cryogenic microcooling ~ a micromachined cold stage ...by two coaxial glass-tube counterflow heat...

CRYOGENIC MICROCOOLING

A MICROMACHINED COLD STAGE OPERATING WITH A SORPTION COMPRESSOR IN A VAPOR COMPRESSION CYCLE

Johannes Burger

The research described in this thesis was carried out at the MESA+ Research Institute of the University of Twente. It was a cooperative project between the Low Temperature Group and the Micromechanical Transducers Group in the Faculty of Applied Physics. The research was financed by the Dutch Technology Foundation (STW). De promotiecommissie: Voorzitter en secretaris: Prof. dr. ir. J.H.A. de Smit Universiteit Twente Promotoren: Prof. dr. H. Rogalla Universiteit Twente Prof. dr. M. Elwenspoek Universiteit Twente Assistent promotor: Dr. ir. H.J.M. ter Brake Universiteit Twente Leden: Prof. dr. Y. Bäcklund Mälardalen University, Sweden Prof. dr. A.T.A.M. de Waele Technische Universiteit Eindhoven Prof. dr. ir. J. van Amerongen Universiteit Twente Prof. dr. ir. T.H. van der Meer Universiteit Twente Deskundige: L.A. Wade Jet Propulsion Laboratory, USA Cover: A cold stage consisting of three micromachined silicon components that are interfaced by two coaxial glass-tube counterflow heat exchangers. The glass-tube heat exchangers are visible as the two thick tubes and consist of two tubes that are placed concentrically around each other; the orange color is caused by a coating. The two thin glass tubes that are visible are included to add mechanical stability to the system. Thin-film heaters with a gold layer on top of it are located on the three silicon parts. The left part combines the high and low pressure gas lines in the first counterflow heat exchanger, the middle part is a condenser where a vapor-liquid transition occurs, and the right part contains a flow restriction and an evaporator. This is the actual cold part. The interior of these three components is visible on the background photo, which shows part of a processed silicon wafer. Cryogenic microcooling – A micromachined cold stage operating with a sorption compressor in a vapor compression cycle / Johannes F. Burger Ph.D. Thesis, University of Twente, Enschede, The Netherlands ISBN 90-365-1536-X Copyright © 2001 by Johannes Burger, Enschede, The Netherlands

CRYOGENIC MICROCOOLING

A MICROMACHINED COLD STAGE OPERATING WITH A SORPTION COMPRESSOR IN A VAPOR COMPRESSION CYCLE

PROEFSCHRIFT

ter verkrijging van de graad van doctor aan de Universiteit Twente,

op gezag van de rector magnificus, prof. dr. F.A. van Vught,

volgens besluit van het College voor Promoties in het openbaar te verdedigen

op vrijdag 12 januari 2001 te 16.45 uur.

door Johannes Faas Burger

geboren op 20 oktober 1969 te Doornspijk

Dit proefschrift is goedgekeurd door: Prof. dr. H Rogalla (promotor) Prof. dr. M. Elwenspoek (promotor) Dr. ir. H.J.M. ter Brake (assistent promotor)

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Contents

NOMENCLATURE..................................................................................................................................... V

1 INTRODUCTION................................................................................................................................ 1

1.1 GENERAL INTRODUCTION ...............................................................................................................1 1.2 CRYOGENICS .................................................................................................................................2 1.3 RESEARCH GOALS ..........................................................................................................................3 1.4 OUTLINE OF THESIS ........................................................................................................................4 1.5 REFERENCES..................................................................................................................................4

2 CRYOCOOLER THEORY................................................................................................................. 7

2.1 INTRODUCTION ..............................................................................................................................7 2.2 ELEMENTARY REFRIGERATOR THERMODYNAMICS ...........................................................................8 2.3 REGENERATIVE COOLING CYCLES .................................................................................................13

2.3.1 Classification and common aspects of regenerative cooling cycles ..........................................13 2.3.2 The regenerator ......................................................................................................................15 2.3.3 Stirling cycle..........................................................................................................................16 2.3.4 Gifford-McMahon and Solvay cycles......................................................................................25 2.3.5 Vuillemier cycle .....................................................................................................................27 2.3.6 Pulse tube cycle ......................................................................................................................29 2.3.7 Regenerative cooling losses ....................................................................................................30 2.3.8 Twente-Stirling cycle .............................................................................................................31

2.4 RECUPERATIVE COOLING CYCLES..................................................................................................37 2.4.1 Classification and common aspects of recuperative cooling cycles ..........................................37 2.4.2 Vapor compression cycle........................................................................................................39 2.4.3 Linde-Hampson cycle.............................................................................................................41 2.4.4 Joule-Brayton cycle ................................................................................................................43

2.5 OTHER COOLING PRINCIPLES.........................................................................................................44 2.5.1 Thermoelectric coolers ...........................................................................................................44 2.5.2 Magnetocaloric cooling ..........................................................................................................47 2.5.3 Optical cooling.......................................................................................................................47

2.6 CONCLUSIONS..............................................................................................................................48 2.7 REFERENCES................................................................................................................................48

3 MINIATURIZATION OF CRYOCOOLERS .................................................................................. 51

3.1 INTRODUCTION ............................................................................................................................51 3.2 MICROFABRICATION ....................................................................................................................53

3.2.1 Materials................................................................................................................................53 3.2.2 Micromechanical fabrication techniques.................................................................................55

3.3 THEORY AND SCALING .................................................................................................................58 3.3.1 Mechanics..............................................................................................................................62 3.3.2 Actuators................................................................................................................................63 3.3.3 Fluid mechanics .....................................................................................................................71 3.3.4 Heat transfer...........................................................................................................................73

3.3.4.1 Steady-state conduction .............................................................................................................. 73 3.3.4.2 Transient Conduction ................................................................................................................. 76 3.3.4.3 Radiation.................................................................................................................................... 78 3.3.4.4 Convective heat transfer ............................................................................................................. 81 3.3.4.5 Boiling and condensation ........................................................................................................... 84 3.3.4.6 Thermal regenerative heat losses ................................................................................................ 85

3.3.5 Fluid mechanics and heat transfer in microchannels...............................................................85 3.3.6 Scaling conclusions................................................................................................................87

3.4 MINIATURIZATION OF REGENERATIVE COOLING CYCLES.................................................................88

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3.5 MINIATURIZATION OF RECUPERATIVE COOLING CYCLES................................................................. 95 3.6 MICROCOOLER OPPORTUNITIES AND REQUIREMENTS ..................................................................... 96 3.7 CONCLUSIONS ............................................................................................................................. 99 3.8 REFERENCES ............................................................................................................................. 100

4 SORPTION COOLER THERMODYNAMIC ANALYSIS............................................................105

4.1 INTRODUCTION.......................................................................................................................... 105 4.2 SORPTION COOLER OPERATION AND HISTORY .............................................................................. 106 4.3 APPROACH OF ANALYSIS ............................................................................................................ 110 4.4 SORPTION COMPRESSOR ............................................................................................................. 111

4.4.1 Adsorption materials............................................................................................................ 111 4.4.2 Sorption compressor thermodynamics .................................................................................. 114 4.4.3 The exergy potential ............................................................................................................ 117 4.4.4 Compressor modelling ......................................................................................................... 118 4.4.5 Case study: xenon adsorption on highly porous charcoal ...................................................... 120 4.4.6 Compressor conclusions....................................................................................................... 123

4.5 LINDE-HAMPSON COLD STAGE ANALYSIS .................................................................................... 124 4.6 COMBINATION OF SORPTION COMPRESSOR AND COLD STAGE........................................................ 125

4.6.1 Two stage sorption compressor ............................................................................................ 125 4.6.2 Precooling of the cold stage.................................................................................................. 127

4.7 SORPTION COOLER SYSTEM SPECIFICATIONS................................................................................ 128 4.8 CONCLUSIONS ........................................................................................................................... 129 4.9 REFERENCES ............................................................................................................................. 130

5 GAS-GAP HEAT SWITCH .............................................................................................................133

5.1 INTRODUCTION.......................................................................................................................... 133 5.2 HEAT-SWITCH REQUIREMENTS.................................................................................................... 134 5.3 GAS-GAP HEAT TRANSFER .......................................................................................................... 135

5.3.1 Theory................................................................................................................................. 135 5.3.2 Limiting ON and OFF thermal resistances ........................................................................... 137 5.3.3 Experiments......................................................................................................................... 139

5.4 HYDROGEN GAS-GAP ACTUATION BY METALHYDRIDES ................................................................ 140 5.4.1 Metal hydride theory............................................................................................................ 140 5.4.2 Material selection................................................................................................................. 142 5.4.3 Actuator modelling .............................................................................................................. 145

5.5 ZRNI THIN FILMS ....................................................................................................................... 147 5.5.1 ZrNi/Pd thin film preparation and characterization .............................................................. 147 5.5.2 Results and discussion.......................................................................................................... 149

5.6 CONCLUSIONS ........................................................................................................................... 153 5.7 REFERENCES ............................................................................................................................. 153

6 SORPTION COMPRESSOR...........................................................................................................155

6.1 INTRODUCTION.......................................................................................................................... 155 6.2 MODELLING OF THE COMPRESSOR THERMAL BEHAVIOR ............................................................... 156 6.3 DESIGN CONSIDERATIONS AND INTRODUCTORY EXPERIMENTS ..................................................... 162

6.3.1 Inner pressure cylinder......................................................................................................... 162 6.3.2 Support ................................................................................................................................ 163 6.3.3 Adsorption material ............................................................................................................. 164 6.3.4 Heater .................................................................................................................................. 168

6.4 DESIGN AND FABRICATION ......................................................................................................... 172 6.5 EXPERIMENTS............................................................................................................................ 174 6.6 CONCLUSIONS ........................................................................................................................... 177 6.7 REFERENCES ............................................................................................................................. 178

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7 HIGH PRESSURE CHECK VALVE UNIT ................................................................................... 179

7.1 INTRODUCTION ..........................................................................................................................179 7.2 CHECK VALVE REQUIREMENTS ....................................................................................................181 7.3 DESIGN .....................................................................................................................................182 7.4 MECHANICAL AND FLUIDIC MODELLING ......................................................................................183 7.5 FABRICATION AND RESULTS........................................................................................................189

7.5.1 Processing scheme................................................................................................................189 7.5.2 KOH etching (wafer 2) .........................................................................................................190 7.5.3 Deep RIE etching (wafer 3) ..................................................................................................194

7.6 EXPERIMENTS............................................................................................................................195 7.7 CONCLUSIONS............................................................................................................................198 7.8 REFERENCES..............................................................................................................................199

8 MINIATURE LINDE-HAMPSON COLD STAGE........................................................................ 201

8.1 INTRODUCTION ..........................................................................................................................201 8.2 LINDE-HAMPSON COOLER WITH GLASS TUBE HEAT EXCHANGER ...................................................201

8.2.1 Design and fabrication .........................................................................................................202 8.2.2 Experiments and discussion..................................................................................................203

8.3 MINIATURE SILICON/GLASS COLD STAGE WITH TE PRECOOLING ...................................................205 8.3.1 Cold stage requirements .......................................................................................................205 8.3.2 Design considerations...........................................................................................................206 8.3.3 Design..................................................................................................................................208

8.3.3.1 Counterflow heat exchangers .................................................................................................... 210 8.3.3.2 Condenser ................................................................................................................................ 211 8.3.3.3 Restriction/evaporator .............................................................................................................. 213

8.3.4 Fabrication and results .........................................................................................................215 8.3.4.1 Processing scheme.................................................................................................................... 215 8.3.4.2 KOH corner compensation........................................................................................................ 217 8.3.4.3 Glue connections ...................................................................................................................... 218 8.3.4.4 Heater deposition ..................................................................................................................... 220

8.3.5 Experiments .........................................................................................................................220 8.4 CONCLUSIONS............................................................................................................................228 8.5 REFERENCES..............................................................................................................................228

9 CONCLUSIONS AND OUTLOOK ................................................................................................ 231

9.1 CONCLUSIONS............................................................................................................................231 9.2 OPPORTUNITIES FOR FURTHER RESEARCH ....................................................................................233

APPENDIX A: PROCESSING SEQUENCE OF THE CHECK VALVES ............................................ 235

APPENDIX B: PROCESSING SEQUENCE OF THE COLD STAGE.................................................. 251

SUMMARY............................................................................................................................................... 259

SAMENVATTING.................................................................................................................................... 263

DANKWOORD......................................................................................................................................... 267

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Nomenclature

Nomenclature* A [m2] area a [m/s2] acceleration a [m2/s] thermal diffusivity B [T] magnetic field b [m] width C [J] heat capacity C [-] constant in expression of the friction factor, f = C/Re c [J/kg] specific heat COP [-] coefficient of performance D [m] diameter D [m] characteristic length Dh [m] hydraulic diameter, 4A/P d [m] thickness dp [m] particle size Ey [Pa] Young’s modulus E [J] exergy E [V/m] electric field e [J/kg] specific exergy F [N] force f [1/s] cycle speed f [-] friction factor f [1/s] frequency f [-] volume fraction of pores in adsorption material G [J] Gibbs energy g [m/s2] acceleration due to gravity H [J] enthalpy h [J/kg] specific enthalpy I [kg m2] moment of inertia k [-] spring constant kB [J/K] Boltzman’s constant L [m] mean free path l [m] length m [kg] mass m [-] number of sorption cells m& [kg/s] mass flow N [-] number (of moles, radiation shields, sorption cells, etc.) O [m] perimeter P [W] power p [N/m2] pressure Q [J] heat q [J/kg] specific heat R [m] radius R [J/K] 8.31 J/K, universal gas constant

* Symbols are only listed if they are used more than once in the text.

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R [K/W] thermal resistance Rh [Pa-s/m3] hydraulic resistance S [J/K] entropy s [J/kgK] specific entropy T [K] temperature t [s] time U [J] energy u [J/kg] specific energy V [m3] volume v [m/s] velocity vm [m/s] mean velocity v [m3/kg] specific volume W [J] work w [J/kg] specific work X [kg] mass of gas x [m] position x [-] normalized position x [kg/kg] mass of gas per mass of sorber material Y [m] stroke of piston Bi Biot number Fo Fourier number Kn Knudsen number Nu Nusselt number Pr Prandtl number Re Reynolds number α [-] dead volume fraction α [1/K] thermal expansion coefficient α [W/m2K] heat transfer coefficient β [-] scale factor β [-] accomodation coefficient χ [-] ratio of convective heat transfer and pressure drop power loss χ [-] ratio of sorption compressor heat losses and useful input power δ [m] displacement ε [-] strain ε [F/m] dielectric constant ε [-] porosity φ [-] AS / ACS, ratio of the cold stage solid conduction area and the cross

sectional area γ [W/m3] cooling power per unit of cold stage volume γb [J/m2] bond energy η [-] Coefficient of Performance, efficiency η [-] Gas-gap heat switch ON-OFF ratio κ [-] compression ratio κ [-] fraction of active actuator volume to total actuator volume λ [W/mK] thermal conductivity µ [Pa-s] dynamic (absolute) viscosity

vii

µ [-] VC,1 / (VA,1 + VC,1), cold volume fraction of Twente Stirling cooler µm [-] mass fraction ν [-] Poisson ratio ρ [kg/m3] density σ [Pa] stress σB [W/m2K4] Stefan-Boltzman constant, σB = 5.67⋅108 W/m2K4

τ [s] time constant τ [Pa] shear stress υ [V] voltage ω [rad/s] angular velocity ξ [m] molecule diameter ψ [W/m3] heat dissipation per unit of volume Indices 0 reference value 2p two phase A ambient act actuator ads adsorption av average C cold c cross sectional cd conduction CFHX counterflow heat exchanger cl closed cs cold stage cv convection cyl cylinder eff effective el electrostatic F Fermi f friction g gas g gravity H hot H at constant enthalpy HS heat switch h hydraulic I inertia irr irreversible

l liquid lam laminar m mean m magnetic o open oc outer container p at constant pressure pl pressure loss prec precooling pu pumping r relative (permittivity) rad radiation rev reversible s solid s surface s sorber sat saturation sh shuttle si heat sink spr spring T at constant temperature tot total turb turbulent v vapor v at constant volume

1

1 Introduction

Chapter 1

Introduction

This chapter presents the motivation and project goals of the work presented in this thesis. The work was motivated by the idea that miniature low-temperature electronic applications would benefit from the development of small micromachined cryocoolers or small cryocooler components. Project goals include a ‘top-down’ and ‘bottom-up’ approach to investigate microcooler opportunities, as well as the development of miniature components for a demonstrator cooler.

1.1 General introduction

This thesis is the result of a five year cooperative project between the low-temperature division and the micromechanical transducers group at the University of Twente; both groups are part of the MESA+ Research Institute. The project was motivated by the idea that miniature low-temperature electronic applications would benefit from the development of small micromachined cryocoolers or small cryocooler components. The collaboration between the two groups facilitated a close interaction between a number of engineering disciplines, which include: cryogenic system engineering, precision engineering and micromechanical engineering. Cryogenic systems are systems capable of reaching temperatures below roughly 120 K; precision engineering concerns the accurate fabrication of very small components and systems using conventional production techniques; and micromechanical engineering refers to the fabrication of micrometer-sized components in substrate materials such as silicon and glass by the use of etching, deposition and waferbonding techniques.

During recent years, a rapid development has taken place of low-temperature (LT) electronics and especially of superconducting devices. However, there exists a gap between this development and the availability of enabling technologies that are essential for the commercialization of LT-electronics [1.1]. These enabling technologies are low-cost, highly reliable cryogenic refrigeration systems and energy-efficient cryogenic packaging of the LT-electronic device with the cryogenic refrigerators. Much effort is currently put in the development of such reliable and cheap coolers, but typically small systems are still rather large in terms of size (> 1 kg) and cooling power (> 1 W). Low-temperature applications requiring very little cooling power, such as a single chip with a low noise amplifier or a superconducting magnetometer, would benefit from very small closed-cycle coolers. Such coolers do not exist

Chapter 1

2

and in this respect it was suggested [1.2] that MEMS (Micro Electro Mechanical Systems) techniques can be attractive for developing miniature cooler components, such as heat exchangers, check valves or compressors.

Recently, there has also been much interest for chip cooling to remove locally produced heat, essentially around normal ambient temperatures [1.3]. Such cooling systems should not be confused with cryogenic cooling systems that operate well below ambient temperatures, although there are common aspects. The history, applications and some typical characteristics of cryogenic (cooling) systems are briefly discussed in the next section.

1.2 Cryogenics

The word cryogenics is a product of the early twentieth century and means, literally, the production of icy cold; however, the term is used today to indicate the science and technology of very low temperatures – typically below 120 K [1.4]. The study of cryogenics started back in the nineteenth century as scientists and engineers competed with each other to liquefy gases and reach ever lower temperatures. This process started in 1887 with the liquefaction of oxygen by Pictet and Cailletet. In 1898, James Dewar first liquefied hydrogen. Dewar also developed the vacuum-insulated flask with reflective walls for containing cryogenic liquids. His design is still used in the cryogenic containers of today, which in tribute are called Dewars. The last and most difficult gas to be liquefied was helium; this was achieved by Kamerlingh Onnes in Leiden (The Netherlands) in 1908. He promptly used helium to discover superconductivity. Another development which started earlier in the nineteenth century is nowadays in the heart of many cryocoolers: the invention of the gas expansion engine in 1815 by the clergyman Robert Stirling. In 1834 Herschel suggested to reverse the engine into a cooler, but it took another 30 years before Kirk succeeded to realize this.

Nowadays, cryogenics plays a major role in modern science and industry. Large-scale air separation plants use cryogenics to break down air into its components for industrial and medical uses. The resulting products are frequently transported as cryogenic liquids in large Dewars. Magnetic resonance imaging (MRI) systems, that use superconducting magnets cooled by liquid helium, have become a common feature in modern hospitals. In space technology, cryogenics is found in the liquid hydrogen and oxygen fuels used in rocket engines and in applications such as the Cosmic Background Explorer (COBE) satellite, whose superfluid cooled sensors have detected remnants of the Big Bang. The particle accelerators used at the European CERN institute use many cooled superconducting magnets to study the fundamental laws of matter. At a smaller scale, cryocoolers are used to provide cooling in, for example, night-vision systems, modern high frequency telecommunication systems, or cryo vacuum pumps. The further miniaturization of these types of cryogenic cooling systems, that operate without the use of liquid Dewars, is the topic of this thesis.

To illustrate what kind of aspects play a role in a small cryogenic refrigeration system, figure 1.1 shows a schematic picture of an electronic chip that is directly mounted to the cold tip of a cryocooler. The depicted cryocooler typically consists of a separate gas compressor that is connected to the cold stage, where the active refrigeration is generated from ambient to the low temperature by some kind of compression/expansion sequence of the refrigeration fluid. Often, drive electronics is required to obtain proper compressor operation. The cold stage typically consists of a high aspect-ratio construction that is made of a material with a low

Introduction

3

thermal conductivity to reduce heat conduction losses through the cold stage itself. A vacuum chamber is mounted around the cold stage to prevent thermal conduction losses through air, as well as condensation/sublimation of gas on the cold tip. A radiation shield may be required around the cold stage to reduce thermal radiation losses from the ambient temperature environment. Proper mounting of the electronic chip on the cold stage is required to guarantee a high thermal conduction and a small temperature difference between the two systems. Proper mounting techniques are not trivial at cryogenic temperatures because of thermal expansion differences between different materials. The electronic chip requires wiring to the ambient temperature, which will lead to thermal conduction losses through the wires. Therefore, often careful optimization is required for the wiring design. To monitor the temperature of the electronic device and the cooler, one or more temperature sensors need to be mounted, including its wiring to the ambient temperature environment. If very low temperatures need to be reached (typically below 20 K), a cryogenic cooling system may consist of two or more cascaded cooling systems.

The discussed topics of the cooling system in figure 1.1 accommodate the following fields, applied under cryogenic conditions: thermodynamics, heat transfer, fluid mechanics, fluid and solid material properties, vacuum techniques, instrumentation, and mechanical and electronic design. For more general information about cryogenics, the reader is referred to the literature [1.4 - 1.7].

1.3 Research goals

Figure 1.2 shows a sketch of how a micromechanical cryocooler with integrated cold electronic chip and vacuum chamber might look like. A small compressor element could either be integrated or connected externally. The development of such a micromachined cryocooler was the initial project goal. To make this wide and ambitious goal more specific, the following four project goals were defined: 1. Investigate the opportunities and limitations of the miniaturization of common

thermodynamic fluid cooling cycles (‘top-down’ approach). 2. Investigate how micromechanical techniques and components can be used to build a small

cryocooler or cryocooler components (‘bottom-up’ approach).

controlelectronics

compressor

vacuum chamber

radiation shield (’superisolation’)

cold electronics

temperature sensor + wiring

wiring of cold electronics

cold tip

heat sink at ambient temperature

gas connection tube(s) betweencompressor and cold stage

cold stage (cylindrical cross section)

> 15 cmtypically

Figure 1.1 Schematic picture of an electronic chip that is directly mounted to the cold tip of a cryocooler.

Chapter 1

4

3. Choose a cooling cycle that can be used to define specifications for the development of small cooler components.

4. Develop the necessary components for this demonstrator cooling system and, if possible, combine the components into a working system.

1.4 Outline of thesis

Chapter 2 presents an overview of a number of cooling cycles that can be applied in cryocoolers. Emphasis is put on thermodynamic theory, conceptual operation and possible loss mechanisms. This chapter serves as a conceptual framework on cryocooler theory which is referred to throughout this thesis. In chapter 2 also a new regenerative cooling cycle is proposed which appears particularly suitable to be applied on micro-scale. Miniaturization of cryocoolers is discussed in chapter 3. It is divided in three sub-topics: microfabrication, the influence of downscaling on the different fields that play a role in coolers, and the possible miniaturization of the cooling cycles that were discussed in chapter 2. Chapter 4 presents the operation and thermodynamic analysis of a sorption cooler, which consists of a sorption compressor and a Linde-Hampson cold stage. This cooling cycle was chosen for the development of small cooler elements because it appeared suitable to be applied on a small scale. The remainder of the thesis discusses the components that were developed; the requirements for the individual components are based on the specifications of the cooling cycle which are presented in section 4.7. Chapter 5 discusses the operation of a gas-gap heat switch as well as the fabrication of a thin-film metal hydride layer that can be used to control the hydrogen pressure in the gas gap. Chapter 6 describes the design, fabrication and testing of the individual sorption compressor cells. Chapter 7 deals with the development of miniature high pressure check valves, which are required in the sorption compressor. Finally, chapter 8 presents the design and operation of two different miniature cold stages, both employing Joule Thomson expansion. Conclusions and a future outlook are given in chapter 9.

1.5 References [1.1] M. Nisenoff, Cryocoolers and high temperature superconductors: advancing toward commercial

applications, Cryocoolers 8, Plenum Press, New York (1995), pp. 913-917. [1.2] G. Walker and R. Bingham, Micro and nano cryocoolers: speculation on future development, Proc. of

the 6th Int. Cryocooler Conf. (1990), pp. 363-375. [1.3] D.B. Tuckerman and R.F.W. Pease, High performance heat sinking for VLSI, IEEE Electron Dev Let,

EDL-2 (1981), pp. 126-129.

compressor cold stage sensor

wiring

crosssection

top view

cold stage sensor

sealed vacuum

~ 1.5 mm

~ 0.5 - 1 cm

compressor

Figure 1.2 A sketch of how a micromechanical cryocooler might look like.

Introduction

5

[1.4] J.G. Weisend II (ed.), Handbook of cryogenic engineering, Taylor and Francis (1998). [1.5] R. Barron, Cryogenic systems, McGraw-Hill Book Company, New York (1966). [1.6] R.G. Scurlock (ed.), History and origins of cryogenics, Oxford University Press (1992). [1.7] G. Walker, Cryocoolers, Part 1: Fundamentals, Plenum Press, New York (1983).

7

2 Cryocooler theory

Chapter 2

Cryocooler theory

In this chapter an overview is presented of a number of cooling cycles that can be applied in cryocoolers. Emphasis is put on thermodynamic theory, conceptual operation and possible loss mechanisms. The chapter serves as a conceptual framework on cryocooler theory which is referred to throughout this thesis. The following regenerative cooling cycles are discussed: Stirling, Gifford-McMahon, Vuillemier and pulse-tube. A new regenerative cooling cycle is proposed which appears particularly suitable to be applied on micro-scale. Furthermore, the following recuperative cooling cycles are discussed: Vapor compression cycle, Linde-Hampson and Joule-Brayton cycle. Some alternative solid-state cooling cycles are also discussed: thermoelectric cooling, magnetocaloric and optical cooling.

2.1 Introduction

Research towards miniaturization of cryocoolers requires conceptual knowledge of the different cooling cycles that can be applied in cryocoolers. This chapter discusses the conceptual operation and important physics of some major cooling cycles currently in use. Emphasis in the discussion is put on the thermodynamic behaviour of the cycles, on possible variations of the cooler configurations and on different loss mechanisms of the cycles. Less emphasis is put on technological and mechanical developments, which can be found more suitably in engineering publications. Also, in this chapter no comparison is made between the different cycles. Chapter 3 focuses in more detail on opportunities for downscaling of the different cooling cycles, whereas this chapter serves as a theoretical background on cooling cycles that will be referred to in the discussions throughout this thesis.

In section 2.2 elementary refrigerator theory is discussed. Next, a distinction is made between regenerative and recuperative coolers, which both operate with a fluid as the working medium. In regenerative coolers the fluid is alternating between the warm (ambient) section and the low temperature section of a cooler. Such cooling cycles are discussed in section 2.3. In recuperative coolers the working fluid is continuously circulating in a closed loop between the ambient and low temperature part of a cooler. Such cooling cycles are discussed in section 2.4. The chapter finishes with section 2.5 which discusses alternative cooling cycles that do not operate with fluids, such as thermoelectric coolers.

Chapter 2

8

During the study of regenerative cooling cycles a cycle was found that appears particularly suitable to be applied on micro-scale. No description of this cycle was found in the literature and it was, therefore, named the Twente-Stirling cycle since it has some similarities with the Stirling cycle. Thermodynamic operation of the cycle is discussed in section 2.3.8 and a MEMS-based design is presented in the next chapter in section 3.4.

2.2 Elementary refrigerator thermodynamics

Figure 2.1 shows a schematic representation of a refrigerator. Heat QC is taken away from a cold body at a low temperature TC to a working substance in the refrigerator. At the warm (ambient) side of the refrigerator, heat QA is subsequently transferred from the working substance to the environment at a temperature TA.# The first and second law of thermodynamics require that work is done on the system (the working substance) to transfer heat from the cold to the warm side. Dependent on the working cycle, the working substance can be an ideal or a van der Waals gas, or another medium*.

TA

TC

-QA

QC

W

Figure 2.1 Schematic representation of a refrigerator. The energy transport in coolers (both on component and system level) is governed by the

first and second law of thermodynamics. The change of the internal energy$ of a thermodynamic system is given by the first law of thermodynamics, which can in a general way be expressed for open and closed systems as:

∑ ∑∑ ∑ ++=+++= dmhdWdQdmp

udWdQdU )(ρ

(2.1)

# In this thesis a sign convention is assumed in which heat and mass flow from the environment to the system are positive. The heat flow from the refrigerator to ambient can, therefore, be represented as a negative heat flow to the refrigerator. * Some parts of this section are adapted from a paper of Radebaugh [2.3], where he discusses the fundamentals and possibilities of alternative cooling systems. This section, however, focuses mainly on (conventional) cooling cycles with fluids as the working medium because we believe that these cooling cycles are currently the only serious candidates for reaching temperatures below 100 K, operating from room temperature. The discussion presented in this section can be generalized to alternative cooling media by replacing the (varying) pressures by generalized forces and the (varying) volumes by generalized displacements. $ In this thesis it is assumed that the internal energy is made up by the thermal energy of the fluid, i.e. for an ideal gas u = cRT. However, dependent on the considered system, more energy terms could play a role that should in that case be added to the internal energy. For example, in liquid flows often kinetic and potential energies need to be considered and u = uthermal + ukin + upot = cRT + ½ρv2 + gh.

Cryocooler theory

9

In this expression, ∑dQ represents the sum of various heat flows to the system, dW is the (shaft) work done on the system and ∑(u + p/ρ)⋅dm represents the energy and work added to the system due to various mass flows going into the system. This last term equals the enthalpy flow into the system. The entropy increase of the same thermodynamic system equals the entropy increase due to the heat flows, due to the mass flows, and due to irreversible entropy production in the system, dSirr:

∑ ∑ ++= irrdSdmsT

dQdS (2.2)

where the second law of thermodynamics requires that in any process:

0≥irrdS (2.3)

The first and second law of thermodynamics are illustrated in figure 2.2 for a situation with two heat flows and two mass flows going into the system.

dW

T1

T2

dSirr

dQ2

dQ1

h dm1 1

h dm2 2

dU = dQ + dQ + dW + h dm + h dm1 2 1 1 2 2 (first law)

dS = dQ /T + dQ /T + s dm + s dm + dS dS > 01 1 2 2 1 1 2 2 irr irrwith (second law)

Figure 2.2 The first and second law of thermodynamics applied on a system with two heat and mass flows going into the system.

The path used in any refrigeration cycle can be drawn in a temperature-entropy plane, or

T-s diagram. Figure 2.3 shows the three most common cycles in a T-s diagram: the Carnot cycle, the Stirling cycle and the Ericsson cycle. The three cycles are different in the way in which the hot and cold isotherms are connected. In the Carnot cycle an adiabatic path (no heat exchange) is used, in the Stirling cycle an isochoric path (constant volume) and in the Ericsson cycle an isobaric path (constant pressure). Common for all three cycles is that the entropy of the working medium can be changed significantly at (nearly) constant temperature to take up or give away heat. Heat dQ absorbed at a temperature T is related to an entropy change of the working medium, dSmedium, by:

mediumdSTdQ ≤ (2.4)

T T T

S S S

TA TA TA

TC TC TC

Carnot cycle Stirling cycle Ericsson cycle

V1V2p1p2

Figure 2.3 Temperature-entropy diagrams for the (a) Carnot cycle, (b) Stirling cycle, and (c) Ericsson cycle.

Chapter 2

10

The equal sign is applicable if the process is performed reversibly, so that

mediumrev dSTdQ = (2.5)

Integration of this equation over the entropy change at temperature TC and TA gives the heat QC and QA absorbed and rejected at the cold and warm isotherms, assuming reversible steps.

According to the first law of thermodynamics, the internal energy of the system in a complete cycle remains constant, and the net work required to drive the cycle equals:

CA QQW −−= (2.6)

In the following discussion it is assumed that all steps of the cooling cycle are reversible. Consequently, no net entropy production occurs in moving the system between both isotherms and –∆Smedium,A = ∆Smedium,C = ∆S. Therefore, Eq. (2.6) can be written as

STTSTSTQQW CACmediumCAmediumACA ∆−=∆−∆−=−−= )(,, (2.7)

The efficiency, η, of a refrigerator is defined by η = QC/W (often also called the Coefficient of Performance, COP). From Eq. (2.7) the efficiency of the ideal Carnot, Stirling and Ericsson cycle becomes

CA

C

CA

CCCarnot TT

TSTT

STWQ

−=

∆−∆

==)(

η (2.8)

where ηCarnot is called the Carnot efficiency and represents the highest possible efficiency for a cycle operating between TC and TA. Any real cycle will have irreversibilities which lead to a lower efficiency. Figure 2.4 shows the Carnot efficiency as a function of the low temperature, as well as some realistic efficiencies of typical coolers on the market.

So far, only the net work for a complete cycle was discussed in terms of QC and QA, based on the fact that the state or energy of a complete cycle does not change. A complete cycle, however, consists of separate parts in which the state or energy of the system may change. These parts can also be analyzed separately, particularly to find in which way a reversible change of the entropy can be accomplished at the hot and cold sides of the refrigerator.

In the Carnot cycle of figure 2.3, heat crosses the system boundary only during the

0.001

0.01

0.1

1

10

100

0 50 100 150 200 250 300 350T (K)

CO

P

Carnot2.2 W, 4.2 K GM, Mitsubishi Electr. Corp.10 W, 20 K PT, Aisin Seiko Co.1.5 W, 77 K Stirling, Signaal Usfa5 W, 123 K PT, Kelvin Int. Co.50 mW, 170 K 6 stage TE cooler, MELCORtyp. household refr.

Figure 2.4 Carnot efficiency as a function of the low temperature TC for TA = 300 K, as well as the efficiency of some typical coolers on the market (most cooler data from [2.4]). Abbreviations: GM = Gifford-McMahon; PT = pulse tube; TE = thermoelectric. The different coolers are discussed in more detail in sections 2.3 - 2.5.

Cryocooler theory

11

isothermal processes at TC and TA, During the adiabatic parts the temperature of the system is changed by means of work that is performed on or by the system. However, in the Stirling and Ericsson cycles heat crosses the system boundary during the constant-volume or constant-pressure curves as well. The system absorbs heat in going from TC to TA and gives off heat in going from TA to TC. In an ideal system the two lines are parallel so that the two heat transfers are equal. In practice this heat transfer is accomplished by placing a heat exchanger between the two lines, which gives rise to some irreversibilities because of the necessary temperature differences required to obtain heat transfer.

An important part of the cycle is the absorption of heat at low temperature. This heat transfer to the system is governed by the first and second law of thermodynamics. A distinction can now be made between the situation in which the working medium at the cold side of a refrigerator operates as a closed system and as an open system. An example of a closed system is the gas in a closed cylinder that is expanded against a piston to provide refrigeration in the regenerative Stirling cycle (see section 2.3.3). An example of an open system is the continuous production and evaporation of liquid in the boiler of the recuperative Linde-Hampson cycle (see section 2.4.3). For a closed system, dm = 0 in equations (2.1) and (2.2). For a reversible process, the entropy change of the medium is related to the absorbed heat by Eq. (2.5), and can now by application of Eq. (2.1) be expressed as:

closed system: dWdUdSTdQ mediumrev −== (2.9)

For a stationary two-port open system, dU = 0 in Eq. (2.1) and dS = 0 in Eq. (2.2). The entropy change of the medium is now obtained as a change of the molar entropies of the mass flowing into and out of the system, resulting in the following expression for the absorbed heat:

open system: dWdmhhdmssTdSTdQ mediumrev −−−=−== )()( 2121 (2.10)

where si and hi are the molar entropy and enthalpy of the medium flowing in and out of the system.

In order to absorb heat at low temperature, Equations (2.9) and (2.10) show that the entropy of the working medium can be changed under two fundamentally different conditions: when dW = 0 and when dW ≠ 0 (where in the last case dU or dH may or may not be zero). Notice that for the complete cycle, obviously, W ≠ 0 for all situations.

Cycles with dW = 0 during the absorption of heat. For this case, a change in the internal energy or enthalpy is responsible for the (reversible) entropy increase required to take up heat from the environment. This is possible for a medium where disordered and ordered states are in equilibrium at a temperature T or, in other words, where a phase transition occurs. Examples are boiling liquids like helium and nitrogen or, alternatively, a magnetic material at the transition from the ferromagnetic to the paramagnetic state. Ideal gases, often used in regenerative cooling cycles (described in section 2.3), cannot be used as cooling medium for the case that dW = 0 because their energy or enthalpy has a fixed value at a certain temperature. Notice again that the condition dW = 0 is only valid at the cold side of the cooling cycle; at the warm side work is required to compress the fluid from a low to a high pressure, or in other words, to move the medium from the disordered state back to the ordered state.

The advantage of this cycle is the simplicity of the no-work condition at the cold side of the cooling cycle: no mechanical or physical mechanism is required to take away work from the cold side. The disadvantage is that the refrigerating temperature is dictated by the equilibrium

Chapter 2

12

temperatures of the phase transition of the used cooling medium. This can only be adjusted in a limited temperature range by variation of the pressure (or generalized force if the medium is not a fluid). Recuperative cooling cycles like the vapor compression cycles used in household refrigerators or the Linde-Hampson cycle used in cryogenic refrigerators are based on the dW = 0 condition. These cycles are discussed in more detail in section 2.4.

Cycles with dW ≠ 0 during the absorption of heat. Such cooling cycles perform reversible work on the warm surroundings when heat is absorbed at the cold side of the system. Examples of these cooling cycles are the regenerative Stirling cycle (described in section 2.3.3) and the recuperative Joule-Brayton cycle (described in section 2.4.4). An advantage of these cycles is that the cooling temperature can be adjusted over a wide range of temperatures, more or less independent of the working fluid (often an ideal gas like helium). The disadvantage is that a means must be provided to the system, which is at the low temperature TC, to interact and perform work on the warm surroundings.

As an illustration, figure 2.5 shows a realistic T-s diagram of hydrogen, a typical gas that may be used in both types of refrigerators. Isobars and isenthalps of the gas are plotted. In the graph the two types of cycles are illustrated: the dW = 0 type in the van der Waals regime and the dW ≠ 0 type in the ideal gas regime.

0

50

100

150

200

250

300

5 15 25 35 45 55 65

s (J/gK)

T(K

)

p = 1

bar

5 ba

r

20 ba

r

50 b

ar

W = 0, H = 0∆

W = 0, H = 0∆

H = 1000 J/g

H = 1500 J/g

H = 3000 J/g

Figure 2.5 T-s diagram of hydrogen with isobars and isenthalps. In the diagram a typical Ericsson cycle (dW ≠ 0 during the absorption of heat) is depicted in the ideal-gas regime and a Linde-Hampson cycle (dW = 0 during the absorption of heat) in the van der Waals regime.

There are essentially two ways in which a working substance can be made to go around a

cycle in a T-s diagram. The first is the time domain. In this case the system remains physically stationary and is connected to the reservoirs TA and TC by heat switches which open and close at the appropriate times. A pressure (or generalized force) does work on the system or receives work from the system at the appropriate times to carry out the cycle. The advantage is that some systems then do not require moving parts; however, this is obviously not the case if the working medium is a fluid. The other mode of cycle operation is in the physical or space domain. In this case the working substance moves to different locations for the various parts of the cycle in the T-s diagram. This is particularly easy to do with a liquid or gas system and has the advantage of continuous refrigeration – in contrast to systems that operate in the time

Cryocooler theory

13

domain which have intermittent refrigeration. Besides the two modes of cycle operation discussed above, it is possible to combine the two, as is done in most of the regenerative coolers that are discussed in section 2.3. Certain combinations can make it difficult to show the cycle on a T-s diagram and to analyze it. For these systems each portion of gas follows a single curve on the T-s diagram, for instance because the system pressure varies during a particular part of the cycle. For such cases the thermodynamic cycle involves a continuum of lines in, for instance, the T-s and p-v planes.

2.3 Regenerative cooling cycles

2.3.1 Classification and common aspects of regenerative cooling cycles

Four major classes of regenerative cooling cycles can be identified, often named after their inventors: Stirling, Gifford-McMahon (GM), Vuillemier (VM) and pulse-tube (PT) [2.1, 2.5]. Many different variations of cooler designs exist for each of these regenerative cycles; in terms of design, cooling power and low temperature. Common to all regenerative coolers is that dW ≠ 0 at the cold side: refrigeration is obtained by allowing the cold fluid to perform work on the warm surroundings. Also common in regenerative coolers is that the gas reciprocates between the warm and cold sides of the cooler through a regenerator, which is placed in the gas-flow between the hot and cold sides of the cooler. Generally, reciprocating frequencies between 1 and 100 Hz are used. Operation of regenerative coolers can be summarized as follows. The gas is compressed at the hot side of the cooler, rejecting compression heat to the environment. Subsequently, it moves through the regenerator where the gas is cooled to the low temperature by delivering heat to the heat capacity of the regenerator. At the cold side of the cooler the gas is expanded isothermally, thus performing work on the warm environment and taking up heat from the cold side. Finally, the gas moves back to the hot side of the cooler through the regenerator, taking up heat from the regenerator heat capacity (that was given off previously).

Variations between the different regenerative cooling cycles consist essentially of the method of compression at the hot side, the method of gas movement through the regenerator, and the method how work is performed by the expanding gas at the cold side. Figure 2.6 shows the schematic diagrams for the four regenerative cooling cycles which are discussed in the next sections. In the (basic) Stirling cycle two reciprocating pistons are used at the warm and cold sides to perform compression, displacement and expansion. In the VM cycle the gas is not compressed mechanically, but thermally. To accomplish this, so called displacers are used to shift the gas between the different parts of the cooler. In the GM cycle, a compressor is used that generates a stationary pressure difference. This compressor is via active valves connected to a cylinder that contains a displacer with integrated regenerator. Proper movement of the displacer and opening/closing of the valves generates a cooling effect. In the pulse-tube refrigerator cooling is obtained by a pressure wave that shifts the gas between the cold and warm side of the cooler. The compression side is similar to that of the Stirling cooler.

Chapter 2

14

Essential elements of regenerative coolers are pistons and displacers, two elements which are very different from each other. A piston maintains a high pressure difference between the upper and lower faces. A piston must, therefore, have a good fluid seal to prevent leaks and must act as a structural element with high pressure forces acting on it. Generally, there is no significant temperature difference between both faces of a piston. In contrast, a displacer is an element with a very low pressure difference between both faces but with a large temperature difference over it. It can, therefore, be a lightweight structural element with minimal forces on the seal. It requires, however, a very low thermal conduction between both faces to minimize thermal heat leaks. In most cases a displacer is used to shift gas through a regenerator between the warm and cold sections of a cooler. Such movement of a displacer requires only a small driving force to overcome the fluidic pressure drop over the regenerator and possible seal friction of the displacer. Figure 2.7 shows two possible and equivalent arrangements for the combination of the displacer and the regenerator. The regenerator can be placed either in a separate loop parallel to the displacer (external), or it can be part of the displacer itself (internal). In the discussion of the cooler concepts in the following sections it is always assumed that the regenerator is part of the displacer, but in most cases the displacer and regenerator can also be separated from each other.

In the next sections, the operation of the four mentioned cooling cycles is discussed in more detail. First, however, the regenerator operation is discussed, which is common for all

QT

A

A

QT

C

C

QT

A

A

QT

C

C

QT

H

HQT

A

A

QT

C

C

WA

Q ’T

A

A

plphQT

A

A

QT

C

C

WC

WA

Q ’T

A

A

WA

Stirling Vuillemier Gifford-McMahon Pulse-Tube

heatexchanger

regenerator

heatexchanger

compressor

valve

orifice

reservoir

Figure 2.6 Schematic diagrams for four different regenerative coolers.

(a) internal (b) external

Figure 2.7 Two possible arrangements for the combination of the displacer and the regenerator: internal (a) and external (b).

Cryocooler theory

15

regenerative cycles. The last section on regenerative cooling cycles discusses the various loss mechanisms that decrease the net cooling power.

2.3.2 The regenerator

The regenerator acts as a large thermal capacity that exchanges heat with the gas when it moves through it: it takes up heat when the gas moves from the hot to the cold side, and it gives off heat when the gas moves back from the cold to the hot side. Regenerator operation can be achieved by a solid (heat capacity) matrix; in practical regenerators often stacked screens or spheres are used. To facilitate proper operation, the regenerator must fulfill some partly conflicting requirements [2.1]: 1. A maximum ratio of the regenerator heat capacity to the heat capacity of the gas. The

temperature of the regenerator should stay virtually constant when heat is ab- or desorbed from the gas that moves through it. This can be obtained by making a large, solid matrix.

2. A minimum heat conduction from the hot to the cold side of the regenerator. Heat conduction through the regenerator is a loss term that is directly subtracted from the gross cooling power. The heat conduction can be minimized by making a long matrix that is preferably subdivided with low conductivity parts (e.g. stacked screens that are almost not touching each other).

3. A maximum heat transfer between the gas and the regenerator. This can be achieved by using a long and fine-meshed matrix with a large contact area.

4. A minimum pressure drop over the regenerator. This can be achieved by using a short, highly porous matrix.

5. A minimum dead volume in the regenerator relative to the compression and expansion stage. This can be achieved by using a small, dense matrix.

6. Complete penetration of the heat in the regenerator material when it is heated or cooled. This can be achieved by using finely divided regenerator material with a small characteristic dimension.

It is clear that it is impossible to satisfy all these conflicting requirements, and in practice compromises need to be made. Often a pragmatic ‘trial and error’ method is used to find the proper regenerator configuration, circumventing the complicated dynamic modelling of heat transfer and hydrodynamics in the regenerator material [2.6]. An example for this pragmatic approach is a rule of thumb given by Walker [2.2] in a chapter about heat exchangers: “A satisfactory compromise design for many Stirling cryocoolers will be found with a regenerator length at least three times the frontal diameter of the flow section, a matrix of wire or spheres having a diameter of 0.025 to 0.05 mm and with a regenerator void volume of one to two times the swept volume in the expansion space.” This pragmatic approach can partly be explained by the limited number of regenerator material geometries that are available (i.e. stacked screens and spheres). Consequently, an opportunity exists for regenerator improvement if the regenerator material can be shaped in more detail to obtain a better compromise for the conflicting requirements. An example of such improvement is Yaron’s etched foil regenerator [2.7], which is discussed in more detail in section 3.4.

Chapter 2

16

2.3.3 Stirling cycle

Although there are many different configurations for a Stirling-cycle refrigerator, the two-cylinder type, as shown in figure 2.8, is most suitable for analysis purposes because it represents the most general case. It consists of a compression and an expansion cylinder, each fitted with a piston, and maintained at ambient temperature TA and low temperature TC, respectively. The two cylinders are connected via a regenerator, which has a temperature difference (TA – TC) across it. For this analysis, it is assumed that the pistons move without friction or leakage of the working fluid, that there is perfect heat transfer between the gas in the cylinders and the environment, and that the regenerator behaves ideally (i.e. infinite heat capacity, perfect heat transfer, no pressure drop, no dead volume). Figure 2.8 illustrates the steps of the cycle, as well as the associated p-v and T-s diagrams.*

TC TATA

1)

2)

3)

4)

p

V

TA

S

TA

TC

1

2

34

QA

QC

TC

QA

QC

12

3 4

compressorcylinder

disp

lace

men

t

time time

regenerator

expansioncylinder

exp.

displ.

compr.

displ.

exp.

displ.

compr.

displ.

1 2 3 4 11 2 3 4 1

discontinuous piston motion harmonic piston motion

Figure 2.8 Model of a two-piston Stirling-cycle refrigerator with p-v and T-s diagrams. The lower graphs show discontinuous and harmonic displacement-time diagrams for the two pistons. The shaded area is proportional to the volume occupied by the gas.

From state 1 to 2 the gas is compressed isothermally by the compressor piston, rejecting

heat of compression QA to the environment. From state 2 to 3 the gas is displaced through the regenerator in a constant volume process by simultaneous movement of both pistons. In this step the gas exchanges heat with the regenerator material and is cooled to a temperature TC. Next, in step 3-4, the gas is allowed to expand isothermally against the expansion piston. In this step the expansion piston performs work on the environment and the gas absorbs heat QC from the cold environment: this is the actual cooling step. Notice that the expansion work done

* Notice that the cycle is a simplified thermodynamical description. T-S and p-v diagrams cannot be given for all gas simultaneously in a complete cycle, but only for small amounts of moving gas in the system.

Cryocooler theory

17

by the cold piston must be dissipated or used at the warm side of the cooler (this is indicated by the connecting rod of the right piston that extends and delivers work at the environmental temperature TA); any dissipation of this work term at the cold side is subtracted from the cooling power. In the last step from 4 to 1, the gas is displaced back through the regenerator to the compression space by simultaneous movement of the pistons. In this step the same amount of heat that was transferred to the regenerator from step 2 to 3 is transferred back from the regenerator to the gas. Figure 2.8 shows also discontinuous and harmonic piston displacements as a function of time.

The efficiency of the idealized Stirling cycle equals the Carnot efficiency, given by Eq. (2.8). Practical Stirling coolers exhibit various loss mechanisms that decrease the efficiency. These losses will be summarized in section 2.3.7.

Essential elements of a Stirling cooler are two spaces, at different temperatures, whose volumes can be varied cyclically and which are connected by ducts containing heat exchangers and the regenerator. These simple elements can be combined in a very wide range of mechanical arrangements. A classification scheme of the different arrangements is shown in

single acting (1)double acting (2)



integral (7)split (8)



integralsplit

Stirling

two-piston-Stirlingα

piston/displacer-Stirlingβ

disciplinedpiston/displacer

free piston/displacer

one actuator, oneresonantly coupled

two actuators

disciplinedpistons

free pistons

hysteresismechanism

resonant

hybrid systems

1

7

2

8

3

9

4

10

5

11

6

12

piston actuator (voice coil, piezo, etc.)

regenerator or displacer with integrated regenerator

hysteresis mechanismflywheel

Figure 2.9 Classification scheme of Stirling cryocoolers. The numbers in the scheme correspond to the numbered models below the scheme.

Chapter 2

18

figure 2.9; the classification is mainly according to physical mechanisms and principles, and is not necessarily complete. Many of the different configurations were invented in the 19th century, or in the beginning of the 20th century. These were often designated as Stirling engines instead of coolers, and named after their inventors. Some of the configurations were actually never conceived as a cooler, but should not be ruled out in search for principles that can be applied on a micro-scale. Many of the coolers in the scheme can be found back in the scheme of Finkelstein that is discussed by Walker [2.1]. However, the structure of the scheme is different from that of Finkelstein’s scheme.

α-Stirling or β-Stirling. A first important distinction can be made between two-piston and piston-displacer cycles, also denoted by α-Stirling and β-Stirling cycles [2.11]. The Stirling cycle of figure 2.8, used for illustration of the Stirling cycle, is an example of a two-piston cycle. Both on the warm and the cold sides of the cooler a piston is used to compress-displace-expand-displace the gas. In contrast, a piston-displacer cycle has only a piston on the warm side of the cooler and a displacer to shift the gas between the warm and the cold volumes of the cooler. Figure 2.10 illustrates the operating principle of a β-Stirling cycle. The cooler consists of a displacer and piston operating in a single cylinder. The space above the displacer is the expansion space at temperature TC and the space between the piston and displacer is the compression space at ambient temperature TA. The regenerator is integrated in the displacer. The cooling cycle is almost the same as with the two-piston cycle depicted in figure 2.8. In state 1 and 2 the displacer is located at the cold side of the cooler, leaving all gas on the warm side. From state 1 to 2 the gas is isothermally compressed by the compressor piston, rejecting heat of compression QA to the environment. From state 2 to 3 the gas is displaced through the regenerator in a constant volume process by the displacer. From state 3 to 4 the gas is allowed to expand isothermally against the compression piston, performing work on the warm environment so that heat QC is taken up by the cold gas. Here the essential difference with the two-piston cycle emerged: work can now be done easily on the compression piston on the warm side of the cooler instead of the difficult expansion piston at the cold side of the cooler. In the last step from 4 to 1 the gas is shifted back to the compression space by means of the displacer.

1) 2) 3) 4)

TC

TA

Figure 2.10 Piston and displacer movement of an (integral) piston-displacer β-Stirling cooler. Disciplined or free piston. Common in α and β-Stirling coolers is that a proper phase-

difference is required between the motion of the compressor piston and the expansion piston or displacer. One classic method to obtain this phase-difference is by connecting the elements in a proper way to a kinematic drive mechanism (e.g. cranks and connecting rods or a rhombic drive mechanism). Machines with a kinematic drive mechanism are called disciplined piston

Cryocooler theory

19

(and displacer) coolers, see figure 2.9 for an illustration. Machines without such drive mechanism are called free piston coolers: the piston (and displacer) can move freely in the cylinders and are driven by fluidic motion and some kind of actuating principle, for instance a voice-coil electromechanical transducer. For β-Stirling coolers also hybrid systems can be considered, for instance with a disciplined piston and a free displacer. The expansion piston of the α-Stirling disciplined piston cooler performs work on the crank of the cooler that may be re-used for the compression piston somewhat later during the cycle. To facilitate this, a flywheel can be used as energy buffer; see figure 2.9.

α-Stirling: two actuators or one actuator and a resonantly coupled piston. For the α-Stirling free piston coolers a distinction can be made between a cooler with two actuators and a cooler with one actuator and the second piston resonantly coupled. For the two-actuator cooler the expansion work performed at the cold side is transferred at the cold side to the electrical domain by an actuator, and electrically dissipated at the ambient environment. The actuator can, for instance, be a voice coil or piezoelectric disc. Such a configuration is very difficult to apply in practice, since all losses in the actuator itself are dissipated at the cold side and subtracted from the net cooling power. To obtain net refrigeration power, a very energy-efficient electromechanical actuator is required. Only one theoretical description of this configuration was found in the literature [2.12], without experimental data.

Figure 2.11 shows a simplified physical model of the α-Stirling free piston cooler with resonantly coupled expansion piston [2.11]. The system can be considered as two masses suspended by three springs which can be driven as a coupled oscillating system with two degrees of freedom. The springs connected to the masses of the two pistons represent a combination of the gas springs and linear flexural springs required to stabilize the pistons. The gas springs are made up by the sealed volumes at the back of the pistons (for a single acting cooler – see below for the difference between single and double acting coolers). The spring between the two masses (not drawn in the figure) is made up by the gas in the volumes between the two pistons.

massactuator

Figure 2.11 Simplified physical model of the α-Stirling free piston cooler with resonantly coupled expansion piston [2.11].

By choosing a proper driving frequency of the compression piston relative to the resonance

frequency of the expansion piston, the required phase difference between the compression and expansion piston can be chosen; see figure 2.8. In order for the system to remain stable, a damping effect must be imposed on the cold-side oscillating mass to dissipate a portion of the compression work being supplied by the actuated compression piston. This dissipation effect is provided by the working fluid flowing through the regenerator (if the regenerator does not provide all the dissipation required, a flow restriction can be added to the warm end of the regenerator). The damping effect is represented by the dash pots drawn in the physical model of figure 2.11.

Chapter 2

20

The expansion work performed in this cycle is transferred back to the warm side of the system due to the resonant coupling between the two pistons. In this process it is essential to notice that, with sinusoidal motion of the pistons, the compression of the working fluid is not accomplished entirely by the hot-side piston but also by the cold-side piston. Analogously, the expansion of the working fluid is not accomplished by the cold-side piston alone, but again by both pistons. In the continuous process of compression and expansion, the following schematic steps can be distinguished. Assuming that irreversibilities are small, the expansion work performed at the cold side of the cooler accelerates the cold-side piston and is transferred into kinetic energy of the piston. This kinetic energy is subsequently turned in direction by means of the (gas) spring and used to shift and re-compress the gas, the majority of which resides at that time in the hot section of the cooler. Therefore, a significant part of the expansion work is rejected as compression heat at the warm side of the cooler. Of course part of the expansion work is dissipated in irreversibilities occurring in, for instance, the gas spring at the cold side and in the regenerator.

Figure 2.12a shows an α-Stirling free piston cooler with resonantly coupled expansion piston, as proposed by Peterson [2.11]. This cooler contains membrane pistons with bellows instead of normal pistons, but that does not affect the principle of operation.

α-Stirling: single or double acting. Another distinction that can be made for α-Stirling coolers is between single and double acting coolers. In a single acting cooler each cylinder contains one compression/expansion space, the other side of the piston is a gas reservoir that acts as a gas spring. In double acting coolers both sides of the piston are used as compression/expansion space, see figure 2.9. Double acting systems were invented primarily as (automotive) engines aiming at large powers (> 10 kW). Under such conditions double acting engines are economically more attractive because of increased work output per engine volume

Figure 2.12 Large (a) and miniature (b) version of the α-Stirling free piston cooler with resonantly coupled expansion piston, as proposed by Peterson [2.11].

TH

TA

Figure 2.13 Double acting α-Stirling engine configuration, investigated by Philips and General Motors for automotive applications [2.1].

Cryocooler theory

21

[2.1]. Double acting engines with disciplined pistons were investigated at the Philips Laboratories and by General Motors in the configuration as shown in figure 2.13; in that configuration the temperature difference stands from top to bottom over the cylinders and pistons. One engine is made up by the top part of a cylinder and the bottom part of an adjacent cylinder. Of more interest for cooler configurations is configuration (6) in figure 2.9. It is a symmetric system with a double acting compressor at the warm side and a double acting expander at the cold side. Figure 2.14 shows a displacement-time diagram for the system. The displacement diagram of the expansion cylinder is drawn at the top and bottom of the displacement diagram of the compressor cylinder, so that the movement of gas between both systems can be indicated by the shaded and double shaded areas in the diagrams. The compression - displacement - expansion - displacement sequence occurs with a 180 degrees phase difference between both systems. Figure 2.12b shows an example of a miniature double acting α-Stirling free piston cooler with resonantly coupled expansion piston, as proposed by Peterson [2.11].

β-Stirling: integral or split. An important distinction for β-Stirling coolers can be made between integral and split systems. For integral systems the piston and displacer are located in the same cylinder; the cycle shown in figure 2.10 illustrates the operation of this system. Figure 2.15 shows a split Stirling configuration: piston and displacer are located in separate cylinders which are connected by a split-pipe and which can be driven in a number of ways discussed later in this section. Thermodynamic operation of split β-Stirling coolers is slightly different from operation of integral coolers. Again the gas is compressed isothermally from state 1 to 2.

compressorcylinder

disp

lace

men

t

gas movement of system 1 (in top compartments)gas movement of system 2 (in bottom compartments)

time

expansioncylinder

regenerator

regenerator

expansioncylinder

exp.

displ.

compr.

displ.

exp.

displ.

compr.

displ.

exp.

displ.

exp.

displ.

compr. compr.

displ.displ.

Figure 2.14 Displacement-time diagram for a double acting α-Stirling cooler.

1) 2) 3) 4)

TC

TA

Figure 2.15 Piston and displacer movement of a split β-Stirling cooler.

Chapter 2

22

Apart from the compression volume, also the volume of the split-pipe and the warm end of the displacer contributes to the compression volume where compression heat QA is rejected to the environment. From state 2 to 3 the compressed gas is displaced from the compression to the expansion space by the movement of the displacer. So far, the steps are equivalent to the steps of an integral β-Stirling cooler. The difference comes in the expansion process 3 to 4. All gas is expanded against the compression piston, but only the gas that remains at the cold side of the displacer contributes to the cooling effect. During the expansion step, gas flows through the regenerator, constantly reducing the amount of gas that generates a net cooling effect at the cold side. If all steps are made reversibly, the performance of a split β-Stirling cooler resembles that of an integral β-Stirling cooler. However, the amount of cooling obtained per mass of compressed gas that is shifted through the regenerator to the cold side is reduced. Since irreversibilities during the different steps are inevitable, the Coefficient of Performance of the split β-Stirling cooler is somewhat lower than that of a comparable integrated β-Stirling cooler.

Split β-Stirling coolers with a free (resonant) displacer are favored for infrared sensors and electronic applications because of the possibility to separate the compressor from the cold head. This reduces the EM and mechanical interference levels at the cold head caused by the vibrating linear compressor heads. Moreover, a compact design can be made of the separate cold head so that it can easily be integrated with an application. A significant number of vendors sell split β-Stirling coolers. As an example, figure 2.16 shows three Signaal Usfa split-Stirling coolers.

Figure 2.16 Photograph of three Signaal Usfa Stirling coolers. Cooling powers range from 0.5W to 1.5 W at 80 K. Diameter of the smallest cold tip: 8 mm.

In order to obtain cooling power, a β-Stirling cooler requires a proper phase-difference

between the displacements of the compressor piston and the displacer, similar to the phase difference required for the α-Stirling cooler. As was discussed before, this phase-difference can be obtained by attaching the piston and the displacer to a kinetic drive mechanism, resulting in a disciplined piston/displacer β-Stirling cooler. An important difference with α-Stirling coolers is that no work is performed on or by the displacer, apart from the small amount of work required to overcome the irreversibilities in moving the fluid through the regenerator. Two different methods of moving the displacer in a free piston/displacer system

Cryocooler theory

23

are distinguished in the scheme of figure 2.9. One option is a resonant system, similar to the one discussed for the α-Stirling cooler. As an example of such a system, figure 2.17 shows a cross section of a commercial resonant split β-Stirling cooler [2.13]. The displacer with integrated regenerator is connected to a spring. The required phase difference between piston and displacer can be obtained by choosing a proper driving frequency relative to the resonance frequency of the mass-spring system of the displacer.

β-Stirling: hysteresis mechanisms. Another method to obtain a proper phase difference is denoted in figure 2.9 by a ‘hysteresis mechanism’, which stands for any mechanism that is able to shift the displacer at the right moment between both ends of the cold cylinder. This hysteresis-like movement may, for example, be induced by the varying fluid pressure, or by some mechanism that interfaces the compressor piston and the displacer. Figure 2.18 shows one example of a split β-Stirling cooler, originally developed by Walter Higa at Jet Propulsion Laboratory and described by Horn [2.14]. The expander contains a regenerative displacer with a displacer rod added at the ambient temperature end extending through the seal into a so called ‘bounce space’. The movement of the displacer is based on a force balance acting upon it. When the compressor operates, the pressure of the working fluid pc fluctuates periodically at the same frequency as the compressor. The pressure in the bounce space remains essentially constant at the mean cylinder pressure pb due to a limited gas leakage past the seal. Therefore, a net fluidic force acting on the displacer is present which is equal to the pressure difference, ∆p = pc – pb, times the area of the displacer rod. This force tends to move the displacer towards the ambient end of the cold finger if ∆p > 0. When this net force exceeds the seal and

compressionvolume

displacer/regenerator

thin-walledcylinder

Figure 2.17 Cross section of a commercial resonant split β-Stirling cooler [2.13].

p

Vexpansion space

1

12

2

3

3

bounce space

seal

Figure 2.18 (a) Schematic cross section of a displacer with bounce space of a free split β-Stirling cooler with (b) work diagrams [2.14].

Chapter 2

24

fluidic friction forces, the displacer begins to move. Figure 2.18 illustrates the movement of the displacer for three different (quasi-static) conditions in which only 3) is a hysteretic mode: 1) a displacer without mass and friction forces acting on it; 2) a displacer with mass (inertia) but without friction forces acting on it, and 3) a displacer with mass and friction forces acting on it. In both situations 1 and 2 the displacer moves in both directions along the same line and there will, consequently, be no net refrigeration effect. In situation 3 the hysteretic effect of friction is used to create the required phase difference so that refrigeration can be obtained.

Figure 2.20 (a) Schematic diagram of snap-action spring with (b) force-displacement diagram [2.15].

Another hysteresis mechanism is demonstrated by Nakajima in a miniature Stirling engine

[2.15]. Figure 2.19a shows a schematic cross section of the miniature engine. It consists of two cylinders containing a compressor piston and a displacer which are connected together via a mechanical spring. A temperature difference is imposed from top to bottom on the cylinder of the displacer. A snap-action spring connected between the displacer and the cylinder causes the hysteretic characteristic of the displacer relative to the movement of the compression piston. A schematic diagram of such snap-action spring (well known from switches) and a force-displacement diagram are given in figure 2.20. Due to the presence of this snap-action spring, the movement of the piston and that of the displacer look like the diagrams given in figure 2.19b. Experiments have confirmed this operating principle [2.15]. Other optional hysteresis

Figure 2.19 (a) Miniature Stirling engine with snap-action spring and (b) displacement-time diagrams [2.15].

Figure 2.21 Alternative hysteresis mechanisms formed by electrostatic and magnetic forces.

Cryocooler theory

25

mechanisms suggested by Nakajima are an electrostatic type and a magnetic type, as illustrated in figure 2.21.

2.3.4 Gifford-McMahon and Solvay cycles

Gifford-McMahon and Solvay cycles form a class of regenerative coolers which are driven by a separate DC-compressor that generates a stationary pressure difference [2.1]. The expansion stage is connected to the compressor with flexible lines that may be several meters in length. Cooling is obtained by opening/closing of active valves and proper shifting of the gas between the warm and cold side of the expansion stage. Two types of expansion stages can be distinguished, which are named after their inventors. The first is the Gifford-McMahon (GM) cycle which operates with a displacer, and the second is the Solvay cycle which operates with an expansion piston.

Figure 2.22 Idealized Gifford-McMahon cycle. The operation of the GM cycle is illustrated in figure 2.22. The expansion stage consists of

a closed cylinder that contains a displacer with regenerator. The displacer is connected to a light drive mechanism so that it can be moved between both ends of the cylinder. In this way the volumes at the ambient and cold side of the displacer can be varied from zero to maximum but the total volume remains constant. Four steps can be distinguished in the operation. In step a, the displacer is located at the cold side and the high-pressure valve is opened so that gas can flow into the volume located at the warm side. Consequently, the pressure in the expansion stage increases from pL to pH and compression heat is rejected at ambient temperature. In step b, the displacer is shifted to the warm side of the expansion cylinder, forcing the gas through the regenerator to the cold side. In that step, the gas is precooled by the regenerator to the low temperature and the density of the gas is increased. During step b the high-pressure valve remains open so that the high pressure pH is kept constant. Consequently, more gas flows through the valve into the expansion stage to compensate for the increased density of the gas that is at the cold temperature. When the displacer is located at the warm side and the volume of the expansion stage is at its maximum V2, then the high-pressure valve is closed. In step c, cooling is obtained by opening the low-pressure valve and expanding the gas at the cold side to the low pressure pL. The gas flows through the regenerator where it is heated to ambient level, and from there back to the compressor. In step c it is important that the low-pressure valve is opened slowly to facilitate a constant flow of gas through the regenerator. Slight flow variations are permissible but very large surges of fluid through the matrix seriously affect the

Chapter 2

26

regenerator effectiveness. In step d, the low-pressure valve remains open and the displacer shifts back to the cold side. Consequently, the low-pressure gas is shifted to the warm side of the expansion stage, and some more gas flows back into the compressor at a constant pressure pL due to the decreased gas density at ambient temperature.

The intrinsic COP of GM-coolers is somewhat lower than the Carnot efficiency, in contrast to the intrinsic COP of Stirling coolers. A large pressure drop over both valves exists when they open, and this pressure drop causes entropy generation. This intrinsic loss is, however, for many applications not of practical importance.

GM-coolers with helium gas as the working fluid were primarily developed for cryopumping and are now available from a large number of suppliers among which the bigger companies in vacuum equipment. The coolers are mostly manufactured in single-stage and double-stage versions. The latter type has cooling powers of several Watts at the coldest stage (typically at 20 K) and several tens of watts at the other stage (typically at 80 K). As an example, a 2-stage GM cold head and a 4 kW compressor of Leybold are depicted in figure 2.23.

The Solvay cooler is illustrated in figure 2.24. The expansion stage consists of a cylinder with piston that is connected to a drive mechanism, a separate regenerator and high and low-pressure valves. The temperature difference stands over the cylinder and piston so the piston

Figure 2.23 GM cold head and separate compressor (Courtesy of Leybold). Typical compressor size: 0.5 m x 0.5 m x 0.5 m.

Figure 2.24 The Solvay cooler.

Cryocooler theory

27

should be made of a low conductivity material. A dynamic gas seal is located at the ambient temperature end of the piston to keep the gas in the cylinder. For the Solvay cycle also four steps can be distinguished in the operation (not drawn). In step a, the piston is located at the cold end of the cylinder and the high pressure valve is opened. High pressure gas enters compressing the small amount of gas that remains in the void volumes of the cylinder and the regenerator from pressure p1 to p2. In step b, when the maximum pressure is reached, the piston is raised increasing the cold volume from V1 to V2. The pressure remains constant at p2 since gas is admitted via the opened high pressure valve. All gas reaching the cold end is precooled with the regenerator. In step c, the high pressure valve is closed and the piston continues to expand from V2 to V3, reducing the pressure from p2 to p1. In this step, the gas in the cold end performs work on the piston and performs refrigeration. In step d, the low pressure exhaust valve is opened and the low pressure gas in the cold end is pushed out of the volume by the piston which reduces the volume from V3 to V1. When the minimum volume V1 is reached, the low pressure valve is closed again.

Compared to the GM cycle, the Solvay cycle has a somewhat higher theoretical efficiency. This is caused by the complete reversible expansion against the piston, in contrast with the GM expansion, where part of the expansion (over the low pressure valve) is irreversible. This advantage of the Solvay cycle is in practical machines, however, overruled by the disadvantages of the sliding seals of the piston that should withstand high pressure differences. Not many practical examples exist of the Solvay cycle, in contrast to GM machines that are widely used for a number of different applications.

2.3.5 Vuillemier cycle

The Vuillemier cycle is a cooling cycle that is driven by thermal energy instead of electrical or mechanical energy that is used to drive other regenerative cooling cycles [2.1]. The VM cycle can, therefore, in fact be viewed as a thermodynamic cooler that is interfaced to a thermodynamic engine, see figure 2.25. High temperature heat, QH, is supplied to the engine-side of the system, which is then converted into mechanical work (compressed gas) and ambient temperature waste heat, QA1. The produced mechanical work (compressed gas) is transferred to and used by the cooler part of the system to drive a cycle in which heat is adsorbed at low temperature, QC, and rejected at ambient temperature, QA2. Physically, a VM cooler consists of two regenerative displacers: a larger one for the engine-side of the system and a smaller one for the cooler-side. The displacers are cyclically moved by some light drive

TH

TA

QH

-QA1

TA

TC

-QA2

QC

W

(a) (b)

Figure 2.25 (a) In thermodynamic terms, a Vuillemier cooler can be viewed as a cooler that is interfaced to an engine. (b) Essential elements of a Vuillemier cryocooler [2.16].

Chapter 2

28

mechanism. Proper phasing is required between the movement of both displacers, which can, for instance, be obtained with some form of kinematic drive mechanism such as a crankshaft. The power required to drive the displacers can be very small compared to the thermal power required to drive the cycle since only friction of the fluid and seals must be overcome by the drive mechanism.

Figure 2.26 illustrates schematically the steps for a complete cycle of a VM cooler. From state 1 to 2, the hot displacer is moved from the hot to the ambient side so that there is a gas flow through the regenerator into the hot volume. As the gas flows through the regenerator, heat is exchanged from the regenerator material to the gas. As a consequence, the average temperature of the fluid in the system rises and, since the total volume remains constant, the pressure and density in the system rises as well: the gas is thermally compressed. In this step heat is rejected by the gas in the ambient and hot volumes to the environment. A similar step will be discussed in more detail in section 2.3.8. Next, from state 2 to 3, the cold regenerator is moved from the cold to the ambient side so that the compressed gas is allowed to flow into the cold end. Because the average temperature of the gas in the system reduces slightly, the pressure also drops slightly and some heat is absorbed due to this gas expansion. Heat is absorbed partly at TA and partly at TL. From state 3 to 4, the hot displacer is moved back to the hot side allowing the gas to flow through the hot regenerator into the ambient volume. In this step the fluid pressure is reduced significantly and the gas in the system expands, taking up heat from the environment including the cold end. The pressure drop and gas expansion causes some gas to flow from the cold end through the regenerator to the ambient volume. From state 4 to 1, the cold displacer moves back to the cold side returning the cycle in its initial state. The regenerative steps are discussed in more detail in section 2.3.8.

An advantage of VM cryocoolers is the potential for a long life which is made possible by the low mechanical forces acting on the drive mechanism, bearings and seals. These lower forces arise as a consequence of the low pressure ratios (1.1 to 1.2) in VM coolers compared with, for instance, Stirling coolers (about 2). These lower pressure ratios also result in a disadvantage, which is a low cooling power per cooler mass. The real advantage of VM coolers is the ability to use a thermal energy input to produce refrigeration. This can be supplied by solar energy or radioisotopes (important for space applications), combustion of fuels or waste heat. In chapter 3 it will be shown that the ability to use thermal energy input is also an important advantage for miniaturization of such a system.

1) 2) 3) 4)

TC

TH

TA

Figure 2.26 The four essential states of a complete cycle of the Vuillemier cooler.

Cryocooler theory

29

2.3.6 Pulse tube cycle

A pulse tube (PT) refrigerator is a variation of the Stirling cycle where the moving displacer is eliminated and replaced by a fixed tube configuration (without moving components) in which a pressure wave is generated. The result is a cryocooler which has the potential for lower cost, longer life, and less vibration at the cold tip. Several variations of the PT refrigerator now exist. The three main types were, among others, compared by Radebaugh et al. [2.17] and the basic operation of two of them will be described briefly in this section.

Q ,TA A Q ,TC C

WCWA

Q ,TA A Q ,TA AQ ,TC C Q ,TC C

WA WAWC

A A A A

regeneratorcompressor

reservoir

compressibledisplacer

orifice

ambient HXambient HX

cold HX expander

Orifice Pulse-Tube cooler Basic Pulse-Tube cooler

a-Stirling cooler

Figure 2.27 Schematic of the basic pulse tube and the orifice pulse tube. For comparison, a schematic of an α-Stirling cooler is drawn above the orifice pulse tube.

Development of the pulse tube started relatively recently (in 1963) when Gifford and

Longsworth discovered that a pressure wave could generate a temperature gradient along a tube because of a surface heat pumping mechanism [2.18]. Such refrigerator is now called the basic pulse tube and is schematically depicted in figure 2.27. The basic pulse tube is closed at one side where a heat exchanger is located to transfer heat between the working gas and the surroundings in order to reject heat QA’. The other side is open but contains also a heat exchanger to absorb refrigeration power QC. The open end is connected to an alternating compressor via a regenerator, a configuration similar to that used in the α-Stirling cooler. During the compression part of the cycle, any part of the gas in the pulse tube moves toward the closed end and at the same time experiences a temperature rise due to adiabatic compression. At that time, the pressure is at its maximum and during the maximum plateau in the pressure wave the gas is cooled somewhat by heat transfer to the tube walls. In the expansion part of the cycle the same element of gas moves towards the open end of the pulse tube and experiences a cooling due to the adiabatic expansion. During the minimum plateau in the pressure wave, the gas is warmed through heat transfer from the tube walls. The net result of cycling the pressure in this manner is a shuttle heat transfer process in which each element of gas transfers heat toward the closed end of the pulse tube. The lowest temperature that was reached with a single stage basic pulse tube is 124 K using a pressure ratio of 4.25. Because of this modest temperature not much work occurred on pulse tubes since the end of the 1960s.

In 1984, however, an important new pulse tube concept was introduced by Mikulin et al. [2.19] and later adapted by Radebaugh and co-workers [2.17]. In this concept an orifice was inserted at the warm end of the pulse tube to allow some gas to flow into a relatively large

Chapter 2

30

reservoir volume, see figure 2.27. Operation of an orifice pulse tube (OPT) is similar to operation of the two piston α-Stirling cooler (see figure 2.8), with the difference that the cold mechanical piston is replaced by a compressible gas volume within the pulse tube, see figure 2.27. This volume of gas acts as a displacer, adiabatically transferring work from the cold end to the hot end of the pulse tube. Compressing the gas displacer also requires work, but this is recovered when the displacer re-expands later in the cycle. Compared to the α-Stirling cooler, the mechanical work of expansion transferred to the hot end is not recovered but is dissipated as heat at the hot end of the pulse tube. The orifice and reservoir provide the phase shift required to produce the work flow. Other than what happens to the expansion work, the ideal OPT behaves just as an α-Stirling cooler. Essential for proper operation of the OPT is that the gas volume in the pulse tube behaves adiabatically and that it does not exchange heat with the walls – this in contrast to the basic pulse tube [2.5]. This makes it intrinsically difficult to scale the OPT to small dimensions since interaction with the wall becomes more dominant for smaller dimensions, as will be discussed in chapter 3.

2.3.7 Regenerative cooling losses

The theoretical Carnot efficiency given by Eq. (2.8) can never be obtained because of various loss mechanisms in regenerative coolers.* Detailed knowledge and modelling of these losses is important during the design phase of a regenerative cooler. Moreover, scaling of regenerative coolers is strongly dependent on the way these losses scale. Below, the most important loss factors are discussed, and based on that, in section 3.3.4 the scaling behavior is discussed. Losses that occur in the compressor actuator are not taken into account. Examples of such losses are resistance losses in magnetic actuators, magnetic hysteresis losses, etc.

Thermal conduction. The temperature gradient from TA to TC is present over the walls of the cold stage, over the regenerator/displacer and over the gas in the regenerator. This gradient causes a heat flow from the warm to the cold side that is subtracted from the gross cooling power. Therefore, the cold stage and displacer walls should be made long and as thin as possible to reduce the heat transfer due to conduction.

Regenerator losses. As discussed in section 2.3.2, a perfect regenerator does not exist and, therefore, regenerator losses are present. These losses can be divided in two types: heat losses and flow losses. Heat losses occur because not all heat can be transferred from the gas to the regenerator and vice versa. This is caused by a limited heat transfer coefficient and a limited regenerator heat capacity. As a result, when the gas flows through the regenerator to the cold end, it will have a higher temperature than the gas present at the cold side. There is, therefore, a net heat flow through the regenerator from the hot side to the cold side. In a typical regenerator, between 95 and 99% of the available heat is transferred between the gas and the regenerator; the rest is a loss factor. Regenerator flow losses are caused by the pressure drop over the regenerator when the gas flows through it.

* In this thesis it is assumed that the net cooling power equals the gross cooling power minus the various loss terms that occur in the cooler itself, such as heat conduction through the cold stage and dissipation losses. As a consequence, produced heat at the outside of the cooler should be cooled away by the net cooling power. This heat may include terms such as: radiation on the outside of the cold stage and the attached load, heat conduction from ambient to the cold temperature through wires and support structures, dissipation within the load itself, etc.

Cryocooler theory

31

Gas leakage losses. Use of clearance seals or gas bearings to levitate moving parts involves leakage of gas. This leaking gas constitutes a loss of available work in a regenerative cooler.

Shuttle heat losses. Shuttle heat losses are caused by the mismatch of thermal gradients between the displacer and the cylinder. The displacer is shorter than the cylinder wall by the length of the stroke but it has, however, the same temperature extremes. As a consequence, the displacer picks up heat from the cylinder when it is at the warm end and it gives off heat to the cylinder when it is at the cold end of its stroke: the displacer shuttles heat from the warm to the cold end. Leo [2.21] approximates the shuttle heat transfer by:

cyl

CAgsh l

TTd

OfYP)(

186.0 2 −⋅=

λ (2.11)

where f is the cycle frequency, Y is the displacer stroke, O is the perimeter, d is the radial clearance, lcyl is the length of the cylinder and λg is the heat conductivity of the gas.

Pumping losses. The pumping losses occur as a result of the cyclic filling and draining of the clearance volume between the displacer and the cylinder. Generally, this volume is at the warm end closed by a seal and at the cold end open to the cold volume. As a consequence, when the gas is compressed high pressure gas flows from the cold end into the clearance volume taking up heat from the walls. When the pressure falls the warmed gas flows back into the cold end and reduces the gross cooling power. Leo [2.21] gives the following expression for the pumping losses:

6.16.06.1

6.26.16.16.1minmax

6.0

25.1

)()(2

+

−−=

CAg

CApcylpu

TTZR

dTTcfpplOP

λ

(2.12)

where Z is the compressibility of the gas and R is the gas constant. Non-ideal cold and ambient heat exchangers. While a temperature gradient is necessary to

effect heat transfer through the wall of a heat exchanger, it is also a deviation from ideal behavior for the system and results in a generation of entropy.

Friction. Some seals, particularly ring seals, rely on friction between components to create a seal. This friction acts as a drag on the moving component consuming power. The effects of this drag can easily be predicted knowing the forces involved.

2.3.8 Twente-Stirling cycle

In this section a new cooling cycle is proposed that has similarities with the Stirling cycle and the Gifford-McMahon cycle. No description of the proposed cycle was found in the literature and it is, therefore, named the Twente-Stirling cycle. It appears that this cycle is suitable for scaling to miniature dimensions. In section 3.4 a microcooler design will be discussed that is based on the Twente-Stirling cycle.

The configuration and steps of the cycle are illustrated in figure 2.28; it could be classified as a free-displacer β-Stirling cooler with a hysteresis-like mechanism. The cooler consists of a regenerator/displacer with integrated flow restriction on the warm side of the regenerator. The displacer is suspended from a spring that is in the neutral position when the displacer is positioned against a stopper, which is located at the warm side of the displacer. At the ambient side a compression piston is required that is able to generate relatively rapid pressure changes.

Chapter 2

32

The cycle starts from state 1 to 2 with rapid compression of the gas from pressure p1 to p2. The combination of spring and flow restriction is chosen such that not much gas flows from the ambient to the cold volume during the rapid compression step and as a consequence, the displacer is forced to move down. From state 2 to 3 the spring forces the displacer to move slowly to the warm end, shifting the ambient temperature compressed gas through the regenerator to the cold volume. From state 3 to 4 the force on the compression piston is released, reducing the pressure in the ambient volume to p1 and pulling the displacer against the stopper. From state 4 to 1 gas flows through the regenerator and flow restriction out of the cold volume, moving the compression piston upward. As will be discussed in section 3.4, this cycle has significant advantages when applied on a micro scale. Below the ideal cycle of this cooler is described to establish elementary understanding. The following crude assumptions are made for this: • the gas behaves ideally • the regenerator behaves ideally (the void volume is zero, perfect regenerative heat transfer

occurs, no aerodynamic pressure drops exist) • the piston and regenerator movement occurs with non-sinusoidal rapid steps (which is

essentially the case for this cooler) • compression and expansion occur isothermally • heat conduction and radiation losses can be neglected • the displacer and spring are considered massless

1) 2) 3) 4)

TA

TC

1 2

xpiston

xpiston

xdispl

xdispl

3 4 1 2time

pres

sure

flow restriction

p1

p2

VA

VC

stopper

pressure in V and VA C

pressure in VC

pressure in VA

a)

b)

Figure 2.28 (a) Twente-Stirling cooler, making use of a flow restriction and spring to obtain the proper phase difference between compression and expansion of the gas (see text for a description of the cycle). (b) Schematic timing diagram of the piston and displacer movements, and of the pressures.

Cryocooler theory

33

Step 1-2. During the isothermal compression step, the internal energy of the gas at the ambient and cold sides of the cooler remains constant. Consequently, the work performed on the gas equals the heat rejected to the environment at the ambient and cold sides of the cooler. The work and heat added to the gas at the ambient and cold side can be derived by integration of the pdV terms:

∫ =−=−= −−

2,

1,

)ln(2,

1,1,121,21,

A

A

V

V A

AAAA V

VVpdVpQW (2.13)

∫ =−=−= −−

2,

1,

)ln(2,

1,1,121,21,

C

C

V

V C

CCCC V

VVpdVpQW (2.14)

where p1 is the pressure at state 1, and where VA,i and VC,i are the ambient and cold volumes at state i. For convenience, in this section all work and heat contributions are expressed in the following reference parameters: p1, VA,1, TA, TC and a parameter µ which represents the fraction of the initial cold volume to the total volume: µ = VC,1 / (VA,1 + VC,1). VC,1 can now be expressed as:

1,1, 1 AC VVµ

µ−

= (2.15)

The pressure and volumes at state 2 can be derived by application of the ideal gas law:

12

1pp

µ= (2.16)

1,2, AA VV µ= (2.17)

1,2, CC VV µ= (2.18)

Equations (2.13) and (2.14) can now be rewritten as:

)1

ln(1,121,21, µAAA VpQW =−= −− (2.19)

)1

ln(11,121,21, µµ

µ−

=−= −− ACC VpQW (2.20)

The total compression work during step 1-2 equals:

21,21,21 −−− += CA WWW (2.21)

Step 2-3. Although the total gas volume remains constant during movement of the displacer from state 2 to 3, there is a ‘work’ term pdV associated with the regenerative process. When the displacer/regenerator moves a distance dx from the cold to the ambient side, dN moles of gas (or a mass dm) flow through the regenerator and cool from TA to TC. Because of this cooling, the volume of these dN moles is reduced from dVA to dVC: the gas is thermally compressed in the regenerating process. Since the pressure p is determined by all N molecules in the cooler and dN << N, the pressure remains essentially constant during the movement of the dN moles. The (negative) heat flow from the regenerator to the gas can be calculated by application of the first law on the gas flowing through the regenerator:

dmTTcdmhhdQ ACpACgasreg )()(32, −=−=−→ (2.22)

Chapter 2

34

which equals the heat capacity of the molecules at constant pressure times the temperature difference.* Because the total volume at both sides of the displacer remains constant, the remaining gas in these volumes must undergo an isothermal expansion to compensate for the thermally compressed gas that flowed through the regenerator. The first law for an open system (see Eq. (2.1)) can be applied on the gas in the two volumes. Taking into consideration the isothermal condition and the ideal gas law, this leads to:

dpVdmhdVpdUdQ −=−+= (2.23)

This expression can be integrated over both gas volumes for the movement of the displacer, yielding the total heat taken up by the gas in the cold and ambient volume, QC,2-3 and QA,2-3 respectively. To make this possible, the volumes and the pressure must be expressed as a function of the normalized position x = VC,x / VC,1 of the displacer. For the pressure it can be found that:

)1(1

)( 0

−+=

C

A

TT

x

pxp (2.24)

where p0 is the pressure at x = 0 (displacer completely at the bottom), given by

)(1,

1,10

C

A

C

A

TT

V

Vpp += (2.25)

For the volumes follows:

1,)1()( CA VxxV −= (2.26)

1,)( CC VxxV = (2.27)

Now QC,2-3 is given by:

∫ ∫∫=

− ⋅∂∂

⋅−=−==1

32, )()(µx

CCCC dxxxp

xVdpVdQQ (2.28)

A similar integral can be found for QA,2-3. Integration of both integrals yields:

−+−

−+

+−=− )(ln1

1,132,CAC

A

CA

AC

A

CAC TTT

TTT

TT

TT

VpQµ

µµ

(2.29)

−+−

−+

−=− )(ln111,132,

CAC

A

CA

AC

AA TTTT

TT

TTVpQ

µµ

µ

(2.30)

The total heat taken up by the gas in the volumes, QC,2-3 + QA,2-3, is equal to a flow-work term performed on (or a heat flow to) the regenerator. This flow-work term is a part of the

* Notice that cp should be used to calculate the heat transfer to the regenerator, although the gas movement seems to be a constant volume process! The use of cp is explained by the infinitesimal steps that occur at constant pressure. Some textbooks on coolers erroneously suggest the use of cv for similar regenerating steps.

Cryocooler theory

35

total heat that flows from the gas to the regenerator, which can be obtained by integration of Eq. (2.22). This leads to:

A

ACAACpgasreg T

TTcVpTTmcQ

−+=−=−− )1()( 1,132, (2.31)

where m is the total amount of gas that flowed through the regenerator and c = 3/2 for mono-atomic and c = 5/2 for di-atomic gas molecules.

Step 3-4. In principle, no heat or work term is associated with this step since only the force on the piston is released and no volume change is associated with that.

Step 4-1. A gas volume dV flowing out of volume VC performs work on the gas in the regenerator. Assuming isothermal steps in the cold volume, the work and heat term added to the gas in VC is given by:

dpVdVpdQ CC −== (2.32)

The pressure at state 3 and 4 in VC equals:

)11

()1( 11,

1,143 +⋅

−=+==

A

C

AC

CA

TT

pTV

TVppp

µµ

(2.33)

Integration of Eq. (2.32) yields:

A

CA

p

p

CCC TT

VpdpVdQQ 1,114,

1

4

=−== ∫ ∫− (2.34)

At the same time work is performed on the compression piston; the associated work performed on the gas equals:

∫ −=−=−

1,

4,

1,114

A

A

V

V

AVpdVpW (2.35)

The heat transferred from the regenerator to the gas is, of course, the negative value of the heat term in Eq. (2.31).

Using the above-calculated values of the heat and work terms, the efficiency of this cooler

can be calculated. It is given by:

1421

14,32,21,

,

,

−−

−−−

+++

==WW

QQQ

W

Q CCC

totin

totCη (2.36)

Figure 2.29 shows η as a function of TC, for different values of µ, as well as the Carnot efficiency. It should be noted that the calculated efficiencies are very theoretical and of little practical use, since only the basic thermodynamic behavior is modelled to clarify the operating principle of this cycle. The only intrinsic loss in this model is the entropy being generated in the flow restriction during step 4-1, making the efficiency always smaller than the Carnot efficiency (similar to the entropy loss in the valves of GM coolers). Theoretically, the best performance is obtained for large values of µ (i.e. a relatively small VA,1 compared to VC,1) because this leads to a relatively small pressure drop over the flow restriction.

Chapter 2

36

Figure 2.30 illustrates some other first-order effects of the parameter µ on the thermodynamic behavior of the cooling cycle. Figure 2.30a shows that for large values of µ the cooling power per mole of ambient-temperature compressed gas (which flows subsequently through the regenerator) is limited, which will result in relatively large regenerator losses. For small values of µ the cooling power per mole of compressed gas is larger, but the required pressure ratio of the compressed gas is also large (see figure 2.30b). This will put more demanding requirements on the compressor. Clearly an optimum has to be found by detailed modelling of the different loss mechanisms that occur in a practical cooler, but that does not fall within the scope of this review.

T = 50 KC

T = 100 KC

T = 200 KC

µ

Q p

er m

ole

gas

(J/m

ole)

C

µ

pres

sure

rat

io

p /p2 1

p /p , T = 50 K3 1 C

p /p , T = 100 K3 1 C

p /p , T = 200 K3 1 C

(a) (b)

Figure 2.30 (a) Cooling power per mole of ambient-temperature compressed gas, as a function of µ and for different values of TC. (b) Pressure ratio p2/p1 and p3/p1 as a function of µ. p3/p1 is calculated for different values of TC. TA = 300 K for all curves.

50 100 1500

0.1

0.2

0.3

0.4

Cold temperature (K)

CO

P

Car

not

µ = 0.01

0.1

0.2

0.4

0.60.8

0.95

Figure 2.29 Efficiency η as a function of the cold temperature TC for the Twente-Stirling cooler. η is calculated for different values of µ = VC,1 / (VC,1 + VA,1). Furthermore: TA = 300 K for all curves.

Cryocooler theory

37

2.4 Recuperative cooling cycles

2.4.1 Classification and common aspects of recuperative cooling cycles

In a recuperative cooler a compressor generates a steady circulating fluid flow through some cooling system; an example of a recuperative cooler is a household refrigerator. In contrast to regenerative coolers where cooling power is almost always obtained by an ideal gas that performs work on the warm environment, in most recuperative coolers cooling is obtained by evaporation of a liquid that was obtained by consecutive compression and Joule-Thomson expansion. However, also expansion turbines performing work on the environment can be found in recuperative systems, both with ideal and non-ideal gases [2.1].

1 2

flow

flow restriction

Q = 0

p , ,T1 1 1ρ p , ,T2 2 2ρ

Figure 2.31 Schematic representation of the Joule-Thomson process. The Joule-Thomson throttling process is discussed in most textbooks on thermodynamics

[2.22, 2.23], but is summarized here since it is essential in the cooling cycle under study in this thesis. Consider the system shown in figure 2.31. It consists of a constant area duct containing some flow restriction which can, for instance, be a porous plug or a small capillary. Fluid at a high pressure enters through cross section 1 and expands through the flow restriction to a low pressure at cross section 2. If it is assumed first that the duct is thermally isolated so that no heat is transferred, second that the fluid velocities are small so that the change in kinetic energy can be neglected, and third that the change in potential energy can be neglected as well, then application of the energy equation for open systems (see Eq. (2.1)) results in:

21 hh = (2.37)

For any individual gas it is possible to draw lines of constant enthalpy on a pressure-temperature diagram; figure 2.32 shows a typical example. The initial temperature and high pressure in a throttling process determine a particular isenthalp. The final low pressure then

Figure 2.32 Typical constant enthalpy curves for a gas on the pressure-temperature plane.

Chapter 2

38

determines a point on this same isenthalp, thereby determining the final temperature. If the initial temperature and pressure lie to the left of the maximum the throttling process cools the gas. If the initial temperature lies to the right of the maximum a small pressure drop heats the gas, though a large pressure drop may cross the maximum and can either heat or cool the gas. By connecting the maxima of the isenthalpic curves, the striped curve in figure 2.32 results which is a plot of the inversion temperature as a function of pressure.

Point A on the inversion curve is called the maximum inversion temperature. It occurs where the pressure is zero. Maximum inversion temperatures for different gases are given in table 2.1. Gases with maximum inversion temperatures below ambient temperature (helium, hydrogen and neon) must be precooled to a temperature within the inversion envelope to ensure a decrease in temperature on isenthalpic expansion.

Table 2.1 Properties of gases that are eligible for use in cooling cycles which employ the Joule-Thomson effect. Boiling

point (at 1 bar) (K)

Maximum inversion temp. (K)

Critical temp. (K)

Critical pressure (bar)

Triple temp. (K)

Triple pressure (bar)

Helium-4 4.2 40 5.2 2.3 2.2 0.05 Hydrogen 20.2 205 32.9 12.8 13.8 0.07 Neon 27.1 250 44.4 26.5 24.6 0.43 Nitrogen 77.2 621 126.2 34.0 63.1 0.13 Argon 87.2 794 150.9 49.1 83.8 0.69 Oxygen 90.1 761 154.6 50.4 54.4 1.5⋅10-3 Methane 111.5 939 190.6 46.0 90.7 0.12 Krypton 119.6 209.4 55.0 115.8 0.73 Xenon 164.8 289.7 58.2 161.4 0.82 Ethylene 169.0 282.3 50.4 104.0 1.2⋅10-3 Ethane 184.3 305.3 48.7 90.3 1.1⋅10-5 Refriger. 32 221.2 351.4 58.0 137.0 5.4⋅10-4 Propane 230.8 369.9 42.5 85.5 1.7⋅10-9 Refriger. 22 234.1 369.3 49.9 180.0 0.03 Ammonia 239.6 406.7 116.3 220.0 0.34 Refriger. 12 243.1 385.2 41.2 198.2 0.09 Butane 272.3 425.2 38.0 134.9 6.7⋅10-6

Increase or decrease of the temperature upon a small pressure change can be written as:

dpdppT

dT H

H

µ=

∂∂

= (2.38)

where the differential µH = (∂T/∂p)H is referred to as the JT coefficient. Using Maxwell’s equations and the definition of the enthalpy, the JT coefficient can be converted to:

)1(

11

−=

+

∂∂

−−=

+

∂∂

−=

∂∂

∂∂

−=

Tcv

vTv

Tc

vps

TcT

hph

p

ppTppT

H

α

µ (2.39)

where α is the (temperature dependent) volumetric thermal expansion coefficient. If αT > 1, then a small decrease in pressure cools the gas. The inversion temperature is determined by αT

Cryocooler theory

39

= 1. For an ideal gas the coefficient of thermal expansion is equal to 1/T, so that there is no change in temperature in a JT expansion.

In recuperative coolers JT expansion occurs at the cold side of the cooler, as a step that is part of a closed cycle. Although the discussed JT effect illustrates the mechanisms that play a role in such cooling cycles, the performance of cooling cycles with JT expansion is, in fact, not determined by the JT effect at the cold side of the cooler, but by the enthalpy difference that is created upon compression of the gas at the ambient side of the cooler. Very effective cooling cycles can be obtained when the compression temperature is lower than the critical temperature of the working fluid; such cycles are called vapor compression or Rankine cycles, and will be discussed in section 0. Cooling cycles with JT expansion that should reach cryogenic temperatures often employ fluids with a critical temperature much lower than the compression temperature; examples of such fluids are nitrogen or oxygen. Such cooling cycles are called Linde-Hampson cycles and will be discussed in section 2.4.3. For both types of cycles the low temperature is determined by the boiling temperature at the low pressure of the cycle. Table 2.1 lists the boiling temperature for a number of gases at 1 bar vapor pressure, as well as the triple and critical pressures and temperatures, and the maximum inversion temperature.

2.4.2 Vapor compression cycle

A schematic diagram of a typical vapor compression cooler is given in figure 2.33a. It consists of a compressor, a condenser, a JT throttling valve and an evaporator. Basically, the cycle makes use of the pressure dependent saturation temperature of a liquid-vapor transition. The steps of the thermodynamic cycle are illustrated in the T-s diagram in figure 2.33b. After adiabatic compression (step 1-2), high pressure gas is condensed at a high temperature rejecting the latent heat of condensation to ambient temperature (step 2-3). Next, the high pressure liquid is expanded at constant enthalpy to a low pressure into the evaporator (step 3-4). After this step, the temperature of the fluid is reduced to the saturation temperature corresponding to the low pressure of the cycle. In the evaporator, heat is absorbed from the low temperature surroundings, in that way evaporating the low pressure liquid (step 4-1).

Since heat is rejected at ambient temperature TA (during section 2-2’ at a temperature slightly above TA) and absorbed at a low temperature TC, the cycle can be compared with the

T

s

liquid

compressor

evaporator

condenser

QC

QA

JT valve

1

2

3 TA

TC low pressure

high pressure

(a) (b)

2

3

44

1

2’

Figure 2.33 (a) Schematic diagram of the vapor compression cycle and (b) TS-diagram.

Chapter 2

40

efficiency of a Carnot cycle operating between TA and TC. If it is assumed that no irreversibilities are present in the compressor, then the only irreversibility occurs in the JT isenthalpic expansion process. The entropy change during expansion, ∆s34, is due to these irreversibilities and is not available for cooling and, therefore, reduces the efficiency of the cycle below the Carnot efficiency. The heat absorbed at the cold side of the cycle equals the heat of evaporation and is given by:

41sTQ CC ∆= (2.40)

The loss of cooling power due to the irreversibilities in the JT expansion process equals:

34, sTQQ CCCarnotC ∆=− (2.41)

When the low pressure and temperature of the cycle are reduced, ∆s34 increases relative to ∆s41 and the efficiency of the cycle reduces relative to the Carnot efficiency. This explains why vapor compression cycles with a small temperature difference can operate with an efficiency very close to the Carnot efficiency (typically 75 – 95% of the Carnot efficiency).

T

s

liquid

compressor

evaporator

counterflowheat exchanger

condenser

QC

QA

JT valve

1

2

3

45

6

TA

TC low pressure

high pressure

(a) (b)

123

4

5 6

Figure 2.34 (a) Schematic diagram of the vapor compression cycle in which isothermal compression and a counterflow heat exchanger are applied; (b) TS-diagram.

Before discussing the operation of the Linde-Hampson cycle, it is illustrative to consider the

vapor compression cycle in a slightly different configuration. If adiabatic compression is difficult because of a somewhat larger temperature difference between the low and high pressure gas, also (near) isothermal compression at ambient temperature could be applied. In such a configuration, low pressure gas that exits the evaporator has to be heated to the compressor inlet temperature before entering the compressor. This enthalpy change can be employed in a counterflow heat exchanger to precool the high pressure fluid before expansion occurs, see figure 2.34a. For both configurations of the vapor compression cycle it can be shown that the majority of the enthalpy difference that is available for cooling is created during the gas-liquid phase transition of condensation. For the complete cycle depicted in figure 2.34, the change in energy and enthalpy of the fluid is zero, yielding:

00 615645342312 =∆+∆+∆+∆+∆+∆⇒=∆ hhhhhhh (2.42)

Cryocooler theory

41

If the counterflow heat exchanger is assumed to operate perfect, it follows that ∆h34 = -∆h61. Furthermore, ∆h45 = 0 for isenthalpic JT expansion. Then it follows that

231256 hhh ∆−∆−=∆ (2.43)

For most fluids and operating conditions it can be shown that ∆h12 << ∆h23, so that

2356 hh ∆−≅∆ (2.44)

In conclusion, the enthalpy of cooling is created in the condenser by vapor compression (as was already mentioned at the end of section 2.4.1).

2.4.3 Linde-Hampson cycle

A schematic diagram of a Linde-Hampson cooling system is given in figure 2.35a; the steps of the thermodynamic cycle are illustrated in the T-s diagram of figure 2.35b. The system consists of a compressor, an optional aftercooler, a counterflow heat exchanger, a JT throttling valve and an evaporator. The system is very similar to the vapor compression cycle depicted in figure 2.34; the essential difference is the absence of the condenser. The vapor compression cycle makes use of the enthalpy of condensation, whereas the Linde-Hampson cycle makes use of the enthalpy change that is created by compression of a real gas in the van der Waals regime.

T

s

compressor

evaporator

counterflowheat exchanger

QC

QA

JT valve

12

45

TA

TC

(a) (b)

aftercooler

2’

3

12

3

4 5

2’’

3’x1-x

pH

pL

pM

2’

Figure 2.35 (a) Schematic diagram of a Linde-Hampson cooling cycle with (b) T-s diagram The Linde-Hampson cycle operates as follows. The working fluid is compressed

isothermally from a low to a high pressure (step 1-2). The compression step itself may also be adiabatic (step 1-2’) or polytropic (step 1-2’’), but in that case it should be followed by an aftercooling step so that in the end the low and high pressures at state (1) and (2) are at the same temperature. Next, the high pressure gas enters the counterflow heat exchanger and is precooled to state (3) by the returning low pressure gas that is simultaneously heated from state (5) to state (1). From state (3) to (4) isenthalpic JT expansion of the fluid takes place from a high to a low pressure. State (4) is generally located in the liquid vapor envelope and the fluid will partially condense during expansion. The entropy at state (4) is, in fact, the

Chapter 2

42

average entropy of the two-phase fluid that exists in a fraction x as saturated liquid in state (6) and in a fraction (1-x) as saturated vapor in state (5). Dependent on the fluid and the applied high pressure, state (3) may also be located inside the liquid-vapor envelope. As an example, such state is depicted by (3’). From state (4) to (5) the precooled liquid is evaporated by the heat that is supplied by the refrigeration load. The available cooling power corresponds to a load that maintains the amount of liquid in the evaporator on a stable level. As a last step, the low pressure gas is heated in the counterflow heat exchanger to the compression temperature.

For the complete cycle depicted in figure 2.35, the change in enthalpy of the fluid is zero, yielding:

00 5145342312 =∆+∆+∆+∆+∆⇒=∆ hhhhhh (2.45)

If the counterflow heat exchanger is assumed to operate perfectly, it follows that ∆h23 = -∆h51. Furthermore, ∆h34 = 0 for isenthalpic JT expansion. If these assumptions are valid, then it can be concluded that the enthalpy available for cooling equals the enthalpy change that is produced during the isothermal compression of the gas (as was already mentioned at the end of section 2.4.1):

1245 hh ∆−=∆ (2.46)

and the cooling power equals:

45hmPC ∆= & (2.47)

where m& is the mass flow. Cooling is only obtained if the compression temperature is below the inversion temperature of the applied fluid (∆h12 < 0), otherwise the fluid is heated upon expansion and the cooling cycle does not cool down at all.

An essential element in the operation of the Linde-Hampson cycle is the counterflow heat exchanger. In the discussion of the cycle it was assumed that the heat exchanger operates ideally, and hence that ∆h23 = -∆h51 in figure 2.35b. In practice this is never the case. A non-ideal heat exchanger operates with an efficiency thatcan be defined as (see figure 2.36a):

51

5'1

32

'32

max, hhhh

hhhh

qq

CFHX

CFHXCFHX −

−=

−−

==ε (2.48)

and the cycle changes to cycle (1’-2-3’-4’-5-1’). In this expression the maximum heat

T

s

TA

TC

12

3

45

pH

pL

1’

3’

4’

x

T1

T1’

T3

T3’

T5

non-ideal heatexchanger

ideal heatexchanger

Figure 2.36 (a) T-s diagram for a Linde-Hampson cycle that operates with a non-ideal heat exchanger. (b) Typical temperature distribution along the counterflow heat exchanger, both for an ideal and a non-ideal heat exchanger.

Cryocooler theory

43

transferred can also be defined as:

)( 52min,max, TTcq pCFHX −= (2.49)

where min,pc is the minimum of the specific heats of the high pressure gas and the low pressure

gas, Hpc , and Lpc , respectively, averaged over the required temperature range. For the Linde-

Hampson cycle Hpc , > Lpc , , which also explains why the temperature change of the high

pressure fluid is smaller than the temperature change of the low pressure fluid. In Eq. (2.48) the actual heat transfer through the heat exchanger can be defined as:

)()( 5'1,'32, TTcTTcq LpHpCFHX −=−= (2.50)

Figure 2.36b shows a typical temperature distribution for the high and low pressure gas in the counterflow heat exchanger, both for an ideal and a non-ideal heat exchanger. The design of the heat exchanger for a given mass flow should be such that the heat exchanger efficiency is above an acceptable level; heat exchanger modelling and design is discussed in more detail by Boersma [2.25]. Because of a non-ideal heat exchanger, the enthalpy available for cooling, ∆h45, is reduced with ∆h44’ = ∆h1’1. Therefore, the efficiency of the cooling cycle is reduced; it can be expressed as a function of the efficiency of the heat exchanger:

45

51

45

1'1

45

5'4

max,

)1(11hh

hh

hh

PP

CFHXC

Ccooler ∆

∆−−=

∆∆

−=∆∆

== εε (2.51)

The fraction ∆h51/∆h45 is dependent on the cooling cycle and the applied fluid. A Linde-Hampson cycle operating with nitrogen gas which is compressed from 1 to 100 bar and which cools from 300 K to 77 K, for example, has ∆h51/∆h45 = 12.2. As a consequence, the counterflow heat exchanger should operate with an efficiency of at least 92% to obtain a cooling power at all!

A number of adjustments exist on the discussed basic Linde-Hampson cycle, some of which are discussed later in this thesis. The addition of a precooler is discussed in section 4.6.2. Another small heat exchanger can be applied to pre-liquefy the high pressure fluid at the cold side; this is discussed in chapter 8.

Figure 2.37 shows two examples of Linde-Hampson coolers, both without compressor. The cooler in figure 2.37a is a small scale stainless-steel based cooler for cooling infrared sensors, including a vacuum housing around it. The cooler in figure 2.37b is made of etched glass layers which are glued together. It operates with nitrogen gas supplied at 100 bar from a bottle. The cooler produces a cooling power of about 250 mW.

2.4.4 Joule-Brayton cycle

To complete the discussion on recuperative cooling cycles, it is important to mention the Joule-Brayton cycle. Cycles based on Joule-Thomson expansion exhibit intrinsic thermodynamic irreversibilities which are especially large for cycles cooling from ambient to cryogenic temperatures. For small scale coolers these losses are not always problematic, but for large scale applications more efficient processes are required. For such processes an adiabatic expansion engine or turbine can be included at the cold side, so that the expanded fluid can perform work on the environment. In this way the efficiency can theoretically be

Chapter 2

44

increased close to the Carnot efficiency, also with the use of a gas that does not operate in the van der Waals regime.

2.5 Other cooling principles

In addition to gas-expansion coolers, many coolers are conceivable starting from the basic equation dQ = TdS, which was discussed in section 2.2. Any system that can be moved from an ‘ordered’ state with relatively low entropy So to a ‘disordered’ state with relatively high entropy Sd, is able to take up heat at a certain temperature T equal to T (Sd - So). An excellent survey of alternate cooling systems based on the entropy concept was written by Radebaugh [2.3]. In the following sub-sections two cooling methods are described based on this concept: thermoelectric cooling (2.5.1) and magnetocaloric cooling (2.5.2). Subsequently, an additional alternative that was developed recently, optical cooling, is considered (2.5.3).

2.5.1 Thermoelectric coolers

Electrons in a conductor or a semiconductor behave as a Fermi fluid with Fermi temperature

Th n

kmF =( )

*

3

2

2 2 3π (2.52)

where n is the electron density, k is Boltzmann’s constant, and m* is the effective mass of the electron [2.3]. Below the Fermi temperature, ordering occurs, and much below TF, the entropy is proportional to T. Because of the small effective mass TF, is relatively large in electron systems, in metals typically 6×104 K.

(a) (b)

Figure 2.37 (a) Small-scale Joule-Thomson expansion unit for cooling infrared sensors (roughly 12-cm high, courtesy of Hymatic Engineering Co. Ltd.). (b) MMR miniature Joule-Thomson cooler consisting of etched glass layers making up the counterflow heat exchanger and JT-expansion stage (courtesy of MMR Inc.).

Cryocooler theory

45

According to Eq. (2.52), the Fermi temperature can be lowered by reducing the electron density, as depicted in Figure 2.38. At a fixed temperature T0 a reduction of TF (from TF1 to TF2 in Figure 2.38) means an increase in entropy (∆S0 in the figure). Therefore, a transport of electrons from a metal to a semiconductor (e.g., Bi2Te3) or a semimetal (e.g., Bi) gives an increase in electron entropy, and heat is absorbed. This is the Peltier effect, and utilizing this effect for cooling is called thermoelectric cooling. The thermoelectric power is expressed by the Seebeck coefficient α, which is proportional to the electron entropy [2.3]. In thermoelectric cooling two loss mechanisms are relevant: ohmic losses which are proportional to the resistivity ρ (= 1/σ, with σ the electrical conductivity) and conductive losses which are proportional to the thermal conductivity λ. As a result, a figure of merit can be defined for a material as

Z = α σ λ2 (2.53)

If the parameters α, σ and λ are temperature independent, the maximum temperature drop ∆T that can be established is

∆T ZTL= 2 2 (2.54)

with TL the temperature of the cold end [2.26, 2.27]. In practical thermoelectric coolers, an n-type semiconducting material is combined with a

p-type material. In that way a current can be established with a double Peltier effect: one for the electrons that leave the junction through the n-type material, and one for the holes that leave via the p-type material. There is not only an entropy flow away from the junction in the n-type material, but also in the p-type material. A cooler formed by such a combination of two materials (1 and 2) has an overall figure of merit given by

( ) [ ]Z12 1 2

2

1 1 2 2

2= − +

−α α λ σ λ σ (2.55)

The Z values of thermoelectric materials are temperature dependent, and there is a marked distinction in this respect between n-type and p-type materials. With decreasing temperature the figure-of-merit of n-type materials increases from roughly 2×10-3 K-1 at 300 K to 6×10-3 K-1 at 100 K, whereas that of p-type materials typically decreases from 3×10-3 K-1 at 300 K to 1×10-3 K-1 at 100 K. Therefore, the limiting factor in cryogenic applications is the poor thermoelectric performance of the p-type leg.

Figure 2.38 Entropy of electron systems with high and low electron densities (n1 respectively n2).

Chapter 2

46

Furthermore, to achieve at low temperatures multiple Peltier stages are required. With each stage, a temperature step given by Eq. (2.54) can theoretically be realized. Starting from a warm-end temperature TH, Eq. (2.54) yields a cold-end temperature TL

( )T ZT ZL H= − + +1 1 2 (2.56)

This equation clearly shows the problem for cryogenic thermoelectric cooling: the lower the temperature, the more TL will approach TH, and the more so if Z becomes smaller. Assuming a constant figure-of-merit of 2×10-3 K-1, Eq. (2.56) gives successive stage temperatures of 300-242-201-172-149-132-118-107.... K in a multistage cooler. In this hypothetical case, a six-stage cooler could reach about 130 K. In practical coolers, however, this performance cannot be established. Figure 2.39 shows the typical COP that can be achieved as a function of the temperature difference for commercial more stage coolers [2.28]. For temperatures below 200 K (∆T ≈ 100 °C) the required number of stages increases rapidly whereas the COP of the coolers drops dramatically, to values well below 1% of the Carnot efficiency. Although thermoelectric coolers have a number of clear advantages (small size, simple use, reliable, cheap, no vibrations), they are currently not suitable for cryogenic applications because of this poor efficiency at lower temperatures. A further drawback is that a current of a few amperes is required, and this may produce considerable EMI. They can, however, be very useful for precooling purposes, for example to precool the fluid in Linde-Hampson coolers [2.29]. This can increase the efficiency of the Linde-Hampson cycle and in that way reduce the overall input power of the system. Such a precooling configuration is discussed in more detail in section 4.6.2.

Figure 2.39 Maximum COP as a function of the temperature difference and the number of thermoelectric stages [2.28].

Cryocooler theory

47

2.5.2 Magnetocaloric cooling

By demagnetizing a paramagnetic material, the magnetic domains become disordered and entropy increases. Thus heat can be absorbed. The magnetocaloric cycle is schematically depicted in the T-s diagram of Figure 2.40. The curve for the magnetized state (i.e., B > 0) has a lower entropy than that of the demagnetized state (i.e., B = 0): A → B: The material is magnetized in good thermal contact with the warm reservoir at temperature TH. (The associated heat of magnetization due to the decrease in entropy is rejected to the warm reservoir). B → C: The magnetized material is cooled to the temperature of the cold reservoir TL. C → D: Demagnetization of the material in good thermal contact with the cold reservoir. In the stationary case the heat of demagnetization TL ∆S is absorbed by the material, and the cold reservoir is cooled by the same amount. D → A: The demagnetized material is warmed to the temperature of the warm reservoir TH.

Figure 2.40 Magnetocaloric cooling represented in a T-s diagram. Magnetocaloric cooling has a number of disadvantages: it has a poor efficiency due to poor

regeneration of heat in steps B → C and D → A, it is bulky and heavy, and it requires high magnetic fields (of a few tesla); all of them make it not suitable to be applied on a small scale. The most important uses have been in two temperature ranges: (sub)-kelvin and near ambient. Initially, research was concentrated on extremely low temperatures, because in that range the contribution of the lattice to the entropy is small compared to the magnetic entropy changes. The materials used are cerium-magnesium-nitrate (CMN) for the range 1 mK - 1K and gadolinium-sulfate for 1 K - 10 K [2.3]. For applications near room temperature, large systems have been designed based on gadolinium as first suggested by Brown in 1976 [2.30]. The latter applications mostly concern large-scale air conditioning.

2.5.3 Optical cooling

Another interesting alternative cooling concept is cooling by means of anti-Stokes fluorescence. The essentials of this cooling principle can best be explained by considering a three-level atom imbedded in an otherwise transparent solid. Laser light of photon energy EL = E3 - E2 pumps an atom from energy level 2 to level 3. A subsequent radiative de-excitation moves the atom either back to level 2 or to the ground state, level 1. In the former case the emitted photon has the same energy EL as the absorbed laser photon and the system is unchanged. In the latter case the fluorescing photon carries away energy EF = E3 - E1 > EL and there is a net shift of an excitation from level 2 to level 1. The relative populations of levels 1

Chapter 2

48

and 2 are thus pushed out of thermal equilibrium. To restore thermal equilibrium, the atom makes a transition from level 1 to 2 by absorbing a phonon of energy EP = E2 - E1, thereby decreasing the solid’s thermal energy and thus cooling the transparent solid.

This idea of optical cooling is not new and dates back to 1929 [2.31]. The most important requirement for establishing net cooling is that the fluorescent efficiency is close to unity. That is, an atom of level 3 may not decay nonradiatively to a lower level by producing phonons. High fluorescent efficiencies are possible if the energy gap E3 - E2 is relatively large, and if the transparent solid is of extreme purity. It was only quite recent that such materials became available. This work was pioneered at Los Alamos National Laboratory by Epstein and co-workers, who used a heavy-metal fluoride glass doped with trivalent ytterbium ions. Their proof of principle was published in Nature in 1995, with a reported temperature drop of 0.3 K [2.32]. Gradually, the experimental results have been improved and the best result at the moment of this writing is a temperature difference of 56 K [2.33]. Based on this work, a system was designed to achieve a temperature of 80 K with a COP of 1% and a specific mass of 4 kg per Watt of cooling power [2.34].

2.6 Conclusions

Research towards the miniaturization of cryocoolers requires conceptual knowledge of the different cooling cycles which can be applied in cryocoolers. Elementary refrigerator theory tells that refrigeration can be obtained in two different ways: by changing the energy or enthalpy of a working medium during the absorption of heat or by performing work on the warm environment while absorbing heat to a working medium. A number of cooling cycles are based on both methods. Often fluid cooling cycles are classified according to the method of movement of the fluid. A large variety of regenerative cooling cycles exists, all of them using a fluid that moves periodically through a regenerator between the warm and cold side of the cooler. A new regenerative cooling cycle was proposed which appears particularly suitable for miniaturization because it reacts passively and non-resonant on a pressure wave from the compressor. Recuperative cooling cycles employ a continuous fluid flow through the cooling system. Often Joule-Thomson expansion is applied, after which the heat of evaporation of a liquid is used to generate refrigeration. The vapor compression cycle and the Linde-Hampson cycle are often treated as different cooling cycles, but from thermodynamic point of view they are almost identical. Other cooling techniques which are of particular interest for miniaturization are thermoelectric cooling and cooling based on anti-Stokes fluorescence. However, these cycles are currently not suitable for reaching cryogenic temperatures.

2.7 References [2.1] G. Walker, Cryocoolers, Part 1: Fundamentals, Plenum Press, New York (1983). [2.2] G. Walker, Cryocoolers, Part 2: Applications, Plenum Press, New York (1983). [2.3] R. Radebaugh, Fundamentals of alternate cooling, in G. Walker, Cryocoolers part 2: Applications,

Plenum Press, New York, pp. 129-175. [2.4] Cryo Cooler Database, version 1.0, Naval Research Laboratory (1999). [2.5] R. Radebaugh, A review of pulse tube refrigeration, Adv. in Cryogenic Engineering, vol. 35, Plenum

Press, New York (1990), pp. 1191-1205. [2.6] W.M. Kays and A.L. London, Compact heat exchangers, McGraw-Hill Inc., New York (1984).

Cryocooler theory

49

[2.7] R. Yaron, P. Alto, M.P. Mitchell, Foil regenerator, US Patent 5429177 (1995). [2.8] H.J.M. ter Brake, Cryogenic systems for superconducting devices, Applications of Superconductivity

(NATO-ASI), ed. H. Weinstock. [2.9] P.A. Rios, J.L. Smith, E.B. Qvale, An analysis of the Stirling-cycle refrigerator, Adv. in Cryogenic

Engineering, 14 (1969), pp. 332-342. [2.10] W.D. Stacy, Diaphragm Stirling cryocooler developments, Cryogenics, Vol. 32 (1992), pp. 138-142. [2.11] R.B. Petersen, Resonantly coupled α-Stirling cooler, US Patent 5813235 (1998). [2.12] L. Bowman, J. McEntee, Microminiature Stirling cycle cryocoolers and engines, US Patent 5749226

(1998). [2.13] Signaal Usfa, P.O. Box 6034, 5600 HA Eindhoven, The Netherlands. [2.14] S.B. Horn, M.E. Lumpkin, B.T. Walters, Pneumatically driven split-cycle cryogenic refrigerator, Adv.

in Cryogenic Engineering, Vol. 19 (1974), pp. 216-220. [2.15] N. Nakajima, K. Ogawa, I. Fujimasa, Study on microengines: Miniaturizing Stirling engines for

actuators, Sensors and Actuators, Vol. 20 (1989), pp. 75-82. [2.16] G.K. Pitcher and F.K. du Pre, Miniature Vuillemier cycle refrigerator, Adv. Cryog. Eng., vol. 15

(1970), pp.447-451. [2.17] R. Radebaugh, J. Zimmerman, D.R. Smith and B. Louie, A comparison of three types of pulse tube

refrigerators: new methods for reaching 60 K, Adv. in Cryogenic Engineering, vol 31, Plenum Press, New York (1986) pp. 779-789.

[2.18] W.E. Gifford and R.C. Longsworth, Pulse-tube refrigeration, ASME paper No. 63-WA-290 presented at Winter Annual Meeting of the American Society of Mechanical Engineers, Philadelphia, Pennsylvania (Nov. 17-22, 1963).

[2.19] E.I. Mikulin, A.A. Tarasov and Shkrebyonock, Low-temperature expansion pulse tubes, Advances in Cryogenic Engineering, vol. 29, Plenum Press, New York (1984), pp. 629.

[2.20] R. Radebaugh, A review of pulse tube refrigeration, Adv. in Cryogenic Engineering, vol. 35, Plenum Press, New York (1990), pp. 1191-1205.

[2.21] B. Leo, Vuillemier cycle cryogenic refrigeration system technology report, AFFDL-TR-71-85, WPAFB, Hughes Aircraft Co. (1971).

[2.22] H.B. Callen, Thermodynamics and an introduction to thermostatics, 2nd ed., John Wiley, New York (1985).

[2.23] J.P. Holman, Thermodynamics, 4th ed., McGraw-Hill, New York (1988). [2.24] J.G. Daunt, The production of low temperatures down to hydrogen temperature, in Encyclopedia of

Physics, ed. by S. Flügge, vol. 14, Low temperature Physics 1, Springer-Verlag, Berlin (1956). [2.25] N. Boersma, A counter flow heat exchanger for microcooling: modelling & characterization set up,

M.Sc. thesis, Twente University (1997). [2.26] H.J. Goldsmid, Thermoelectric refrigeration, Plenum Press, New York (1964). [2.27] D.M. Rowe (ed.), CRC Handbook of Thermoelectrics, CRC Press, Boca Raton (1995). [2.28] MELCOR Corp., 1040 Spruce Str., Trenton, NJ 08648, USA, http://www.melcor.com. [2.29] H.B. Lyon Jr. and J. Bierschenk, The potential for improved cycle efficiency by combining

thermoelectric coolers with vapor compression cycles in hybrid systems, Proc. 14th Int. Conf. on Thermoel., St. Petersburg (1995).

[2.30] G.V. Brown, Magnetic pumping near room temperature, Journal of Applied Physics, vol 47 (1976), pp. 3673-3680.

[2.31] P. Pringsheim, Zwei Bemerkungen über den Unterschied von Lumineszenz- und Temperaturstrahlung, Zeitung der Physik, vol. 57 (1929), pp. 739-746.

[2.32] R.I. Epstein, M.I. Buchwald, B.C. Edwards, T.R. Gosnell and C.E. Mungan, Observation of laser-induced fluorescent cooling of a solid, Nature, vol. 377 (1995), pp. 500-502.

[2.33] B.C. Edwards, J.E. Anderson, R.I. Epstein, G.L. Mills and A.J. Mord, Demonstration of a solid-state optical cooler; A new approach to cryogenic refrigeration, Journal of Applied Physics, vol. 86 (1999), pp. 6489-6493 (48 K step reported, 56 K was claimed in private communication with R.I. Epstein, November 3rd 1999).

[2.34] R.I. Epstein, B.C. Edwards, C.E. Mungan, The Los Alamos solid-state optical refrigerator, Cryocoolers 9, Plenum Press, New York (1997), pp. 681-686.

51

3 Miniaturization of cryocoolers

Chapter 3

Miniaturization of cryocoolers

This chapter discusses the opportunities and difficulties that appear when cryogenic coolers are miniaturized. First, a number of important micromachining techniques to structure silicon and glass are reviewed. These two materials exhibit, respectively, a very high and very low thermal conductivity which makes a combination of the two materials attractive to construct cryocooler components. Next, the theory and scaling behavior are discussed of a number of fields that play a role in coolers: mechanics, actuator theory, fluid mechanics and heat transfer. The results can be summarized as follows: active mechanical components encountered in a number of cooling cycles are difficult to fabricate in MEMS; most heat transfer mechanisms are enhanced upon downscaling, having both positive and negative effects; the development of a powerful, small and efficient MEMS compressor is an important condition for a complete integrated MEMS microcooler. Based on the discussed scaling theory, opportunities for downscaling of several cooling cycles are discussed. An example is given of a design of a MEMS based regenerative cooler, based on the Twente-Stirling cycle. Finally, an overview is presented of existing coolers and existing low-temperature applications, which is useful for determining potential applications of a microcooler.

3.1 Introduction

MEMS (Micro Electro Mechanical Systems) technologies make it possible to construct miniature cooler components and constructions which are difficult or impossible to make with conventional machining techniques. Moreover, different materials can be used, like silicon, glass and ceramics. In order to fully exploit these new technologies and materials it is important to understand what kind of effects influence the scaling of coolers and their components to a miniature size. As a first empirical approach, the correlation between cooler size and cooling power or efficiency of different existing coolers will be examined.

Figure 3.1 shows the mass of a large number of coolers as a function of the cooling power, and figure 3.2 shows the efficiency normalized to the Carnot efficiency as a function of the cooling power. The numbers are taken from a recent database containing a large number of cryocoolers currently on the market or in an advanced R&D state [3.1]. Single-stage coolers in the temperature range of 60 − 100 K were selected from the database and used to create the graphs. The smallest cooler is the 150 mW Inframetrics Stirling cooler [3.2] (denoted by

Chapter 3

52

number 1) and the largest cooler is a 3.5 kW Stirling cooler from Stirling Cryogenics and Refrigeration BV [3.3] (formerly a part of Philips).

Figure 3.1 illustrates the trend that smaller (lighter) coolers produce less cooling power. This is, however, not necessarily true as is illustrated by the coolers denoted by numbers 2 and 3. Analysis of the data showed, in first order, that relatively heavy coolers located above the trendline operate with a low COP and relatively light coolers located below the trendline operate more efficiently (compare, for example, the data points 1 - 4). A simple explanation is that less efficient coolers produce more losses and require, therefore, more compression work and associated compressor size, regenerator size, etc. To be able to construct a microcooler with a small mass and volume it is, therefore, important to look in detail how different loss terms scale and to reduce these losses as much as possible. This scaling analysis is presented in section 3.3. In figure 3.1 a possible 10 mW microcooler is depicted which, according to the trendline, should weigh about 20 grams.

0.01

0.1

1

10

100

1000

10000

0.01 0.1 1 10 100 1000 10000

Cooling power (W)

Ma

ss(k

g)

Gifford-McMahanJoule-ThompsonPulse TubeReverse BraytonSolvayStirlingMicrocooler??

1

Microcooler??

3

2 4

Figure 3.1 Cooler mass as a function of cooling power for different single-stage coolers reaching 60 – 100 K. Data from [3.1].

0.001

0.01

0.1

1

0.01 0.1 1 10 100 1000 10000Cooling power (W)

CO

P/C

arno

t

Gifford-McMahanJoule-ThompsonPulse TubeReverse BraytonSolvayStirling

1

2

3

4

Figure 3.2 Cooler efficiency normalized to the Carnot efficiency as a function of cooling power for different single-stage coolers reaching 60 – 100 K. Data from [3.1].


53

Two other interesting remarks can be made about the graphs. Firstly, it appears from figure 3.2 that smaller coolers tend to be slightly less efficient than larger coolers. In 1972 a similar database was collected by Strobridge [3.4]. A comparison of the data reveals that small coolers at that time were significantly less efficient than current small coolers. Apparently, 25 years of cooler development has reduced the thermodynamic losses in small coolers significantly and these losses were, therefore, not fixed by fundamental limits associated with scaling effects. Secondly, the smallest closed cycle cryocooler currently on the market, the 150 mW Inframetrics Stirling cooler, has a remarkably high efficiency and small mass. This suggests that limits can be pushed to a small size.

In the next section, first a brief discussion is given of the opportunities and limitations of

MEMS technologies that could be specific for microcooler fabrication. Next, in section 3.3 theory and scaling behavior of various effects that play a role in coolers are discussed. Opportunities for microminiature regenerative and recuperative cooler components and configurations are illustrated in sections 3.4 and 3.5. As a part of this, a novel MEMS design of the Twente Stirling cooling cycle, that was discussed in section 2.3.8, is presented. Finally, in section 0 some possible applications for miniature coolers are discussed.

3.2 Microfabrication

Several recent publications give an excellent overview of the numerous different technologies and applications that are available in the field of MEMS [3.5, 3.6]. In this section a summary is presented of micromechanical materials and processing techniques that may be relevant to miniaturization of cryocoolers.

3.2.1 Materials

The basis of micromechanics is that silicon, besides its traditional role as an electronic material, can be exploited as a high-precision high-strength high-reliability mechanical material. Much advantage can be taken from the advanced microfabrication, originating from the IC technology. Furthermore, Single Crystal Silicon (SCS) is available in an extremely high quality, both electrical and mechanical. SCS is a brittle material that fails by fracturing, unlike most metals that first deform non-elastically. However, silicon is not as fragile as it may seem. The Young’s Modulus (7.0 · 109 Pa) is similar to that of stainless steel, but the yield strength is several times higher. Therefore, if surface and bulk defects are prevented, elastic structures made of SCS do not show mechanical fatigue, and mechanical structures can be obtained with strengths and lifetimes exceeding that of the highest strength alloy steels [3.7]. With respect to the application of silicon in microcooling devices, it is important to note the high thermal conductivity of silicon (especially for T < 300 K), which may be a condition or a limitation for certain applications. This is illustrated in figure 3.3, where the thermal conductivities of some relevant materials are compared.

Other important micromechanical wafer materials are glass and quartz. These materials can also be patterned and structured using microfabrication technologies. In contrast to silicon, glass and quartz show a lower thermal (and electrical) conductivity. In MEMS, silicon and glass wafers are often combined by anodic wafer bonding. Because this type of bond is made at

Chapter 3

54

approximately 450 °C, it is important that the thermal expansions of both materials are similar to prevent stress development during cool-down to room temperature. Often Pyrex glass is used in combination with silicon. Figure 3.4 shows the small difference between the thermal expansions of both materials between room temperature and 600 °C. However, the figure also shows a deviation of the expansions at temperatures below –50 °C. As a consequence, stresses in the order of tens of MPa develop in silicon/glass structures which are cooled below 100 K. Preliminary tests were done to verify if a silicon/glass structure would show damage after repeated cooling to liquid nitrogen temperature (77 K). No damage was observed by visual and microscopic inspection. However, for the development of cooler components this stress development could be a factor that should be taken care of in the design.

0.01

0.1

1

10

100

1000

10000

1 10 100 1000T (K)

Con

duct

ivity

(W

/mK

)

Helium

Pyrex glass

Copper

Silicon, high purity

Stainless steel, 304

Quartz, single crystal

Figure 3.3 Thermal conductivities as a function of temperature for a number of materials [3.8, 3.9].

-0.001

0

0.001

0.002

0.003

0 200 400 600 800 1000T (K)

Line

ar e

xpan

sion

(-)

Lead glass

Fused silica

Silicon

Pyrex glass

Figure 3.4 Linear expansion as a function of temperature for silicon and Pyrex glass; reference temperature: 293 K. Expansion of lead glass (Corning 0120) and fused silica are included to illustrate the perfect matching of silicon and Pyrex between 300 K and 800 K. Data from [3.10].


55

3.2.2 Micromechanical fabrication techniques

Two different MEMS techniques are often distinguished: bulk and surface micromachining [3.11]. For bulk micromachining etching processes are applied to structure the bulk material of a wafer, which may in subsequent steps be combined with other wafers. In surface micromachining, structural parts are embedded in layers of a sacrificial material during the fabrication process. The sacrificial material is then etched or dissolved in a chemical etchant that does not attack the structural parts. The processing steps in surface micromachining allow a maximum structure thickness of about 5-10 µm. For microcooler components, gas channels and volumes of significant size are required, together with strong structural parts which can stand high gas pressures. Therefore, bulk micromachining is needed for the development of microcooler components.

Patterns are transferred to the substrate or a thin film by means of photolithographic techniques, after which the substrate or thin film can be processed further, for instance by means of etching. In the photolithographic process, a patterned glass layer is used as a mask during the exposure of a photosensitive layer that is applied on top of the substrate or thin film. The wavelength of the light that is used determines the ultimate pattern resolution (typically about 1 µm).

A key technology in micromechanics is the removal of (substrate) material at non-covered locations: etching. In general, one distinguishes isotropic and anisotropic etching (see figure 3.5) with wet and dry agents. Another important etch parameter is the etch selectivity, which is the ratio between the etch rate of the material to be etched and that of the mask material.

Numerous chemical etchants can be used for wet etching of silicon. KOH is a common etchant often used for bulk micromachining; it etches anisotropically along the crystal surfaces, making it possible to realize unique geometries. Also, wet etching with suitable etchants is used for etching a wide range of thin films.

Dry etching stands for the use of a plasma to dissociate and ionize relatively stable gas molecules, forming chemically reactive and ionic species [3.12]. Under the condition that a proper chemistry is chosen, these species can be used to react with the solid substrate to form volatile products. Dependent on the mechanism that is applied, dry etching can be differentiated in 1) chemical plasma etching, 2) physical ion beam etching and 3) synergetic reactive ion etching (RIE), each with its own characteristics. Etch profiles resulting from the

mask

(a) (b) (c) Figure 3.5 The difference between isotropic (a) and anisotropic (b) etching. The profiles are etched using chemical plasma etching (a), synergetic RIE (b) and physical ion beam etching (c) [3.12].

Chapter 3

56

different etch mechanisms are illustrated in figure 3.5. The main advantage of dry etching (especially RIE) over wet chemical etching is its capability to etch highly anisotropic patterns, not limited by crystal anisotropy - also in polycrystalline and amorphous materials. In addition, etch profiles and mask-underetching can be controlled by varying the plasma chemistry [3.6]. A very high selectivity with respect to mask materials can be obtained, see figure 3.5b.

Being an IC technology spin off, micromachining is best performed on silicon. Because of the high thermal conductivity of silicon, other materials than silicon are required in some parts of the cold stage of a microcooler. However, these materials are much harder or impossible to pattern with conventional MEMS etching techniques. For that reason, in an early phase of the microcooling project we introduced powderblasting in MESA+ as a potential and new technique for patterning in MEMS. In this technique a particle jet of e.g. alumina particles is directed towards a target for mechanical material removal. With large particles this technique is widely used to remove paint, to clean houses and to decorate (grave)stones and glass. With small particles (< 100 µm), it is used for e.g. device marking in electronic industry, surface preparation, rapid prototyping and flat panel display production. It was also used by Little for the realization of gas channels in glass layers for small Joule-Thomson coolers [3.13]. By application of a suitable ductile masking material (such as copper) and very small alumina particles (< 10 µm), it was shown at MESA+ that powderblasting can also be used to pattern brittle materials with feature sizes less than 50 µm and a maximum aspect ratio of 2.5 [3.14]. Figure 3.6 shows a perspective view of a 400 µm deep channel structure in glass, as well as a deep trench.

(a) (b)

Figure 3.6 (a) Perspective view of a 400 µm deep channel structure in glass, fabricated by powderblasting. (b) Cross section of a trench in glass with a width of 60 µm at the top. The mask material is removed [3.14].

Besides removal of bulk silicon, the deposition and selective removal of thin films is also

very important in micromechanics. Thin films can be deposited on a substrate, or realized in or grown from an existing material (e.g. oxidation), with a thickness of nanometers to several micrometers. Deposition can be done in a physical process, like sputtering, or in a chemical process, like chemical vapor deposition. In MEMS, the physical processes are often used to deposit a number of metals, whereas the chemical processes are used for materials such as silicon nitride, silicon oxide and polysilicon. The choice of an appropriate thin film technology depends on factors such as: desired material, deposition rate, maximum substrate temperature, adhesion between layer and substrate, layer morphology, etc. Examples of thin film applications in MEMS are: electrical isolation, electrical signal tracks, membranes, strain sensors, capacitor plates, mask materials, passivation/protection layers, intermediate layers for


57

bonding of two substrates, sacrificial layers, heater material, junction material, optical mirrors, valve-seat material, etc.

Different bonding techniques can be used to fix two or more wafers together, a technology that is of great importance for micromachining [3.15]. Bonding techniques make it possible to realize constructions in three dimensions, besides the conventional planar constructions. Both silicon and glass wafers can be used, as well as a combination of both. The wafers may be processed partly or completely prior to a bonding step, giving an enormous freedom in design.

Another new development at MESA+ is glass molding with a silicon mould. This bulk micromachining technology may be of great importance for the development of microcooler components, as will be explained in section 3.4. Silicon melts at 1412 °C, whereas most glasses melt at much lower temperatures. It was shown that structures etched in silicon with the smallest resolution available (< 1 µm) can perfectly be transferred to glass by means of molding. Figure 3.7 illustrates the featuring steps of glass molding. In step a) first a desired shape is etched in silicon. In step b) the silicon structure is covered by a desired thickness of glass powder or a glass slurry. Next, in step c) the combination of silicon and glass is heated until the glass is melted, reflown and coalesced into the silicon mould. After careful cooling, a number of different following steps can be made. In option 1, the silicon mould is etched away completely (by KOH), freeing the molded glass structure. In option 2, the glass layer that is located above the silicon surface is removed by a combination of grinding, polishing and/or etching. This leaves the individual glass structures inside the silicon mould which can subsequently be treated in a number of normal processing steps. In option 3, which may follow after option 2, the silicon mould is patterned from the backside to make an in-plane patterned silicon-glass structure. So far, the only other method to make in-plane silicon-glass structures is by deposition or growing of SiO2 thin films in patterned silicon structures. However, for these methods the film thickness is limited to a few micrometers only.

a) b) c)

d)

1

2

3

Si

glass

Figure 3.7 Steps made to shape glass in a silicon mould.

Essential in the molding process is that the thermal expansion of the used glass is similar to

that of silicon to prevent stress development during cool down. This is a similar requirement that also holds for bonding of glass and silicon. Experiments were carried out with borosilicate glass (Schott type 8447) which has a melting zone between 700 °C and 1300 °C and a thermal expansion coefficient of about 4.8⋅10-6 K-1. This is close to but not equal to the expansion coefficient of silicon, which is about 3.5⋅10-6 K-1. The glass was melted at 900 °C. Figure 3.8

Chapter 3

58

shows SEM photos of the introductory experiments. Fig 3.8a shows a cross section of a silicon mould with etched steps and the molded glass connected to it. The silicon is etched back slightly to reveal the obtained glass structure. Detailed SEM photographs of these and other shapes revealed that perfect ‘wetting’ of the silicon was obtained. Figures 3.8b and 3.8c show a top view and detailed cross section of molded glass with very deep wells in the glass [3.16]. This structure was obtained by etching thin long spikes in silicon, molding these spikes and removing the silicon. The thin film that can be observed on photo (c) was located between the silicon mould and the glass structure. Presumably, this layer is the passivation layer deposited on the silicon sidewalls during RIE of the silicon pillars.

(a) (b) (c) Figure 3.8 SEM photos of glass structures created with silicon moulds. (a) Cross section of glass/silicon structure; (b) Top view and (c) cross section of molded glass with deep wells [3.16].

Similar molding processes were recently reported in the literature. Yasseen et al [3.17] used

a 10 µm thick spin-on glass film to planarize 10 µm thick polysilicon surface-micromachined structures. After polishing, a perfect flat glass/polysilicon surface was obtained that could be used for subsequent normal processing steps. Liu et al [3.18] used the LIGA technique (deep X-ray lithography combined with electrodeposition and molding) to fabricate a high aspect ratio nickel mould, about 100 µm in height. Spin-on glass was applied on this mould, and after curing the nickel mould was removed by reverse electroplating.

3.3 Theory and scaling

A number of different fields play an important role in coolers, such as mechanics, fluid transfer, thermodynamics, etc. In this section, important aspects of these fields are summarized and geometric scaling analysis is used to examine how relevant parameters change in relation to size changes and what are consequences of this scaling behavior [3.19]. The results of this section can be used to assess qualitatively what factors become ‘easier’ or ‘more difficult’ when different cooling cycles are scaled to a miniature size. This is done in more detail in sections 3.4 and 3.5, in which the miniaturization of recuperative and regenerative cooling cycles is discussed. It is important to notice that this scaling analysis was developed with assumptions that are specific for cryocoolers; the results should, therefore, be evaluated critically when used for other applications.

The size of the system is represented by a single scale variable β, which represents the linear scale of the system. It is assumed that the dimensions on all three axes scale proportionally to β. As a consequence, length scales with β, area with β 2, and volume with


59

β 3.* It follows directly that the ratio area/volume increases for smaller systems. This is a central issue in the scaling analysis since all area related effects are enhanced. This includes diffusion limited processes such as conduction and convection, as well as radiation, friction, etc. These enhancements can contribute both positively and negatively to the operation of small coolers as will be shown later.

In the analysis of this whole section it is assumed that the physical characteristics of materials (such as Young’s modulus, density, viscosity, etc.) are independent of size. Furthermore, it is assumed that working gas pressures and the ambient and low temperatures remain constant. These parameters strongly influence the cooling power of a cooler (as well as the input power). For a regenerative cooling cycle (see section 2.1 for the difference between a regenerative and recuperative cooling cycle), this cooling power is, in first order, proportional to:

VfpgPC ∆⋅⋅= )( (3.1)

where g(p) is some function of the working pressure, f is the operating frequency of the regenerative cycle, and ∆V is the volume change of the compressed gas per cycle. For a recuperative cooling cycle, the cooling power is, in first order, proportional to:

VphPC&⋅= )( (3.2)

where h(p) is some function of the working pressure and V& is the volume flow of gas through the cycle. Under the assumption that the operating pressure and the operating frequency of a regenerative cycle remain constant, PC ∝ ∆V ∝ β 3. Similarly, under the condition that the

operating pressure in a recuperative cycle remains constant, PC ∝ V& ∝ β 3. An interesting parameter is, therefore, the scaling factor per unit of volume which, under these conditions, equals the scaling factor per unit of cooling power. The scaling factor per unit of volume is simply the scaling factor divided by β 3. For a number of parameters (especially those associated with power or heat), the scaling factor per unit of volume tells directly if the parameter has a positive or negative effect after scaling.

It is important to notice that the assumptions of constant gas pressures, temperatures and operating speed are only a working assumptions to obtain understanding in the complex scaling behavior. In practice, some of these parameters could be scaled with size as well, yielding a somewhat different overall scaling behavior (see, for instance, the discussion on the cycling frequency of sorption compressor cells in section 3.3.4.2).

A list of parameters that can play a role in cryocoolers is shown in table 3.1 for the following fields: mechanics, actuators, fluid mechanics and heat transfer processes. In the next sections, these scaling effects are discussed in detail.

* This is a logic choice for general scaling considerations, but not always appropriate for realistic design considerations. Often, one or two dimensions are fixed due to fabrication constraints (for instance wafer thickness) and only one length or one area can be scaled. Sometimes also other parameters or assumptions that were taken constant in the analysis can be changed with scale. Because of that, these geometric scaling considerations should be used with great care in actual design considerations. Nevertheless, scaling analysis is very useful to obtain qualitative understanding of scaling behaviour.

Table 3.1 Geometric scaling of some parameters that could play a role in cryocoolers. The parameters and expressions are discussed in the text in the same order as they appear in this table, except for the power-related parameters which are grouped together in the last part of the table. Parameter Expression Symbols Scaling Scaling

p. vol.* Remarks

Mechanics (section 3.3.1) Inertia force FI = ma = m d2x/dt2 m = mass, a = acceleration β 4 Gravity force Fg = mg g = acceleration due to gravity β 3 Spring force (of loaded beam) Fspr = kx ∝ bd3/l3⋅x k = spring const., l = length, b = width,

d = thickness, x = spring deflection β 2

Friction force Ffr = µFN µ = friction coeffient, FN = normal force Friction scales proportional to normal force Tensile stress in pressurized tube σ = pR/d R = radius, d = wall thickness 1 Max. bending stress in pressurized plate

σ ≈ pl2/2d2 l = length, d = thickness 1

Interface stress of bonded materials σ ∝ β β Scales with thickness of bonded layer Linear (gas) spring constant k = F/x = 2UV/x2 U = strain energy per unit volume

(=const.), V = spring volume, x = defl. β

Natural frequency ω0 = √(k/m) β -1 Moment of inertia I ∝ mR2 R = radius β 5 Actuators (section 3.3.2) Magnetic actuation force Fm ∝ β 2.5 β 2.5 For permanent magnet + wire with constant

surface heat flux [3.32] Electrostatic actuation force Fel ∝ β β For increased insulator breakdown field with

a smaller scale [3.32] Piezoelectric actuation force Fpz ∝ β 2 β 2 Pneumatic (actuation) force Fp = pAc Ac = loaded cross sectional area β 2 Fluid mechanics (section 3.3.3) Knudsen number Kn = L/D L = mean free path, D = char. length β -1 Reynolds number Re = ρvmDh/µ vm = mean velocity, Dh = hydraulic

diam., ρ = density, µ = visc. β 2

Pressure drop for internal laminar flow

chlam

AD

mlp 2

&∝∆ l = length, Dh = hydraulic diameter,

Ac = cross sectional area

1 Downscaling of l (and associated m& and vm)

reduces ∆p, downscaling of Ac increases ∆p

Pressure drop for internal turbulent flow (Re < 2⋅104) 75.125.1

75.1

chturb

AD

mlp

&∝∆ l = length, Dh = hydraulic diameter,

Ac = cross sectional area

β 1.5 Downscaling of l (and associated m& and vm)

has major scaling impact

* Scaling per unit of volume is only mentioned if there is a physical meaning of this parameter.

Parameter Expression Symbols Scaling Scaling p. vol.*

Remarks

Gas leakage (laminar flow through narrow slit) p

lOd

m ∆=3

121

µρ

& O = perimeter of slit, d = width of slit, l = length of slit

β 3

1

Scaling of d has major impact

Heat transfer (section 3.3.4) Steady state conduction Pcd = λ(Ac/l)∆T λ = thermal conductivity β β -2 Length scale controls scaling p. unit of vol. Transient RC-time constant τRC = (ρVcp)/(hAs) β β -2 For body with const. surface heat transf. coeff. Biot number Bi = hD/λ β Fourier number Fo = at/D2 β -2 Radiation Prad ∝ As(T1

4 − T24)

ρ = body density, V = body volume, cp = body spec. heat, h = surface heat transf. coef., As = surface area, D = body char. length, a = thermal diffusivity, t = time β 2 β -1

Nusselt number Nu ≈ 4 1 Fully developed laminar flow Convection in internal laminar flow

Pcv,lam = hAs∆T h = λ Nu/Dh, heat transfer coefficient β β -2 Notice that hlam is independent of m& !!

Convection in int. turbulent flow 8.02.0

8.0

,ch

turbcvAD

mOlP

&∝ O = perimeter, l = length, Dh = hydr.

diameter, Ac = cross sectional area

β 2.6

β -0.4 Downscaling of l (and associated m& and vm) reduces Pcv, downscaling of As increases Pcv

Film condensation in internal flow P2p = hAs(Tsat – Ts) β 1.75 β -1.25 Pool boiling Pboil = hAs(Ts − Tsat)

h: see text, As = surface area, Ts = surface temp., Tsat = saturation temp. ~β 1.5 ~β -1.5

Regenerative shuttle losses see Eq. (2.11) β β -2 Regenerative pumping losses see Eq. (2.12) β 4.2 β 1.2 Power (input, losses, etc.) Compr. power with magn. actuator ∫= dxFfP mm

f = cycling frequency (=constant) β 3.5 β 0.5

Compr. power with piezoelectr. act.

∫= dxFfP pztpz β 3 1

Compr. power with electrostatic act.

∫= dxFfP elel β 2 β -1

Compr. power with (pneumatic) sorption compr. ρρ

pmfpmP s

s

∆∝

∆=

& m& = massflow, ms = sorber mass, ρ = gas density, f = cycling frequency

β 3 1 For constant f, but f may be increased significantly at a smaller scale (see section 3.3.2)

β 3 1 Internal laminar flow Pressure drop power loss ρ

pmPpl

∆=

& ∆p = pressure drop for internal flow – see above β 4.5 β 1.5 Internal turbulent flow

β -2 Internal laminar flow Ratio of convective heat transfer and pressure drop power loss

χ = Pcv / Ppl Pcv and Ppl: see above β -1.9 Internal turbulent flow

Kinetic energy of rotation U = ½ Iω2 I = moment of inertia, ω = angular velocity

β 5 β 2

Heat input Ph = Vψ ψ = dissipation per unit of volume V β 3 1 Often ψ can be incr. sign. at smaller scale

Chapter 3

62

3.3.1 Mechanics

Important forces that can play a role in coolers are those due to pressure, inertia, friction, springs, thermal expansion differences and actuator forces. The characteristics of actuator forces determine the compression power that can be achieved with these actuator forces and are discussed in the next section. Other important mechanical effects are stresses, spring constants, natural frequencies of mass-spring systems and moments of inertia. The (scaling) behavior of some of these mechanical effects is reviewed below.

Inertia forces are proportional to mass times acceleration. If it is assumed that velocities and accelerations scale with size and, therefore, with β, then inertia forces scale with β 4. As a consequence, jerky movements or sudden stop/accelerations are less problematic in small coolers than in large coolers. Stress due to a collision of two masses, for instance, is proportional to the ratio of the force and the impact surface area and scales accordingly with β 2.

Since friction is a complicated phenomenon dependent on a large number of conditions and assumptions, it is rather useless to make general statements on the scaling behavior of friction. Nevertheless, some interesting remarks can be made. In cryocoolers friction and associated wear plays especially a role in the sliding bearings between pistons or displacers and their containing cylinders. Recently, significant reduction of these friction effects was reached by application of clearance seals [3.20, 3.21]. To maintain such a clearance seal, thin springs are connected between the moving component and the cylinder housing. Seals of less than 10 µm were applied. Similar spring constructions are widely used in micromechanical applications and, if designed well, can be integrated in the same production steps that are used to make the actual moving construction [3.22]. Dependent on the production steps, seals down to 1 µm could be feasible. If friction still plays a role, control of the applied structural materials and the surface topography is very important.

Stresses occur in pipes and plates under pressure or another type of load, and should be limited below a safe value, typically 10% of the ultimate stress. For a certain pressure load these stresses are quite independent of scaling. As an example, the tensile stress in a pressurized tube can be obtained by assuming a force balance through a longitudinal cross section of the tube, yielding:

dpR

pRdFF wallongaswallin =⇒=⇒= σσ (3.3)

where σ is the stress in the wall, d is the wall thickness and R is the tube radius, and it is assumed that d << R. If the wall thickness scales with the tube radius, then the stress has a scale factor of 1. Another type of stress is the interface stress of two bonded materials with dissimilar expansion coefficients. The interface stress is a result of temperature variations and scales, fortunately, with β (in fact, the thickness of the bonded layers) [3.23].

For a specific spring, the scale factor of the spring constant can be obtained by evaluation of the analytic expression of the spring constant (see the spring force in table 3.1). A more general approach, however, assumes the strain energy per unit spring volume and keeps it constant during scaling. For a certain deflection x, the strain energy per unit volume equals [3.19]:


63

∫ ==x

VFx

dwwfV

u0 2

)(1

(3.4)

where f(w) is the (linear) spring force as a function of the deflection w. Using this definition of the strain energy, the spring constant for a linear spring follows as:

2

2xuV

k = (3.5)

and the linear spring constant scales accordingly with β (if it is assumed that the spring deflection scales with β). The scaling behavior of a mechanical spring is often not so important because the spring constant can easily be adjusted by variation of the spring geometry (that was assumed constant during scaling). A gas spring, however, in which gas in a cylinder is compressed by a piston, cannot easily be adjusted because it is much more fixed by the system design that it is part of. By application of the gas law it can be shown that the spring constant of a gas spring scales with β as well.

The natural frequency of a mass-spring system is proportional to √(k/m) and scales accordingly with β -1. This scaling behavior has especially impact on the natural frequency of a mass-spring system formed by a piston and gas spring, as will be discussed in section 3.4.

The moment of inertia equals mR2 and scales accordingly with β 5. As a consequence, the kinetic energy of rotation per unit of volume reduces drastically as the system size is reduced. The use of a flywheel mechanism (to buffer mechanical energy between different stages of a cooling cycle) is, therefore, unsuitable at a small scale.

3.3.2 Actuators

In the compressor of a cryocooler an actuator is needed to transform some kind of non-mechanical input energy into mechanical output energy that is used to compress the refrigeration medium. The required compression power is determined by the cooling power and the efficiency of the cooler. In section 3.3.4.3 it is argued that an 80 K microcooler should have at least a net cooling power of a few milliwatts. If it is assumed that a microcooler operates with 10% of the Carnot efficiency (see section 3.1) and that it has a compressor that operates with 70% efficiency, it follows for an 80 K cooler that about 20 times the cooling power is required as compression power from the actuator. For a cooling power of 10 mW this would mean a required mechanical compression power of 200 mW. This seems a relatively small power for miniature cm-sized systems, but it is a very large mechanical power for MEMS based systems. No description of such a powerful MEMS-based compressor was found in the literature and it is certainly a challenge to produce one.

Although the required compression power and gas pressures are similar for regenerative and recuperative coolers, other requirements for the compressor and actuator are somewhat different. Regenerative coolers require a rapid pulsating pressure wave and recuperative coolers a continuous flow of compressed gas. In principle, it is most logic to apply fast pressure actuators in combination with regenerative coolers and slower actuation principles in combination with recuperative cooling cycles, but opposite combinations are not impossible. A rapid pressure wave generated by a strong oscillating actuator can, for instance, be rectified by check valves such as described in chapter 8. On the other hand, a DC pressure difference

Chapter 3

64

generated by some kind of compression principle can theoretically be converted into a rapid AC pressure wave using small active valves.

In most conventional cryocoolers, actuation is based on magnetic effects; examples are linear voice-coil motors used in many split-Stirling coolers and conventional electromotors used in GM compressors [3.4]. In MEMS, a number of different actuation principles have been investigated [3.24]. Microactuators employing electrostatic, magnetic and piezoelectric effects have been realized. Also microactuators based on thermal effects such as thermal expansion and bi-metal effects, thermopneumatic and phase change actuators as well as Shape Memory Alloy actuators have been fabricated. Beside these methods other mechanisms like giant magnetostrictive alloy actuators, electrochemical actuators and mechanochemical actuators have also been used. To compare the different microactuation methods, factors such as the produced force or torque, downscaling, speed, efficiency, material issues, fabrication technology, size, integration and application can be considered. Because the required mechanical compression power in a microcooler is very significant, the efficiency of the microactuator is a major requirement. To make it possible to construct an integrated MEMS actuator, compactness of the actuation principle is also an important topic. Integration of the actuator with the microcooler is, however, not necessarily a major requirement. Dependent on the detailed system requirements, it is also a good possibility to interface a somewhat larger actuator with a MEMS based microcooler. If, for instance, some small system needs a small cooler without any moving components, a small sorption compressor can be interfaced to a MEMS based cold stage. In that way the distance between the compressor and the cold stage may also be increased, which may be an advantage for certain applications.

Because of the efficiency requirement, the discussion on actuators is limited to electrostatic, magnetic, piezoelectric and phase-change actuators (including adsorption compressors); most other actuation principles are intrinsically inefficient [3.5]. Electrochemical actuation could theoretically also be an efficient actuation principle [3.25], but it is not discussed here.

A simple but effective approach to compare the actuator size, effectiveness and scaling behavior is to compare the stored energy densities of the different actuator principles [3.26]. From thermodynamic point of view, an actuator can be described as an energy buffer connected via energy ports to two domains, often the mechanical and the electrical domain. Energy may flow via both ports into or out of the buffer, carried by a flow of one of the extensive variables such as displacement, charge or entropy. By definition, the energy is a unique function of these extensive variables. For an electrostatic actuator, for instance, the energy is a function of the charge q on the capacitor and the distance x between the plates: U = U(x,q). As a consequence, a change in the energy is given by:

dqdxFdqqU

dxxU

dUxq

υ+=

∂∂

+

∂∂

= (3.6)

where F is the force between the capacitor plates and υυ the voltage across the plates. When such an actuator is applied to perform work on the mechanical domain, it will be driven in a cyclic process in both the Fx and υq plane – similar to the Carnot or Stirling cycle discussed in chapter 2. The cycle can be chosen such that in one part of the cycle energy flows from the electrical domain to the energy buffer and in another part of the cycle from the energy buffer to the mechanical domain: the actual compression work for instance. Different variations of the cycle are possible, but it is common to all cycles that the change of the buffered energy is


65

closely related to the work performed onto the mechanical domain. For that reason a good method to compare different actuators is to compare the maximum energy densities of the active parts of the actuator, i.e. the parts that participate in the cyclic actuation process.

For electrostatic actuators the energy density is dependent on the electric field that is present in the gap between the actuator plates:

2

21

Euel ε= (3.7)

where ε is the dielectric constant and E the electric field in the gap. The maximum electric field that can be applied is limited by electrical breakdown described by the Paschen curve [3.27]. For large air gaps (> 100 µm) in atmospheric air, the breakdown field is constant and equals about 3⋅106 V/m. For a decreasing gap-size at constant pressure the breakdown field increases rapidly to compensate for the reduced number of collisions per ionized molecule before they reach the wall. Recently, electrostatic actuators with gap widths down to 2 µm have been fabricated [3.11]. For 2 µm gaps breakdown fields of about 2⋅108 V/m are reported [3.28, 3.29], leading to an energy density of 2⋅105 J/m3. The increased maximum electric field at smaller dimensions explains the attractive scaling behavior of electrostatic forces. Different electrostatic actuator configurations and driving conditions are possible, but when a constant electric field in the gap is assumed, it can be shown that the electrostatic force equals [3.30]:

xV

ExV

ux

UF el

elel ∂

∂=

∂∂

=∂

∂= 2

21

ε (3.8)

where V is the active volume between the actuator plates. For a constant electric field that is independent of scale, this force scales with β 2. If it is supposed that the electric field changes with β -0.5 (due to the increased breakdown field at smaller gaps), then the force scales with β. This last assumption has been made in table 3.1. It can be shown that for other driving conditions the scaling behavior is similar [3.30].

V υ υV

(a) (b)

Figure 3.9 (a) Gap closing actuator and (b) comb-drive actuator. The volume V containing the electric field is drawn in light grey.

Figure 3.9 shows two different electrostatic actuator types that are often used in MEMS:

the gap-closing actuator and the comb-drive actuator [3.30]. The comb-drive actuator has the advantage of a constant electric field and associated constant actuation force for a certain applied voltage and is suitable for larger deflections, currently up to 30 µm [3.11]. Generally, only a small fraction of the electrostatic actuator volume can be used as active gap volume that participates in the energy conversion; the rest of the volume is required to produce the

Chapter 3

66

electrostatic gaps and to incorporate them into a working solid device. The produced actuator power can now be approximated by:

uVfPact κ= (3.9)

where f is the operating frequency, V is the actuator volume, κ the active fraction of the actuator and u the energy density. For a typical operating frequency of 100 Hz, an active volume of 5% and an actuator power of 200 mW it follows that an actuator volume of about 200 mm3 is required. From MEMS point of view, such a volume for an electrostatic actuator is enormous and with the current technology not feasible [3.31]. To put this number in the right perspective, surface micromachined electrostatic comb drives with 2 µm gaps have been produced successfully with overall actuator sizes in the range of 1 mm x 200 µm and a height of 5 µm, leading to an actuator volume of about 10-3 mm3. Such a structure is depicted in figure 3.10. Higher structures can be fabricated by bulk micromachining, but currently not together with the desired small gaps. Other characteristics of electrostatic actuation are summarized in table 3.2, in which the different actuation principles are compared.

Figure 3.10 SEM photograph of a fabricated comb drive actuator for large deflections [3.11]. The total width of the actuator is about 1 mm. There are eight long thin springs that form a so called ‘folded-flexure’ system to keep the moving electrode in a stable position. The maximum deflection of the actuator is about 30 µm.

For magnetic actuators the stored energy density is dependent on the magnetic field B that

is induced in the moving actuating part [3.26]:

2

21

Bum µ= (3.10)

where µ is the magnetic permittivity of the material (in most cases air). The maximum achievable magnetic field is not limited by breakdown such as with the electric field, but by saturation of the magnetic material that is used to induce the field. Very high fields can be achieved by using 10 to 15 T superconducting magnets yielding energy densities up to 108 J/m3. More realistic are fields up to 1.5 T for materials such as iron, yielding an energy density of about 106 J/m3. Because strong magnetic fields can also be maintained in larger gaps and volumes, long strokes are possible for magnetic actuators. This can be combined with the very large forces that can be created. Below a certain size of magnetic actuators, however, the maximum achievable magnetic fields are limited by the dissipation losses that increase relative


67

to the actuation power when the system scale is reduced. This can be understood by considering Ampere’s law that is used to calculate the induced magnetic field:

∫∫ ⋅

∂∂

+=⋅SC

dt

d sD

JlH (3.11)

Here, H is the magnetic field intensity vector, J is the current density vector and ∂D/∂t is the varying electric displacement that equals zero for quasi static conditions. If this law is applied to calculate the magnetic field in the actuating gap of figure 3.11 and if it is assumed that the magnetic field intensity in the yoke is zero, then it follows that B ≈ µ0JAc/d where Ac is the total cross sectional area of the current carrying wires and d is the width of the gap. For downscaling of all dimensions, Ac/d scales with β so that B scales with β as well if J is kept constant. If larger systems are scaled down, Ac/d can often be kept constant because the coil size is still small compared to the rest of the system. Below a certain system size, however, the size of the coil will become very significant and finally Ac/d will scale with β. Increasing of J may be possible, up to a level where the thermal losses or the temperature becomes too high. Trimmer [3.32] distinguishes three cases for the current through the wires of an electromagnet: constant current density, constant heat flow per unit surface area and constant temperature rise across the windings. For the interaction of a wire in combination with a permanent magnet or yoke he finds respectively β 3, β 2.5, β 2. In table 3.1 β 2.5 is assumed. To obtain the required compression power, a displaced actuator volume of at least 2 mm3 is required (and a much larger actuator volume) which is very large for a MEMS based magnetic actuator. A small relays-type magnetic actuator mounted on top of a MEMS based cooler with integrated piston appears to be a more logic choice.

The piezoelectric effect is a bulk material property which translates an applied voltage into a stress and/or strain in the piezoelectric material. When an electric field E is applied, a stress σ develops which can be written as [3.5]:

εσ yEe +−= E (3.12)

where e is a piezoelectric constant, Ey the Young’s modulus and ε the strain in the material. The applied force equals the developed stress times the active surface area and scales accordingly with β 2. The energy density in piezoelectric actuators is also given by Eq. (3.7). Compared to electrostatic actuators, the breakdown field of piezoelectric material is in the same order of magnitude but the dielectric constant is about three orders of magnitude larger than that of air. Moreover, the active fraction of a piezoelectric actuator is close to one: the piezoelectric effect is a bulk material property and in principle no other volume consuming components are required to make a piezoelectric actuator working. All together, piezoelectric

I

dC

Figure 3.11 Magnetic actuator in which an air-gap is closed by the application of an induced magnetic field.

Chapter 3

68

actuators are efficient, small and powerful. For commercially available PZT (lead zirconate titanate), an electrical field of at least 3⋅106 V/m is allowed in the direction of poling, resulting in an energy density of at least 1.2⋅105 J/m3 (εr = 3000) [3.33, 3.34]. In experimental PZT thin films, breakdown fields up to 3⋅108 V/m are reported [3.35]. If a more conservative field of 1⋅108 V/m is assumed for these thin films, an energy density of 5.8 x 107 J/m3 is found (εr = 1300). With these numbers for the energy densities the required actuator volumes can again be estimated. To obtain the required compression power of 200 mW with an actuating frequency of 100 Hz, about 17 mm3 of commercially PZT material would be required or 0.03 mm3 of thin film PZT material. Based on these numbers, a small commercial PZT actuator mounted on top of a MEMS based compressor could be a good solution. Also application of thin film PZT material in a MEMS based compressor seems possible. For example, a circular bimorph membrane with a diameter of 3 mm and a 5 µm thick PZT film could fulfill the required PZT actuator volume. With a proper design it should be possible to fulfill the requirements of force and stroke [3.36].

The principle of phase-change actuation is mentioned in some MEMS reviews [3.24], but actual implementation is shown in a limited number of papers. Phase-change actuation is based on the principle that mechanical work can be performed by an evaporating liquid. A nice feasibility study is done by Bergstrom et al [3.37]. They constructed a sealed cavity that contains a silicon free-standing heating element and a membrane to measure the pressure development. The heater was specially designed to wet easily during cool-down of the cycle. The cavity was partially filled with a small amount of methanol, which has a vapor pressure of 1 bar at 297 K. With an input power of 20 mW and a temperature increase of 21 K, they were able to produce a pressure difference of 1.2 bar and a displacement of 50 µm with a response time of 100 ms. Best performance for this type of actuator is obtained when just enough liquid is present to produce the required amount of gas for the pressure rise. Abundant liquid reduces the performance since this liquid must be heated and cooled without contributing to the actuation process. This type of actuation is intrinsically slow or inefficient: to reduce heat conduction losses from the heater to the environment it should be isolated from the environment resulting in a slow cool-down process.

An important fundamental difference with most other actuation principles is that two-phase actuation converts thermal energy instead of electrical energy. As a consequence, the principle is intrinsically less efficient than electrically driven actuators because of the limiting Carnot efficiency for thermal engines. The thermodynamic steps of the cycle can be clarified by focussing on a large scale application that operates a similar cycle in the space domain instead of the time domain: the continuous steam or Rankine cycle that is used in most modern power plants [3.38]. Figure 3.12 shows a schematic diagram of the cycle, together with the steps in a T-s diagram. In its basic configuration, the cycle consists of three components: an evaporator, a (turbine) expander and a condenser. For continuous operation of the cycle also a liquid compressor is required. Evaporation takes place at high temperature, producing high pressure vapor. Next, mechanical shaft work is obtained by expansion of the gas in the turbine until the condensing pressure is reached. In large applications, usually adiabatic expansion from the high to the low temperature is used (see figure 3.12), but theoretically also isothermal expansion followed by cooling of the low pressure gas could be applied. After expansion, the low pressure vapor is condensed at low temperature, rejecting low grade heat to the environment.


69

In the case of a continuous process, the liquid is in a last step compressed to high pressure. This step requires very limited compression power because of the small change in liquid density. If this compression work is neglected, the efficiency of the cycle is given by:

H

AH

in

out

QQQ

QW −

==η (3.13)

For this type of cycle it can be shown that the efficiency is only slightly smaller than the intrinsic engine Carnot efficiency (see also the discussion in section 2.2), given by:

H

AHengineC T

TT −=,η (3.14)

It follows that the intrinsic efficiency of a phase-change actuator increases with the temperature difference between evaporation and condensation. For liquid-vapor equilibria, these temperatures are in first order proportional to the vapor pressures, so that two-phase actuators operating at higher temperatures and producing larger pressure differences are intrinsically more efficient than actuators operating with smaller temperature differences and pressures. Obviously, this is only true if the thermal conduction losses associated with the higher temperature differences can be limited.

Basically, the thermodynamic behavior of the phase-change actuator operating in the time-domain, such as described by Bergstrom et al. [3.37], is not much different from the described behavior of the Rankine cycle operating in the space domain. One essential difference is that compression and expansion takes place via a locus of vapor pressures and temperatures instead of a constant pressure and temperature. Practical implementation of the principle in the time domain is difficult and inefficient because of a number of reasons: large thermal conduction losses in the heating phase due to the requirement to cool down rapidly, a relatively low operating speed, the requirement to use a separating membrane between the actuator fluid and the environment, etc. The energy conversion per unit of volume fluid is very large for a phase-change actuator. By application of Eq. (2.10) it can be shown that, for example, steam expansion from 10 to 0.1 bar (at saturation temperatures of 453 and 319 K) yields about 109 J per m3 of liquid or about 7⋅105 J per m3 of steam at 0.1 bar. No example was found in the literature of a continuous flow cycle on a MEMS scale. Although it is relatively

WQH

QA

evaporator

condenser

expander

liquidcompressor

T

s

453 K

319 K

p = 10 bar

p = 0.1 bar

liquid

adiab.exp.

isoth.exp.

Figure 3.12 Schematic diagram of the steam or Rankine cycle that is used in most power plants to convert thermal energy into mechanical work. The dotted compressor is only required for continuous operation (instead of batch operation).

Chapter 3

70

straightforward to produce the required pressure difference by means of a MEMS based evaporator and condenser, it is probably difficult to construct an expansion stage that can make use of the pressure difference. In that respect it is important to notice that the produced pressures are vapor pressures; expansion can only take place at the high temperature or under adiabatic conditions from the high temperature to the low temperature, see figure 3.12. Cooling of the vapor before expansion will reduce the vapor pressure accordingly. Obviously, this effect makes it also impossible to apply the produced pressure difference as a direct input for a recuperative cold stage. However, by application of the phase transition between free gas and adsorbed gas in or on a sorber material, the temperature of the gas can be reduced without a reduction of the gas pressure as soon as it is physically separated from the sorber material. This makes actuation based on ad- and desorption an attractive concept for application in cryocoolers. More details on operation of sorption compressors are discussed in chapter 4. In section 4.4.5 it is shown for a typical xenon-charcoal adsorption combination that the energy density equals approximately 3⋅106 J per m3 sorber material. In chapter 5 it is shown that hydrogen can reversibly be ab- and desorbed on a thin-film metal-hydride material. This illustrates the feasibility of a MEMS-based sorption compressor.

Concerning the scaling behavior of pneumatic forces generated by a phase change actuator, it is important to distinguish between scaling of the force when a certain pressure is present, and scaling of the pneumatic power that can be generated with a certain pressure source. Since F = p⋅As, the force scales with β 2. The generated compression power can be written as:

ρρ

pmfpmP s

s

∆∝

∆=

& (3.15)

where m& is the mass flow, ∆p is the pressure difference, ρ is the gas density, ms is the sorber

Table 3.2 Comparison of some general characteristics of different actuation principles. Electrostatic Magnetic Piezoelectric Phase change Sorption

Type rapid alternating (AC) batch-continuous (DC) Conditions 2 µm gap 1.5 T magnet commercial PZT H2O 10-0.1 bar xenon-charcoal (Field) energy density

2⋅105 J/m3 9⋅105 J/m3 1.2⋅105 J/m3 1⋅109 J/m3-liquid 7⋅105 J/m3-gas

3⋅106 J/m3-sorber

Force scaling β β 2.5 β 2 β 2 β 2

Power efficiency very good good; worse for smaller systems with more heat

dissipation

good good, but limited by the engine

Carnot efficiency

moderate; limited by the engine

Carnot efficiency and heat capacity

Speed fast fast very fast slow; trade-off with efficiency or

heat switch required

slow; trade-off with efficiency or heat switch required

Size per unit of power output

moderate moderate small large large

Range (deflection)

small large small - -

Miniaturization and MEMS integration

excellent difficult good (thin film) difficult possible

Complexity low high moderate high high Remarks Until now only

actuators for small powers were made

No expansion turbine known for

small scale

Can directly be combined with

recuperative cold stage


71

mass (or liquid mass for a liquid-vapor phase transition) and f is the cycling frequency. For a constant cycling frequency the compression power scales with β 3. In section 3.3.4.2 it will be shown, however, that the cycling speed of sorption compressors can be increased with β -2 if the system size is reduced with β. With regard to compression power per unit of compressor volume, downscaling of sorption compressors is, therefore, attractive.

3.3.3 Fluid mechanics

In small coolers gas flow, liquid flow and sometimes two-phase flow take place. The gas and liquid flows are essentially characterized by a continuum, viscous, laminar, incompressible and internal flow. Dependent on the configuration, in recuperative coolers compressible flow effects may play a role, but these are not considered in this scaling analysis. A number of dimensionless parameters are used to describe the transport mechanisms and to distinguish between the different flow regimes.

For gases, the transition between free molecular flow and continuum flow is given by the dimensionless Knudsen number. It is defined as the ratio between the mean free path of a molecule and a characteristic length such as the diameter of a channel. According to the Knudsen number the flow can be divided into three regimes. For Kn < 0.01 the fluid can be considered as a continuum, for 0.01 < Kn < 1 it is in the transition flow regime, for Kn > 1 it is in the molecular regime. The mean free path of a molecule is given by [3.39]:

p

TkL B

22πξ= (3.16)

where kB is Boltzman’s constant and ξ is the molecule diameter. The Knudsen number scales with β -1 and for a certain small channel dimension the continuum dynamics will not be valid anymore. In coolers, gas pressures are generally larger than 1 bar. At 300 K and 1 bar the mean free path has a typical length of about 100 nm, and it reduces linearly with temperature. As a consequence, the continuum theory can be used for channels with a characteristic length down to micrometer size.

Another essential dimensionless number in fluid mechanics is the Reynolds number, which describes the ratio of inertia to viscous forces. It is given by [3.40]:

µ

ρ hm Dv=Re (3.17)

where ρ is the density of the fluid, vm is the mean velocity, µ is the viscosity and Dh is the hydraulic diameter of the duct through which the fluid flows, given by:

OA

D ch

4= (3.18)

Here Ac is the cross sectional area and O is the perimeter of the duct. In fact, the hydraulic diameter is directly related to the smallest dimension of the cross sectional area of a duct. The Reynolds number indicates whether the flow is laminar (smooth tubes: Re<2300) or turbulent (smooth tubes: Re>6000). Both pressure drop losses and heat transfer depend strongly on the regime of the flow. In the laminar regime particles move along streamlines. The turbulent flow is irregular and the fluid is mixed. Due to this mixing, the temperature and velocity profiles in the flow in the radial direction are different than in laminar flow conditions. From the

Chapter 3

72

assumption that the mass flow scales with β 3, it follows directly that vm scales with β and the Reynolds number scales accordingly with β 2. In the considered miniature constructions it is expected that Re<100 and as a consequence, only laminar flows have to be considered.

Pressure drops are important loss effects and sometimes also required to obtain certain functions in coolers. In internal incompressible fully developed flow, pressure drops are caused by viscous forces, both for gases and liquids. By application of Newton’s momentum equation, the pressure drop can be derived as [3.40]:

2

2m

h

vDl

fpρ

=∆ (3.19)

In this expression f is the friction factor that is dependent on the Reynolds number, the geometry of the channel and whether the flow is laminar or turbulent. For laminar flow, the friction factor can be calculated analytically and is given by:

ReC

f = (3.20)

The constant C in this relation is dependent on the shape of the cross-sectional area of the tube. For several geometries the coefficient can be found in literature [3.41], e.g. for a circular tube C=64, for parallel plates C=96 and for a square tube C=57. For fully developed turbulent flow, the analysis is much more complicated and the friction factor is determined experimentally. It is dependent on the Reynolds number and the tube surface condition. For smooth tubes different expressions can be found in literature, which are quite similar [3.42]. Incropera gives the following equations [3.43]:

425.0 102ReRe316.0 ⋅≤⋅= −f (3.21)

42.0 102ReRe184.0 ⋅>⋅= −f (3.22)

By substitution of the appropriate expressions in Eq. (3.19), the pressure drop for laminar and turbulent flows follow as:

mAD

lCv

D

lCp

chm

hlam &

22 22 ρµµ

==∆ (3.23)

75.175.125.1

25.075.1

25.1

25.075.0

2316.0

2316.0

mAD

lv

D

lp

ch

m

h

turb &ρµµρ

==∆ (3.24)

where all relevant parameters are assumed to be constant over the length of the duct. In the derivation of Eq. (3.24) it is assumed that Re < 2⋅104. According to these expressions, the pressure drop for laminar flow scales with 1 and for turbulent flow with β 1.5 (recall that m& scales with β 3). In fact, it is illustrative to distinguish between scaling of the cross sectional diameter and scaling of the length. If it is assumed that the flow velocity is proportional to the length scale, it follows that scaling of the length (for constant cross sectional area) reduces the pressure drop significantly. This is true for laminar flow, but even more significant for turbulent flow. On the other hand, downscaling of the cross sectional area (for constant length) adversely increases the pressure drop, more or less nullifying the gain of downscaling the length and velocity.


73

A pressure drop over a tube leads to a power loss. This power loss can be written as:

ρρρ

pmppmP

in

in

out

outpl

∆≈−=

&& )( (3.25)

where ρ is the average density of ρin and ρout. The last approximation is valid if the pressure drop is small compared to the absolute pressure. By combining Eq. (3.25) with Eq. (3.23) and (3.24) respectively, the pressure drop power loss for laminar and turbulent flows can be found. These power losses scale with β 3 for laminar flow and with β 4.5 for turbulent flow and play an important role in the discussion about convective heat transfer in heat exchanger tubes; see the next section.

Gas leakage can take place through the gap between a piston or displacer and the cylinder

around it. Such leakage gives rise to a loss term and should be limited by application of small gaps. Eq. (3.19) can be used to calculate the mass flow through a narrow gap:

pl

Odm ∆=

3

121

µρ

& (3.26)

in which O is the perimeter of the piston or displacer and d is the width of the gap. From this expression if follows that the leakage flow scales with β 3. This scaling factor is mainly determined by the possible scaling of the gap width d. By application of MEMS technologies very small gaps down to the µm size can be created.

3.3.4 Heat transfer

A number of heat transfer mechanisms can play a role in coolers: heat conduction, heat transfer by convection, condensation and boiling, and radiation. All of these mechanisms are strongly influenced by scaling. Moreover, as was discussed in section 2.3.7, shuttle and pumping losses occur in regenerative coolers. These heat losses are also strongly affected by scaling.

3.3.4.1 Steady-state conduction One-dimensional, steady-state heat conduction through a continuum (solid, liquid or gas) is

governed by [3.43]:

dxdT

APcd λ= (3.27)

where λ is the (temperature dependent) thermal conductivity of the material, A is the cross-sectional area normal to the temperature gradient and the heat flow, and dT/dx is the temperature gradient. From this expression it follows that Pcd scales with β, and per unit volume with β -2. Recall that it was assumed earlier in this section that the cooling power scales with the system volume and, therefore, Pcd scales with β -2 per unit of cooling power. As was discussed in section 2.3.2, thermal conduction from ambient to the cold temperature through the construction of the cold stage is a loss term that is subtracted from the produced cooling power. This scaling factor reveals that, at a certain critical minimum size of the cooler, thermal conduction through the cold stage itself will conduct away all cooling power. This is a fundamental limit for downscaling of coolers, which is strongly dependent on the thermal

Chapter 3

74

conductivity of the applied material. To investigate the scaling effects of the conduction losses in more detail, it is useful to distinguish between the 2-dimensional scaling of the cross sectional area and the 1-dimensional scaling of the length of the conduction path. The scaling factor of the cross sectional area is β 2 (or 1 per unit of volume if the length scale is kept constant), whereas the scaling factor of the length is β -1 (or β -2 per unit of volume if the cross sectional area is kept constant). From these separate scaling factors it can directly be concluded that, instead of a critical size, a minimum critical length of the cold stage will conduct away all cooling power – more or less independent of the cross sectional area. To illustrate this more quantitatively, below a first order scaling analysis of the conduction losses through a typical regenerative cold stage is presented. In the analysis the following assumptions are made: 1. This analysis focuses on a regenerative cold stage with internal displacer/regenerator (see

for instance the cold stage of the cooler in figure 2.15 or 2.17). A similar discussion can be made for recuperative coolers, yielding somewhat different numbers.

2. The cooling power of the cold stage, PC, is a gross cooling power, which does not include the conduction losses Pcd (other loss mechanisms are not important in this discussion, and therefore assumed to be included in PC).

3. To compare the conduction losses to the cooling power for different sizes of the cold stage, it is assumed that the cooling power scales linearly with the volume of the cold stage.

The cross sectional solid area of the conduction path, Ac, consists of the cross section of the pressure resistant tube around the cold stage plus the solid conduction path through the regenerator material (see, for instance, figure 2.15 or 2.17) . For a cylindrical pressurized tube configuration, the minimum required ratio of the wall thickness and the tube radius can be found by application of Eq. (3.3), where σ is the maximum allowable stress in the tube material. This maximum stress of typical materials like stainless steel and glass is about 100 MPa. With a typical gas pressure of 1 MPa, it follows that Awall/Acs > 0.01, where Awall is the cross section of the wall and Acs is the cross section of the complete cold stage. Including the cross section of the solid conduction path through the regenerator, it is assumed that φ = As/Acs = 0.05.

Now empirical data from a typical Stirling cooler (type: UP 7058/01 from Signaal Usfa [3.44] with 1.5 W of cooling power at 80 K) is used to calculate a cooling power per unit of cold stage volume, γ = Pc / Vcs. This cooler, that has an efficiency normalized to the Carnot efficiency of about 0.1, yields γ = 2.6⋅105 W/m3. The cold stage cooling power and the heat conduction can now be estimated as:

γγ cscscsC lAVP == (3.28)

TlA

TlA

Pcs

csav

cs

savcd ∆=∆= φλλ (3.29)

where λav is the averaged thermal conductivity over the temperature range of the cold stage. Figure 3.13 shows a plot of the heat conduction and cooling power as a function of the cold stage length, for a diameter of 5 mm. Notice from Equations (3.28) and (3.29) that the ratio of the heat conduction and the cooling power is independent of this diameter; it determines only


75

the absolute value of the conduction losses and cooling power. From the plot the following conclusions can be drawn: 1. The impact of the thermal conductivity of different materials is obvious. Stainless steel, a

very common construction material for cold stages, gives significant conduction losses. These losses are limited to acceptable values by making the cold stage sufficiently long, preferably longer than about 4 cm.

2. The use of silicon as a construction material for the cold stage is impossible. Even if only a small fraction of the conduction area would be made of silicon, enormous conduction losses would result.

3. The use of SiO2 (glass) for the construction of the cold stage is very attractive from thermal conduction point of view. Dependent on the detailed design, a length of 1 or 2 cm should be possible.

4. The feasibility of a cold stage length in the millimeter range is very unlikely because of conduction losses, even for glass.

This last conclusion results in an important design rule for a miniature cold stage based on MEMS technologies. MEMS technologies are tailored to the fabrication of constructions in a plane. This plane can be made up by one or more wafers bonded together and is seldom thicker than 1 or 2 mm. As a consequence, if conventional MEMS technologies are used, it is virtually impossible to put the cold stage temperature difference normal to the wafer-plane – for instance from top to bottom of a wafer stack. It is much more attractive to put the cold stage temperature difference in the plane of the wafer; in this way the length of the cold stage can easily be adjusted over a wide range, up to several centimeters if necessary. For this reason, the ‘Microminiature Stirling Cycle’ patented by Bowman et. al [3.46] is a conceptual design that most probably will never work. Figure 3.14 shows a cross section of one of Bowman’s designs. It consists of two identical Stirling coolers placed in parallel. The bottom side contains the actuators connected to the two compression membranes and the top side is the cold end where the electronics is located. In between the regenerative displacers are located, suspended on thin diaphragms.

Except for conduction through the cold stage itself, thermal losses also occur due to conduction through wires and support structures. If no significant current is flowing though

0

0.2

0.4

0.6

0.8

1

0 0.02 0.04 0.06 0.08 0.1

length (m)

P (

W)

P coldP cond, SS316P cond, SiO2P cond, silicon

SS316

silicon

SiO2

Figure 3.13 Cooling power and heat conduction losses as a function of the cold stage length. For the cross-sectional area of the cold stage is taken: Acs = 5 mm2. Average heat conductivities between 80 K and 300 K are: λav, SS316 = 12.4 W/mK, λav, Si = 408.1 W/mK, λav, SiO2 = 0.89 W/mK [3.45].

Chapter 3

76

wires, then the cross sectional area can be made very small by application of thin film technologies; otherwise conduction losses through wires may become significant and a limiting factor for downscaling of coolers.

3.3.4.2 Transient Conduction In many cryocoolers dynamic or transient heat conduction plays an important role as well.

One example is the regenerator, which periodically exchanges heat with the working fluid. Another example are sorption compressor cells which are periodically heated and cooled to desorb and adsorb gas. Often such transient problems can be described by an energy balance in which a lumped thermal capacitance Ct is heated or cooled by a surface heat flux which is characterized by a thermal resistance Rt:

dtdT

CTTRdt

dTVcTTAUQ t

tpsbodysurface =−⇔=−⇒= ∞∞ )(

1)( ρα&& (3.30)

where α is the heat transfer coefficient, T is the body temperature and T∞ is the temperature of the environment. This differential equation yields the body temperature as a function of time:

τ/t

i

eTTTT −

∞

∞ =−−

(3.31)

where the thermal time constant τ is given by

)()1

( ps

tt VcA

CR ρα

τ ⋅== (3.32)

This time constant, that characterizes the speed of heating or cooling, scales with β: small things heat and cool faster. The validity of this lumped capacitance method can be checked by evaluation of the Biot dimensionless number, which is defined as the ratio of the thermal conduction resistance within the body and the resistance to convection across the body surface or fluid boundary layer [3.43]:

λ

ααλ DAAD

R

RBi

s

s

extconv

cond ===/1/

,

int, (3.33)

where D is the characteristic dimension of the body. If Bi < 0.1, the error associated with using the lumped capacitance method is generally considered small and no significant temperature gradients develop within the body. The Biot number also scales with β. The consequence of

Figure 3.14 Cross section of a double ‘Microminiature Stirling cycle’ as described by Bowman et. al [3.46].


77

this is that small things can easier be heated or cooled uniformly with a certain surface heat flux; this adds to the fact that small things can be heated and cooled faster. One important implication is the clear advantage to make sorption compressor cells with a small size (and diameter): they can be heated and cooled more uniformly and more rapidly than large ones, yielding an improvement of the compression work per unit of compression volume which scales with β -2.

For larger Biot numbers, the lumped capacitance method is often inappropriate and other methods must be used to account for gradients within the body. In general, the variation of the body temperature with both time and the spatial coordinates can be obtained by solving Fourier’s heat diffusion equation, given by:

)( TgraddivatT

⋅=∂∂

(3.34)

where a = λ/ρcp is the thermal diffusivity. Eq. (3.34) is valid under the condition that no heat generation or convection is present within the body. For a large number of different configurations and boundary restrictions solutions to this differential equation can be found in the literature [3.47]. Two interesting cases are heat penetration in a semi-infinite and in a finite medium resulting from a temperature step imposed at the surface boundary of the medium. It can be shown that the temperature distribution in a semi-infinite medium is given by the error (erf) function, see figure 3.15a [3.48]. The tangent to the temperature curve at x = 0 goes through T = T0 at xt = √(πat). The distance xt is the thermal penetration depth, which represents the distance x over which the temperature difference T1 – T0 at x = 0 has dropped to 20% of its original value. The condition for semi-infiniteness of the medium is only valid if xt < D/2, where D is the characteristic dimension of the system. This condition is often expressed by using the dimensionless Fourier number, given by:

2D

atFo = (3.35)

This number represents the ratio of the processing time and a characteristic time for the heat to penetrate the medium. A medium is considered to be semi-infinite if Fo < 0.1. For Fo > 0.1, the penetration depth is larger than the dimension of the body and a finite medium must be assumed. This situation is illustrated in figure 3.15b. After a certain period of time (in the figure for t > t2 which corresponds with Fo > 0.1), the consecutive temperature distributions remain geometrically similar. In that region the development of the average temperature Tav of

(a) (b)

Figure 3.15 Temperature distribution in a semi-infinite (a) and finite medium (b) as a function of time.

Chapter 3

78

the body can be described by:

FoNuDat

NuTTTT av −=−=

−−

201

1ln (3.36)

where Nu is a dimensionless heat transfer coefficient that depends only on the geometry of the body. From this expression the required Fourier number (or the time t) can be calculated at which Tav has reached T1 within a certain margin. For example, Nu ≈ 5 for an infinite cylinder [3.48] and to reach (T1 – Tav)/(T1 – T0) < 0.01, it is for a cylinder required that Fo > 0.9. Such a condition holds for geometries of a different scale if the Fourier number remains constant. From Eq. (3.35) it can now be concluded that the settling time, at which Tav reaches a certain temperature, scales with β 2. Once more, smaller things can uniformly be heated and cooled much faster than larger things.

The Fourier number can also be used to assess heat penetration times for different materials and sizes; this is of particular interest with respect to regenerator materials. Table 3.3 shows a list of materials that are currently in use as regenerator material and that may be used in future MEMS based regenerators. The values for the thermal diffusivities are listed, as well as a characteristic thermal penetration time and feature size. The meaning of the time constant is the time required to reach equilibrium within 99% (Fo = 0.9) after a thermal disturbance, for a long cylinder with a 100 µm diameter. Oppositely, the meaning of the listed feature size is the maximum cylinder diameter that can reach a 99% equilibrium within 1 ms after a thermal disturbance. For large scale cryocoolers, a typical regenerator feature size is 100 µm or less and the operating frequency is 50 Hz or slower. It can, therefore, be concluded that even glass is suitable for regenerator use – even if no downscaling of the regenerator feature size is applied.

Table 3.3 Thermal material properties, characteristic thermal penetration time and feature size for a number of materials that are of interest for regenerator use. Values at T = 300 K. λ (W/mK) ρ (kg/m3) cp (J/kg⋅K) a (m2/s) τD = 100 µm (ms) Dτ = 1 ms (µm) Copper 394 8.96⋅103 386 1.14⋅10-4 0.079 356 Lead 35.0 11.3⋅103 130 2.38⋅10-5 0.38 163 SS 304 15.1 7.86⋅103 477 4.03⋅10-6 2.23 67 Silicon 148 2.33⋅103 715 8.88⋅10-5 0.10 314 Pyrex glass 1.02 2.21⋅103 737 6.25⋅10-7 14.4 26 Helium, 10 bar 0.157 1.60 5.19⋅103 1.89⋅10-5 0.48 145

3.3.4.3 Radiation Heat transfer due to radiation for a convex object in a cavity (two-surface enclosure, see

figure 3.16) can be written as [3.43]:

−+

−=

out

out

out

in

in

inoutBinrad

AA

TTAP

εε

ε

σ11

)( 44

(3.37)

where Ain, Aout, εin and εout are the areas and emissivities for the inner and outer surfaces and σB is Stefan-Boltzman’s constant. This equation holds for two parallel surfaces (and Ain/Aout = 1). According to Eq. (3.37), radiation scales with β 2.


79

Radiation in coolers occurs essentially from the vacuum enclosure at ambient temperature to the cold stage with attached load at low temperature. From Eq. (3.37) it follows that these radiation losses are strongly dependent on the enclosure temperature Tout and also on the emissivities of both surfaces. A reduction of εin directly translates in a reduction of the radiation losses. If Ain ≈ Aout, then a reduction of εout also reduces the radiation losses. If the cold stage, however, is located in a much larger vacuum enclosure such that Aout >> Ain, then a reduction of εout is of limited influence on the radiation losses. Table 3.4 lists the emissivities for a number of relevant materials at different temperatures. The smallest emissivities can be found for polished metals with the highest electrical conductivity, such as gold, silver, copper and aluminium. Contamination of the surface, addition of other elements (alloys) and surface roughness increases the emissivity. For metallic elements at lower temperatures, the emissivity increases approximately proportional with temperature.

Table 3.4 Emissivities at different temperatures for a number of materials. No distinction was made between the hemispherical and normal emissivities. 77 K 300 K other temperature gold electropolished [3.9] 0.012 0.027 silver electropolished [3.9] 0.009 0.018 aluminium electropolished [3.49] 0.018 0.010 at 175 K aluminium commercial sheet [3.50] 0.05 copper electropolished [3.9] 0.024 0.030 copper lightly oxidized [3.9] 0.49 at 590 K platinum polished [3.9] 0.065 at 370 K stainless steel 316 polished [3.9] 0.16 stainless steel 316 cleaned as-received [3.9] 0.29 at 350 K silicon 0.8 0.9 silicon nitride [3.51] 0.89 at 590 K pyrex [3.52] 0.87 0.86

Instead of reducing the emissivity of all cold stage parts, radiation in conventional cryogenic

systems is often reduced by application of solid radiation shields or Multi Layer Insulation (MLI or superisolation). In these methods, one or more shielding layers of low emissivity (high reflectivity) material are placed in the vacuum space around the cold stage reflecting the radiation load. The net radiation between two parallel surfaces 1 and 2 with one radiation shield (3) placed in between can be derived as [3.43]:

2,3

2,3

1,3

1,3

21

42

41

1111)(

εε

εε

εε

σ−

+−

++

−=

TTAP Bs

rad (3.38)

A , , Tin in inε

A , , Tout out outε

Figure 3.16 Schematic of a convex object in a cavity.

Chapter 3

80

where ε3,1 and ε3,2 are the emissivities of both sides of the radiation shield. Notice that Prad becomes very small when ε3,1 and/or ε3,2 is small, even if ε1 and ε2 stay close to 1. For the case that N shields are placed between the warm and cold surface and the special condition that all emissivities are equal, it can readily be shown that

0,, 11

radNrad PN

P+

= (3.39)

MLI often contains 10-30 layers of highly reflecting material such as aluminized Mylar. To prevent thermal contact between the layers they are crinkled or a low conductivity spacer material is applied. However, for larger layer densities the thermal conductivity between successive layers starts to play a role, reducing the effective shielding factor. Often an effective (temperature dependent) thermal conductivity is applied to account for these losses, which is about 7⋅10-5 W/mK for an optimum 30 layers per cm for typical NRC-2 MLI used to shield 300 K radiation [3.53]. Both for solid radiation shields and MLI it is very important that the shields are optically closed; a small hole can significantly reduce the effectiveness of the shielding.

For a miniature cold stage the application of optically closed MLI around the system seems quite cumbersome. Another option could be a solid miniature radiation sheath that is accurately positioned around the cold stage. However, probably an easier, more elegant and more effective solution is a coating of a low emissivity layer on the cold stage surface itself. The substrates used in MEMS are often highly polished, so that a deposited thin film of gold or aluminium directly translates into a very small emissivity. To make this an effective solution, the cold surface should be completely covered with the low emissivity coating. Typical MEMS surface materials are silicon, silicon nitride or silicon oxide (pyrex) which all exhibit very high emissivities so that a small fraction of non covered substrate directly translates into higher radiation losses.

To compare the effectiveness of MLI with a solid radiation shield or a low emissivity coating on a miniature cold stage surface, an effective emissivity can be defined for MLI insulation:

)(

)(44

inoutB

inouteffeff

TTd

TT

−

−=

σ

λε (3.40)

where d is the thickness of the MLI layer. If, for example, a 0.5 cm thick 15 layer NRC-2 MLI is applied around a miniature cold stage to shield from 300 K, it follows that εeff ≈ 0.004. This is valid under the assumption that the area of the inner MLI layer joins closely with the cold stage. If this is not the case, εeff increases significantly because of increased surface area. A fixed single radiation shield that is closely fitted around a cold stage yields an effective emissivity about half of the emissivity of the applied metal layers on the shield (both sides work as a shield, see Eq. (3.38)), so that εeff ≈ 0.005. For a thin film coating on the cold stage such as gold or aluminium, ε ≈ 0.01 or 0.02 should be feasible. In conclusion, MLI or a radiation shield theoretically results in a lower radiation load compared to a low emissivity coating on the cold stage, but this is only valid under the assumption that the shields fit closely to the cold stage surface. In practice, the surface area of the radiation shield will at least be twice the surface area of the cold stage which can be considered as the break-even point. Because a thin


81

film coating is relatively easy to apply, such a coating is probably the preferred solution for a miniature cold stage.

For ε = 0.02, radiation from 300 K results in a load of 0.9 mW per cm2 cold area at 77 K. The conduction losses discussed earlier in this section required a cold stage length in the centimeter range. If it is now assumed that the cold stage area (including load) is in the cm2 range, it follows that the net cooling power should be at least in the low mW range to cool away the radiation losses from 300 K (see the footnote on page 16 for a definition of the net cooling power). This is a sort of fundamental lower limit for the cooling power if radiation is present from 300 K on a cold stage area in the cm2 range. A similar argumentation with different numbers can be made for other ambient temperatures.

3.3.4.4 Convective heat transfer In cryocoolers, convection occurs essentially in different types of heat exchangers and

regenerators. Emphasis in this section is, therefore, put on convection in forced internal flow. Although flows in a microcooler are expected to be laminar, it is clarifying to look to scaling of heat transfer effects in the turbulent regime as well, since heat exchangers in large coolers often operate in the turbulent regime. Sometimes boiling and condensation, where latent heat is transferred to or from a fluid, are also classified as convective heat transfer, but these effects are treated separately in the next section.

When a fluid with uniform velocity and temperature profiles enters a tube, a velocity profile develops in the hydrodynamic boundary layer and a temperature profile develops in the thermal boundary layer. After a certain entrance region the boundary layers no longer change and the flow reaches the fully developed region. For laminar flow, the ratio of the thermal entry length xfd,t and the tube diameter D can be expressed as [3.43]:

PrRe05.0, ≈

D

x tfd (3.41)

In this expression Pr stands for the dimensionless Prandtl number, which is the ratio of the hydrodynamic boundary layer to the thermal boundary layer.* The Prandtl number is given by:

λµpc

=Pr (3.42)

For turbulent flow, the thermal entry length is xfd,t / D ≈ 10. In most applications the entry length is relatively short and can be neglected.

A general expression for the convective heat transfer dPcv through a small section of the tube surface area dAs can be given as:

smscv dATTdP )( −= α (3.43)

where α is the local convection heat transfer coefficient of the fluid and Ts and Tm are the surface and mean fluid temperature. Notice that Tm changes in the flow direction since heat is added or removed from the fluid. Ts can vary as well, dependent on the applied boundary restrictions. In general, the heat transfer coefficient is a complicated function of all the

* The Prandtl number is determined by the kind of fluid, the temperature and the pressure. For gases at room temperature and atmospheric pressure the Prandtl number is near unity. If the Prandtl number is high, the temperature difference between the axis and the wall of the tube is concentrated in a relatively thin boundary layer. At low Prandtl numbers the temperature profile between the axis and the wall of the tube is parabolic.

Chapter 3

82

parameters that influence convective heat transfer. It is common to use a dimensionless number, Nusselt, to express the convective heat transfer relative to heat transfer by conduction:

λ

α hDNu = (3.44)

For laminar flows, Nusselt can be calculated analytically and is only dependent on the channel geometry and the type of thermal boundary restrictions that are applied [3.41]. Table 3.5 shows some Nusselt numbers for fully developed laminar flow in different cross sections, and for two different thermal boundary restrictions. In the entrance region, Nusselt is higher because of a smaller thermal boundary layer.

Table 3.5 Nusselt numbers for fully developed laminar flow in different cross sections for two different thermal boundary conditions [3.43].

Configuration Nusselt number for different boundary conditions cross section width/height fixed heat flow fixed wall temperature

circular - 4.36 3.66 square 1 3.61 2.98

rectangular 2 4.12 3.39 rectangular 4 5.33 4.44 rectangular 8 6.49 5.60 rectangular ∞ 8.23 7.54

triangle - 3.11 2.47

For turbulent flows, no theoretical expression exists and different empirical relations are

used to match typical situations. A preferred expression is the Dittus-Boelter equation [3.43]:

nNu PrRe023.0 8.0= (3.45) where n = 0.4 for heating (Ts > Tm) and 0.3 for cooling (Ts < Tm). This equation has been confirmed experimentally for the range of conditions: 0.7 ≤ Pr ≤ 160, Re ≥ 10000, L / D ≥ 10. If, for instance, the duct contains significant surface roughness, other relations are required.

With the above-mentioned expressions, the scaling behavior of internal convective heat transfer can be investigated. For laminar and turbulent flow through a tube, the convective heat transfer can be derived as:

TA

lONuP

clamcv ∆=

2

, 4λ

(3.46)

TmAD

OlcTv

DOlc

Pch

pm

h

pturbcv ∆=∆= 8.0

8.02.05.0

3.07.08.0

2.05.0

8.03.07.0

,

023.0023.0&

µλ

µρλ

(3.47)

From these expressions, it appears that heat transfer in laminar flow scales with β and in turbulent flow with β 2.6 (recall that m& scales with β 3). As a consequence, the heat transfer per unit of volume in the turbulent regime is hardly improving at a smaller scale. In fact, for turbulent flow two dimensional scaling of the cross sectional flow path increases the heat transfer per unit of volume but the reduction of the flow velocity, associated with a reduction of the length scale, strongly reduces the heat transfer rate. This in contrast to the heat transfer per unit of volume in laminar flow, that is significantly improving at a smaller scale. This is caused by the relative increase of surface area, as well as by an increased heat transfer


83

coefficient at a smaller scale. This explains why microminiature heat exchangers can have efficiencies that outperform larger macroscopic heat exchangers that operate in a turbulent regime. Turbulences were normally considered essential for the operation of heat exchangers to allow fluid mixing, which transfers heat from the walls of the exchanger to the body of the fluid. Several miniature heat exchangers for liquid cooling of electronics have indeed demonstrated enormous heat transfer capabilities in the laminar flow regime [3.54, 3.55]. Heat flow densities in these devices could be larger than those of turbulent flow through larger channels.

Another important distinction between heat transfer in laminar and turbulent flows can be illustrated for tubes with a rectangular cross section. If it is assumed that the width b of the channels is much larger than the height d, the heat transfers become proportional to:

dlb

P lamcv ∝, (3.48)

d

blmP turbcv

2.08.0

,

&∝ (3.49)

From these expressions, it can be concluded that heat exchangers in the laminar flow regime can be designed with much more freedom since both b and l can be used to enhance the heat transfer. This is in contrast to heat transfer in the turbulent regime, that can hardly be enhanced by increasing b. For turbulent flow, the benefit of an increased surface area (by widening of the channel) is cancelled out by a reduced heat transfer coefficient due to the reduced flow velocity. For laminar flow, slow flow of the fluid over a broad surface can be used without loss of efficiency [3.56].

Heat transfer rates can easily be increased by increasing the flow velocity and by increasing the heat transfer surface, for instance by designing many parallel channels. However, both measures also strongly affect the pressure drop losses over these channels, which can especially for gases become very significant. Pressure drop losses in coolers are in some way or another subtracted from the cooling power, and should be limited. Therefore, an important parameter for convective heat transfer in tubes is the ratio of the convective heat transfer and the pressure drop power loss which is given by Eq. (3.25). For laminar and turbulent flows this ratio can be calculated as:

2

22

,

, 8m

TA

CNu

P

Pc

lampl

lamcv

&

∆=

µλρ

(3.50)

95.105.0

2

75.0

23.07.0

,

, 624.0

mT

PAc

P

Pcp

turbpl

turbcv

&

∆=

µρλ

(3.51)

From these expressions it can be concluded that, both for laminar and turbulent flow, the ratio Pcv / Ppl increases with about β

-2. For laminar flow, this improvement is caused by the relative increase of heat transfer surface area per unit of volume. Meanwhile, the pressure drop losses over these smaller channels (per unit of volume) are kept constant by a reduction of the flow velocity that is associated with the reduction of the length scale. For turbulent flow, no heat transfer improvement is obtained at a smaller scale. The improvement of the power ratio is made possible by the reduction of the pressure drop losses, caused by a reduction of the flow velocities. In summary, the key parameter in scaling is a reduced flow velocity through shorter

Chapter 3

84

channels creating a large ratio Ac / m& . For conventional large scale heat exchangers this scaling behavior translates into a common design rule. Heat exchangers with low pressure drop losses should have a short flow path with low fluid velocities in combination with a large cross sectional and surface area. In addition to this, heat exchangers with microchannels for laminar flow benefit of increased absolute heat transfer rates.

It is important to notice that the result of this discussion is often less relevant for liquids, because of the relatively small pressure drop losses and very large heat transfer rates that occur for liquids. For similar heat exchanger configurations and mass flows, the power ratios in Eq. (3.50) and (3.51) are for liquids four orders of magnitude larger compared to these ratios for gases.

3.3.4.5 Boiling and condensation Condensation occurs when the temperature of a vapor is reduced to below the saturation

temperature. In coolers, condensers can be found at the ambient (warm) side of vapor compression refrigerators and in precoolers of JT-cryocoolers. From these condensers, the latent heat of condensation is rejected to the environment. Dependent on the surface condition inside the condenser and the kind of fluid that is applied, film condensation or dropwise condensation may occur. Either the liquid film or the drops flow from the surface due to gravitational forces. In dropwise condensation, most of the heat transfer is through µm-sized drops, and transfer rates are more than an order of magnitude larger than those associated with film condensation. To estimate heat transfer rates and the scaling trends for micro condensers, film condensation is assumed. Conditions within the tube are complicated and depend strongly on the velocity of the vapor flowing through the tube. If the velocity is small (low Reynolds number), condensation occurs in the manner depicted by figure 3.17a: condensate flow is from the upper portion of the tube to the bottom, from where it flows in a longitudinal direction with the vapor. For such condensation, Chato [3.60] recommends an expression for the heat transfer coefficient of the form:

4/1'2

3

2 )(

)(555.0

−

−=

DTT

hg

ssatl

plvllp µ

λρρρα (3.52)

where g is the acceleration due to gravity, g(ρl − ρv) is the body force arising from the liquid-vapor density difference, Tsat – Ts is the difference between the saturation and surface temperature, D is the tube diameter and h2p

’ is the modified latent heat, given by:

)(83

,2'

2 ssatlppp TTchh −+= (3.53)

vapor vapor

condensate

condensate

a) b) Figure 3.17 Film condensation in a horizontal tube. (a) Cross section of condensate flow for low vapor velocities. (b) Longitudinal section of condensate flow for larger vapor velocities.


85

From these expressions, it can be concluded that the scaling behavior for miniaturization is mainly determined by the relative increase of surface area. Scaling occurs with β 1.75.

Boiling or evaporation occurs at the cold stage of recuperative coolers, where the produced liquid refrigerant is evaporated by a thermal load that is attached to the cold stage. This boiling or evaporation may occur under various conditions. In pool boiling the liquid is quiescent and heat transfer occurs due to conduction, convection and due to mixing induced by bubble growth and detachment. In contrast, for forced convection boiling, fluid motion is induced by external means, as well as by free convection and bubble-induced mixing. If gravity is not present, wetting of the surface may be prevented and a porous wick material can be used to hold the liquid and evaporate it from the enlarged wick surface area [3.61]. All these different evaporation methods are strongly related to the wetted surface area, which is advantageous for scaling to miniature size. Scaling of the heat transfer will likely occur between β and β 2.

3.3.4.6 Thermal regenerative heat losses Shuttle heat losses were discussed in section 2.3.7 and are given by Eq. (2.11). Since shuttle

losses are in fact conduction losses over the outer area of the regenerator, it is obvious that scaling to small dimensions is very unfavorable. When 3D-scaling is considered, shuttle heat losses scale with β. As a consequence, shuttle losses put severe restrictions on the design of a miniature regenerative cooler. One major implication is that a very small gap width d over the whole length of the regenerator is undesirable.

Pumping losses were also discussed in section 2.3.7 and are given by Eq. (2.12). Scaling occurs proportional to β 4.2. Pumping losses are also a strong function of d, but with a dependence opposite to that of shuttle losses. Clearly, careful design is required to find an optimum between these two types of losses.

3.3.5 Fluid mechanics and heat transfer in microchannels

The presented scaling analysis is based on physical laws that are normally used for conventional macro-sized systems. It is important to study if deviations of these theories can be expected when applied in the micro domain that we are focussing on. In the field of mechanics much experience is gathered in the fabrication of all kinds of MEMS systems, such as accelerometers, pressure sensors, valves, etc. From this experience, it follows that no relevant deviation is expected in the discussed mechanical topics. This may be different for fluid mechanics and heat transfer in microchannels, where deviations from normal behavior are reported [3.62, 3.63]. Some relevant results that were found in the literature are discussed below.

Wu and Little [3.64, 3.65] measured both friction factors and heat transfer characteristics for the flow of gases in fine channels used for micro-miniature Joule-Thomson refrigerators. The test channels were fabricated by powderblasting of glass and measured 30 to 60 microns in depth and 130 to 200 microns in width. Typical for powderblasting is a large surface roughness; a roughness of 10 microns or more was reported. The channels were covered by a smooth glass plate which leads to an asymmetric roughness of the channels. To compare the friction factor of rough and smooth channels, samples of similar sizes but without significant roughness were prepared by etching of silicon. The measured friction factors of these smooth channels coincided with theory, both for laminar and turbulent flows. For the powderblasted

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86

channels, the friction factor increased in the laminar zone with a factor of 3 to 3.5 and in the turbulent zone with 4 to 5. Moreover, for rough channels the transition from laminar to turbulent occurred at much lower Re numbers, at Re ≈ 400. Their measurements of heat transfer coefficients are much more difficult to interpret. No reference data for smooth channels was available and the construction of the refrigerator configuration caused large inequalities of heat fluxes and temperatures over the cross section of the channels, leading to a more complicated interpretation of the measurement data. From the measurements they concluded, however, that roughened channels have an improved heat transfer coefficient, especially in the turbulent regime.

Choi et al [3.66] investigated the friction factors and convective heat transfer coefficients for laminar and turbulent nitrogen gas flows in microtubes. The inside diameter of the microtube ranged from 3 µm to 81 µm and the tube roughness was characterized between 10 and 80 nm. The measured friction factors in both laminar and turbulent flows were found to be 10 – 30% less than expected. No explanation was given for this deviation. The measured heat transfer coefficients in laminar flow exhibited a Reynolds number dependence, which is not expected from the theory for fully developed laminar flow in which Nusselt is a constant depending only on the duct geometry. For turbulent flow, the measured heat transfer coefficients were up to one order of magnitude larger than expected; the deviation was larger for large Reynolds numbers. In the paper, it was suggested that suppression of the turbulent eddy motion in the radial direction (but not in the axial direction) due to the small channel diameters could explain this behavior. Another explanation, that was not mentioned, could be as follows. In the paper, it was reported that the fluid velocity and Reynolds number were varied by adjustment of the inlet pressure of the tube, while the outlet pressure was kept constant at 1 bar. Because of the small tube diameter very high pressures were required, up to 100 bar for the smallest and 57 bar for the largest diameter tube. Nitrogen gas, used for the experiments, behaves as a van der Waals gas at these high pressures and exhibits very significant cooling during expansion from high pressure (Joule-Thomson effect), up to 20 °C for expansion from 100 bar. Since the heat transfer coefficient was determined by cooling a hot gas flow through the tube to a cold environment, an extra Joule-Thomson effect would erroneously suggest an enhanced heat transfer coefficient. In the paper no comment was made about correction of the measurement data for this intrinsic gas cooling. This could explain the higher heat transfer coefficients that were found at high Reynolds numbers.

Pfahler [3.67] conducted an experimental investigation of fluid (liquid and gas) flows in very small rectangular channels with a depth of about 1 to 5 µm. The flows were in the fully developed laminar regime. In most of the experiments it was observed that the friction factor could be described as f⋅Re = C, with C being independent of the Reynolds number (see Eq. (3.20)). This behavior is in line with predictions based on the Navier-Stokes equations. However, the experimentally obtained C was consistently 15% lower than the theoretically predicted one. Pfahler mentioned that inaccuracies of the measured channel depth could be one explanation for the difference.

In a continuation of this effort, Pfahler et al [3.68] presented measurements of the friction factor for fluids in channels between 0.5 and 40 µm. For liquid flows, a different behavior was observed for the polar isopropanol and the non-polar silicone oil. In the largest channel using isopropanol, the flow behaved as predicted by the Navier-Stokes equations. However, with


87

decreasing channel size, the friction factor reduced approximately proportional with the channel size, leading to a deviation of about 19% for the channel with a depth of 0.5 µm. For silicone oil also a smaller friction factor was measured, but independent of channel size. For nitrogen and helium gas flow, the obtained C was again about 15% smaller than expected in channels with a depth of 4.5 µm. For the smallest channel with a depth of 0.5 µm, C showed a decreasing trend with decreasing Reynolds number which could very well be attributed to rarefaction effects due to small Knudsen numbers.

3.3.6 Scaling conclusions

Below a summary is given of the most important discussed scaling effects. Mechanics: • Since inertia forces are very small for small systems, jerky movements are less problematic

than in large systems and vibrations will be relatively small as well. • Stresses in mechanically loaded or pressurized structures are quite independent of system

scale. • The natural frequency of a mass (gas) spring system increases for smaller systems with β -1. • The possibility to buffer energy in rotation is virtually impossible at a small scale. Actuators: • A typical microcooler with a cooling power of 10 mW at 80 K and a COP of 0.1⋅COPCarnot

will require about 200 mW of mechanical compression power. Such compression power is very large for MEMS based actuators, but theoretically not impossible.

• Forces and powers in electrostatic actuators scale attractively when the gap size is reduced because of the large electric fields that can be present in small gaps. However, the required compression power would still require a very large actuator volume which seems not feasible with the current MEMS technologies.

• Magnetic actuators exhibit a somewhat difficult scaling behavior because heat dissipation becomes more dominant at a smaller scale. This, together with the large required compression power, makes integration in MEMS unlikely. A small relays-type magnetic actuator mounted on top of a MEMS based cooler with integrated piston appears to be a more logic choice.

• Because the piezoelectric effect is a bulk material property, it is quite independent of scaling. Integration of a thin film piezoelectric actuator in a MEMS cooler or mounting of a small external actuator are both serious options.

• Theoretically, phase change actuators can deliver significant power densities but no solution is known for the implementation of the actual power conversion step.

• An actuator in which a pressure difference is made by ad- and desorption of a gas on a sorber material can directly be connected to a recuperative cold stage. Real integration in MEMS is unlikely because of the slow thermal processes which requires a very significant sorber mass.

• In general, thermal energy can be produced at a very high rate at small dimensions by dissipating electrical energy.

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88

Fluid mechanics: • The continuum theory for gases at atmospheric pressures starts breaking down for channel

sizes smaller than 1 µm. Microcooler channel sizes are expected to be larger than 1 µm and fluids can, therefore, still be considered as a continuum.

• Because of the reduced hydraulic diameters and fluid velocities, low Reynolds numbers and laminar flows are expected in microcooler components.

• Pressure drops in internal laminar flow have a scale factor of 1. Because of that, it is not expected that pressure drops cause more problems in smaller systems.

• Gas leakage along a narrow slit is to the third power dependent on the width of the slit. So, very small openings between two moving parts will create very effective clearance seals. MEMS technologies make it possible to fabricate such very small openings.

Heat transfer: • Since steady-state conduction is inversely proportional to the length of the conduction path,

conduction through the cold stage of a microcooler puts a fundamental lower limit on the length scale of a cold stage. This minimum length can be pushed to millimeter or small centimeter size by choosing a suitable construction material with a low thermal conductivity. Glass is a suitable material in this respect.

• Also thermal conduction through support structures and especially wires can become dominant.

• The heat transfer rate (transient conduction) is enhanced at a smaller scale, making it possible to heat and cool small devices both faster and more uniformly.

• For larger cryocoolers ambient temperature radiation is often reduced by application of radiation shields around the cold stage. For very small cooler configurations this is not so practical anymore. Radiation can better be reduced to the low milliwatt range by direct deposition of a low emissivity thin film on the polished surface of cold stage components.

• Convective heat transfer is greatly enhanced for laminar flow in small channels. Moreover, the design freedom is larger than in turbulent flow heat exchanger configurations. As a bonus, the ratio of convective heat transfer to pressure drop losses can be increased significantly at smaller dimensions.

• Transfer of latent heat in condensation and boiling is easier at small dimensions, mainly because of the increased surface area.

• Regenerative shuttle and pumping losses are both related to the interaction between a regenerative displacer and its encapsulating cylinder. Pumping losses benefit from downscaling but shuttle losses clearly deteriorate and will, therefore, need much attention in a regenerative microcooler design.

• Some cooling cycles such as the Vuillemier cycle are powered by heat input. Large heat densities can easily be produced at small scales which makes a heat powered microcooler an interesting option.

3.4 Miniaturization of regenerative cooling cycles

In section 3.3 the theory and scaling behavior was discussed of several physical phenomena that play a role in coolers. This section discusses briefly some opportunities and difficulties in downscaling of regenerative coolers, both on component and system level. On component


89

level, downscaling of the compressor, regenerator, displacer and vacuum housing is discussed. On system level, downscaling of some regenerative cooling cycles is discussed.

Compressor. In figure 3.18 two different methods are depicted to create the pulsating pressure wave that is required in regenerative coolers. Figure 3.18a shows some kind of static pressure source connected to the cold stage via two active valves, a configuration similar to those used in GM coolers (see section 2.3.4). Figure 3.18b shows an alternating compression piston generating a pressure variation that is directly connected to the cold stage, a configuration similar to those used in (split) Stirling coolers. The static pressure source in figure 3.18a is probably difficult to integrate in MEMS, but the required active valves could be integrated in MEMS. The pressure will typically vary between 10 and 20 bar and the active valves should be able to switch against the maximum pressure difference of 10 bar. In the literature, active MEMS valves were described that indeed can operate against such a pressure difference [3.69].

In the alternating compressor of figure 3.18b, some kind of compression piston is required that is interfaced to an actuator. The required compression power is determined by the cooling power and the efficiency of the cooler. In section 3.3.2 it was argued that a 80 K microcooler with a cooling power of 10 mW would require a compression power of approximately 200 mW. The compression power of a simple isothermal recuperative piston compressor can be expressed as:

κln00 ⋅⋅= VpfPcompr (3.54)

reg.coldstage

reg.coldstage

DCcompr.

ACcompr.

pH pL

valves

(a) (b)

Figure 3.18 Two different methods to create the pulsating pressure wave that is required in regenerative coolers: (a) by application of a static pressure source and active valves or (b) by application of an alternating compression piston.

0.001

0.01

0.1

1

10

0 5 10 15 20piston diameter (mm)

pist

on s

trok

e (m

m)

0

100

200

300

400

pist

on fo

rce

(N)

stroke (mm)

force (N)

(a)

10

100

1000

10000

100000

0 5 10 15 20piston diameter (mm)

reso

nanc

e fr

eque

ncy

(Hz)

(b) Figure 3.19 (a) Estimated compression piston stroke and piston force as a function of the piston diameter for a regenerative 80 K cooler with a cooling power of 10 mW. (b) Resonance frequency as a function of the piston diameter. Assumptions: operating frequency = 100 Hz; filling pressure = 10 bar; compression ratio = 2; ambient temperature = 300 K; COP = 0.1⋅COPCarnot; COPcompr = 0.7; Pcompr = 0.2 W; (fictive) piston mass = 0.2 gram.

Chapter 3

90

where p0 and V0 are the reference pressure and volume, f is the operating frequency and κ is the compression ratio. If, for example, a regenerative cooling cycle operates with 100 Hz and has a reference gas filling pressure of 10 bar and a compression ratio of 2, then a stroke volume of about 1.5 mm3 is needed to obtain the estimated compression power of 200 mW. For a certain stroke volume, the design of a compression piston is strongly influenced by the chosen piston diameter. Figure 3.19a shows a plot of the required piston stroke and piston force (at the beginning of the stroke) as a function of the piston diameter, under the assumption of a circular piston. To reach the required stroke volume, it is obvious that a compression piston with a small diameter requires a long stroke and a compression piston with a large diameter requires a short stroke. Free piston compressors of many typical Stirling and pulse tube coolers currently on the market operate with a small diameter piston and a long stroke; see for instance the Stirling cooler in figure 2.16. Such a long stroke piston compressor typically operates with a piston inside a sealed chamber; the piston may be suspended by thin springs combined with a clearance seal between the piston and the cylinder wall. For large diameter pistons, however, a membrane can be applied around the piston since bending and tension stresses in the membrane are limited because of the short stroke. Such a membrane makes it possible to seal the compressor chamber from the other side of the piston. Moreover, it prevents sliding contacts and maintains the compression piston in position. Figure 3.20 shows an illustration of how a large diameter membrane compressor and a small diameter piston compressor could be implemented using MEMS technologies. It is probably easier to combine the membrane compressor with an actuator because the actuator can be interfaced externally outside the gas compression chamber. For the planar small diameter piston compressor at least part of the actuation principle must be integrated with the piston which is located inside a sealed gas chamber.

Because of some distinctive advantages, many commercial free piston compressors are designed to operate in a resonant condition; see for instance the discussion on resonant Stirling coolers in section 2.3.3 or Hofman [3.70]. For such systems, the compressor resonance

Factuatormembrane spring

compression volume(stroke 10 m)∼ µ

compression volume(stroke ~ 1.5 mm)

cros

s se

ctio

n

cros

s se

ctio

n

1.5 cm

1.5 mmFactuator

actuator

flexure springs

(a) (b) Figure 3.20 Illustration of how a large diameter membrane compressor (a) and a small diameter piston compressor (b) could be implemented using MEMS technologies.


91

frequency is determined by the mass of the piston and the gas spring. In section 3.3.1 it was explained that the natural frequency of a mass spring system scales with β -1 if the system size is scaled with the same proportion in all three dimensions. This scaling behavior can be clarified by focussing in more detail on the expression for the resonance frequency. For small displacements of a piston which compresses a gas volume, the gas spring constant can be written as:

0

20

VAp

xF

k c≅∂∂

= (3.55)

where p0 and V0 are the starting pressure and volume of the gas spring and Ac is the cross sectional area of the piston. Using this expression, the resonance frequency of the mass spring system can be written as:

mVAp

mk

f c

0

20

0 21

21

ππ== (3.56)

where m is the mass of the piston. From this expression it follows immediately that especially large diameter microcompressors with a small stroke volume will result in very high resonant frequencies (i.e. relatively large Ac with a small V0 and m). Figure 3.19b illustrates the resonance frequency as a function of the piston diameter for a (fictive) fixed piston mass of 0.2 grams, a stroke volume of 1.5 mm3 and a gas pressure of 10 bar. Although miniature regenerative coolers can probably be operated at relatively high frequencies due to reduced flow losses at smaller scales (see the discussion in sections 3.3.3 and 3.3.4.4), the resonance frequency of at least large area membrane compressors is much too large. A small diameter piston compressor of 1 or 2 mm could perhaps be operated in a resonant condition but such a compressor is probably more difficult to fabricate.

Regenerator and displacer. The regenerator acts as a large thermal capacity that exchanges heat with the gas when it moves through: the regenerator takes up heat when the gas moves from the hot to the cold side, and it gives off heat when the gas moves back from the cold to the hot side. Some essential regenerator requirements were discussed in section 2.3.2. Regenerator theory indicates that the best geometric configuration for a regenerator is a parallel plate arrangement with small clearances in between the plates and discontinuities (e.g. slits) in the plate material from the warm to the cold side [3.71]. For such a configuration, the heat transfer rate is maximum for a specified flow rate and pressure drop; this follows also from the discussion in section 3.3.4.4. The discontinuities are required to interrupt the conduction of heat in the direction of flow and to allow cross flow between parallel flow passages. Long channels without openings to allow cross flow cause instabilities of the flow distribution between parallel flow sections. This means that flow passing through the regenerator in one direction does not follow exactly the same path as flow passing through it in the other direction, resulting in a reduction of the regenerator effectiveness [3.71].

Current regenerator technology for cryocoolers operating above 50 K is based on stacks of screens woven from metallic wire since no other serious alternatives are available. Although cross flow is guaranteed for this configuration, stacked screens have several disadvantages that can be improved by using MEMS technologies for the regenerator fabrication. For stacked screens, the parallel plate condition is not satisfied so that the ratio of pressure drop losses to heat transfer effectiveness is relatively high. Using MEMS technologies to create a well

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92

controlled etched geometry, the parallel plate condition could be improved significantly. Another advantage of a MEMS based regenerator is that the passage size and regenerator geometry can be varied continuously from the warm to the cold end of the regenerator. In that way a gradual adjustment can be made to match the (strongly) temperature dependent material properties of the gas and the regenerator material.

A similar regenerator fabrication is shown in a patent by Yaron [3.72], in which etching technologies typical for MEMS are proposed to create favorable regenerator geometries in thin foils. By etching slits and slots in foils and subsequently stacking of these foils, effective regenerator material can be created. These stacks or rolls of regenerator material can then be used to build conventional regenerators, see figure 3.21.

The temperature difference of the cold stage is present over the regenerator and, as was discussed in section 3.3.4.1, conduction losses through the regenerator can become very significant when it is scaled to small dimensions. To limit these conduction losses, the solid support structure of the regenerator cannot be made of silicon due to its high thermal conductivity and the temperature difference should be established in the plane of the MEMS construction to create a sufficiently long thermal conduction path. The glass molding technology, that was discussed in section 3.2.2, could be used to manufacture a regenerator. It could, for example, be made of silicon pillars which are mechanically interfaced by a glass support structure that limits the heat conduction. Another possibility is a complete glass regenerator since the thermal penetration time constant for glass is still acceptable under most conditions, see the discussion in section 3.3.4.2. An example of a silicon-glass regenerator incorporated in a displacer structure is drawn as part of the Twente-Stirling cooler, which is discussed later in this section.

Vacuum housing. Conventional cryocoolers are always used in combination with some kind of bulky vacuum housing around the cold stage to guarantee thermal isolation from the environment. If a microcooler would become available, a complete small system package can only be obtained when the vacuum housing around the micro cold stage is also miniaturized. One attractive approach is to integrate a MEMS based vacuum house around the cold stage. A schematic illustration of such a miniaturized vacuum house around a microcooler is given in figure 1.2

gas flow

(a) (b) Figure 3.21 (a) Stack of etched regenerator foil material, such as proposed by Yaron [3.72]. The gas flow is intended in the vertical direction. (b) Regenerator foil rolled and packaged to make up a conventional regenerator.


93

Miniaturization of regenerative cooling cycles. Possible miniaturization of the regenerative cooling cycles from section 2.3 will be discussed below. The scaling theory presented in section 3.3 will be taken into account, as well as remarks made in this section about miniaturization of cooler components.

Stirling. The α-Stirling cycle with disciplined pistons (cycles 1 and 2 in figure 2.9) requires a strong mechanical link between the two pistons. This link should be able to transfer the expansion work back to the actuator and it should maintain the proper phase difference between the two pistons. Such a configuration appears difficult to realize in MEMS. The α-Stirling cycle with two actuators (cycles 3 and 4 in figure 2.9) requires an actuator at the cold side that is able to convert the expansion work reversibly to electrical energy. Real actuators do not fulfill this requirement, which makes the cycle unlikely to succeed. The α- and β-Stirling cycles with resonantly coupled expansion piston or displacer (cycles 5, 6, 9 and 10) could perhaps be applied on a small scale, but only with a small diameter large stroke piston. For a large diameter small stroke piston, the resonance frequency becomes very high and this would lead to unacceptable flow losses in the regenerator. For that reason, the cooler depicted in figure 2.12b and proposed by Petersen [3.73] will probably not be feasible. The β-Stirling cycle could be applied with some kind of mechanical link between the piston and displacer that would maintain the required phase difference between the piston and the displacer. This could, for instance, be a kind of snap-action spring, as was illustrated in figure 2.20. Another possibility is a separate small actuator located at the ambient side of the displacer that moves the displacer at the appropriate moment.

Gifford-McMahon. The GM-cycle as discussed in section 2.3.4 could perhaps be applied on a micro-scale, but it requires an actively controlled displacer, active high pressure valves and some kind of high pressure source. Such high pressure source could, for instance, be a small sorption compressor (see chapter 4) that is interfaced to the MEMS-based cold stage.

Vuillemier. The Vuillemier cycle appears rather suitable for miniaturization. It is driven by heat, which can easily be supplied in miniature devices. Only two additional small actuators are required to move the displacers and which can both be located at the ambient temperature side of the displacers.

Pulse-tube. Miniaturization of the orifice pulse tube appears intrinsically difficult. For proper operation the gas in the volume of the pulse tube should behave adiabatically. For smaller dimensions the surface area of the wall increases rapidly which makes the adiabatic condition more difficult. More research is needed to find out if the basic pulse tube configuration could use this increased surface area as an advantage at smaller scale.

An example of a regenerative microcooler. A number of Stirling cycles and the Gifford-McMahon cycle require mechanical links or active control of the displacer or expansion piston. A more attractive solution for a MEMS-based cooler is a displacer that reacts passively on the fluidic forces generated by the compressor. A resonantly coupled displacer is one example of such a passively reacting displacer, but this cycle is not easy to implement on a small scale as was discussed before. Another example of a cooling cycle with a passively reacting displacer is the Twente-Stirling cycle discussed in section 2.3.3. Figure 3.22 shows a design of an integrated MEMS regenerative microcooler that is based on this cycle. The cooler consists of a large diameter, short stroke, membrane compression piston and a planar displacer with integrated regenerator which are both machined in the same silicon wafer. Machined glass

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94

wafers are bonded on the top and bottom side of the center silicon wafer to create a sealed gas volume inside the cooler. The compressor actuator is not included in the drawing, but it should be interfaced externally on top of the membrane piston and it could, for example, be a strong electromagnetic actuator or a piezoelectric actuator. The membrane piston consists of a thick circular boss which is suspended on a thin circular membrane. This membrane should be able to resist the gas pressure inside the cooler, in addition to the piston deflection when it is actuated. The compression chamber is interfaced to the displacer via a gas channel that is etched in the bottom glass wafer.

The displacer with integrated regenerator consists of a glass frame which is suspended by thin silicon flexure springs and which contains silicon pillars that act as the regenerative thermal capacity. Such a construction could be fabricated by glass molding, as was discussed in section 3.2.2. In the current design, the displacer is open at the top and the bottom side and a clearance seal, that is manufactured between the displacer and the top and bottom glass wafers, forces the gas flow through the regenerator pillar structure. The folded flexure springs are anchored on one side to the displacer and on the other side to the top and bottom glass wafers. A flow restriction is integrated at the entrance of the warm side of the regenerator, for instance by a reduction of the gap size between the regenerator pillars.

Thermal conduction losses through the glass wafers that cover the cold stage should be limited by proper shaping of the glass, so as to reduce the cross sectional area of the thermal conduction path. Next to the regenerative displacer, the silicon of the center wafer is etched into separated plates to break the thermal conduction path; plates fabricated of glass could also be used here. The shown dimensions of this microcooler match first order calculations carried

compression piston

Factuatormembrane spring

flow restriction

compression volume

expansion volume

flexure spring

displacer withregenerator(~ 25 m pillars)µ

glass frame thatholds siliconpillars

glass support beams

cros

s se

ctio

n

gas channel between compressor and displacer

1 m gas sealµ

siliconglasssi membraneflow restriction

silicon supports

postion of displacer justafter the compression step (step 2 of the cycle)

1.5 cm

1.5 mm

cross section

Figure 3.22 Top view and cross sections of a possible regenerative microcooler. Operation of this cooler is based on the Twente Stirling cycle, described in section 2.3.3.


95

out on this cooling cycle, but detailed modelling is required to investigate the behavior of the cooling cycle and its proposed subcomponents.

3.5 Miniaturization of recuperative cooling cycles

Until now, no publication exists about a realized and operating MEMS-based regenerative microcooler. On the other hand, the Linde-Hampson cooler of MMR that is depicted in figure 2.37b illustrates that MEMS technologies can successfully be used to construct recuperative coolers. It should, however, be noticed that this cooler is not really a microminiature cooler in terms of size and cooling power and that no miniature compressor exists for this cooler. On the other hand, it demonstrates that MEMS technologies clearly offer opportunities to fabricate passive fluidic components like heat exchangers, flow restrictions and boilers, components which are used in cycles employing Joule-Thomson expansion. Miniaturization of expansion engines, which are required for the recuperative Joule-Brayton cycle, seems to be rather difficult using MEMS technologies.

Compressor. Cooling cycles which employ the Joule-Thomson effect and which are used to cool to cryogenic temperatures require rather high pressure ratios, often a ratio of 20 or more. Currently, no miniature or MEMS based compressor exists that can create such pressure ratios. From the actuators that were discussed in section 3.3.2, a piezoelectric actuator is a logic choice for creating high pressure ratios and high pressures. Another proposed solution is a miniature compressor based on the ad- and desorption of gas on a sorber material. This compressor solution will be investigated in more detail in the chapters 4 and 6 of this thesis. In order to get continuous flow operation from such sorption cells, at least four cells are required which are interfaced by check valves. Design and realization of MEMS-based check valves is discussed in chapter 1.

Counterflow heat exchanger. Three basic requirements can be formulated for a counterflow heat exchanger: 1. The geometry should allow a certain heat transfer between the fluid flows in the two channels; 2. The pressure drop losses should be limited below a certain value; 3. Heat conduction losses along the length of the heat exchanger should be limited. In section 3.3.4.4 it was discussed that the ratio of heat transfer to pressure drop power losses increases rapidly when heat exchangers are scaled to smaller dimensions. Therefore, if the heat exchanger is properly designed, the heat transfer and pressure drop requirements should be satisfied easily. On the other hand, heat conduction losses along the length of the heat exchanger become relatively more significant due to the adverse scaling behavior of conduction losses. Moreover, when microchannels are etched in a solid substrate using MEMS technologies (like in Little’s glass-based Linde-Hampson cooler of figure 2.37b), then the solid cross sectional area of the heat exchanger will become relatively large compared to the cross sectional area of the channels. This will increase the conduction losses even more. Traditional large scale counterflow heat exchangers, on the other hand, are often constructed of a long stainless steel tube-in-tube configuration for which the cross sectional area can be optimized to a relatively small value. The use of a substrate material with a lower thermal conductivity (such as glass) will clearly help in reducing heat conduction losses in a MEMS based heat exchanger. Instead of etching channels in glass such as done by Little [3.13], chapter 8 shows a method in which glass capillary tubes with a small cross sectional area are used to create a counterflow

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heat exchanger. Clearly, other methods to pattern glass (such as glass molding discussed in section 3.2.2) could also be applied to create a heat exchanger configuration.

Joule-Thomson flow restriction. A fixed flow restriction can easily be constructed using MEMS-technologies. In fact, any etched capillary channel that exhibits the required flow restriction could be used. Some optimization could be required to create a flow restriction that is the least sensitive to clogging, a problem that could occur in Joule-Thomson restrictions. Large scale refrigerators employing Joule-Thomson expansion sometimes use controllable flow restrictions to supply a fluid flow that matches the required cooling power [3.74]. For a small cooler it is probably easier to dissipate the excess cooling power by supplying heat from an electrical heater; this solution is used in chapter 8. A MEMS based active Joule-Thomson restriction would require some kind of actuation principle at the cold side of the cooler, which is not an easy solution.

Condensers and evaporators. Condensers and evaporators can rather easily be fabricated using MEMS etching technologies. Because a liquid-vapor phase change should occur basically at a uniform temperature, a material with a high thermal conductivity is preferred to prevent temperature gradients across the condenser or evaporator. In chapter 8 some designs of condensers and evaporators in silicon are discussed. Also, fabrication details and experiments are presented.

3.6 Microcooler opportunities and requirements

Opportunities for microcooling can be found by focussing on the interaction of existing cooling technologies and low temperature applications. To study this interaction in more detail, in figure 3.23 two charts are depicted of a number of existing coolers and existing applications in the plane of cooling power versus cooling temperature. The figures are adapted from Radebaugh [3.75]. Much of the data on coolers in figure 3.23a can be traced in Nichols’ Cryocooler Database [3.1]. Cooler data was changed or added on Joule-Thomson coolers (He, H2 and N2), vapor compression coolers, space radiators and thermoelectric coolers

1

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(Special)

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ing

Mixed-gas JTHe JT

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1 TJLarge-size

SMES

1MJMicro-SMES

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VacuumH O cryotraps2

IRIR

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HTSelectronics

GaAssub-mm

Bolometers

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X-raydet.

HTSSQUIDs

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IR

Low-temp.material research

HEMTs

Bearings

Figure 3.23 (a) Most commonly used coolers in the plane of cooling power versus cooling temperature. (b) A number of applications in the plane of required cooling power versus required temperature (adapted from [3.75]).


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[3.76 - 3.82]. Operation of most of the cooling cycles was discussed in chapter 2. The figures should give an impression of the opportunities for microcooling. In this respect roughly three different types of opportunities can be distinguished: 1. For applications requiring very little cooling power, existing coolers are oversized in terms

of mass/volume/cooling power and a microcooler could be applied. For such applications it is, of course, possible to apply oversized coolers, but this increases the system size and mass unnecessarily. For existing small coolers, further downscaling of the cooling power is most likely fixed by fabrication constraints.

2. Novel microcooling technologies can lever new types of applications that were formerly impossible to achieve. An example of such new application is a MEMS-based cooler with an integrated application as well as an integrated MEMS-based vacuum enclosure around the cold stage. Such a sealed package could then be integrated with, for instance, conventional electronics on a printed circuit board. Another example is distributed cooling by application of one large compressor and many distributed MEMS-based micro cold stages.

3. New microcooling technologies can improve or extend existing cooling technologies by the addition of essential MEMS-based components. In this respect it is important to notice that cryocoolers reaching lower temperatures (T < 20 K) are frequently constructed of more stages, often stages of the same type of cooler but sometimes also of different types. The sizes of the stages reduce with temperature because the amount of heat lifted reduces with temperature. The lower temperature stages require, therefore, smaller components which could utilize MEMS techniques.

A typical example of such a multistage cooling system that could benefit of microcooling technologies can be found in a space application: the Planck mission of the European Space Agency that is currently being prepared [3.83]. This satellite is designed to study cosmic background radiation for cosmological and astrophysical purposes. The detectors of the system consist of a number of bolometers that operate at 0.1 K and High Electron Mobility Instruments (HEMTs) operating at 20 K. Precooling of the system to 50 K with 1.5 W of cooling power is obtained by a radiator. In a next stage, a Joule-Thomson cooler operating with hydrogen gas cools to 20 K with 1.5 W of cooling power. This stage precools the helium gas that is in a next stage used to cool to 4 K with 10 mW of cooling power. Finally, 0.1 K and 0.05 mW of cooling power is reached by dilution of 3He in 4He [3.84]. An additional stage at 1.6 K with 0.2 mW of cooling power is added to intercept heat inputs along the mechanical support of the 0.1 K stage. The lower temperature stages are rather small and could benefit from microcooling technologies [3.76, 3.85].

For the applications depicted in figure 3.23b, the required cooling powers and temperatures

are not necessarily fixed to values currently found and depicted in the figure. For a certain application, it is important to distinguish between the cooling power that is intrinsically fixed, for instance due to dissipation of the sensor/electronics, and additional thermal losses which are determined by the overall system design and which can often be reduced a lot. For many existing applications with a small cooling power there was, up till now, no need to optimize the system with respect to the required cooling power because all available existing cooling techniques are largely oversized anyhow. Therefore, opportunities for microcooling can be

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generated if applications are optimized with respect to the required cooling power in synergy with the (micro)cooler itself.

Concerning the temperatures, for a number of applications in figure 3.23b the depicted applied temperature is in fact determined by the available cooling method. If a cooling method would be available in a somewhat different temperature range, a number of applications could also operate in that range. An example of such artificially fixed temperature is for instance 4.2 K, the boiling temperature of liquid helium at a vapor pressure of 1 bar - a pressure which can relatively easy be applied.

The applications depicted in figure 3.23b are now briefly discussed below. Applications that

could operate with a small cooling power are underlined. Accelerators & Fusion. Large superconducting coils are used to confine charged particle bundles in accelerators and plasmas in fusion reactors. SMES. Superconducting Magnetic Energy Storage (of magnetic flux in a large coil). Maglev. Magnetic Levitation, for instance for application in trains. MRI. Magnetic Resonance Imaging (of the human body). Superconducting coils are used to generate the required large magnetic fields of approximately 1.5 T. LTS electronics. Low Temperature Superconducting electronics, for instance used to make very fast digital circuits. The intrinsic dissipation of the circuits is very small, but may become larger for complex circuits with a large number of junctions. Cooling power is mainly required to compensate heat leakages through the connecting wires; but by using thin film technologies the cross sectional area of wires can be minimized. LTS SQUIDS. Low Temperature Superconducting Quantum Interference Device. Superconducting system used to sense very small magnetic signals. Dissipation is virtually zero. The required cooling power is mainly determined by the system size, which may be significant for a system consisting of more squids. Moreover, sometimes a spatial distribution is required which adds to the system size. A small cooling power could apply for a single squid or distributed cooling. SiS. HEMT’s. High Electron Mobility Transistors, for instance used in space applications as detectors for radio spectra. Bolometers. NbN electronics. Electronics based on Niobium Nitride, a material that yields good superconducting devices operating around 10 K. See also comments for LTS electronics. IR. Infrared detectors. Dependent on the required wavelength and sensitivity, a number of different IR detectors are available at different operating temperatures. Cryopumps. Cryo vacuum pumps are commonly used in ultrahigh vacuum applications and are based on the adsorption of gases on low temperature surfaces. Air liquefaction/LNG. Large scale applications for the industrial production of cryogenic liquids such as liquid nitrogen, oxygen, methane and air. Transmission lines. Experimental projects in which conventional transmission lines for electricity are replaced by superconducting transmission lines. Transformers. Transformers operating with superconducting coils.


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Vacuum H2O cryotraps. Used in vacuum applications to freeze out water vapor. FCL. Fault Current Limiter, a protection method used in the power supply industry. Motors. By using superconducting coils, compact high power motors or generators can be created. Bearings. Superconductivity can be applied to create effective bearings. Wireless. In Wireless-basestations, superconducting filters are applied to improve performance. CMOS Si electronics. Cooling of conventional electronics has two advantages: it increases the maximum operating speed due to increased carrier mobility at lower temperatures (for instance with a factor of two by cooling from 300 K to 150 K) and it reduces the thermal noise. A low-temperature low-noise amplifier could be an important application for microcooling. Cryosurgery. Joule-Thomson coolers are applied to locally freeze and destroy human tissue inside the body. HTS electronics. High Temperature Superconducting electronics. See also comments for LTS electronics. HTS SQUIDS. Superconducting Quantum Interference Device operating with high temperature superconductors. See also comments for LTS SQUIDS. Low-temperature material research. There are many applications in chemistry, physics and materials science in which material properties need to be studied as a function of temperature. GaAs sub-mm. X-ray detectors. As an example, small X-ray detectors are used in electron microscopy for Energy Dispersive X-ray analysis (EDX).

3.7 Conclusions

An overview of existing cryocoolers shows an opportunity to construct microcoolers with a cooling power in the milliwatt range. MEMS materials and technologies offer an opportunity to construct such a small system. Silicon, mostly used in MEMS, has a very high thermal conductivity which limits its application in microcoolers to isothermal components. In contrast, glass has a very low thermal conductivity which makes it suitable for the construction of thermally isolating components. To structure glass and to combine it with silicon, somewhat more specialized micromachining techniques are required such as sandblasting, molding, bonding and glass-welding. Some of these techniques were discussed.

The scaling behavior of a number of effects in mechanics, actuator theory, fluid mechanics and heat transfer determines the opportunities and difficulties encountered in downscaling of cryocoolers. These scaling effects were investigated. In the field of mechanics, inertia forces and stored kinetic energies become relatively small when systems are miniaturized. Furthermore, the resonance frequency of a mass-spring system increases rapidly when such a system is miniaturized, which makes the miniaturization of resonantly operating cryocoolers difficult.

For an 80 K microcooler, it was shown as an example that at least a few milliwatts of cooling power is required to cool away the parasitic radiation losses on the cold stage. To obtain 10 mW of cooling power at 80 K, the compressor actuator should at least produce 0.2 W of compression power which is very large for most integrated MEMS actuators. By comparing the stored energy densities of a number of actuation principles, it was shown that there appears only an opportunity for a thin-film piezoelectric actuator to be truly integrated

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with a microcooler compressor. Other actuation principles, such as magnetic and sorption-based, require actuators of a larger scale that could be interfaced to a MEMS-based microcooler.

No significant influence of scaling is expected in the field of fluid mechanics. Low Reynolds numbers and laminar flows are expected in microcooler components. If it is assumed that mass flows scale with the system volume, then pressure drops in internal laminar flow are quite independent of scale.

In the field of heat transfer, all area related effects such as radiation, convection, boiling and condensation are relatively enhanced at a smaller scale. As a consequence, the ratio of convective heat transfer to pressure drop over a channel increases for smaller systems, which is attractive for the construction of miniature heat exchangers operating with gas. Heat conduction is relatively strongly enhanced at a smaller scale, primarily because of a reduction of the length of the conduction path. This puts a lower limit on the length scale of a microcooler cold stage and requires the use of a low conductivity material such as glass. Also transient conduction is enhanced at a smaller scale, making it possible to heat and cool small devices both faster and more uniformly. For the expected channel sizes and fluid flows, no significant deviations are expected in fluid mechanics and heat transfer theory.

A miniaturized planar regenerative cooler was discussed that illustrates the use of MEMS technologies. The cooler is based on the Twente-Stirling cycle, which is particularly attractive for miniaturization because the cold displacer reacts passively on the generated pressure wave. Another regenerative cycle that could be suitable for miniaturization is the Vuillemier cycle since this cycle is driven by heat input, which can easily be supplied in small systems.

MEMS technologies clearly offer opportunities to fabricate passive fluidic components like heat exchangers, flow restrictions and boilers, components which are used in cycles employing Joule-Thomson expansion. Unfortunately, the large pressure differences which are required for such cycles are probably difficult to generate with a MEMS based compressor. A miniature sorption compressor appears to be an attractive alternative.

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4 Sorption cooler thermodynamic analysis

Chapter 4

Sorption cooler thermodynamic analysis

In this chapter the operation and thermodynamic analysis is presented of a sorption cooler that consists of a sorption compressor and a Linde-Hampson cold stage. This cycle is promising because it has no moving parts. This facilitates scaling down to small sizes, it eliminates interference, and it contributes to achieving a long life time. In the thermodynamic analysis, the behavior of compressor and cold stage are analyzed separately, leading to a better understanding of sorption coolers. It is found that the considered compressor performs well at relatively low pressures, whereas the Joule-Thomson cold stage requires high pressures for proper performance. Two solutions were discussed to overcome this conflict: a novel two stage compressor and precooling of the gas in the cold stage. In this way, a COP of about 3 % can be obtained for a carbon/xenon cooler operating between 300 K and 165 K.

4.1 Introduction

In the previous chapter a sorption compressor in combination with a Linde-Hampson cold stage was suggested as a potential candidate for the development of a microminiature cooler aiming at a cooling power in the order of 10 mW at 80K. An advantage of this cycle is the absence of wear-sensitive moving parts, except for some check valves. This facilitates scaling down of the system to very small sizes, it minimizes electromagnetic and mechanical interference (which is important for many applications), and it offers the potential of a long life time. Moreover, the efficiency of such coolers is quite independent of scale which makes them suitable for small dimensions.

This chapter discusses the operating principles and the thermodynamic modelling of a sorption based cooler, which consists of a sorption compressor connected to a Linde-Hampson cold stage. Section 4.2 describes the system aspects of the cycle and some history of sorption coolers. A key issue in this chapter is the choice to analyze the compressor and the cold stage separately, which is different from the limited number of analyses presented in the literature. This approach is motivated in section 4.3. Next, in section 4.4 the operation of a sorption compressor is treated. Such a compressor can, in fact, be viewed as a thermodynamic engine, which makes its description completely different from normal compressors. No useful fundamental thermodynamic description of the sorption compressor cycle was found in the literature, and for that reason such a description was developed. This will be described in

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section 4.4.2. After that, a more detailed compressor model is presented which is used to illustrate the influence of different operating parameters. In section 4.5 the Linde-Hampson cold stage is analyzed and it is shown that a straightforward combination of a sorption compressor and a Linde-Hampson cold stage can lead to a poor cooler performance. Finally, in section 4.6 two solutions to this problem are considered in the form of a novel two stage compressor arrangement and a precooling configuration.

It should be emphasized that the analysis and the parameter studies in this chapter are based on our specific case of a microcooler with a warm-end temperature of 300 K. Also, a specific combination of sorbent and gas was considered: activated carbon and xenon. Nevertheless, the results are applicable in a very general sense. Other gases, materials or temperatures yield different numbers but the trends in the thermodynamic behavior and the physics behind it remain the same. In this study the combination of carbon and xenon appeared to be appropriate for a microcooler design to construct a first stage that cools from 300 K down to roughly 165 K.

4.2 Sorption cooler operation and history

Operation of a sorption compressor is based on the principle that large amounts of gas can be adsorbed on certain solids such as highly porous carbon. The amount of gas adsorbed is a function of temperature and pressure; it increases with a reduction of the temperature and an increase of the pressure. If a pressure container is filled with a sorber material and gas is adsorbed at a low temperature and pressure, then a high pressure can be created inside the closed vessel by an increase of the temperature of the sorber material. Next, a controlled gas flow out of the vessel can be maintained at a high pressure by further increase of the temperature until most of the gas is desorbed. By nature, a sorption compressor is an intermittent system in which the sorbent bed alternates between gas generation and adsorption. However, by combining at least four sorbent beds in a single compressor and sequencing these sorbent beds out of phase, it is possible to produce a constant flow of gas through the cold stage and thus achieve continuous refrigeration.

Figure 4.1 shows a schematic drawing of a sorption compressor unit connected to a Linde-

Gas-gap heat switchwith metal hydridepressure controller

Sorption compressorcell with heater

Check valve unit

Counterflow heatexchanger

J-T valve + cryostat

Aftercooler

Com

pressor unitcold stage

Refrigeration load

T environment

Q

Insulating vacuumhousing

Figure 4.1 Sorption cooler consisting of a sorption compressor unit and a Linde-Hampson cold stage.


107

Hampson cold stage that consists of a counterflow heat exchanger and a Joule-Thomson expansion valve. The sorption compressor unit generates a DC flow of gas that is isothermally compressed in the Van der Waals regime, thus reducing the internal energy of the fluid. Compressed fluid coming out of the compressor moves through the counterflow heat exchanger to the cold side where Joule Thomson (JT) expansion to low pressure occurs through a restriction. After evaporation, the low pressure vapor returns through the counterflow heat exchanger to the compressor unit. In this way the heat exchanger facilitates effective precooling of the high-pressure gas using the returning cold low-pressure gas. The cold stage is packaged in a vacuum container to minimize conductive heat losses. A more detailed description of the thermodynamic behavior of the Linde-Hampson cycle is given in section 2.4.3.

The compressor unit contains four sorption cells and several check valves to control the gas flows. Low and high pressures are generated by the cyclic ad- and desorption of the working gas on the sorption material, which is accomplished by cooling and heating of the sorption material. Usually, heating occurs with an electrical heater and cooling is done by turning on a heat-switch between the sorption cell and a heat sink on the outside. Figure 4.1 shows a configuration with a gas-gap heat switch around the cylinders. Adjusting the gas pressure in the gap between the cylinder and the heat sink can vary the heat conduction through the gap. This pressure adjustment can, for instance, be done with another small sorption pump. Chapter 5 discusses more details about the operation of the gas-gap heat switch. In that chapter also the feasibility is shown of a miniature thin film metal-hydride absorption pressure controller that can be used to adjust hydrogen pressure in a gas-gap heat switch.

A compressor cycle of one cell is schematically shown in figure 4.2. Figure a) shows the cycle in a so-called sorption diagram which depicts the amount of gas adsorbed as a function of the pressure for the used gas-sorber combination. Figure b) illustrates some essential parameters of one cell during a complete cycle. The cell is heated during sections A and B, and cooled during C and D. During sections A and C both valves of the cell are closed, and the cell is in a regenerating phase. During sections B and D one of the valves is opened; the cell generates a high-pressure gas flow out of the cell during B, and a low-pressure gas flow into

T(K)

pressure(bar)

flow(mg/s)

heat-switch

check-valves

OFF OFF ON ON

closed closedp highopen

p lowopen

A B C D

time300

600

1

30

heater ON ON OFF OFF

flow out ofcompr. cell

flow intocompr. cell

(b)(a)

A

B

C

D

C T

T: temperature (isotherms from low temperature on the upper left to high temperature on the lower right)

∆xnet

∆xdvxL

xH

pHpL pressure

TL

TH

∆xgross

A

B

C

D

x: amount of gas adsorbed (mass gas per mass sorbent material)

1

2

3

4

Figure 4.2 Schematic of compressor cycle in adsorption diagram with isotherms (a) and as a function of time (b).

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the cell during D. It is important to notice that the valves are passive check valves; the cycle is driven by the temperature induced pressure variations of the compressor cells. The time required for a complete cycle depends, among other parameters, on the volume of the compressor cells and the required gas flow. For the sorption compressor discussed in this thesis a complete compressor cycle typically takes about 10 minutes.

There are two types of sorption processes that can be used by sorption compressors in

cryogenic coolers: physical adsorption and chemical absorption [4.1]. Physical adsorption relies mainly on the relatively weak van der Waals forces between the gas molecules and the surface of the sorbent material. Microporous activated carbons (with a specific area up to 2000 m2 per gram), zeolites and silica gels are some of the materials used in physisorption compressors [4.2]. During chemical absorption a chemical bond, usually covalent, is formed between the gas and the sorbent. Chemisorption materials include: metal-hydrides (e.g. ZrNi and LaNi4.8Sn0.2) for use with hydrogen gas and praseodymium cerium oxide (PCO) for use with oxygen gas. The difference between physical adsorption and chemical absorption can be summarized as follows [4.2]: 1. Physical adsorption, like condensation, is a general phenomenon and will occur with any

gas-solid system provided only that the conditions of temperature and pressure are close to those required for liquefaction. On the other hand, chemisorption is dependent on the chemistry involved between gas and sorber material.

2. The heat of physical adsorption is of the same order of magnitude as the heat of liquefaction of the associated gas, whereas the heat of chemisorption is of the same order as that of the corresponding bulk chemical reaction which is often much larger than the heat of liquefaction.

3. Under suitable conditions of temperature and pressure, physically adsorbed layers of several molecular diameters in thickness are frequently found on the surface. No bulk effects exist for physisorption. In contrast, chemisorption on the surface is limited to a monomolecular layer but dissociated gas molecules may diffuse into the bulk of the chemisorption material.

4. Physical adsorption is per definition instantaneous but, with highly porous or finely powdered adsorbents, diffusion of the gas into the adsorbent can be slow, particularly at low pressures. Chemisorption may also be instantaneous, but there are many systems where chemisorption involves an activation energy or diffusion into the bulk material, which both may slow down the process.

The nature of physical adsorption enables the use of almost any type of gas. However, only significant amounts of gas can be adsorbed if the temperature of the adsorber is not much higher than the critical temperature of the gas so that van der Waals forces still can cause some adsorption. This limits the refrigerator temperature drop from the compressor heat sink temperature to the low pressure boiling temperature at the cold side of the cooler. For the xenon stage discussed in this chapter, for example, it will be shown that the temperature drop is limited to about 150 K. On the other hand, chemical absorption is dependent on the chemistry involved between gas and sorber material and occurs often at a much higher temperature than the refrigerant boiling temperature. For PCO, for instance, the oxygen is absorbed and desorbed around 600 and 900 K, respectively. This means that no precooling of


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the compressors is required below ambient temperature. Unfortunately, chemical absorption is only possible for certain specific gas-sorber combinations and associated refrigeration temperatures. Also, continuous reversibility of the ab- and desorption is often very difficult to achieve – this in contrast to physical adsorption. Table 4.1 lists a number of typical gas-sorber combinations that can be used for cryogenic cooling purposes [4.1].

The development of cryogenic sorption coolers started in 1963. Earlier, the somewhat

dissimilar absorption refrigerators (e.g. ammonia/water refrigerators) had already been used for many years in industrial and household applications. In addition, adsorption pumps are commonly used for ultrahigh and ultraclean (no oil) vacuum applications. In 1963 Vickers of NASA’s Jet Propulsion Laboratory proposed to use silica gel as the sorbent and a JT expander to provide refrigeration for space applications [4.3]. After that, a number of different cooler configurations have been proposed [4.4 - 4.8] but only a very limited number of sorption coolers were actually built and characterized. Most work was done for the space industry because of some typical advantages of sorption coolers for space applications [4.9]. These advantages include: a long life time, limited interference levels, the possibility of periodic refrigeration driven by a continuous low input power spread over a longer period of time. The developments focussed mainly on metal-hydride sorption compressors using hydrogen refrigerant to reach temperatures below 20 K, a development which was started in 1971 by van Mal and Mijnheer at the Philips Research Laboratories [4.10]. At these low temperatures, the efficiency of hydrogen sorption coolers becomes very competitive in comparison with other cooling cycles. One reason for this is that hydrogen compressors using chemical absorbers are quite efficient. Another reason is that competitive regenerative cooling cycles experience substantial losses below 30 K because of a decreased regenerator effectiveness [4.11].

An important demonstration of the feasibility of a metal-hydride hydrogen sorption cooler was the Brilliant Eyes Ten-Kelvin Sorption Cryocooler Experiment (BETSCE), which flew on a Space Shuttle in 1996 [4.12 - 4.15]. The cryocooler was designed to cool infrared detectors to 10 K and below. It could cool down from 70 K to 10 K in less than 2 minutes and sustain a 100 mW heat load for 10 minutes. The size and weight of the complete cooler was significant: about 2.5 m3 and 300 kg. Duband et al [4.16, 4.17] have developed physisorption compressors for operation with 3He and 4He capable of reaching very low temperatures down to 260 mK with cooling powers of ten to a few hundred microwatts.

In our application we would like to cool from 300 K down to 80 K. Starting from ambient temperature, a number of refrigerant gases are available that can be adsorbed by a physisorption compressor. The major drawback of physisorption coolers is their limited efficiency. However, the coolers being investigated are intended to supply very little cooling power (range: 10 mW – 50 mW) and for such a small cooler, efficiency is not necessarily the most important parameter to compare with the established performance of other cooler types.

Table 4.1 Some typical gas-sorber combinations that may be used in cryogenic sorption coolers (adapted from [4.1]). Sorption type physical adsorption chemical absorption Sorbent highly porous charcoal metal-hydride PCO Gas ethane xenon krypton methane nitrogen helium hydrogen oxygen Cooler low T (K) 170-220 160-200 120-150 100-140 70-100 3-5 20-30 65-110 Compr. low T (K)

300-350 300-350 240-300 200-260 160-220 25-35 300-400 350-500

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110

This is because a cooler with a small cooling power can be very attractive, despite a limited efficiency, if the input power is below a certain limit (e.g. 10 W).

4.3 Approach of analysis

In this chapter the thermodynamics involved in a sorption cooler are systematically categorized so as to investigate the physical limitations to its overall efficiency. This thermodynamic analysis assumes quasi-static conditions, in which the system is considered in thermal equilibrium. In a practical design, however, dynamical effects can occur that lower the performance of the cooler such as temperature profiles in the sorbent beds, pressure drops across the beds, an imperfect heat sink, etc. Therefore, the quasi-static analysis is a best-case consideration. It is applicable in a general sense to understand the physics behind a sorption cooler and as is shown, can usefully identify several important design issues and opportunities. Influence of dynamical effects is discussed in chapter 6, in which the design of the sorption compressor cells is considered.

In the limited published literature where the thermodynamic (quasi-static) efficiency of a sorption cooler is optimized, always the Coefficient of Performance of a complete sorption cooler is calculated as a function of the relevant parameter settings [4.18, 4.19]. This is a quantitatively sound method, but it does not give a good qualitative insight what exactly influences the COP of the system if the parameters are varied. The system consists of a compressor with aftercooler and of a cold stage, and variation of most of the system parameters has different effects on these two system components - see figure 4.3. Therefore, these components are considered separately. For that purpose, the exergy potential is introduced in this chapter*. This thermodynamic potential makes it possible to express the available useful energy of the pressure difference produced by the compressor (before and after

the aftercooler), as well as the required energy to drive the cold stage. In this way, the COP of the compressor and that of the cold stage can be calculated separately. This greatly clarifies the influence of compressor temperatures and pressures on the performance of the system

* In some textbooks on thermodynamics the term ‘available work’ or ‘availability’ is used instead of ‘exergy’.

COPcompressor

COPcold stage

COPtotal cooler

Sorptioncompressor

Cold stage

Sorption cooler

sorberTH

Twall material

(number of stages)

A

gasPP

H

L

T(precooler)

A

Figure 4.3 Separate analysis of the sorption compressor and the cold stage.


111

components separately, as well as the influence of compressor container materials and dead volumes. The separate analysis of compressor and cold stage is illustrated in figure 4.3.

4.4 Sorption compressor

4.4.1 Adsorption materials

Because activated carbon is reported to have a higher adsorption capacity per gram of sorption material compared to zeolites and silica gels [4.20 - 4.22], in this work activated carbon is the preferred material to construct a sorption compressor. Common materials that are used to fabricate activated carbons are: turf, coal, wood, coconut-shells and also organic materials such as polyvinyl chloride (PVC) [4.23 - 4.25]. The large surface area is created in the form of pores, slits and slots, often by a two-step activation process. In the first step of such a process, the raw material is carbonized, yielding the basic pore structure. The diameter of these pores is mostly too small for sufficient adsorption. Therefore, in a next step the size of the pores is increased by a reaction with, for instance, high temperature water vapor, KOH, phosphoric acid or air [4.23]. The resulting porous material can exhibit a surface area up to about 2000 m2 per gram activated carbon [4.26]. Pores are often divided in micro, meso and macro pores according to the pore size. Micro pores (pore diameter < 2 nm) and meso pores (pore diameter: 2 – 50 nm) generally account for the major part of the surface area, whereas macro pores (pore diameter > 50 nm) especially determine the diffusion transport of gas into the micro and meso pores. It should be noticed that pores in most charcoals have, in fact, the shape of grooves, slits and slots instead of a cylindrical shape as suggested by the term ‘pore diameter’. Many charcoals consist of grains; dependent on the application, different grain size distributions are available. The dead volume between the grains can be significant, see table 4.2 later in this section where some important properties of high capacity charcoals are compared.

The adsorption behavior of a gas-sorber combination can be measured using a gravimetric or volumetric method and is typically expressed as isotherms in a plot of the amount of adsorbed gas as a function of pressure. Figure 4.4 shows an example of isotherms for xenon adsorption on activated carbon. In the gravimetric method, the mass of a small amount of adsorption material is weighted accurately before and after adsorption of gas at a certain

0

0.4

0.8

1.2

1.6

2

0 10 20 30 40p (bar)

x (g

/g)

T=300 K

T=350 K

T=400 K

T=500 K

T=550 K

T=600 K

Figure 4.4 Adsorption isotherms for xenon adsorption on Maxsorb activated carbon [4.27].

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112

temperature and pressure. In the volumetric method, the amount of gas is measured that is flowed into a cell filled with sorption material. To obtain the amount of physically adsorbed gas in both methods, the unadsorbed gas present in the voids and pores must be subtracted from the total mass of gas in the sorber material. Knowledge of the void volumes is, therefore, essential. After the measurement of one or more isotherms, it would be nice to obtain a generalized correlation that can be used to predict other isotherms and, preferably, even the adsorption behavior of other gases on the same adsorption material. A generalized correlation theory valid for all materials, temperatures and pressures does not exist, but a number of adsorption theories have been developed in the past that can be used for certain adsorption materials and certain temperature and pressure regimes [4.28]. Most of these theories are based on a theory originally proposed by Polanyi [4.29], in which he uses the adsorption potential to calculate the volume of adsorbed gas. In this thesis, no correlation techniques are used because the compressor calculations were directly based on measured isotherms that were available for the adsorption materials under consideration [4.27].

There are two essential requirements for activated carbon to be applied in a sorption compressor: a large adsorption capacity per mass of sorber material and a minimum void volume. This can be understood as follows. During cycling of the compressor cells, most input power is lost in heating of the heat capacity of the sorption material (see also sections 4.4.2 and 4.4.4). To minimize this heat loss, the adsorption capacity per unit of sorber mass should be maximized. Since adsorption of refrigerant fluid takes place at significant higher temperatures than the critical temperature of the fluid, no capillary condensation takes place but instead essentially monolayer adsorption on the internal surface of the sorber material [4.2]. Consequently, adsorbers with large surface areas should be effective adsorbers. Since micro pores and small meso pores contribute especially to the surface area, a carbon with a large micro and meso pore volume should be an effective adsorber for a sorption compressor. Macro pores and large meso pores, on the other hand, have minimum influence on the total adsorption (but may determine the transport of gas to the smaller pores). The total sorber void volume should be minimized since, after pressurization of a sorption compressor, the high pressure gas stored in the void volumes and the larger pores can be very significant and is lost for operation of the cooler. Minimization of the void volume and the macro pores of the sorption material should occur without obstructing the transport of gas to the smaller pores.

Table 4.2 lists properties of four different activated carbons: a typical commercial activated carbon, two high surface area carbons (Maxsorb& and Saran#) and a new type of composite activated carbon. Relative to the sorber mass, the Maxsorb carbons have been identified as showing the greatest adsorption capacity of any commercial carbon reported to date [4.33, 4.35]. It has a large micro- and mesopore volume, but it has also a very large macropore and void volume and, as a consequence, a low apparent density. It is only available in fine

& Maxsorb is currently available from The Kansai Coke and Chemicals Corp. [4.30], but was originally developed in the 80’s by Amoco Corp. [4.31] and commercialized by the Anderson Development Company. Maxsorb is also known as ‘Anderson charcoal’. It is especially used in the electronics industry for use in batteries and capacitors [4.33]. # Saran was discovered in 1935 and is currently, to our knowledge, not commercially available. The material has been investigated sporadically since its discovery, most recently by Quinn for use in storing natural gas [4.32]. We obtained some Saran from Jet Propulsion laboratory, where a batch of Saran carbon was produced and investigated for application in sorption compressors [4.34].


113

powder form. The polymer polyvinylidene chloride (PVDC), which is often referred to by the Dow Chemical trade name Saran, on thermal degradation produces a carbon which has quite different characteristics to the KOH-activated Maxsorb carbon [4.34, 4.37 - 4.38]. The powdered polymer PVDC can be molded or pressed into a form and pyrolyzed to produce a solid porous carbon block. Without further activation, it has a high micro- and mesopore volume, a very small macropore volume and hardly any void volume. The internal surface area per sorber mass can be further increased by activation, but then also the macropores and associated void volume are increased significantly [4.33].

In a recent study an attempt was made to combine the attributes of Maxsorb and Saran carbons to produce an optimized composite suitable for gas storage [4.39]. By mixing PVDC polymer and finely powdered Maxsorb carbon and pressing in a mould, it was shown that monolithic pieces could be formed and then pyrolyzed to produce a composite carbon. These composites maintained the high density of the PVDC (Saran) carbon and the high adsorption capacity on a mass basis of Maxsorb carbon. The PVDC used in this study was obtained as a copolymer in latex form, which was able to enter and fill the macropore volume and voids of the KOH-activated Maxsorb carbon and remain there as a porous carbon after subsequent pyrolysis. It was claimed that the polymer in the macropores did not block entrance of gas to the micropores. A composite with 60% Maxsorb carbon was identified as an optimum with a high volumetric storage capacity and a low void volume, see table 4.2.

Very recently, carbons were developed with an increased micropore volume compared to the commercial Maxsorb carbons [4.40]. Their adsorption capacity is reported to be about 20-25% higher, but these carbons also suffer from a relatively large void volume.

The reported surface area of the Maxsorb carbon exceeds the maximum surface area that is physically possible; this is attributed to the measurement method [4.41]. In this so called BET-method, nitrogen gas is adsorbed at a certain temperature and pressure where it is assumed to adsorb as a uniform monolayer of gas molecules. It is reported, however, that in this method multi-layer adsorption is still likely to occur in the micropores and smallest mesopores, leading to exaggerated surface areas for these types of activated carbon.

The influence of the different sorber materials on the compressor behavior is studied in section 4.4.5.

Table 4.2 Material properties for some relevant activated carbons. Typical AC Maxsorb Saran unact. Composite carbon apparent density (g/ml) 0.44 0.30 0.93 0.77 volume fractions (%) solid carbon (density: 2.2 g/ml) 20.0 13.6 42.3 34.9 micro pores (< 2 nm) 17.6 12.0 35.2 meso pores (2 – 50 nm) 4.4 44.4* 15.5

49.7

macro pores + void volume 58.0 30.0 7.0 15.4 BET surface area (m2/g) 1160 3250 1000 1800 average part. size (µm) 1000 92 solid solid adsorption cap. per unit mass moderate very high high high adsorption cap. per unit volume moderate moderate high very high reference [4.36] [4.33, 4.36] [4.33, 4.34] [4.39] * Meso pores of 2 – 4 nm especially contribute to this volume fraction.

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114

4.4.2 Sorption compressor thermodynamics

In order to present a proper thermodynamic description of the sorption cycle, first a thermodynamic description of the ad- and desorption process is required. Following Hill [4.42] and Everett [4.43], adsorbed gas can be regarded as a single component system in equilibrium with the unadsorbed gas. For such a first-order phase transition, the molar Gibbs potentials of the adsorbed and unadsorbed gas are equal, or µs = µg. With µ = h – Ts, the (differential) heat of adsorption follows as

sgsgads hhssTq −=−= )( (4.1)

The heat of adsorption is related to the difference in molar entropies of the unadsorbed and adsorbed gas or, alternatively, it equals the difference in the molar enthalpies. The heat of adsorption can directly be derived from the measured adsorption isotherms. Consider an infinitesimal pressure and temperature change at a constant amount of adsorbed gas, x. This requires that the phase equilibrium is maintained so that dµs = dµg, or:

sg

sg

xggss vv

ss

Tp

dpvdTsdpvdTs−−

=

∂∂

⇒+−=+− (4.2)

Since vg >> vs and pvg ≈ RT, after integration follows:

R

qR

ssT

Tp adssg

x

−=−

−=

∂∂ )(

)/1(ln

(4.3)

where it is assumed that the heat of adsorption, qads, is constant over the region of integration. Eq. (4.3) shows how adsorption isosteres (p versus T at a constant amount of adsorbed gas) can be used to find the heat of adsorption. The heat of adsorption may vary slightly with the amount of adsorbed gas [4.2], unlike the heat of evaporation associated with a liquid-vapor transition that is constant for a certain vapor pressure. Figure 4.5 shows for xenon adsorption on Maxsorb carbon some plots of ln(p) as a function of 1/T for different values of x. From the figure, it can be concluded that for this type of adsorption the heat of adsorption has an approximately constant value, independent of the amount of gas adsorbed.

To study the thermodynamic behavior of a sorption compressor, focus should be put on the

8

9

10

11

12

13

14

15

16

0.0015 0.002 0.0025 0.003 0.00351/T (1/K)

ln p

x=0.1x=0.2x=0.3x=0.4x=0.5x=0.6

Figure 4.5 Adsorption isosteres for xenon adsorption on Maxsorb carbon, for different amounts of gas adsorbed. The data was derived from the isotherms in figure 4.4.


115

relevant thermodynamic steps of the gas that participates in the cycle. A sorption compressor basically consists of a high and a low-pressure cell which generate a pressure difference that can be used to perform some useful work on the environment (or that can be used to drive a cooler). Consider the cycle 1-2-3-4-5 in the T-s diagram of figure 4.6, representing desorption, cooling, expansion, adsorption and heating of the gas. In order to focus on the basic thermodynamic steps, the following simplifying assumptions are made: 1. The heat capacity of the sorption material is not taken into account. 2. The dead volume within the sorption material and the compressor cells is neglected. 3. Ad- and desorption of the gas take place, respectively, at a fixed low and high temperature

and pressure. All of these assumptions are not realistic, but make it possible to create a clear description

of the essential steps involved in the cycle. These are as follows: 1-2: High pressure gas is desorbed at a high temperature TH. This requires heat of adsorption, qads, and increases the entropy of the gas from s1 to s2 as given by Eq. (4.3). 2-3: The high-pressure gas is cooled to ambient temperature, TA. 3-4: The gas is expanded isothermally at ambient temperature from high to low pressure, performing work on the environment and taking up heat from the environment. By application of Eq. (2.1), this work term can be expressed as (w3-4 < 0):

)( 34434343 ssThqw A −−≅∆+−= −−− (4.4)

The approximation in Eq. (4.4) is valid for near-ideal gas behavior where ∆h3-4 << q3-4, which is generally the case. It should be noticed that, instead of route 2-3-4, also a different route could be used to obtain the useful work from the generated pressure difference. For instance: expansion at high temperature and subsequent cooling of the low-pressure gas (route 2-6-4) or adiabatic expansion followed by isothermal expansion (route 2-7-4). These alternative routes yield similar results. 4-5: The low-pressure gas is adsorbed at ambient temperature, TA. Heat of adsorption is rejected and the entropy of the gas is reduced from s4 to s5 as given by Eq. (4.3). 5-1: The low-pressure adsorbed gas is heated from TA to TH, resulting in high pressure adsorbed gas.

T

S

pH pL

TH

TA

1 2

3 475

adsorbedphase

6

Figure 4.6 Schematic representation of a sorption compressor cycle in a T-s diagram.

Chapter 4

116

To relate the performed work, w3-4, to the process of ad- and desorption, the entropy change s4 – s3 in Eq. (4.4) first has to be related to the pressure change. For a near-ideal gas, this entropy change can be written as [4.44]:

L

H

pp

Rss ln34 =− (4.5)

Finally, by application of Eq. (4.3), the performed work described by Eq. (4.4) can be related to the temperatures of ad- and desorption and to the heat of adsorption:

)1()11

(ln)( 3443H

Aads

HAadsA

L

HAA T

Tq

TTqT

pp

TRssTw −−=−−=−=−−=− (4.6)

In this step, it is assumed that the heat of adsorption is constant between ad- and desorption, which is the case for the gas-sorber combinations under consideration as was illustrated in figure 4.5.

To calculate the coefficient of performance of the described sorption cycle, the total heat that is put in the cycle is required. It is useful to write first a heat balance for the complete cycle:

00 155443433221 =+++++⇒=∆ −−−−−− qqwqqqu (4.7)

Since q1-2 = −q4-5 = qads and q3-4 ≈ −w3-4, it follows that q2-3 ≈ −q5-1. This means that, theoretically, the heat that is rejected by cooling of the high pressure gas from state 2 to 3 can be used to heat the adsorbed gas from state 5 to 1. In that theoretical case, the only heat input of the cycle is the heat of adsorption required to desorb the gas at a high pressure, q1-2 = qads. Using this heat input, the COP of the cycle can be written as:

H

AH

TTT

qw

COP−

=−

=12

34 (4.8)

This coefficient of performance equals the Carnot efficiency of an engine. This is not surprising because a sorption compressor is basically a thermodynamic engine which converts heat into mechanical work and, furthermore, all loss terms are neglected.

Two useful conclusions can be derived from the above-mentioned theoretical description of the sorption cycle. 1. For a certain gas-sorber combination, Eq. (4.3) directly reveals that a relatively high value

of the heat of adsorption results in a relatively high pressure ratio for a given temperature difference between ad- and desorption. Alternatively, a relatively small temperature difference is required to obtain a high pressure ratio. Chemical absorbers exhibit in most cases a much higher heat of absorption than physical adsorbers. As a consequence, pressure ratios for a given temperature rise are indeed much larger for chemisorption systems than for physisorption systems.

2. According to the Carnot efficiency of Eq. (4.8), the theoretical performance of a sorption compressor improves for larger temperature differences between ad- and desorption.

In a real sorption compressor, a number of loss mechanisms dominate the thermodynamics

and severely disturbs the described theoretical cycle. This makes it necessary to do detailed numerical modelling for finding proper operating conditions. Major loss mechanisms include:


117

1. Especially for physical adsorbers, the heat capacity of the sorption material is very significant compared to the heat of adsorption. As a consequence, during step EA much heat is required to heat up the sorption material. Especially for small sorption cells it is difficult to re-use this heat, so that it has to be rejected without being used during cooling (regeneration) of the sorption cells.* This loss term increases with increasing TH – TA, counter-acting the theoretical improvement of the Carnot efficiency as given by Eq. (4.8).

2. Cooling of the high pressure gas from state 2 to 3 can in practice not easily be used to heat the adsorption material and adsorbed gas from state 5 to 1, as was suggested in the theoretical description above. Therefore, step 23 is in practice associated with a loss term. It reduces the available work or exergy of the gas, a thermodynamic potential which is explained in section 4.4.3 and which is used in the modelling of the sorption compressor and cold stage.

3. Adsorption material contains a lot of dead volume, up to 85% of the total volume. When a sorption cell is heated and pressurized, high pressure gas must first fill this dead volume before high pressure gas can flow out of the cell. This high pressure gas in the dead volume must be desorbed but does not contribute to the compressor performance.

4. During ad- and desorption, the temperature of the sorption material is not constant at TA and TH, but it is gradually decreased towards TA during adsorption and increased towards TH during desorption. This is not really a loss mechanism, but it makes a real thermodynamic description of the cycle more complicated than is suggested in figure 4.6.

After a discussion about the exergy potential in the next section, the above-mentioned loss mechanisms will be included in a thermal model of the sorption compressor that is described in section 4.4.4 and that is used to do a case study in section 4.4.5.

4.4.3 The exergy potential

To study the COP of a sorption compressor, a thermodynamic potential is required to express the maximum available work that can be obtained with the produced pressure difference. Figure 4.7a shows a sorption compressor connected to some kind of system at ambient temperature in which the pressure difference of the gas is converted to mechanical work (w < 0). For a stationary open system the first law of thermodynamics (Eq. (2.1)) gives:

24 hhqw −+−= (4.9)

where the gas at the high pressure side of the compressor is in state 2 and at the low pressure side in state 4. Using this pressure difference, theoretically the maximum amount of work can be performed if no thermodynamic losses are introduced in the work generating process. This means that no net entropy is generated in the system and as a consequence ∆stot = 0. With application of Eq. (2.2) it follows that:

04242 =∆−=−+=∆+∆=∆ −sTq

ssTq

sssAA

flowmassflowheattot (4.10)

* Theoretically, this heat can, at least partly, be used to heat up other low temperature cells upon cooling of a high temperature cell. For larger sorption compressor systems, this may conveniently be implemented by using a fluid circulation system [4.5].

Chapter 4

118

So that the heat flow q to the system can be written as:

42−∆⋅= sTq A (4.11)

Combination of Eq. (4.9) and (4.11) results in the maximum work that can be generated, which is called the exergy of the pressure difference of an open system:

4242max42 −−− ∆−∆== sThwe A (4.12)

where ∆h2-4 is the enthalpy difference between the two states expressed in J/g, and ∆s2-4 is the entropy difference expressed in J/gK. The exergy reduces to the change in the Gibbs free energy if TH = TA.

As an example, figure 4.7b shows qualitatively the situation for a sorption compressor, in which gas is desorbed at a high pressure and temperature (state 2) and adsorbed at a low pressure and temperature (state 4). The maximum amount of work in a process from state 2 to state 4 is obtained along 2-3’-4: adiabatic expansion 2-3’ from TH to TA followed by isothermal expansion 3’-4 at ambient temperature TA towards the final pressure pL. During this route no entropy is generated and w = wmax. Net entropy is produced, however, if the gas is first precooled from state 2 to 3 with heat rejection to the environment, which results in a loss of exergy (w3-4 < e2-4).

4.4.4 Compressor modelling

By using the definition of exergy, the COP of the compressor can now be expressed as follows:

totin

comprcompr Q

ECOP

,

= (4.13)

where Ecompr is the exergy of the gas that flows out of the compressor during a certain period of time, and Qin,tot is the total heat put into the compressor over the same period of time. In this definition, it is convenient to relate Ecompr and Qin.tot to a combination of a high and a low pressure cell that operate during half a compressor cycle, i.e. in figure 4.2 to sections A and B of the high pressure cell and to sections C and D of the low pressure cell. Ecompr is then found

(sorption)compressor

system

pLpH

42

qH q (< 0)A

q w (< 0)

TA

T

S

pH pL

2

3 3’ 4

TH

TA

(a) (b)

Figure 4.7 (a) Schematic representation of a sorption compressor connected to a system operating at ambient temperature in which the pressure difference is converted to work. (b) T-s diagram to illustrate application of the exergy potential.


119

by multiplying the specific exergy of the gas, egas, with the amount of gas that is flowing between the two compressor cells during one cycle:

gasnetsgasgascompr exmemE ∆== (4.14)

In this expression, ms is the mass of the sorber material of one cell and ∆xnet is the mass of the gas that flows between the two cells normalized to ms. This gas mass equals the amount of gas freed from the sorber surface, ∆xgross, corrected for the high pressure gas that remains in the dead volume of the sorber material and that does not take part in the mass flow out of the cell, ∆xdv (see figure 4.2). Hence,

dvgrossnet xxx ∆−∆=∆ (4.15)

HLgross xxx −=∆ (4.16)

)( 1,3,1,3, gasgass

dvdvdv xxx ρρρα

−=−=∆ (4.17)

where α is the fraction of the total dead volume in the sorber material (interparticle voids and pores), ρgas is the density of the gas at state 1 or 3 and ρs is the density of the sorber material. The value of the specific exergy of the gas in Eq. (4.14), egas, depends on the state (temperature) that is assumed for the high pressure gas coming out of the compressor. The exergy can be calculated with the state of the high pressure gas before or after the aftercooler, corresponding to states B and C in figure 4.6b. The difference is the loss of exergy due to the (after)cooling of the gas.

The total heat put into one compressor cell during one cycle consists of the heat required to heat up the thermal mass of the sorber material and the container (including heater, thermocouple, etc.), plus the heat required to heat up the adsorbed gas (approximated by ms⋅xL⋅cv,gas), plus the desorption energy of the gas that is desorbed from the surface of the adsorption material:

adsgrosssLHgasvLscpcspstotin qxmTTcxmcmcmQ ∆+−++= ))(( ,,,, (4.18)

In this expression mc is the mass of the container, TH – TL is the temperature difference of the cycle and qads is the adsorption energy of the gas/sorber combination expressed in J/g. Furthermore, spc , , cpc , and gasvc , stand for the specific heat of respectively the sorber material,

the container material and the adsorbed gas which must be averaged over the required temperature range by application of:

∫−=

H

L

T

Tp

LHp dTTc

TTc )(

1 (4.19)

The minimum required mass of the container is determined by the minimum wall thickness that is required to withstand the high pressures. For a typical cylindrical configuration, this thickness is given by:

maxσ

Rpd H= (4.20)

In this expression R is the radius of the cylinder and σmax is the maximum allowed tensile stress in the container material. If, for a cylinder with a high aspect ratio, the mass of the end-caps of

Chapter 4

120

the cylindrical container is neglected compared to the mass of the cylinder itself, then the ratio of the container-sorber mass can be determined as follows:

max

2σρ

ρµ H

s

c

s

cm

pmm

⋅== (4.21)

As can be seen, this ratio is independent of the container mass or size itself. Combining equations (4.18) and (4.21), the input power follows as:

]))([( ,,,, adsgrossLHgasvHcpmspstotin qxTTcxccmQ ∆+−++= µ (4.22)

The COP in Eq. (4.13) can now be calculated by dividing equations (4.14) and (4.22). For a given adsorber material with associated properties and adsorption isotherms and a given gas, COPcompr is a function of TL, TH, pL, pH because the following parameters depend on these variables: ∆xgross = ∆xgross(TL, TH, pL, pH); egas = egas(TL, pL, pH); ∆xdv = ∆xdv(TL, TH, pL, pH); µm = µm(pH); xL = xL(TL, pL); xH = xH(TH, pH). Obviously, COPcompr is also strongly dependent on material properties.

4.4.5 Case study: xenon adsorption on highly porous charcoal

In this section a parameter study is described that shows the influence of the compressor temperature and pressure settings and of the material properties. As an example of the process, the compressor performance is calculated with xenon as the working gas and one of the two described high surface area active carbons, Maxsorb and Saran, as sorber material. Calculations with both types of charcoals are compared. The sorption data of xenon on Maxsorb and Saran carbon were measured at NIST [4.27], and the gas properties were calculated with Cryodata's fluid property program GASPAK [4.45]. The following material properties were assumed in the analysis. Maxsorb carbon: ρ = 0.3 g/cm3, cpc , = 1.054 J/gK,

dead volume fraction α = 0.86; Saran carbon: ρ = 0.93 g/cm3, cpc , = 1.054 J/gK, α = 0.577;

heat of adsorption for xenon on both carbons: qads = 174 J/g; stainless steel container: ρ = 7.9 g/cm3 , cpc , = 0.52 J/gK, σmax = 0.5⋅σstrain=0.002 = 110 MPa. In general, the low and high

temperatures and pressures of the sorption compressor (denoted by TA, TH, pL, pH, respectively) are the main parameters that have to be chosen, and are, therefore, of major interest in this parameter study.

The compressor COP is directly proportional to the amount of gas that flows between the two cells, ∆xnet, see equations (4.15) - (4.17). Figure 4.8a shows xL, xH, ∆xgross, ∆xdv and ∆xnet

0

0.1

0.2

0.3

0.4

0.5

0.6

0 10 20 30 40 50 60pH (bar)

x (g

/g) xH

xgros

xdv

xnet xnetxgross

xL

xdv

TH = 600 KTH = 500 K

(a)

xH

0

10

20

30

40

50

60

70

80

90

100

0 20 40 60 80 100pH (bar)

exer

gy g

as (

J/g)

T H=300 KT H=350 KT H=400 KT H=500 KT H=550 KT H=600 K

(b) Figure 4.8 (a) xL, xH, ∆xgross, ∆xdv and ∆xnet as a function of pH for TL = 300 K, pL = 1 bar, TH = 500 K and TH = 600 K. (b) Exergy as a function of pH for TL = 300 K, pL = 1 bar and a number of values for TH.


121

as a function of pH for TL = 300 K, pL = 1 bar and for two values of TH. The parameter xL, the amount of gas adsorbed at state 1 in figure 4.2, is strongly dependent on TL and pL as can be seen from the isotherms in figure 4.4, and it is independent of TH and pH. The parameter xH, the amount of gas adsorbed at state 3 in figure 4.2, increases with pH. The parameter ∆xdv, the gas lost in the dead volume, increases with pH due to the increased gas density but decreases with increasing TH. ∆xnet follows with Eq. (4.15); it reduces with increasing pH and decreasing TH; ∆xnet drops to zero when all desorbed gas from the adsorber surface is lost in the dead volume of the adsorber material, and no gas is vented from the compressor.

The compressor COP is also proportional to the exergy of the pressure difference, see Eq. (4.13) and (4.14). Figure 4.8b shows the exergy as a function of pH for TL = 300 K, pL = 1 bar and a number of values of TH. The exergy for TH = 300 K corresponds to the exergy with the high pressure gas located after the aftercooler, i.e. the exergy between states 3 and 4 in figure 4.6. The difference between the exergy with the high pressure gas at TH > 300 K and the exergy with the high pressure gas at TH = 300 K is the loss of exergy due to cooling of the high pressure gas.

0

0.01

0.02

0.03

0.04

0.05

0 20 40 60 80 100pH (bar)

CO

P c

ompr

esso

r

700 K

650 K

600 K

550 K

500 K

400 K

350 K

(a)

0

0.01

0.02

0.03

0.04

0.05

0 20 40 60 80 100pH (bar)

CO

P c

ompr

esso

r two stagecompressor,TH = 600 K

700 K

650 K

600 K

550

500 K400

(b)

Figure 4.9 The compressor COP as a function of the high pressure for TL = 300 K, pL = 1 bar and a number of values of TH. Figure (a) is calculated with the high pressure gas located before the aftercooler (i.e. for the exergy between states B and D in figure 4.6) and figure (b) is calculated with the high pressure gas located after the aftercooler (i.e. for the exergy between states C and D in figure 4.6). The calculated points for a two stage compressor in figure (b) are discussed in section 4.6.1.

In figure 4.9a a plot is shown of COPcompr as a function of pH for TL = 300 K, pL = 1 bar and

a number of values for TH. In this plot, COPcompr is calculated with the high pressure gas that is still at a high temperature located before the aftercooler, i.e. for the exergy between states 2 and 4 in figure 4.6. Essentially two competing effects influence the compressor COP as pH increases: the reducing ∆xnet in figure 4.8a and the increasing exergy in figure 4.8b. As a result, the COP peaks at an optimum pH, which is dependent on TH. Apart from a reduction of ∆xnet, the COP at higher values of pH also decreases because of the increased wall-thickness that is required at higher pressures, see equations (4.20) - (4.22). As a consequence, for higher pressures relatively more heat is lost in the walls of the compressor.

In general, an increase in TH increases the net amount of gas that is desorbed from the compressor and it increases the exergy. However, a higher TH also increases the required input power. At very low values of pH, an increase of TH does not desorb a significantly higher amount of gas out of the compressor and it, therefore, does not improve the COP. At these values of pH, most of the gas is already liberated from the adsorber surface at lower

Chapter 4

122

temperatures. Above a certain value of pH, the increased amount of liberated gas at higher values of TH is of significant benefit and it improves the COP.

Figure 4.9b shows the compressor COP with the high-pressure gas located after the aftercooler (i.e. for the exergy between states C and D in figure 4.6). Comparison of figures 4.9a and 4.9b illustrates the influence of this cooling step on the compressor COP. The exergy after aftercooling corresponds to the actual ‘work’ that is available to drive the cold stage.

An increase of pL has two effects on Ecompr in Eq (4.14) and is illustrated in figure 4.10a. Firstly, egas is decreased and, secondly, the amount of gas adsorbed at pL and TL is increased. For small adsorption ratios xL, the adsorption ratio increases approximately linearly with pL (see figure 4.4), whereas egas decreases less than linearly with increasing pL (for xenon gas at 300 K, egas decreases 20% when pL increases from 1 to 2 bar). The net result is an increase of the COP with increasing pL. At higher adsorption ratios, xL does not increase linearly with pL anymore because the isotherms enter the saturation region. In that region the maximum COP starts to decrease with increasing pL because of the decreasing egas, see figure 4.8b. Saturation of the adsorption material is, therefore, a limit for compressor performance. This saturation shifts to higher values of pL with increasing TL.

There are several other parameters that influence the general described behavior, these are discussed separately below.

Isotherms. It is clear that the compressor performance improves for adsorption materials with higher ratios of gas adsorption at the same temperatures and pressures. These adsorption ratios are strongly related to the internal surface area that is available for adsorption, see the discussion in section 4.4.1.

Dead volume fraction. The large influence of the dead volume fraction that was mentioned before, has been highlighted in several publications [4.46]. The influence on the analyzed xenon system is illustrated in figure 4.10b, where the COP is compared for Maxsorb (α = 0.86) and Saran carbon (α = 0.577). It appears that the reduced dead volume fraction increases the maximum COP slightly at low pressures, but much more at higher pressures. A high dead volume fraction and associated low sorbent density also reduces the COP at higher pressures indirectly, because relatively more heat is lost in the container wall, see also the discussion about material choices below.

0

0.01

0.02

0.03

0.04

0.05

0 2 4 6 8 10pL (bar)

CO

P c

ompr

esso

r, m

ax

(a)0

0.01

0.02

0.03

0.04

0.05

0.06

0 20 40 60 80 100pH (bar)

CO

P c

ompr

esso

r

Maxsorb + Stainless SteelMaxsorb + TitaniumSaran + Stainless SteelSaran + Titanium

(b)

Figure 4.10 (a) The maximum compressor performance as a function of the low pressure, for TL = 300 K and optimized pH and TH. (b) Influence of the dead volume fraction (Maxsorb: α = 0.86, Saran: α = 0.56) and container material on the compressor COP for TL = 300 K, pL = 1 bar and TH = 600 K.


123

Material choices. The ratio of the heat capacities of the container and the sorber materials is a measure for the relative amount of heat that is lost in the compressor container. By using Eq. (4.21), this ratio can be written as:

sp

cpH

s

c

sp

cpm

sps

cpc

sp

cp

c

cpc

c

cm

cm

C

C

,

,

max,

,

,

,

,

, 2σρ

ρµ === (4.23)

This expression can be used as a simple tool to evaluate the container heat capacity losses as a function of the material properties and the high pressure pH. In table 4.3 a comparison is made between different possible container materials. The parameter ρccp,c/σmax can be used in comparing materials. As an example, in the last column Cp,c/Cp,s is calculated for the density of Maxsorb charcoal and pH = 30 bar. It follows that it can be advantageous to use high strength alloys like Titanium or Inconel if higher pressures are required, and also ceramic containers can be attractive with respect to minimization of heat capacity losses. The use of high strength alloys, however, may result in practical problems in the case of small compressors because a very thin wall thickness is required in that case, which may be difficult to realize. For example, in the case of a 1 cm diameter Titanium compressor suited for a high pressure pH = 50 bar, a wall thickness of only 60 µm is required. Note that, for a certain pH, the container heat capacity losses are reduced if a sorbent is used with a high density and a low dead volume fraction, like Saran, instead of a low density charcoal.

Figure 4.10b illustrates the influence of the container material choice on the compressor COP as a function of the high pressure, as well as that of the dead volume influences. From this figure, it appears that the influence of the container material is relatively small for the pressures of interest, both for Maxsorb and Saran charcoal.

Table 4.3 Comparison between relative amount of heat lost in different container materials. The last column is calculated for the density of Maxsorb carbon and pH = 30 bar.

σmax (MPa) cp,c (J/kg⋅K) ρ (103 kg/m3) ρcp,c/σmax (10-3 K-1) Cp,c/Cp,s Stainless Steel 316 110 520 7.9 37 0.71 Copper 40 390 8.9 87 1.65 Aluminium 90 880 2.7 26 0.50 Inconel 718 210 450 7.9 17 0.32 Titanium 400 520 4.5 5.9 0.11 Si3N4 500 860 3.2 5.5 0.10 SiC 400 880 3.1 6.8 0.13 ZrO2 700 530 5.6 4.2 0.08

4.4.6 Compressor conclusions

Some concluding remarks can be made with respect to the compressor modelling. For the special case of a xenon – Maxsorb carbon compressor operating at TL = 300 K, TH = 600 K and pL = 1 bar, constructed of straightforward stainless steel 316 container material, a maximum COP of 3.5% at pH = 10 - 20 bar can be obtained. At higher pressures the COP decreases rapidly to zero at about 35 bar. The maximum COP can slightly be increased (to about 4%) by using high strength materials, and somewhat higher pressures can be obtained by increasing TH to 700 K. Much higher pressures can be obtained by using an adsorber material with a low dead volume fraction, e.g. with Saran at 40 bar a COP of 2.5 % can be realized.

Chapter 4

124

Since the sorption compressor is in fact a thermodynamic engine, it’s performance should be compared to engine performances, which are typically less than 40% [4.44]. A COP of 4 - 5% for a sorption 'engine' without moving parts that is, therefore, easily scalable to small sizes is, from a fundamental point of view, a promising result. Moreover, if a somewhat larger system is allowed including heat regenerating facilities that can recover more than 75% of the heat [4.5], then COP's close to 20% should be obtainable.

4.5 Linde-Hampson cold stage analysis

Operation of the Linde-Hampson cold stage is described in section 2.4.3. In order to model the cold stage, it is assumed that it operates without losses, except for the intrinsic irreversibilities that are associated with the throttling process and heat exchanger operation with a van der Waals fluid. In that case, the cooling power equals the enthalpy difference, ∆hA, that is created between the low and high pressure sides of the ambient inlet of the counterflow heat exchanger. Now the COP of the LH cold stage can be defined as:

AAA

A

ambient

coldLH sTh

heq

COP∆−∆

∆−== (4.24)

In this expression eambient is the exergy or Gibbs energy at the inlet of the counterflow heat exchanger as defined by Eq. (4.12), or the minimum work of compression that is required.

For a certain working gas the parameters that can be varied are pL, pH and TA; the low temperature TC is determined by the vapor pressure pL. Figure 4.11 gives for xenon a plot of COP/COPCarnot as a function of pH for different values of TA and pL = 1 bar. The COP is normalized to the Carnot efficiency to enable better comparing between the curves for different values of TA. For low values of pH, the performance is rather poor because in that region the gas behaves essentially as an ideal gas, and only small enthalpy differences can be created upon compression. The steep increase of the COP at higher pressures is because the fluid enters the van der Waals region or even liquefies during compression. This transition moves to higher pressures when TA is increased. At the highest values of TA the increase is not so steep because the temperatures are above the critical temperature of xenon, but still reasonable performances

0

0.2

0.4

0.6

0.8

1

0 20 40 60 80 100pH (bar)

CO

P/C

OP

Car

not

TA=240 KTA=250 KTA=260 KTA=270 KTA=280 KTA=285 KTA=290 KTA=295 KTA=300 K

pL = 1 bar, Tcold = 165 K

Figure 4.11 COP/COPCarnot of the xenon cold stage as a function of the high pressure, for pL = 1 bar and different values of the ambient compression temperature TA.


125

can be obtained because of the strong non-ideal behavior of the fluid in that regime. Similar plots can be obtained for larger values of pL.

4.6 Combination of sorption compressor and cold stage

If the heat sink temperature of the sorption compressor is also taken as the precooling temperature of the gas that enters the cold stage, then the COP of the xenon sorption cooler can be obtained by multiplying COPcompr and COPLH. If the curve for TA = 300 K in figure 4.11 is multiplied with one of the compressor curves in figure 4.9b (for Maxsorb carbon), then it appears that a very poor overall performance is obtained. The reason is that the sorption compressor only performs well at low pressures, whereas the cold stage requires high pressures to obtain a reasonable performance. This statement does not hold for compressors that are based on chemical sorption (e.g. hydrogen/metalhydride). These operate relatively well at high pressures [4.1]. We see three possible solutions to overcome the bad matching of the (physical adsorption) compressor and the cold stage: 1. The dead volume fraction of the adsorption material can be reduced by using a high

density charcoal like Saran or a composite carbon. The compressor high pressures are in that case still limited to about 60 bar, but the overall performance does improve.

2. A two stage sorption compressor can be applied to enable generation of much higher pressures.

3. The gas at the inlet of the cold stage can be precooled to lower temperatures with another cooler in order to improve the cold stage performance at low pressures.

In the following subsections, the last two options will be considered in more detail.

4.6.1 Two stage sorption compressor

In a two stage sorption compressor, that was earlier proposed in a different composition by S. Bard [4.46], the gas is compressed from a low pressure to some intermediate pressure pI in a first stage, then flowed into a second stage where the gas is compressed from intermediate to high pressure. The cycle is illustrated in figure 4.12a. Each compressor stage operates in a similar way as the single stage that was described before. Because both compressor stages

TA

TH

pL pHpI

X, a

mou

nt o

f gas

ads

orbe

d(m

ass

gas/

mas

s so

rbe

r)

pressure

A

BCD

E

F

G

H

1 stagest

2 stagend

pH pL

1 stagest

2 stagend

intercooler

uni

t I

uni

t II

uni

t III

uni

t IV

(a) (b)

Figure 4.12 (a) Cycle of a two stage compressor; (b) Integrated two stage compressor (see text).

Chapter 4

126

have a limited pressure ratio, it is possible to operate them close to their thermodynamic optima (i.e. the peaks in figure 4.9b) so that high overall COP’s can be obtained at very high pressures. Moreover, the influence of the dead volume fraction is greatly reduced, and under some conditions completely irrelevant which makes adsorber selection much easier.

Figure 4.12b shows a novel interconnection scheme of the 4 low pressure and 4 high pressure cells that we propose. It was recognized that one specific low pressure cell always blows the gas into one specific high pressure cell, so only one check valve is required to interface these two cells. Moreover, during the cyclic operation the low and high pressure cells are in a constant phase difference with respect to each other. By combining a low and high pressure cell that operate in the same heating or cooling phase, one sorption unit can be created consisting of two compartments. This enables the use of a single heater and heat-switch for a unit of a combined low and high pressure cell. In this way the combined low and high pressure cells are always in a similar cooling or heating phase of the compressor cycle, but at different pressure levels. For instance, the low pressure cell of unit I is in phase B and blows the compressed gas at the intermediate pressure into the high pressure cell of unit III, which is then in phase H. At the same moment the high pressure cell of unit I is in phase F and blows the compressed gas into the cold stage, whereas the low pressure cell of unit III is in phase D and adsorbs low pressure gas that returns from the cold stage.

In a two stage compressor that operates continuously, the amount of gas that flows at intermediate pressure out of the first stage must be adsorbed in the second stage. In a next step, the same amount of compressed high pressure gas that flows out of the second stage must be adsorbed in the low pressure first stage. This means that for continuous operation mg1, net = mg2, net, where mgi, net stands for the net amount of gas that is freed from stage i (i = 1 or 2):

)( ,,,, dvigrossisinetisinetgi xxmxmm ∆−∆=∆= (4.25)

For a certain sorber mass fraction, ms1/ms2, an intermediate pressure pI will be established so that mg1,net = mg2,net or, alternatively, to obtain a certain intermediate pressure pI the condition mg1,net = mg2,net gives the required sorber-mass fraction:

),,,(

),,,(),,,,(

,1

,2

2

1

ILHLnet

HIHLnetHILHL

s

s

ppTTx

ppTTxpppTT

mm

∆∆

= (4.26)

The COP of the two stage compressor can be evaluated by calculating the exergy and the total heat that has to be put into the two stage compressor, and subsequent application of Eq. (4.13). For a certain TL, TH, pL and pH, the COP was calculated for different values of pI. This resulted in an optimum for pI. The calculated optimum COP for different high pressures is added to figure 4.9b, for the case pL = 1 bar, TL = 300 K, TH = 600 K, Maxsorb carbon and a stainless steel container. The intermediate optimum pressure pI ranges from 6 to 18 bar for increasing pH. It can be concluded that a two stage compressor facilitates the generation of much higher pressures compared with a single stage compressor, even with rather straightforward sorber and container materials. Now a reasonable cooler performance can be obtained by combining a two stage compressor with a cold stage that operates from 300 K. For instance, a total COPtot = 0.021×0.767 = 0.016 is obtained for pH = 80 bar.


127

4.6.2 Precooling of the cold stage

The performance of the LH cold stage at lower pressures can be improved by lowering the temperature of the high pressure gas before it enters the counterflow heat exchanger, as was indicated in figure 4.11. A similar effect can be obtained by active precooling of the high pressure gas in the counterflow heat exchanger, see figure 4.13 [4.47]. The total COPtot of this system can be written as:

precLHprecLHcomprcold

preccompr

cold

totin

tot COPCOPCOPCOPP

PP

P

P

COP −

+=+

==111 , (4.27)

where Pcompr and Pprec are the powers required to drive the compressor and the precooler, COPprec is the coefficient of performance of the precooler and COPLH-prec is the ratio of the power that has to be cooled away by the precooler relative to the cooling power at the cold end. Precooling is useful if COPtot can be increased by increasing COPLH. This is only possible if the reduction of Pcompr is not cancelled out by a large increase of Pprec. In the case of a sorption compressor with a relatively low COPcompr, precooling can be very attractive because Pcompr can be reduced significantly with only little required Pprec.

compr

CFHX 1 CFHX 2

precooler PcoldPprec Pheat,prec

Pheat,compr

Pcompr

JT2 3 4 5 6

781

Figure 4.13 Schematic diagram of LH cold stage with precooling arrangement. If the counterflow heat exchanger behaves ideally, the heat taken away by the precooler can

be calculated using an enthalpy balance:

2148128443 )()( −−− ∆−∆=−−−=∆ hhhhhhh (4.28)

If the performance of a certain precooler is known, this expression can be used to evaluate the proper precooling temperature.

It is a logical choice to use another sorption cooler as a precooler by choosing a different gas that operates at a higher temperature. This concept was used in several coolers at JPL [4.48]. Also thermoelectric (TE) precooling has been used. The significant improvement of the

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0 20 40 60 80 100pH (bar)

CO

P to

tal

T prec = 200 KT prec = 220 KT prec = 240 KT prec = 260 KT prec = 280 K

pL = 1 bar, TL = 300 K,TH = 600 K,Maxsorb charcoal,stainless steel cylinder

Figure 4.14 Performance of a Xe sorption cooler with TE precooling for different values of TTE.

Chapter 4

128

performance of the xenon cooler precooled by a TE cooler is illustrated in figure 4.14, in which the total performance is plotted as a function of the high pressure, for different precooling temperatures. The dramatic improvement results from the preliquefaction of the refrigerant by the TE cooler and the subsequent near ideal thermodynamic performance of the cooling cycle. The numbers are calculated by application of equations (4.27) and (4.28), and COP values for the TE cooler that were obtained from Melcor for multi-stage coolers (see figure 2.39) [4.49]. By precooling of the high pressure gas to 230 K, for instance, a reasonable COPtot = 0.032 can be obtained for TH = 600 K, pH = 15 bar and Maxsorb carbon in a stainless steel compressor. This COP can slightly be improved by using Saran instead of Maxsorb carbon.

4.7 Sorption cooler system specifications

It was decided to develop miniature components for a small sorption cooler that consists of a sorption compressor connected to a Linde-Hampson cold stage with thermoelectric precooling. Chapters 5 to 8 of this thesis discuss the development of these components. The requirements for these individual components are based on the specified cooling cycle, which is presented in this section.

During the development of the cooler components, it became apparent that xenon gas is very expensive and, especially for the flow-experiments on the cold stage, a cheaper gas was desired. It was decided to use ethylene for the experiments, which has very similar thermodynamic fluid properties as xenon. However, no adsorption data was available of ethylene adsorption on Maxsorb carbon. Because the fluid properties of ethylene are so similar to that of xenon (on a volume basis), the data of xenon was used for the calculation of the system specifications. This assumption may cause slight deviations between the calculated and real values of xL, xH, ∆xgross, ∆xnet and COPcompr for ethylene gas.

Gas-gap heat switchwith pressure controller

Sorption compressorcell with heater

Check valve unit

Aftercooler

Co

mpressor un

it

T environment

Counterflow heatexchanger 1

J-T valve + cryostat

cold stag

e



Condensor

TE-cooler

Heat-sink

Heat-sink

Q

12

3

4

5

67

8

Refrigeration load

100

150

200

250

300

350

4 5 6 7 8s (J/gK)

T(K

)

12

34

5

6 7

820 bar

1 bar

-32 J/g-87 J/g

-358 J/g-93 J/g

0 J/g

+390 J/g

+93 J/g

+87 J/g

0.01 bar

0.1 bar

5 bar

10 bar

50 bar

100 bar

-200 J/g-100 J/g 0 J/g

-300 J/g 100 J/g

lines of constant enthalpy

(a) (b)

Figure 4.15 (a) Schematic of the complete sorption cooler. (b) Thermodynamic cycle of the cold stage in a temperature-entropy diagram.


129

The gross cooling power equals 67hm ∆⋅& , where m& is the mass flow through the system,

and ∆h67 is the specific enthalpy change available for cooling. For this demonstration cooler, the cooling power can in principle freely be chosen within certain limits. The aim is to demonstrate a working sorption compressor in combination with a cold stage, which is able to reach a stable low temperature with a few tens to hundreds milliwatts of cooling power that can be used to cool a thermal load. Therefore, the minimum net cooling power is determined by the thermal losses on the cold stage (see the footnote on page 30 for the definition of net cooling power). These losses are, among others, dependent on the design of the cold stage but they are assumed to be smaller than 50 mW. The maximum cooling power is either limited by the maximum flow that can be delivered by the sorption compressor, or by the size of the cold stage (i.e. a pressure drop in the return line, the size of the condenser or evaporator, etc.). It was decided to aim at a gross cooling power of about 200 mW, which requires a mass flow of 0.5 mg/s through the system.*

Figure 4.15a shows the schematic of the complete sorption cooler and figure 4.15b shows the chosen thermodynamic cycle of the cold stage in a temperature-entropy diagram. Further system specifications are listed in table 4.4.

Table 4.4 System specifications for the sorption cooler operating with ethylene gas. General system parameters Compressor parameters Cold stage parameters gas: ethylene pL = 1 bar pH = 20 bar m& = 0.5 mg/s COPtot = 0.0293

adsorption material: Maxsorb TL = 300 K TH = 600 K xL = 0.56 g/g xH = 0.20 g/g ∆xgross = 0.36 g/g ∆xdv = 0.14 g/g ∆xnet = 0.22 g/g µm = 0.96 Cp,c/Cp.s = 0.47 COPcompr = 0.0225 Pcompr,in = 5.7 W Pcompr,out = 128 mW

TA = 300 K Tcond = 244 K TC = 169 K COPLH = 1.52 COPTE = 0.19 PLH,in = 128 mW PC = 195 mW Pcond = 179 mW PTE,in ≈ 0.96 W

4.8 Conclusions

The thermodynamic behavior of sorption coolers is explained by a systematic analysis in which the compressor and the cold stage are treated separately, both for quasi-static conditions. The parameter studies in this analysis are based on a specific case of a (micro)cooler with a warm-end temperature of 300 K. Nevertheless, the results are applicable in a much broader sense.

The compressor can be considered as a thermodynamic engine that converts high temperature heat into low temperature heat and mechanical work that appears as compressed gas. The ideal behavior of this Carnot engine is strongly reduced by two loss mechanisms: * The described sorption cooler may in the future be used to cool a very small cascaded sorption cooler operating with nitrogen gas, which is able to cool from 169 K to about 75 K. This second stage cooler could operate with a COP of about 0.03. To obtain 10 mW of cooling power at 75 K, the described first stage should produce about 400 mW of gross cooling power.

Chapter 4

130

much heat is lost in the periodical heating of the heat capacity of the sorption material and container, and much compressed gas is lost in the dead volume of the sorption material. Detailed modelling of these losses showed a clear optimum in compressor performance at moderate high pressures of 10 – 30 bar, which appeared strongly dependent on the operating parameters such as compressor temperatures and the low pressure. Unfortunately, Linde-Hampson cold stages require relatively high pressures for proper operation. Two solutions were discussed to overcome this conflict: a novel two stage compressor and (thermoelectric) precooling of the gas in the cold stage. In this way, a COP of about 3 % can be obtained for a carbon/xenon cooler operating between 300 K and 165 K.

4.9 References [4.1] L.A. Wade, An overview of the development of sorption refrigeration, Adv. in Cryogenic Eng. vol. 37

(1992), pp. 1095-1106. [4.2] D.M. Young and A.D. Crowell, Physical adsorption of gases, Butterworths, London (1962). [4.3] J.M. Vickers, Intermittent type silica gel adsorption refrigerator, U.S. Patent 3270512 (1963). [4.4] S. Bard, Development of an 80-120 K charcoal-nitrogen adsorption cryocooler, Proc. of the 4th Int.

Cryocooler Conf., Easton, MD (1986), pp. 43-56. [4.5] S. Bard and J.A. Jones, Regenerative sorption compressors for cryogenic refrigeration, Adv. in

Cryogenic Engineering, vol. 35b, Plenum Press, NY (1990). [4.6] L. Wade, P. Sywulka, M. Hatter and J. Alvarez, High efficiency sorption refrigerator design, Adv. in

Cryogenic Engineering, vol. 35b, Plenum Press, NY (1990), pp. 1375. [4.7] L. Wade, E. Ryba, C. Weston and J. Alvarez, Test performance of a 2W, 137 K sorption refrigerator,

Cryogenics, vol. 32, no. 2 (1992), pp. 122-126. [4.8] J. A. Alvarez, R.J. Krylo, R.D. Snapp, C. Weston, P. Sywulka and G.C. Abell, Development of an

advanced sorption compressor and its application in a 125 K cryocooler, Cryocoolers 8, Plenum Press, New York (1995), pp. 569-579.

[4.9] L.A. Wade, Advances in cryogenic sorption cooling, Proc. of recent Advances in Cryogenic Engineering, ASME 1993 winter annual meeting, New Orleans (1993).

[4.10] H.H. van Mal and A. Mijnheer, Hydrogen refrigerator for the 20 K region with a LaNi5 hydride thermal absorption compressor for hydrogen, Proc. ICEC 4, ICP Science and Technology Press, Guildford, UK (1972).

[4.11] G. Walker, Cryocoolers, Plenum Press, New York, USA (1983). [4.12] P. Bhandari, J. Rodriguez, S. Bard and L. Wade, Dynamic simulation of a periodic 10 K sorption

cryocooler, Cryocoolers 8, Plenum Press, New York (1995), pp. 581-599. [4.13] R.C. Bowman, D.R. Gilkinson, R.D. Snapp, G.C. Abell, B.D. Freeman. E.L. Ryba and L.A. Wade,

Fabrication and testing of the metal hydride sorbent bed assembly for a periodic 10 K sorption cryocooler, Cryocoolers 8, Plenum Press, New York (1995), pp. 601-608.

[4.14] S. Bard, J. Wu, P. Karlman, P. Cowgill, C. Mirate and J. Rodriguez, Ground testing of a 10 K sorption cryocooler flight experiment (BETSCE), Cryocoolers 8, Plenum Press, New York (1995), pp. 609-621.

[4.15] S. Bard, P. Karlman, J. Rodriguez, J. Wu, L. Wade, P. Cowgill and K.M. Russ, Flight demonstration of a 10 K sorption cryocooler, Cryocoolers 9, Plenum Press, New York (1997), pp. 567-576.

[4.16] L. Duband, C. Alsop and A. Lange, A rocket-borne helium 3 refrigerator, Adv. in Cryogenic Engineering, vol. 35b, Plenum Press, NY (1990), pp. 1447.

[4.17] L. Duband and B. Collaudin, Sorption coolers development at CEA-SBT, Cryogenics, vol. 39 (1999), pp. 659-663.

[4.18] Bard, S., Development of an 80-120 K charcoal-nitrogen adsorption cryocooler, Proc. 4th Int. Cryocooler Conf. (1986), pp. 43-56.

[4.19] Chan, C.K., Optimal design of gas adsorption refrigerators for cryogenic cooling, Proc. 2nd Biennial Conf. on refrigeration for cryogenic sensors and electronic systems (1982), pp. 323-341.


131

[4.20] S. Brunauer, The adsorption of gases and vapors, vol. 1: physical adsorption, Princeton University Press (1945).

[4.21] W.H. Hartwig, Cryogenic refrigeration concepts utilizing adsorption pumping in zeolites, Adv. in Cryogenic Eng. vol. 23 (1978), pp. 438.

[4.22] L.C. Yang, T.D. Vo and H.H. Burris, Nitrogen adsorption isotherms for zeolite and activated carbon, Cryogenics (1982), pp. 625-633.

[4.23] H. von Kienle and E. Bäder, Aktivkohle und ihre industrielle Anwendung, Enke Verlag Stuttgart (1980).

[4.24] J.J. Kipling and R.B. Wilson, Adsorptive properties of polymer carbons (part 1 and 2), Trans. Faraday Soc. (1959), pp. 557-569.

[4.25] Norit Aktivkohle – Einfühhrung, Norit N.V. [4.26] S.J. Gregg and K.S.W. Sing, Adsorption, surface area and porosity, Academic Press, New York

(1982). [4.27] R.Radebaugh, National Institute of Standards and Technology, Boulder (1992). [4.28] W.H. Cook and D. Basmadjian, Correlation of adsorption equilibria of pure gases on activated carbon,

The Canadian J. of Chem. Eng., August (1964). [4.29] M. Polanyi, Verhandl. Deut. Physik. Ges., vol. 16 (1914). [4.30] The Kansai Coke and Chemicals Company, Ltd., Japan. [4.31] A.N. Wennerberg and T.M. O’Grady, Active carbon process and composition, U.S. Patent no.

4082694 (1978). [4.32] D.F. Quinn and J.A. MacDonald, Natural-gas storage, Carbon, vol. 30 (1992), pp. 1097-1103. [4.33] S.S. Barton, J.A. Holland and D.F. Quinn, The development of adsorbent carbon for the storage of

compressed natural gas, Ontario Ministery of Transportation and Communications & Ontario Ministery of Energy, report no. AF-85-01 (1985).

[4.34] A. Yavrouian and H. Schember, Saran carbon sorbent development for sorption cryocooler use, Jet Propulsion Laboratory report no. D-7368 (1990).

[4.35] Norit Activated Carbon, Amersfoort, The Netherlands, personal communication, 1998. [4.36] T. Otowa, R. Tanibata and M. Itoh, Production and adsorption characteristics of MAXSORB: high-

surface-area active carbon, Gas separation & Purification, vol. 7, no. 7 (1993), pp. 241. [4.37] R.V. Culver and N.S. Heath, Saran charcoals (part 1 and 2), Trans. Faraday Soc., vol. 51 (1955), pp.

1569-1583. [4.38] J.R. Dacey and D.G. Thomas, Adsorption of Saran charcoal, Trans. Faraday Soc., vol. 50 (1954), pp.

740-748. [4.39] J.A.F. MacDonald and D.F. Quinn, Carbon adsorbents for natural gas storage, Fuel, vol. 77, no. 1/2

(1998). [4.40] Personal communication with D. Quinn (1999). [4.41] C. Pierce, J.W. Wiley and R.N. Smith, Capillarity and surface area of charcoal, J. Physic. Chem., vol.

53 (1949), pp. 669. [4.42] T.L. Hill, J. Chem. Phys. vol. 17 (1949), pp. 520. [4.43] D.H. Everett, Trans. Faraday Soc. vol. 46 (1950), pp. 453. [4.44] H.B. Callen, Thermodynamics and an introduction to thermostatics, 2nd ed., John Wiley, New York

(1985). [4.45] Cryodata Inc., Niwot, CO, USA, www.sni.net/partners/index.html. [4.46] S. Bard, Improving adsorption cryocoolers by multi-stage compression and reducing void volume,

Cryogenics, vol. 26 (1986), pp. 450-458. [4.47] J. Lester, Closed cycle hybrid cryocooler combining the Joule-Thomson cycle with thermoelectric

coolers, Adv. In Cryogenic Eng., vol. 35 (1990), pp. 1335-1340. [4.48] S. Bard, J.A. Jones, H.R. Schember, A two-stage 80 K – 140 K sorption cryocooler, Proc. ICEC 12,

Butterworths, Guildford, UK (1988). [4.49] Melcor thermoelectronics, Trenton, NJ, USA, www.melcor.com. [4.50] J.P. Holman, Thermodynamics, 4th ed., McGraw-Hill, New York (1988). [4.51] C.B.P. Finn, Thermal Physics, 2nd ed., Chapman & Hall, London (1986).

133

5 Gas-gap heat switch

Chapter 5

Gas-gap heat switch

This chapter discusses the operation of a gas-gap heat switch as well as the fabrication of a thin-film metal hydride layer that can be used to control the hydrogen pressure in the gas gap. First, the heat switch requirements are discussed, based on the design of the sorption compressor. Next, the theory of the heat transfer through the gas gap is described and verified experimentally. In section 5.4 hydrogen absorption by metal hydrides is discussed, a suitable metal hydride is selected, and the actuator behavior is modelled. Finally, the development and characterization is described of ZrNi thin films which are suitable for reversible hydrogen absorption.

5.1 Introduction

In a sorption compressor, a thermal switch is required to isolate the sorption cell during heating, and connect it thermally to a heat sink during cooling. This requirement was discussed in more detail in section 4.2. A number of heat-switch alternatives have been investigated in the past among which mechanical [5.1] and fluid-flow switches [5.2]. Another attractive approach is a gas-gap switch. This type of heat switch consists of two parallel surfaces with a gap in between that can be filled with a gas. The thermal resistance can be regulated by variation of the gas pressure in the gap [5.3]. In principle, a pressure increase can be realized by supplying gas from a storage bottle, and a pressure decrease by pumping away the supplied gas. However, a more convenient method is the use of a small sorption pump that is connected to the gas gap and that can reversibly vary the pressure by ad- or desorbing the gas – see figure 4.1. Dependent on the detailed requirements, different physical or chemical sorbers and gases can be used. Hydrogen gas is a preferred gas because of its high thermal conductivity. Moreover, hydrogen can reversibly be absorbed on a number of so called metal hydrides, which are widely being investigated for application in e.g. fuel storage systems [5.4]. Notice that there is a difference between the sorption pump that is used to vary the pressure in the gas gap around a sorption compressor cell, and sorption compressor cells that are used to drive the cooler.

The gas-gap heat switch appears particularly suitable for a miniature compressor. It can easily be scaled to very small sizes, with suitable thermal resistances and without adding any thermal mass to the compressor cells. Moreover, a sorption pump for the gas-gap actuation

Chapter 5

134

can also be scaled to very small sizes. In contrast, a fluid flow switch, for instance, is much more difficult to scale to a miniature size.

Because of the size requirements of the compressor cells, we investigated the feasibility of thin film ZrNi instead of conventional bulk ZrNi, a metal hydride suitable for gas-gap actuation. Heating, leading to hydrogen release, may easily be accomplished by deposition of the material on a thin film heater resistor. An additional advantage of thin film ZrNi, compared to bulk ZrNi, is that oxidation of the ZrNi may be prevented by a palladium cover layer, which is transparent for hydrogen, but not for oxygen [5.5]. Furthermore, the relatively large surface area of a thin film enables rapid hydrogen ab- and desorption. As a bonus, the feasibility of thin film metal hydrides generates new opportunities for integration in MEMS devices, for instance as actuators in valves, pumps or a micromechanical thermal switch. The basic principle can easily be adapted for higher pressures, by choosing a metal hydride with a different absorption behavior.

In the next section, first the heat switch requirements are formulated. Next, in section 5.3 the theory of the heat transfer through the gas gap is described and verified experimentally. In section 5.4 hydrogen absorption by metal hydrides is discussed, a suitable metal hydride is selected and the actuator behavior is modelled. Finally, section 5.5 describes the development and characterization of ZrNi thin films which are suitable for reversible hydrogen absorption.

5.2 Heat-switch requirements

The requirements for a sorption compressor heat switch are determined by the desired thermodynamic and dynamic properties of the compressor unit. Thermodynamic properties were discussed in chapter 4 and include: the compressor minimum and maximum temperatures and the compressor COP. Dynamic properties will be discussed in chapter 6 and include: the compressor size and associated cycle time, and the compressor cooling behavior. The important heat switch requirements that will be discussed are: ON and OFF thermal resistances and ON/OFF ratio; speed of switching; actuation power; lifetime; heat switch thermal mass.

Thermal resistance in the ON-state. The required heat-switch ON-resistance is related to two different factors: the required speed of cooling of the compressor cell during depressurization and the maximum temperature difference that is allowed between the cell and the heat sink during adsorption of the gas that flows into the cell. This temperature drop results from the heat of adsorption. At the end of the adsorption phase, it determines the minimum temperature of the sorber material and by that the amount of gas adsorbed. Both factors are discussed in detail in section 6.2. There it is found that RHS,ON < 6.1 K/W is required for the following system parameter settings: TA = 300 K, TH = 600 K, pH = 20 bar, pL = 1 bar, Tcond = 244 K, TC = 169 K, PC = 195 mW, Pcompr = 5.7 W, Tmin – TA = 2.5 K.

Thermal resistance in the OFF-state. The heat switch OFF-resistance determines the heat losses that occur between the heated compressor cell and the heat sink, see also section 6.2. If 10% heat losses are tolerated through the heat switch of a sorption compressor that operates with TA = 300 K, TH = 600 K and Pcompr = 5.7 W, then RHS,OFF > 526 K/W is required.

ON-OFF ratio. The mentioned required ON and OFF resistances result in a required ON-OFF ratio of at least 86.

Gas-gap heat switch

135

Heat switch speed. The heat switch should be able to switch in a relatively short period of time, τHS, after the start of the heating or cooling part of the compressor cycle, for instance within the first 10% of it. This would imply τHS < 0.05⋅tcycle. As a consequence, the required heat-switch speed is proportional to the total compressor cycle period. The sorption compressor that is discussed in chapter 6 will operate with tcycle ≈ 650 s; it follows for this situation that τHS < 30 s is required.

Actuation power. If a small metal hydride sorption pump is used to actuate the gas gap, heat must be supplied to the metal hydride to maintain it at a high temperature during the ON-state of the gas gap. This ‘actuation’ power should be much smaller than the sorption compressor input power, for instance Pact < 0.02⋅Pcompr. For Pcompr ≈ 10 W this means that Pact < 0.2 W is required.

Lifetime. Sorption coolers have the potential to reach life times of ten years or more because of the absence of moving parts. If a small sorption compressor is operated with a cycle period of 600 seconds, this would require about 106 switch actions of the heat switch.

Heat switch thermal mass. The relatively large input power that is required for the cyclic heating of the thermal mass of the compressor cells is responsible for the relatively low Coefficient of Performance of sorption compressors and sorption coolers (see also section 4.4.2). This thermal mass should, therefore, be kept as small as possible and as a result the heat switch should not significantly contribute to this thermal mass. Now two different heat-switch arrangements can be considered: an ‘external’ heat-switch device that is connected to the compressor cell via a thermal link, and an ‘internal’ heat switch in which the compressor wall is an intrinsic element of the switch. In general, the thermal conductivity of sorption materials is low and to prevent temperature gradients during heating and cooling, the thermal path of the heat to be conducted away should be kept as small as possible. One important way to reach this is to use the complete outer surface of the compressor cell to conduct away the heat. An ‘external’ heat switch that is connected to the complete outer surface of the cell requires a thermal link that will add much thermal mass to the compressor cell, which deteriorates its performance. In contrast, an ‘internal’ heat switch that connects directly to the outer surface of the compressor cell, using this as the temperature varying part of the heat switch, does not add any thermal mass to the cell at all, but still can use the complete outer surface area to conduct away the heat.

5.3 Gas-gap heat transfer

5.3.1 Theory

The process of heat transfer by gases is in the viscous state different from that in the molecular state. In the viscous state the totality of molecules is responsible for the heat transfer, whereas in the molecular state the individual molecules carry the heat from wall to wall. This difference is illustrated in figure 5.1. The transition between both regimes is determined by the Knudsen number, which is the ratio of the mean free path L and the distance d between the heat exchanging surfaces:

dLKn /= (5.1)

Chapter 5

136

Generally, the gas is considered to be in the continuum regime if Kn < 0.01 and in the molecular regime if Kn > 1. The mean free path can be derived from kinetic theory of gases and equals [5.6]:

p

TkL B

πξ 22= (5.2)

where kB is Boltzman’s constant, ξ is the molecule diameter and p is the pressure. The thermal conductivity λ0 in the continuum regime can be related to the viscosity µ and the volumetric specific heat cv by [5.6]:

vcµγλ )59(41

0 −= (5.3)

where γ = cp/cv is the ratio of the specific heats at constant pressure and volume. The viscosity and the specific heat for a di-atomic gas are given by [5.6]:

MR

cMRT

N vA 2

5998.02 ==

ππξµ (5.4a and b)

where NA is Avogadro’s number, M is the molecular mass and R is the universal gas constant. If the pressure is low enough to be in the molecular regime, the flux of heat between two

surfaces equals the flux of molecules on the walls times the amount of energy they transfer from wall to wall per molecule. The heat transfer coefficient α expressed in W/m2K equals

[5.6]:

pMTR

eff πγγ

βα81

1−+

= (5.5)

The so-called accommodation coefficient β in this expression is used to account for the incomplete energy exchange between a wall and a molecule. An effective accommodation coefficient βeff is used to account for both walls:

β

βββββ

βββ

−≅

−+=

22121

21eff (5.6)

where β1 and β2 are the accommodation coefficients for the two parallel walls. The first expression in Eq. (5.6) reduces to the second for parallel surfaces with a thin gap in between and identical accommodation coefficients. Eq. (5.5) is independent of the gap distance, since d does not influence the particle flux nor the energy transport per molecule, and proportional to the pressure, since the number of particles is proportional to p.

The transition region between the molecular and continuum region covers about two decades of the pressure range and may be an important region for the gas-gap operation. An expression for the heat transfer coefficient in this region can be derived by using the concept of

(a) (b)

Figure 5.1 Illustration of heat transfer through a gas in the molecular (a) and continuum regime (b).

Gas-gap heat switch

137

a temperature jump between the wall and the gas in the presence of a temperature gradient, which reduces the heat transfer by an effective increase of the wall separation [5.7]. This method is mathematically equivalent to the assumption of placing the thermal resistances of the two regimes in series. Using this method, an expression for the heat transfer coefficient (expressed in W/m2K) that covers the three regions was derived:

11

)59(4

10998.0:

)1(0

+−

−⋅=⋅+

=γγ

γβ

κκλ

αeff

whereKnd

(5.7)

It can be shown that for low pressures Eq. (5.7) reduces to Eq. (5.5) and for high pressures it reduces to Eq. (5.3) divided by the gap distance d. Eq. (5.7) can be used as a useful tool to calculate the gas-gap behavior under various conditions. Figure 5.2 shows the heat transfer coefficient as a function of the hydrogen pressure, for different gap widths and calculated with Eq. (5.7). These plots are discussed later in the text together with the measurements that are included in the plot.

0.1

1

10

100

1000

10000

0.1 1 10 100 1000 10000 100000pressure (Pa)

α (

W/m

2K

)

measurements, gap = 0.3 mm

corrected for losses, gap = 0.3 mm

gap = 0.03 mm

gap = 0.3 mm

gap = 3 mm

Figure 5.2 Theoretical and experimental heat transfer coefficients for hydrogen gas. The theoretical values are calculated for three different gap widths. The experimental data is discussed in section 5.3.3.

5.3.2 Limiting ON and OFF thermal resistances

In general, the thermal resistance of a gas-gap heat switch consists of three thermal resistances in parallel which represent, respectively, the heat transfer through the gas, radiation through the gap, and parasitic conduction through the mechanical construction that maintains the gap. In this section, the limiting ON and OFF resistances are estimated under the condition that the pressure can be adjusted without limitations. Next, it is shown what hydrogen pressures are needed to obtain the required ON and OFF resistances.

Thermal resistance in the ON-state. For a heat switch with a reasonable ON-OFF ratio, the ON resistance will be dominated by the gas conduction and RHS,ON ≅ Rgas. The minimal gas thermal resistance is limited by the continuum region:

s

ONHS Ad

R0

min,,

1λ

= (5.8)

and it follows that this resistance is proportional to the gap width and inversely proportional to the conductivity of the gas, which is dependent on the kind of gas and the temperature. For a

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138

given gap width, equations (5.1) and (5.2) can be used to estimate the required pressure to reach this ON resistance. For a sorption cell of 10 cm in length and 10 mm in diameter that we are working on, a gap separation of 300 µm can easily be realized. If hydrogen gas is used, RHS,ON,min = 0.56 K/W can be achieved when p ≈ 4.0 kPa. This resistance can now be compared with the required RHS,ON that was discussed in section 5.2 and which equals 6.1 K/W. To obtain this resistance, it follows with Eq. (5.7) that p ≈ 25 Pa is required. In conclusion, the required RHS,ON can easily be reached with moderate hydrogen pressures for this gas-gap configuration. It can also be concluded that it is attractive to use a smaller gap than strictly required for the desired ON-resistance. In this way, the heat transfer occurs essentially in the molecular regime and relatively low pressures are needed to obtain the required ON-resistance.

Thermal resistance in the OFF-state. The maximum OFF thermal resistance is limited by the parasitic losses: radiation through the gap and conduction through the mechanical construction that separates the gap. The radiation thermal resistance Rrad can be expressed as:

)( 44

AHBeff

AH

radrad

TTA

TTP

TR

−−

=∆

=σε

(5.9)

where TA and TH are the temperatures of the ambient and hot surfaces, εeff is the effective emissivity and σB is Stefan-Boltzman’s constant. It is clear that Rrad is a strong function of especially TH because of the fourth-power temperature dependence of radiation. Rrad can be maximized by application of clean and polished surfaces in the gas gap; in this way εeff = 0.05 can easily be obtained [5.8]. The importance of the thermal resistance of the gap separating construction, RHS constr, depends on the detailed design of the heat switch. The resistance can be made large by choosing a proper construction and low conductance construction materials, e.g. glass etc. For purpose of this study it is assumed that Rrad << RHS constr so that RHS, OFF, max ≈ Rrad. Now the required pressure to make Rgas sufficiently low (for instance Rgas = Rrad) can be calculated by combination of equations (5.5) and (5.9). For a compressor cell of 10 mm in diameter and 10 cm in length, an effective emissivity of 0.05, and TH = 600 K taken as a worst case estimation of the radiation losses, it follows that Rrad = 277 K/W. The pressure should be reduced to below p = 0.5 Pa in order to make Rgas > Rrad. This thermal resistance can be compared with the required RHS,OFF = 526 K/W that was discussed in section 5.2, and it follows that this requirement is critical. In conclusion, for compressor cells with an input power of 5.7 W, the 10 mm diameter and 10 cm length create a significant gas-gap surface area and thermal radiation losses through the gas-gap can become significant relative to the required small input power.

ON-OFF ratio. The limiting ON-OFF ratio for the above mentioned conditions can be calculated by dividing equations (5.9) and (5.8). The ratio is inversely proportional to the gap width and independent of the gas-gap area. For hydrogen gas and an effective emissivity of 0.05, typical maximum ON-OFF ratios that can be obtained are 150/d, where d is the width of the gas gap expressed in millimeters. For d = 300 µm, an ON-OFF ratio follows of about 500. It can be concluded that especially for narrow gaps very high ratios can be obtained, of course under the condition that the required high and low hydrogen pressures can be supplied and that the conduction losses of the gap maintaining construction are reduced to a low value.

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5.3.3 Experiments

To validate the gas-gap model, the heat transfer coefficient α was measured in a test setup as a function of the pressure. When a temperature difference is maintained across a gap

between two parallel surfaces and the heat Q& that flows through the gap is measured, then α

can be calculated from TAQ ∆⋅⋅= α& , where A is the surface area of the gap. The

experimental setup is given in figure 5.3a and a detailed cross section of the experimental gas-gap construction is given in figure 5.3b. It consists of two cylindrical copper parts that fit into each other with a gap of 300 µm in between. The inner cylinder measures 1 cm in diameter and 2 cm in length and is suspended via two thin glass tubes (outer diameter: 360 µm) to obtain a high thermal resistance for the gap separating link. The glass tubes are mounted in a spoke construction that is attached to the outer cylinder; the tubes are free to slide in the inner cylinder to account for thermal expansion effects. The spoke constructions on both sides are also used to adjust the gap width around the cylinder. A small ceramic 100 Ω heating resistance is mounted inside the inner cylinder and two thermocouples are mounted directly below both surfaces of the gap. The pressure in the gap can be regulated via the combination of a gas supply and a two stage vacuum pump, with two adjustable valves incorporated in the lines. The pressure was measured with a two stage membrane pressure transducer, fabricated by MKS Instruments [5.9].

gapspokeconstruction

∆T

Pheater

pumpgassupply

psensor

valve 1 valve 2

T ~ 300 K sealglass tubesheater

thermocouplesvacuum flangewire feedthroughs

(a) (b)

1 cm

Figure 5.3 (a) Experimental set-up to characterize gas-gap behavior. (b) Detailed cross-section.

When a measured input power P is supplied to the heater, and a steady state is established

(i.e. the temperatures are stabilized), then an ‘effective’ heat transfer coefficient α can be calculated if the temperature difference ∆T is also measured. These measurements can be done for different pressures yielding α(p), which is an effective value because the loss terms are included. Measurements were done for hydrogen and nitrogen gas. The results for hydrogen are included in figure 5.2. The results for nitrogen showed a similar behavior, except for the maximum heat transfer at high pressures, which was about a factor 7 lower in comparison to hydrogen. This corresponds to literature values. From the measurements, it can clearly be observed that the minimum effective α at low pressures is limited by the losses, and that the maximum α at high pressures is limited by the gas conduction in the continuum region. From the measured data, also a heat transfer coefficient was calculated which only accounts for the heat transfer through the gas. This was achieved by separately measuring the heat flow losses by pumping the gap to a high vacuum; the losses were measured as a function of ∆T to account

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for the non-linear temperature dependence of the radiation. The corrected transfer coefficient is obtained by subtracting the losses from the measured heat flows, and is included in figure 5.2. The theoretical α in the molecular regime (see Eq. (5.7)) was fitted to these corrected data by adjusting the accommodation coefficient; β ≅ 0.7 was found for hydrogen and β ≅ 1.0 for nitrogen. Values reported in the literature are 0.3 – 0.7 for hydrogen and 0.6 – 0.9 for nitrogen, both around 300 K, and the lower values for clean metallic surfaces [5.6]. Dirty unpolished surfaces with possible adsorbed layers of other gases in our experimental setup may explain the high values for α that were found. In the transition region the measured data for hydrogen deviates from the modelled curve, to a maximum of about 35%; for nitrogen the measured data fitted the model much better. In both cases the deviation was, however, within the range of the measuring accuracy. This accuracy is relatively low at the higher pressures because of the low temperature differences. Furthermore, from the measurements it can be concluded that an ON-OFF ratio of about 170 was obtained for this simple experimental gas-gap configuration. Reduction of the severe parasitic losses would increase this ratio dramatically - up to 500 for the conditions discussed in section 5.3.2.

5.4 Hydrogen gas-gap actuation by metalhydrides

5.4.1 Metal hydride theory

Because of it’s small size, atomic hydrogen is capable of diffusing into a lot of solid materials. A special class of solids in this respect are metal hydrides, a group of elemental metals, alloys and intermetallic compounds which are under certain conditions able to reversibly absorb hydrogen in an exothermic reaction. In table 5.1 the storage density of hydrogen in several metal hydrides is compared to the density of liquid and gaseous hydrogen [5.10]. It can be concluded that the hydrogen density in most metal hydrides exceeds that of liquid hydrogen. For that reason metal hydrides have been studied extensively for e.g. fuel storage applications [5.4]. An additional advantage in this respect is the reduced safety risk associated with absorbed hydrogen. The hydrogen absorption process in a metal hydride can generally be divided in several sub-processes [5.10]: 1. Adsorption. When a hydrogen molecule hits the surface of a metal hydride it can be

adsorbed. 2. Dissociation. Before atomic diffusion into the bulk can take place, the hydrogen molecule

must be dissociated into hydrogen atoms by the catalytic influence of the hydride surface. 3. Diffusion. Hydrogen atoms can now diffuse through interstitial sites of the metal hydride.

Table 5.1 Storage capacity of hydrogen in metal hydrides [5.10]. mass % H-atoms moles H-atoms per ml

H2 (l) 100 4.2 H2 (g), p = 100 bar 100 0.5 MgH2 7.6 6.7 UH3 1.3 8.3 TiH2 4.0 9.1 VH2 2.1 11.4 Mg2NiH4.2 3.8 5.9 LaNi5H6.7 1.5 6.7

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Depending on the hydrogen concentration, the temperature and the pressure, atomic hydrogen may partially or fully occupy different sets of interstitial sites.

4. Chemical bonding. When the free hydrogen reaches a critical concentration, the hydrogen is chemically bonded into the metal forming the actual hydride phase. This phase-change is exothermic and the hydride may change in chemical and crystal structure.

The absorption characteristics are dependent on the type of metal hydride and can conveniently be represented in a Pressure-Composition-Temperature (P-C-T) diagram such as illustrated in figure 5.4. Following an absorption isotherm from low pressure, hydrogen diffuses into the metal forming the α-phase. At a certain concentration, hydrogen starts to occupy particular combinations of interstitial sites to nucleate and form the hydride β-phase. During this phase transition the α- and β-phases co-exist and, according to the Gibbs phase rule, the pressure remains constant. When the transition to the β-phase is completed, the pressure increases much more rapidly as more hydrogen is absorbed. It is possible for a metal hydride to have more plateau pressures and corresponding phases. For an increasing temperature the plateau pressure is higher but the width of the plateau decreases. For a temperature higher than TC the phase change does not occur anymore for one pressure, but is a more gradual process. Figure 5.4 shows also a van 't Hoff plot as derived from the P-C-T diagram. Van 't Hoff plots of different metal hydrides are available and make it possible to compare equilibrium pressures of different materials.

AB

Figure 5.4 P-C-T diagram of a metal hydride with three isotherms and van 't Hoff plot as derived from the P-C-T diagram.

In the P-C-T diagram of figure 5.4 two typical paths are depicted that can be used to switch

a gas volume between a low and high pressure by switching the metal hydride between T1 and T3. Path A is applied when much metal hydride is present relative to the volume that must be filled with gas, so that the amount of desorbed hydrogen per mass of metal hydride is relatively small; path B is applied when the amount of metal hydride is smaller so that relative much hydrogen is desorbed per mass of metal hydride.

Apart from the described general behavior, metal hydrides exhibit some other specific characteristics which are briefly discussed below.

Hysteresis. In practice, the equilibrium pressure for hydrogen absorption is somewhat higher than the equilibrium pressure for hydrogen desorption. This effect is referred to as hysteresis and is attributed to chemical or structural lattice disorder [5.11].

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Plateau sloping. Many metal hydrides exhibit sloping plateau pressures instead of constant equilibrium pressures. Also this effect is attributed to lattice disorder.

Expansion of the lattice. Hydrogen absorption causes an expansion of the host lattice. The volume expansion during diffusion is known to be just a few percent, but upon transition to the β-phase the metal may expand up to 40% of its original volume [5.13]. This expansion process will stress the lattice and will often lead to disintegration of the bulk material into a fine powder.

Irreversibility. Residual impurity gases adsorbed at the surface of the chemical sorber can drastically decrease or completely block the absorption and desorption rates of hydrogen by impeding the dissociation of the hydrogen molecules. Even low impurity concentrations in the hydrogen gas can cause problems in applications if storage alloys are subjected to repeated loading and unloading cycles [5.14]. Gases like O2, H2S, H2O and CO are known to have poisoning effects on the effective surface area of metalhydrides [5.15]. Apart from surface poisoning, also bulk chemical reactions may occur that are irreversible. Certain phases of intermetallic compounds may store hydrogen irreversibly, which may also be dependent on the temperature.

Annealing and activation procedures. After preparation, metalhydrides are usually unintentionally exposed to a number of poisoning gases which block the hydrogen dissociation at the surface. In order to clean the active surface, the material can be annealed under high vacuum to remove the contaminants by either evaporation or diffusion into the bulk lattice. After this annealing step, the clean surface should not react with new gases. Apart from the surface cleaning effect, annealing has the additional advantage that it can reduce the crystal defects within the metal. Crystal defects can getter hydrogen and will reduce the reversible absorption of hydrogen when the hydride is exposed to hydrogen for the first time.

Besides poisoned surfaces, freshly prepared metal hydride samples usually exhibit a very low surface-volume ratio which limits the hydrogen absorption rate. For this reason, metal hydrides are usually initially activated by exposing them to a high hydrogen pressure. Because of the hydrogen absorption the surface layer will expand and eventually crack creating more clean surface. A few absorption-desorption cycles can pulverize the metal hydride completely resulting in small grains separated by cracks, enhancing absorption and dissociation by offering clean surfaces to the hydrogen gas.

5.4.2 Material selection

The requirements for the metal hydride are directly related to the heat-switch requirements. In section 5.3.2 it was shown that pH2 < 0.5 Pa is required to obtain RHS,OFF > 300 K/W and pH2 > 25 Pa is required to obtain RHS,ON < 6.1 K/W for sorption compressor cells measuring 10 mm in diameter and 10 cm in length and Pcompr = 5.7 W. These required hydrogen pressures may vary somewhat for different miniature sorption compressor designs, but a pressure swing between 0.5 Pa and 100 Pa will suit a wide range of compressor designs. The low pressure should be obtained by cooling the metal hydride to a temperature above ambient temperature (300 K). Furthermore, the process of ab- and desorption should be completely reversible and the kinetics should be reasonably fast.

Figure 5.5 shows van 't Hoff plots for the plateau pressures of a number of metal hydrides [5.16]. Of the depicted materials, only ZrNi and U are able to reach a low pressure of 0.5 Pa at

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T = 300 K or above. Bulk uranium has recently been characterized as a suitable reversible hydrogen storage material by M. Prina in another study on gas-gap heat switches [5.17]. The uranium-hydrogen system has only one hydride phase UH3 and it is characterized by broad and flat plateaus. There is a very large discrepancy between the metal (19 g/cm3) and hydride (10.95 g/cm3) densities, which causes the metal to disintegrate into a very fine powder upon hydrogen uptake. It is very likely that this expansion will lead to cracking of the thin-film that we plan to make, which makes this material not a suitable candidate.

Bulk ZrNi has also been tested successfully as a gas gap hydride actuator at JPL by J. Wu [5.3] and M. Prina [5.17] and many other studies were done on its properties. The stoichiometric 1:1 alloy is one of the nine intermetallic compounds of the ZrNi system and among them it has the highest hydrogen storage capacity forming two hydride phases [5.18]. Fig. 5.6a shows absorption isotherms of the first phase change and figure 5.6b shows the ab- and desorption isotherms of the second phase change [5.18]. No hysteresis was reported in the first (α-β) phase transition but significant hysteresis occurs in the second (β-γ) phase transition, as can be observed in the isotherms in figure 5.6b. The lattice parameters of the different phases of the ZrNiHx system are given in table 5.2. It shows clearly that the change in volume of one unit cell for diffused free hydrogen is small (about 0.3%) compared to the change in volume after the first phase change (5 – 6%) and the second phase change (17 – 20%). The pure ZrNi and the ZrNiH3-phase are known to have a orthorhombic structure,

Figure 5.5 Van 't Hoff plots for several metal hydrides [5.16].

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144

the ZrNiH-phase has a tetraclinic structure [5.19]. It has been observed that degradation of the ZrNiHx system occurs especially at a temperature above 675-700 K [5.20], resulting in more stable binary hydride compounds such as ZrHx and a pure nickel phase [5.21] or ZrNi3 [5.18]. For the lower temperatures that are required in a heat switch actuator, degradation in bulk ZrNi appears to be limited or absent.

Table 5.2 Lattice parameters of the different phases of the ZrNiHx system [5.19].

Composition a0 (Å) b0 (Å) c0 (Å) Volume (Å3) ZrNi 3.272 ±0.005 9.965±0.005 4.115±0.005 134.2±0.4 ZrNi(H) 3.28 ±0.01 10.12 ±0.01 4.05±0.01 134.6±0.7 ZrNiH 3.367±0.002 10.313±0.004 4.063±0.002 141.6±0.2 ZrNiH3 3.53±0.01 10.48±0.02 4.30±0.02 159.1±1.5

Also Mg2Ni, ZrCo, Ti and a commercial getter from SAES are reported as potential

actuator materials [5.17]. The capacity of Mg2Ni is reported as promising, but the kinetics at low temperatures is rather slow. For ZrCo, contamination sensitivity and observed disproportionation seemed not encouraging to the selection of this material. TiHx is mentioned as a stable elemental hydride so that a very high temperature is required to desorb hydrogen in the prescribed pressure range arguing against its use as gas-gap sorbent material. The St 172 SAES getter is a sintered porous alloy composed of a mixture of Zr-V-Fe and Zr in about equal proportions. It is reported that the porous getter does not embrittle if the hydrogen concentration is kept below a certain limit. However, for that situation a high temperature of at least 700 °C is required to desorb hydrogen at 30 – 50 Pa.

It was decided to investigate the feasibility of thin film ZrNi for application in a miniature or MEMS based heat switch for the following reasons: 1. Concerning the pressure and temperature requirements, either the first or the second plateau in the P-C-T diagram may be applied for pressure switching. 2. In the required temperature range the reversibility of hydrogen absorption on ZrNi seems to be good. 3. Especially for the first α-β-phase change,

(a) (b)

Figure 5.6 (a) Absorption isotherms of the first (α-β) phase change of ZrNi; (b) Ab- and desorption isotherms of the second (β-γ) phase change of ZrNi [5.18].

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the expansion of the lattice is relatively small compared to other metal hydrides which makes the chance of delamination of a polycrystalline thin film smaller. 4. The fabrication of thin film ZrNi could be carried out in the MESA+ lab.

5.4.3 Actuator modelling

The required amount of ZrNi is determined by the amount of hydrogen gas that is needed to fill the gas-gap volume. This amount of gas, expressed in moles, follows by application of the ideal gas law:

gap

gapHH RT

VpN 2

2= (5.10)

where pH2 is the pressure in the gas-gap during the ON-state, Vgap is the volume of the gas-gap plus other dead volumes around the sorption compressor and Tgap is the average temperature of the hydrogen gas. Next, the required mass of ZrNi follows as:

x

NM

xN

MNMm HZrNi

HZrNiZrNiZrNiZrNi ∆

=∆

== 22 (5.11)

where MZrNi is the molar mass of ZrNi, NZrNi, NH and NH2 are the number of moles of ZrNi, hydrogen atoms and hydrogen molecules, respectively, and ∆x is the amount of desorbed hydrogen atoms per molecule of ZrNi (see figure 5.4). For our compressor cells, the following values can be assumed: pH2 = 50 Pa, Vgap = 1.5 cm3, Tgap = 350 K and ∆x = 0.05; this last value means that, for safety reasons, it is assumed that only a small fraction of the hydrogen gas stored in the ZrNi is actually desorbed during actuation of the gas gap. With these values, the required amount of ZrNi follows as mZrNi = 0.17 mg. With ρZrNi = 7.0 g/cm3, a tiny required ZrNi volume of merely 0.024 mm3 results.

hea

t sin

k

Cact

Ract

i

Pact

Figure 5.7 Thermal system that determines the heating and cooling behavior of the ZrNi actuator. The thermal system of the ZrNi gas-gap actuator is schematically depicted in figure 5.7. In

this system Cact represents the heat capacity of the ZrNi and its holder or container with electrical heater, Ract is the thermal resistance between the ZrNi-unit and the heat sink, and Pact is the input power required to maintain the temperature difference between the ZrNi and the heat sink. The thermal resistance must fulfill two conflicting requirements. Firstly, together with the thermal mass Cact it determines the time constant τRC = RactCact that characterizes the cooling (switching) speed of the ZrNi after switching OFF the heater of the ZrNi. In section 5.2 it was discussed that the heat switch should be able to switch within 30 seconds. As a consequence, τRC should be somewhat less than 30 seconds; the exact number depends on the required low temperature of the ZrNi. Secondly, the resistance should limit the heater input power Pact to a reasonable low value while in the ON-state, for instance below 1 W. If bulk ZrNi is used, the volume ZrNi will in practice be much larger than the tiny required volume, increasing the thermal mass Cact. Moreover, bulk ZrNi must be stored in a container

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because it pulverizes during use, adding even more thermal mass to Cact. It can easily be shown that for an actuator made of bulk ZrNi the conflicting requirements cannot be solved due to this relatively large Cact. Either the system becomes too slow or too much input power is required during the ON-state of the actuator. Thin film ZrNi deposited on a thin membrane such as depicted in figure 5.8 is much more suitable in this respect. A film of 500 nm thickness and an area of 0.5 cm2 already results in the required volume of ZrNi. A thin film heater can easily be integrated with the ZrNi layer deposited on top of the membrane, leading to a small value for Cact. An additional advantage of thin film ZrNi is that a Pd overlayer can be integrated, which increases the speed of hydrogen uptake (this topic is discussed in more detail in the next section).

Figure 5.9 shows Pact and τRC as a function of Ract for mZrNi = 0.17 mg, ∆T = 200 °C and cp,ZrNi = 333 J/kg-K; Cact was estimated by doubling the thermal mass of the required ZrNi to account for the thermal mass of the membrane and the thin film heater. From this figure, it can be concluded that the two conflicting requirements can easily be resolved for such a configuration, for instance by choosing Ract ≈ 2⋅103 K/W, leading to Pact ≈ 0.1 W and τRC ≈ 0.2 s. The thermal resistance of a surface area that radiates to 300 K varies between 3⋅103 and 103 K/W-cm2 for a surface temperature between 300 and 600 K and εeff = 0.5. Therefore, radiation from the membrane to 300 K can be used to realize the required thermal resistance Ract.

silicon carrierheater

heater with bond pads

silicon nitride membraneZrNi/Pd

ZrNi/Pd

cross section

top view

Figure 5.8 Schematic picture of a ZrNi/Pd thin film on top of a silicon nitride membrane that is carried by a KOH-etched silicon device. A thin film heater is located under the membrane.

0.001

0.01

0.1

1

10

1.0E+02 1.0E+03 1.0E+04 1.0E+05R thermal (K/W)

P in

(W

)

0.01

0.1

1

10

100

t RC

(s)

P in (W)t RC (s)

Figure 5.9 Illustration of the trade-off between the required input power Pact and the time constant for cooling down of the ZrNi thin film as a function of Ract.

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5.5 ZrNi thin films

5.5.1 ZrNi/Pd thin film preparation and characterization

Thin films of ZrNi were deposited on silicon nitride-covered silicon substrates with the aid

of magnetron sputtering in a cryogenically pumped system with a background pressure of less than 10-7 mbar. Such a low pressure is required to reduce incorporation of especially oxygen into the alloy film. ZrNi is very susceptible for impurities like oxygen, and unless the film is protected in some way after deposition, it will within a short time become oxidized and therewith unsuitable for hydrogen uptake. Therefore, the sputtering system was equipped with three metal targets: Ni and Zr, which can be mixed to achieve an optimal composition of the ZrNi alloy, and Pd, which acts as the protective layer during further experiments on the ZrNi film. Palladium has been used frequently as a protective layer for easily contaminated metal hydrides [5.22]. The thickness of the Pd cover layer was optimized with respect to its protective and dissociation-catalytic behavior. Palladium is known to dissociate hydrogen gas and allow fast transport of atomic hydrogen through its bulk, and therefore it is an ideal material to facilitate hydrogen uptake into the alloy lattice.

Important properties for reversible and reproducible hydrogen uptake of the ZrNi films are also elemental composition, microstructure and adhesion to the substrate. Concerning the composition of the films, the Zr-Ni phase diagram exhibits nine different stable compounds, some of which, but not all, have the possibility of reversible hydrogen uptake. Pure Zr films will absorb hydrogen irreversibly, whereas pure nickel films are not capable of storing large amounts of hydrogen at low temperatures at all. A homogeneous distribution of Zr and Ni throughout the film is therefore desirable, while from earlier research on bulk ZrNi [5.23] it followed that a 50% Zr - 50 % Ni composition will give the best hydrogen uptake properties.

The deposition conditions were adjusted such that fine-grained polycrystalline films would result. The idea behind this was that such films will have a faster hydrogen ab/desorption behavior and a better adhesion upon hydrogen absorption. This adhesion of the films is important because hydrogen absorption results in an expansion of the alloy lattice, as was discussed in section 5.4.1. In a thin film this expansion will cause stresses, which may result in delamination of the film. To prevent this, it was thought that fine-grained polycrystalline films would be preferable, assuming that fine grains might accommodate the stresses more easily, e.g. by slight rotations of the individual grains. Similar experiments done by Griessen [5.5] on polycrystalline thin film Yttrium metal hydrides showed that these films did not delaminate upon hydrogen absorption from YH2 to YH2.9. In contrast, experiments of Reimer [5.24] showed that epitaxial grown Niobium thin films directly delaminated after only 10% hydrogen uptake. This was attributed to the structured stress that was uniformly introduced in the crystalline layer after hydrogen uptake.

Accurate mass measurements were used to determine the relation between sputtering conditions and deposition rates of the pure metals. These calibration runs were then used to deposit ZrNi films of the desired composition, which was evaluated with AES (Auger Electron Spectroscopy) depth profiles or EDX (Energy-Dispersive X-ray spectroscopy). The microstructure of the films was examined by XRD (X-ray diffraction) and TEM (Transmission Electron Microscopy).

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To relate film structure to absorption behavior and kinetics, several samples were tested in the set-up shown in figure 5.10a. The 3” wafers containing the ZrNi/Pd films were inserted in the vacuum chamber depicted in figure 5.10b. This stainless steel vacuum chamber contains a 3” stainless steel flat heat exchanger with integrated heater. A gas flow through the heat exchanger could be used to rapidly cool down the 3” sample on top of it, and the heater could be used to rapidly heat up the sample. The heat exchanger-heater combination was thermally isolated from the vacuum chamber. Three springs in the top part of the vacuum chamber were used to press the sample on the heat-exchanger/heater and guarantee thermal contact. A thermocouple was integrated in one of the springs to measure the surface temperature of the sample. A MKS Baratron capacitance manometer with a range of 10-4 – 2 mbar was used as pressure transducer [5.9]. High purity hydrogen gas could be flowed into the chamber via a Bronkhorst [5.25] flow controller that could control gas flows as low as 1 µg/s. A turbomolecular pump was applied to evacuate the set-up. The following parameters were recorded by a data acquisition system operated by Labview software [5.26]: sample temperature, heater voltage and current (and indirectly the heater power, resistance and temperature), pressure, gas flow, valve status.

vacuumseal

heat exchangerwith heater

Si wafer withZrNi/Pd film

(a)

(b)

pressuregauge

Hbottle

2

massflow

controller

valves

pumpsample

Figure 5.10 (a) Characterization set-up used for measuring isotherms and cycle tests. (b) Cross section of the vacuum chamber with integrated heat-exchanger/heater to control the temperature of the sample.

To determine absorption isotherms, a controlled amount of hydrogen gas was introduced

into the sample chamber, and the equilibrium hydrogen pressure was measured at a pre-set sample temperature. The absorbed amount of hydrogen can thus be calculated from the pressure change during equilibrium, which might take from a few seconds up to an hour, depending on the temperature and thickness of the Pd cover layer. The kinetics of hydrogen uptake were studied in a similar way.

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5.5.2 Results and discussion

Several thin film samples were prepared, which typically consisted of 200 nm thick ZrNi films covered by a 20 nm thick Pd layer. The temperature in the different sputtering runs was varied between room temperature and 450 oC, while in some experiments the ZrNi was deposited at a different temperature than the Pd cover layer. All other deposition parameters were kept constant, i.e. the Ar pressure was 50 Pa and sputtering powers on 2" targets of ca. 200, 50 and 50-100 W for Zr, Ni, and Pd respectively, leading to deposition rates of ca. 20 nm min-1.

XRD showed that for deposition temperatures below 300 oC the ZrNi film was amorphous, while the Pd film was polycrystalline and exhibited 111 texture for all deposition temperatures. ZrNi films deposited at temperatures above 300 oC were polycrystalline. For deposition temperatures above 400 oC in some samples traces of a second phase, Zr2Ni, were detected by XRD, indicating how difficult it is to adjust the composition of the film with the chosen deposition method. AES depth profiles of the films showed that during deposition no interdiffusion or oxidation of layers had occurred. Figures 5.11 and 5.12 show TEM-pictures

Figure 5.11 (a) TEM-pictures of sample R1, R2 and R3 grown at 20 °C, 150 °C and 300 °C respectively.

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150

of 20 °C, 150°C, 300 °C and 450 °C grown thin films of 200 nm ZrNi and 50 nm Pd; the pictures were made to verify the conclusions of the XRD measurements. The first two photographs clearly show all different layers within the film: the Si substrate, SixNy, ZrNi and Pd. For the 20 °C, 150 °C and 300 °C grown samples no structure is seen in the ZrNi thin film but the Pd appears to be polycrystalline. The close-up photo of the 300 °C grown sample shows a very thin amorphous transition layer between the ZrNi and Pd films. This transition layer is more clear for the 450 °C grown sample, in which the ZrNi can indeed be considered polycrystalline. This transition layer is probably required to match the different lattice parameters of ZrNi and Pd.

A typical example of a series of absorption isotherms for a polycrystalline film is shown in figure 5.13. A sorption plateau can be observed which, after comparison with Luo’s data in figure 5.6a, suggests an α-β phase transition. Absolutely no hysteresis between ab- and desorption was observed, neither for all other samples. Some care has to be taken with the interpretation of the data at the lowest temperatures, for which the isotherms are seen to overlap. This overlap is caused by desorption of other gases from the walls of the set-up during the long experiment, which could not be eliminated completely in this experiment.

Figure 5.12 TEM-pictures of a sample grown at 450 °C before (left) and after (right) several thousands of ab- and desorption cycles (this endurance test is discussed later in this section).

0.0001

0.001

0.01

0.1

1

10

0 0.2 0.4 0.6 0.8 1 1.2

H/ZrNi

Pre

ssu

re (

mb

ar)

2202001801601401201008060

Temperature:

Figure 5.13 Absorption isotherms for a ZrNi thin film deposited at 450 oC, covered with 50 nm Pd deposited at 175 oC.

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Nevertheless, it can be seen that the films absorb considerable amounts of hydrogen. It also demonstrates that the pressure swing required in the heat switch can be accomplished with these films. The heat of absorption was determined from van 't Hoff plots that were made for H/M = 0.5; ∆h = 40.5 kJ/g was found. Exactly the same value was found by Luo [5.18] for the α-β phase transition of bulk ZrNi, whereas he found ∆h = 36.6 kJ/g for the β-γ phase transition.

From the first measurement on the 450 °C grown sample it appeared that 20 % of the amount of the initially absorbed hydrogen was not released from the film when the sample was exposed to a high vacuum. This was concluded from a comparison of the hydrogen uptake of the fresh sample with data of the sample after it had undergone a large amount of successive hydrogen ab- and desorption cycles. This may be explained by the fact that the ZrNi thin film contains some other phases which bind hydrogen at a different ratio than ZrNi. This irreversibility increased to 60% for the 20 °C amorphous grown sample.

The absorption isotherms of an amorphous ZrNi sample, deposited at 200 oC, showed a behavior similar to that depicted in figure 5.13, the only difference being that no plateau was observed. The sorption plateau is related to a phase change during hydrogen uptake. It is unlikely that such a phase change will occur in an amorphous film, since a phase change is thought to be related with a change in crystal structure.

To show the feasibility of hydrogen pressure switching, thousands of hydrogen absorption-desorption cycles were performed by temperature variation of one particular sample; a number of these cycles are shown in figure 5.14. The drift of the lower equilibrium pressure level is caused by gas leakage or gas desorption from the walls of the test chamber. These gases (other gases than hydrogen) could be pumped from the chamber while the ZrNi film was at ambient temperature and all hydrogen gas was absorbed in the film; after such a short pumping step the pressure cycling started again at the lowest pressure. The pressure cycling experiment demonstrates that a significant pressure swing can be accomplished by a variation of temperature in a feasible range.

0.0001

0.001

0.01

0.1

1

10

0 5000 10000 15000 20000 25000 30000Time (s)

Pre

ssu

re (

mb

ar)

60 oC

230 oC

Figure 5.14 Absorption-desorption endurance test for the 450 °C grown sample of figure 5.13.

Chapter 5

152

Figure 5.12 shows TEM pictures of the 450 °C grown sample before and after the endurance test. No interfacial or structural changes were found, indicating that no structural degradation of the film occurred. In all experiments the adhesion of the films remained intact. EDX measurements also showed no changes in composition.

During the experiments, it became clear that the Pd overlayer is very well able to protect the ZrNi from oxidation. However, the catalytic operation of the Pd layer appeared to be sensitive for surface contamination. Repeated absorption-desorption cycles without degradation in time could only be obtained if the vacuum chamber was thoroughly cleaned in advance. In earlier experiments, vacuum grease was used to obtain proper vacuum sealing of the chamber. During these experiments, a brown film formed on top of the Pd layer that strongly degraded the cycling performance in time. This contamination was apparently produced by a chemical reaction between hydrogen gas and the vacuum grease, and clearly showed the importance of a clean environment.

A step response measurement of the hydrogen uptake is shown in figure 5.15 for a ZrNi-Pd thin film deposited at 200 °C. After each measurement hydrogen was removed from the sample by exposing it to a vacuum of 10-6 mbar and a temperature of 230 oC. A comparison of samples with different growth conditions of ZrNi showed that these growth conditions hardly influenced the absorption rate of hydrogen. On the other hand, the temperature of the sample during absorption strongly influenced the absorption rates. Absorption time constants typically varied from 20 seconds for a sample temperature of 60 °C to 3 seconds for a sample temperature of 140 °C. The results of the kinetic measurements suggest that the Pd overlayer limits the absorption kinetics of the ZrNi-Pd thin film, which is strongly temperature dependent. Both its thickness and microstructure were seen to influence the absorption behavior, whereas changes in the ZrNi structure only resulted in changes in the equilibrium pressures. Optimization of the Pd layer properties will give some room for further improvement of hydrogen uptake rates. However, the required switching speed of 30 seconds could be reached by a controlled cool-down behavior of the ZrNi/Pd thin film; a very rapid cool-down to ambient temperature would result in a slow hydrogen uptake because of the limited absorption rates at lower temperatures.

0

0.2

0.4

0.6

0.8

1

1.2

0 10 20 30 40 50time (s)

Pre

ssu

re (

mb

ar)

T=60

T=80

T=100

T=120

T=140

Figure 5.15 Time dependence of hydrogen uptake for a 200 nm ZrNi film with 50 nm Pd cover, both deposited at 200 oC.

Gas-gap heat switch

153

5.6 Conclusions

A gas-gap heat switch around a sorption cell is desired to isolate the cell during heating and to conduct away this heat during cooling of the cell. An ON-OFF ratio of about 50 is suitable for proper operation of the cells. The thermal conduction through a gas gap is varied by adjusting the gas pressure in the gap. For low pressures, conduction occurs in the molecular regime and is independent of the gap-width; the lowest conduction is limited by thermal radiation through the gap. For hydrogen gas, this thermal radiation limit occurs for pressures below about 1 Pa. For high pressures, the maximum conduction is limited by the pressure-independent conduction through a continuum, and this conduction increases inversely proportional with the gap width. Typical maximum ON-OFF ratios that can be obtained for hydrogen gas are 150/d, where d is the width of the gas gap expressed in millimeters. The heat transfer behavior of a gas-gap heat switch in the molecular, transition and continuum regime was described with one simple expression, and fair agreement was obtained with experimental results.

Pressure adjustment in a gas gap can be realized with hydrogen gas that can reversibly be ab- and desorbed from a small amount of metal hydride. From a comparison between different metal hydrides it followed that ZrNi is a suitable candidate. The application of bulk ZrNi will inevitably result in a relatively oversized pressure regulation system which does not fit with the requirements of a relatively small sorption compressor. For that reason, the feasibility of thin film ZrNi was studied.

It was demonstrated that polycrystalline ZrNi thin films are feasible as a small scale hydrogen pressure actuator, both with respect to the pressure swing that can be obtained and the switching times that can be achieved. The pressure could reversibly be varied between 0.03 Pa and 125 Pa by variation of the temperature between 60 °C and 230 °C. The required switching times of 30 seconds and less could be achieved. The pressure variation would result in an ON-OFF ratio of 100 for the 300 µm wide gas-gap heat switch.

5.7 References [5.1] T. Slater, P. van Gerwen, E. Masure, F. Preud'homme and K. Baert, Thermo-mechanical

characteristics of a thermal switch, Techn. Digest 8th Int. Conf. Solid-State Sensors & Act., Stockholm, Sweden, June 25-29, 1995, pp. 341.

[5.2] Bard, S., Jones, J.A., Regenerative sorption compressors for cryogenic refrigeration, Advances in cryogenic engineering, Vol. 35, Plenum Press, New York (1990).

[5.3] D.L. Johnson, J.J. Wu, Feasibility demonstration of a thermal switch for dual temperature IR focal plane cooling, Cryocoolers 9, Plenum Press, New York (1997).

[5.4] D.L. Cummings and G.J. Powers, The storage of hydrogen as metal hydrides, Ind. Eng. Chem. Process Des. Develop., vol. 13, no. 2 (1974), pp. 182.

[5.5] R. Griessen, J.N. Huiberts, M. Kremers, A.T.M. van Gogh, N.J. Koeman, J.P. Dekker and P.H.L. Notten, Yttrium and lanthanum hydride films with switchable optical properties, J. Alloys and Compounds, 253-254 (1997), pp. 44.

[5.6] A. Roth, Vacuum technology, Elsevier, Amsterdam (1990). [5.7] R.J Corruccini, Gaseous heat conduction at low pressures and temperatures, Vacuum (1959). [5.8] Y.S. Touloukian and D.P. DeWitt, Thermophysical Properties of Matter, vol. 7, IFI/Plenum, New

York (1970). [5.9] MKS Instruments, Inc., Six Shattuck Road, Andover, MA 01810. [5.10] G.D. Sandrock and E.L. Huston, How metals store hydrogen, CHEMTECH, dec. (1981), pp. 754.

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[5.11] T.B, Flanagan and C.N. Park, Hysteresis in Metal Hydrides, Materials Science Forum, vol. 31 (1988), pp. 297-324.

[5.12] B. Baranowski, A simplified quantitative approach to the isothermal hysteresis in metallic hydride with coherent interphase, J. Alloys Compounds, vol. 200 (1993), pp. 87-92.

[5.13] G.G. Libowitz, H.F. Hayes and T.R.P. Gibb, Jr., The system zirconium-nickel and hydrogen, J. Phys. Chem., vol. 62 (1958), pp. 76.

[5.14] F. Schweppe, M.martin, E. Fromm, Hydrogen absorption of LaNi5 powders precovered with O2, CO, H2S, CO2 and N2, Journal of Alloys and Compounds, vol. 253 (1997), pp. 511-514.

[5.15] R.L. Cohen and J.H. Wernick, Hydrogen storage materials: properties and possibilities, Science, vol. 214, no. 4525 (1981), pp.1081-1087.

[5.16] R.C. Bowman, Jr., Evaluations of Metal Hydrides and design of Low-Pressure Sorption Bed for the production of Solid Hydrogen via Joule-Thomson Expansion, Report 9786, Aerojet Electronic Systems Division.

[5.17] M. Prina, Hydrogen gas gap heat switches: characterization and life testing, Ph.D. Thesis, Politecnico di Milano (1999).

[5.18] W. Luo, A. Craft, T. Kuji, H.S. Chung and T.B. Flanagan, Thermodynamic characterization of the ZrNi-H system by reaction calorimetry and P-c-T measurements, J. Less-Common Metals, 162 (1990), pp. 251.

[5.19] D.G. Westlake, H. Shaked, P.R. Mason, B.R. McCart and M.H. Mueller, Interstitial site occupation in ZrNiH, J. Less-common Metals (1982).

[5.20] J.S. Cantrell, R.C. Bowman, L.A. Wade, S. Luo, J.D. Clewley, T.B. Flanagan, Thermodynamic Properties and the degradation of ZrNiHx at elevated temperatures, J. of Alloys and Comp., 231, (1995), pp. 518.

[5.21] K. Ichimura, M. Matsuyama, K Watanabe, Alloyng effect on the activation processes of Zr-alloy getters, J. Vac. Sci. Technol., A 5 (2) (1987), p. 220

[5.22] D.E. Azofeifa and N. Clark, Hydrogen absorption in Pd coated Nb and V films, Z. Physik. Chemie, vol. 181 (1993), pp. 387.

[5.23] L.A. Wade, Performance, reliability, and life of hydride compressor components for 10 to 30 K sorption cryocoolers, Adv. in Cryogenic Eng., vol. 39, Plenum Press, (1994), pp. 1483-1490.

[5.24] P.M. Reimer, H. Zabel, C.P. Flynn, A. Metheny and K. Ritley, Elastic properties of hydrogen loaded epitaxial films, Int. J. of Research in Phys. Chem. & Chem. Phys., vol. 181 (1993), pp. 367-373.

[5.25] Bronkhorst High-Tech B.V., Nijverheidsstraat 1A, Ruurlo, The Netherlands., www.bronkhorst.com. [5.26] National Instruments, Inc., 6504 Bridge Point Parkway, Austin, TX 78730-5039, USA,

www.natinst.com.

155

6 Sorption compressor

Chapter 6

Sorption compressor

This chapter describes the design, fabrication and testing of the individual sorption compressor cells. Section 6.2 first discusses the thermal behavior of one sorption cell. Next, in section 6.3 design considerations are presented on the inner sorption cylinder, the support structure between the inner and outer cylinder, the flow resistance of the adsorption material, and the heater. Two different designs of the sorption cell are shown in section 6.4. Finally, cycling experiments and flow tests are discussed in section 6.5.

6.1 Introduction

A sorption compressor for continuous operation consists of at least four sorption compressor cells with integrated heat switches. Operation and thermodynamic modelling of such a sorption compressor was discussed in chapter 4 and operation of the gas-gap heat switch was discussed in chapter 5. This chapter concerns the design and operation of the individual compressor cells with integrated heat switch. Some special attention is given on the effects of miniaturization of the cells.

Chapter 4 discussed the thermodynamic behavior of a sorption compressor based on quasi-static conditions and the system in thermal equilibrium. In a practical design, however, dynamic and parasitic effects will occur that lower the performance of the cooler such as temperature profiles in the sorbent beds, pressure drops across the beds, an imperfect heat sink, etc. Therefore, the quasi-static analysis is a best-case consideration and careful (dynamic) modelling and design of the compressor elements is required to minimize losses due to non-ideal behavior. Section 6.2 discusses a first order lumped thermal model that illustrates how the relevant parameters are linked together and which can be used as a simple design tool for the compressor cells and heat switches. More detailed design considerations on aspects of the compressor cell are discussed in section 6.3. As a part of this, a model on pressure drops due to gas flow through particle beds is discussed in section 6.3.3. Next, two different designs of the compressor cell are presented in section 6.4. Finally, experiments on the sorption cells are presented in section 6.5.

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156

6.2 Modelling of the compressor thermal behavior

Figure 6.1 shows a schematic cross section of a sorption compressor cell with gas-gap heat switch. It consists essentially of five elements: the inner pressure container, sorption material inside this container, an electrical heater in or around the inner container, a gas-gap heat switch, and the outside container that is connected to a heat sink. In addition to these basic elements there are also: a support structure between the two containers, a gas tube through the outside container connecting to the inside pressure container, and a thermocouple inside the sorption material to measure the temperature. A sorption compressor unit consists of (at least) four of these cells; the operation of such a unit is discussed in section 4.2.

cross section

outside containerheat-sink thermocouple

support

gas-tube

inside container

gas-gap heater

sorber material

Figure 6.1 Schematic cross section of a sorption compressor cell with gas-gap heat switch. If a sorption cylinder with a large aspect ratio is assumed (which is attractive for several

reasons, see sections 3.3.4.2 and 4.4.4), then only the radial thermal behavior is of real importance. Figure 6.2a gives a radial lumped thermal model for the five elements of one sorption cell. It consists, respectively, of the sorption cylinder containing sorber material that can be modelled as a distributed heat capacity Ccell and a distributed thermal resistance Rcell; the variable heat switch thermal resistance RHS (assuming that the heat capacitance of the gas gap can be neglected); another distributed heat capacity Coc and a thermal resistance Roc representing the thermal link of the outside container between the heat switch and the heat-sink; and the thermal transition resistance Rsi to the environment. The heat switch resistance RHS is made up by the gas conduction and radiation through the gap and can actively be controlled between a low RHS,ON value and a high RHS,OFF value by variation of the gas pressure in the gas gap. Dependent on the importance of the (non-linear) radiation term, RHS,OFF may be a function of the temperature of the sorption cell. Together with the heater, the heat switch resistance actively controls the thermal behavior of a sorption cell, which subsequently determines the pressure in that cell. Apart from heat supplied by the heater, heat of ad- and

C R C R C R C C R C R C R C

hea

t sin

k

Ccell

sorption cylinderwith sorber mat.

RHS

(variable) heat switchresistance

hea

t sin

k

sorption cylinderwith sorber mat.

thermal linkto heat sink

heat sink thermaltransition resistance

(variable) heatswitch resistance

RHSRsi

compressor centre line

(C and R )cell cell(C and R )oc oc

(a) (b)

Pcompr PcomprPads Pads

Figure 6.2 (a) Typical radial thermal model of a sorption cell. (b) Simplified lumped model (see text).

Sorption compressor

157

desorption may also play a role in the heat balance. From the discussion in section 4.4.5 it follows that, after cooling of the compressor cell, the

minimum compressor sorber temperature should be as close as possible to the ambient heat sink temperature to prevent a reduction of the compressor COP. Temperature gradients in the sorber material, which could emerge during cooling, make it more difficult to obtain this minimum temperature and should, therefore, be prevented as much as possible. Also during heating, a uniform temperature in the sorber material is preferred to prevent local overheating of the sorber material. If these two requirements are met, then the inside compressor container with sorber material can be represented by one lumped thermal capacitance Ccell at a uniform temperature. Huinink [6.1] has developed a numerical model to predict the temperatures and pressures within the compressor more accurately; complete analytical modelling of the dynamic temperature and pressure behavior is impossible because of a number of strongly non-linear effects such as the sorption characteristics and thermal radiation through the gas-gap. From this work it was concluded that temperature profiles within the adsorption material are very limited for the considered compressor size and input power, which justifies the application of the lumped model.

If the values of Roc and/or Rsi are not much smaller than RHS,ON, then the outside container will be heated during the limited cool-down period of the compressor cell to a temperature above ambient temperature. Such behavior is unwanted, because with the increased temperature of the outside container also the minimum approachable compressor temperature is increased. As a consequence, the design of the outside container and heat sink should be such that both thermal resistances can be neglected compared to RHS,ON. If these conditions are met by proper designing, the system reduces to the simple lumped RC model of figure 6.2b. In this system, the temperature difference between the inside compressor cylinder and the ambient temperature falls completely across the heat switch resistance, which then can be used as a tuning variable during design and operation. Starting from this lumped RC model, the compressor dynamic behavior will be discussed and some useful expressions will be developed for the required heat-switch resistance. Essential assumptions in this discussion can be summarized as: 1. A temperature profile is only present in the gas-gap. All other elements are on a uniform

temperature. 2. The major heat flow is in the radial direction. 3. The heat capacity of the gas in the gas-gap is neglected.

Figure 6.3 illustrates qualitatively the temperature and pressure of a compressor cell during one complete cycle of heating and cooling, together with the states in a typical sorption diagram. The total period tcycle is equally divided in four parts in which the cell is pressurized, delivering gas, depressurized and adsorbing gas. To pressurize the cell, it is heated until the desired pressure is obtained. A period of constant temperature will be needed if the second period with flow out of the cell is not yet reached. The pressure is kept constant during the next phase when gas flows out of the cell so that additional heating is required. To depressurize the cell and to generate a low-pressure gas flow into it, it is cooled passively to the ambient temperature TA by switching on the heat switch. In figure 6.3 three different possible curves are depicted for this passive cooling:

Chapter 6

158

1. The gas-gap heat switch is switched to a fixed but very low on-resistance and the cell is cooled rapidly to ambient temperature, within a period of ¼tcycle. As a consequence, the pressure also drops rapidly and, due to the check valve operation, gas flow into the cell will start as soon as the pressure drops below the low pressure of the former low pressure cell in the cycle. In order to synchronize the operation of the four cells, the moment of switching the heat switch to the ON-state should be timed accurately. This method of switching suffers from low pressure variations during cycling because the low pressure gas flow into the cell takes place at a constant temperature instead of a constant pressure.

2. The gas-gap heat switch is switched to a fixed but somewhat larger ON-resistance so that, at the end of the cooling period of ½tcycle, a temperature is reached close to ambient temperature. With this method, control of the starting point of low pressure flow into the cell is rather difficult. Low pressure variations are somewhat less compared to method 1 because the cell still cools during the adsorption phase.

3. This method assumes that the gas-gap resistance can freely be adjusted during the cool-down phase of the cycle. In that way, the temperature and pressure of the cell can be actively controlled by adjustment of the gas-gap resistance. Figure 6.3 illustrates a situation in which the cell is cooled and depressurized with a somewhat larger thermal resistance, and where further cool-down during gas flow into the cell occurs with a relatively small resistance to maintain a constant low pressure in the cell. A somewhat similar behavior can be obtained in method 2 by supplying simultaneously small amounts of heat to the cell, together with cooling of the cell via a fixed thermal resistance. Unfortunately, by supplying extra heat to the cell the COP is deteriorated.

The high and low pressures of the gas can be adjusted by controlling the compressor temperatures and input powers as described above. The cold stage only operates properly if these pressures are chosen as discussed in the parameter study of chapter 4. In other words, the gas pressures are fixed by the thermodynamic system requirements and should be independent of, for instance, the compressor size. The required mass flow is determined by the required cooling power via

coldcold hmP ∆⋅= & (6.1)

TH

TA

Tmin

pH

pL

flow

time

TH

Tmin

x

pHpLA B C D

A

B

C

D

13

2

1

32

out of cellinto cell

3

12

tcycle

Figure 6.3 Temperature and pressure development of one sorption cell during a complete cycle. Three different ways for passive cooling are depicted (see text).

Sorption compressor

159

where ∆hcold is the enthalpy difference that is available for cooling in the evaporator (∆h67 in figure 4.15). For a given pressure difference, this mass flow is entirely fixed by the flow restriction of the cold stage and in that respect also independent of the compressor. The compressor should just be able to supply the required mass flow at the required pressure difference. This mass flow is supplied by one cell and adsorbed by another cell during a period of tflow = ¼tcycle, or:

flow

nets

txm

m∆

=& (6.2)

where ∆xnet is the net amount of gas desorbed from the sorber cell per mass of sorber material during a complete flow period, see figure 4.2. For a certain constant mass flow m& , it follows that the time of flow of one cell scales proportionally with the sorber mass ms. As a consequence, the compressor cells can freely be scaled to small dimensions, until a size is reached where parasitic or dynamic effects start to deteriorate the compressor performance or where fabrication is not possible anymore. Examples of parasitic or dynamic effects are significant temperature profiles or pressure drops in the adsorption material.

The mass flow out of the cell and into the cell are assumed constant in figure 6.3, and independent of the type of cooling curve of the sorption cell (1, 2 or 3). This is because the mass flow is fixed by the pressure difference that is present over the flow restriction of the cold stage or, since the low pressure is much smaller than the high pressure, essentially by the high pressure (that is assumed constant in figure 6.3).

The required heat-switch ON-resistance is related to two different factors: the required

speed of cooling of the cell during depressurization and the maximum temperature difference that is allowed between the inside container and the heat sink during adsorption of the gas that flows into the cell. This temperature drop results from the heat of adsorption and it determines at the end of the adsorption phase the minimum temperature of the sorber material and, because of that, the amount of gas adsorbed. From the three cooling methods depicted in figure 6.3 and described above, method 1 requires the lowest thermal ON-resistance and requires, for the same OFF-resistance, the highest ON-OFF ratio. The required ON-resistances for the other two methods are of the same order of magnitude, but larger in value. An expression will be derived for the required ON-resistance of method 1.

During passive cooling of the cell, the temperature of the cell follows an exponential decrease towards the heat sink temperature TA:

τ/)()( tAHAcell eTTTtT −⋅−+= (6.3)

where τ = RHS,ONCcell is the RC-product of heat-switch resistance and sorption cell heat capacity. The cooling time can now be written as

cellONHScooling CRnnt ,⋅=⋅= τ (6.4)

where n determines how close TA is approached. For example, for n = 5, Tcell approaches TA within 1% of (TH – TA), which is a reasonable value. This cooling period must be synchronized with the other periods of the cycle, so that

cellONHScyclecyclecooling CRnttt ,41 4 ⋅≥⇒≤ (6.5)

Chapter 6

160

The complete cycle period can be related to the average compressor input power.* During operation of a sorption compressor with four cells, the total useful input power, Pcompr, is divided over the four cells, so that each cell is heated with ¼⋅Pcompr during the total cycle period, tcycle. This means that the amount of heat put in one cell during a full cycle equals:

cyclecomprcell tPQ 41= (6.6)

This heat is made up by the heat needed to warm the thermal capacity of the cell and the heat of desorption. Hence,

adsgrosscellcell qXTCQ ∆+∆= (6.7)

where ∆T = TH – Tmin is the temperature increase of the cell, ∆Xgross is the total amount of gas desorbed from the sorber surface and qads is the heat of adsorption. Concerning the ratio of the heat put in the thermal mass and the heat of adsorption, a distinction can be made between physical and chemical sorption. For a number of chemical hydrogen absorbers used in sorption compressors, the heat of absorption is of the same order of magnitude or much larger than the heat put in the thermal mass [6.2]. For physisorption compressors, however, the heat of adsorption is mostly much smaller than the heat stored in the thermal mass; a typical value for the fraction of these two for charcoal compressors is 10 – 20% (see section 4.4.5). If the heat of adsorption is neglected for physisorption compressors, a straightforward expression can be obtained for the heat-switch on-resistance. Eq. (6.7) then reduces to

TCQ cellcell ∆≈ (6.8)

and combining Equations (6.5), (6.6) and (6.8) yields for the on-resistance required to reach a certain value of n:

compr

ONHS nPT

R∆

≤, (6.9)

As can be seen, this required heat-switch on-resistance is independent of the compressor size or geometry, but instead mainly dependent on the compressor input power and the required cooling speed (i.e. the parameter n).

Under the assumption that the passive cooling of the sorption cell has reached an equilibrium temperature at the end of the cooling period ½⋅tcycle (at the end of phase D), the final temperature difference between the compressor cell and the heat sink is static and only proportional to the heat of adsorption, which can be expressed as:

adsads qmP &= (6.10)

Since the mass flow is related to the cooling power via Eq. (6.1), the temperature difference between the compressor and heat sink follows as:

cold

adscoldONHSadsONHSA h

qPRPRTT

∆==− ,,min (6.11)

The heat switch ON-resistance should be able to match both the required speed of cooling (Eq. (6.9)) and the maximum static temperature difference between the compressor cell and the heat sink at the end of the adsorption cycle (Eq. (6.11)). For the charcoal-ethylene compressor presented in section 4.7, a temperature increase of 2.5 K for Tmin causes a reduction in the

* The cycle period could also be related to Eq. (6.2), but this results in less convenient expressions.

Sorption compressor

161

COP of about 10%. If this 2.5 K is taken as the maximum value for Tmin – TA, then with Pcold = 0.195 W, qads = 827 J/g and ∆hcold = 390 J/g it follows from Eq. (6.11) that:

RHS,ON < 6.1 K/W (6.12) Next, with Pcompr = 5.7 W and ∆T = 300 K, it follows from Eq. (6.9) that n ≈ 8. These values for Tmin – TA and n are both acceptable.

The heat switch in the OFF-state should isolate the compressor cell during the heating part of the cycle. The heat conduction through the OFF-resistance during this period is a loss term, and should be minimized. If a linear temperature increase from Tmin to TH is assumed during the heating part (A and B in figure 6.3) and RHS,OFF is considered to be independent of the temperature, then the total average power loss for the four cells is given by:

OFFHSOFFHS

loss RT

RT

P,,

41

4∆

=∆

= (6.13)

Now the total input power equals Ptot = Pcompr + Ploss. The ratio of the loss term and the useful compressor input power can be expressed as χ = Ploss/Pcompr, so that RHS,OFF can be written as:

compr

OFFHS PT

Rχ

∆=, (6.14)

where χ should preferably be much smaller than unity. Apart from this RHS,OFF also an ON-OFF ratio can be defined, for instance by dividing Eq. (6.9) and (6.14), leading to

χ

ηn

R

R

ONHS

OFFHS ==,

, (6.15)

From this expression it can be seen that if, for example, the compressor cells should cool to TA within 1% of TH – TA (n = 5), and at most 10% of heat may be lost during the heating cycle (χ = 0.10), then the ON-OFF ratio should be at least 50. Such an ON-OFF ratio is feasible for a gas-gap heat switch, as was shown in chapter 5.

An interesting effect occurs when η = 1, which means that no thermal switch is present at all, but instead a fixed thermal resistance. If, for instance, n = 5 is chosen, it follows that χ = 5 and Ploss = 5⋅Pcompr. This means that, in principle, a sorption compressor can be operated without heat switch at all with the penalty of a dramatically reduced efficiency, in this example with about a factor of 5. Such losses might be reduced by using more than four sorption cells, so that the cooling period of one cell can be extended over a longer time:

cellONHScyclecyclecooling CRnm

mtt

mm

t ,33

⋅−

≥⇒−

≤ (6.16)

where m is the number of sorption cells (m ≥ 4). Instead of Eq. (6.6), the amount of heat put in one cell during a complete cycle becomes now:

cyclecomprcell tPm

Q1

= (6.17)

Using these expressions, Eq. (6.9) can be recalculated for m sorption cells, yielding:

compr

ONHS nPTm

R∆−

≤)3(

, (6.18)

Chapter 6

162

From this expression an ON-OFF ratio for m cells can be obtained similar to Eq. (6.15) for four cells:

)3(,

,

−==

mn

R

R

ONHS

OFFHS

χη (6.19)

If no heat switches are present then η = 1 and if, for instance, n = 5 and m = 6 is chosen, then χ = 1.67 is obtained instead of χ = 5 for four sorption cells. This means that with a few more than four sorption cells and a slightly higher input power, a sorption compressor can readily be operated without heat switches at all. For some applications this may be an attractive alternative, for instance in the case that no heat-switch alternatives are feasible, e.g. due to small dimensions, reliability issues or price.*

6.3 Design considerations and introductory experiments

6.3.1 Inner pressure cylinder

In this section, a number of issues are discussed that concern the design of the inner compressor cylinder. These include: material choice, fabrication of joints, and the choice of dimensions.

Criteria that play a role in selecting the compressor material are: 1) The material should be machinable in a normal workshop and it should be possible to make joints in a relatively easy way with other components, such as the thermocouple, the gas supply tube, the filter (that keeps the carbon particles inside the cylinder), etc. 2) The material should be resistant to hydrogen gas, which is used to switch the gas gap. 3) The heat capacity of the compressor cylinder reduces the compressor COP and should, therefore, be minimal (see the discussion in section 4.4.5). The first criterion forced a rapid decision towards the use of stainless steel 316. This material is easily available in a variety of shapes, it can easily be machined in the workshop, it is compatible with hydrogen, and it can be welded or brazed to other 316 components or even other types of stainless steel. The disadvantage of an intrinsic larger heat capacity (see table 4.3) was accepted in this initial development stadium of the compressor.

A combination of laser-welding and high-temperature brazing was selected for the assembly of the compressor components. Laser welding melts two metals together in a protective atmosphere. The equipment available at the university workshop [6.3] applies two 1064 nm lasers with a power of 300 W and 150 W. The piece of work can be positioned with an accuracy of less than 2 µm in a XY-table that also facilitates rotation. The minimum spot width is 25 µm. Because a minimum amount of heat is very locally supplied, the heat zone is just a few times the width of the weld. The smallest stainless steel thickness that can still properly be

* Notice that this ON-OFF ratio does not take into account the temperature difference due to the heat of adsorption. The purpose of increasing the number of compressor cells is to increase the required (fixed) heat switch resistance, see Eq. (6.18). As a consequence, the temperature difference due to the heat of adsorption will increase with an increase of the number of compressor cells, thus reducing the compressor COP and counteracting the advantage of the reduced heat losses – under the assumption that all adsorbed gas flows into one compressor cell. However, since more compressor cells are in the cooling phase, the gas may at a certain moment be adsorbed by more than one compressor cell, which subsequently reduces the influence of the increased heat switch resistance on the temperature difference due to the heat of adsorption.

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welded is about 100 µm. For that reason, high-temperature brazing was needed to make joints with the shielded thermocouples that were applied, which have a diameter of 250 µm and a shield thickness of about 40 µm. This brazing occurred with a Au-Ni alloy at 1040 °C under vacuum. Brazing was not an option for all joints because the brazing temperature of 1040 °C is not applied locally which would, therefore, result in unacceptable high temperatures of the activated carbon upon closure and brazing of the sorption cell. Moreover, brazing would fill the applied porous stainless steel filter with the liquid alloy due to capillary forces; this problem was observed experimentally.

The minimum compressor dimensions that can be obtained are fixed by fabrication issues. An important limitation in this respect is the desire to minimize the thermal mass of the compressor container relative to the thermal mass of the adsorption material to prevent a reduction of the (already limited) compressor COP. In other words: upon downscaling of a proper compressor design, the ratio of the compressor thermal mass to the sorber thermal mass should not increase significantly to facilitate that smaller construction. Eq. (4.20) gives the (minimum) required wall thickness for a cylinder that is pressurized with a maximum pressure pH. If a safety factor of four is assumed for σmax/σyield to account for the high number of repeated mechanical strainings of the cylinder [6.4], then for stainless steel 316 and pH = 20 bar it is found that dwall ≈ 0.01⋅Dcyl. The minimum wall thickness that can still be laser-welded is about 100 µm, so that Dcyl > 10 mm to maintain the optimized compressor COP. Apart from being a limit for welding, to our knowledge, 100 µm is also the smallest wall thickness for commercially available stainless steel tubes with diameters between 5 mm and 10 mm [6.5]. Although it was tempting to aim at a compressor with a diameter of 5 mm (and a length of 5 cm) with some sacrifice of the compressor COP, a diameter of 10 mm (and a length of 10 cm) was chosen because the fabrication of the end-caps and other components was considered to be very risky for a 5 mm compressor.

To verify the strength of laser-welded and brazed joints, pressure tests were carried out on two stainless steel 316 tubes with a diameter of 5 mm, a wall thickness of 200 µm and a length of 5 cm. The tubes were on one end closed with an end cap and on the other end connected to a 1/4 inch thick-walled gas tube and from there to a liquid-compressor. The joints on one tube were made by laser-welding, on the other by brazing. For both tubes the pressure was increased repeatedly to 300 bar without any visible change on the tubes. This pressure corresponds to a tensile stress of 375 MPa or 0.82⋅σyield. Further increase of the pressure to 450 bar caused yielding of the 5 mm tube, but the joints did not deform or crack. It was concluded that both laser-welding and brazing can properly be applied on thin-walled tubes to fabricate joints.

6.3.2 Support

A support construction is needed to position the inside compressor container in the outer cylinder, thus creating a gas gap. The following requirements can be formulated for this construction: 1) It should facilitate an accurate radial positioning, for instance within 50 µm to facilitate a gas gap of 300 µm. This positioning should preferably occur with a high mechanical radial stiffness to prevent a variation of the gap-width due to forces acting on the compressor cell. 2) It should facilitate a longitudinal movement of the inside container with respect to the outer cylinder. Such movement results from the thermal expansion of the inside container: the

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300 K temperature variation causes an expansion of 0.5% or 0.5 mm for a 10 cm long cell. 3) To prevent significant thermal conduction losses from the hot inside compressor cylinder to the outer heat sink, the thermal conduction of the support construction should be low. 4) The construction should facilitate easy assembling of the compressor.

A first design of the support was used to construct the set-up that was used for the gas gap characterization, see figure 5.10. It consists of a glass tube with an inner/outer diameter of 0.53/0.67 mm, respectively, that slides on one side in a hole in the radial center of the compressor cell and that is glued to a three-spoke wheel construction on the other side. With this construction, requirements 2 and 3 are met easily. However, proper radial positioning had to be obtained by careful positioning of the wheel-construction and subsequent tightening of the screws, which was a difficult task. Moreover, the radial stiffness of the construction was low.

The final design of the support construction consists of a 100 µm thick stainless steel wheel construction which holds the compressor cell in the center hole, see figure 6.4 (and the pictures in section 6.4). Fabrication is done by laser-cutting techniques, which guarantees a dimensional accuracy of less than 50 µm. The outer circle of the wheel fits accurately in the outer cylinder that is subsequently covered and welded by the closure. This construction fulfills all four requirements.

Figure 6.4 Photograph of the support structure that was used in the final compressor design.

6.3.3 Adsorption material

In section 4.4.1 and 4.4.5, four different activated carbons were compared, with a focus on the storage properties. In this section, the influence is investigated of the carbon particle size and packing characteristics on the pressure drop over the sorption bed, which results from the flow through the bed.

For proper operation, it is required that the pressure drop over the bed is very small compared to the absolute gas pressure. In this study, it is assumed that this pressure drop should be smaller than 1% of the lowest gas pressure (1 bar), so that ∆pmax = 103 Pa. To predict the pressure drop over the sorption bed, a model was used that was developed by Ergun and that is described by Beek [6.6]. The model is based on a calculation of the dissipated energy of flow around a bed of spheres with a uniform diameter. Because the carbon

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bed consists of non-spherical particles that have a certain size distribution instead of one fixed size, the model can only be used as an approximation for the pressure drop over a carbon bed. Experiments were done to investigate the accuracy of the model for this situation; these experiments are described later in this section. For laminar flow, the hydraulic resistance through a particle bed can be written as [6.6]:

3

2

2

)1(1170

εε

µ−

=∆

=pc

hdA

lVp

R&

(6.20)

where V& is the volume flow, l is the length and Ac the cross sectional area of the bed, dp is the diameter of the particles, and ε is the porosity or volume fraction of the voids between the particles. For beds of spheres, in practice 0.35 < ε < 0.45; for particle beds with a wide particle size distribution, also smaller values of the porosity can be obtained (due to small particles that fill the voids between the larger particles). Eq. (6.20) was derived under the assumption that the particle diameter is considerably smaller than the diameter of the bed (< 1/20). Eq. (6.20) was used to calculate the plot depicted in figure 6.5, which shows the flow restriction as a function of the particle diameter for different values of the porosity ε.

1.0E+01

1.0E+02

1.0E+03

1.0E+04

1.0E+05

1.0E+06

10 100 1000particle size (micrometer)

flow

resi

stan

ce(P

a-s/

ml)

porosity = 0.150.200.250.300.350.40

Rh,max

Figure 6.5 Flow restriction of a particle bed as a function of the particle diameter for different values of the porosity. The plots were calculated for ethylene gas flowing at 1 bar through a bed with a length of 10 cm and a diameter of 0.94 cm.

The maximum acceptable hydraulic resistance of the bed can be calculated from the

specified maximum pressure drop over the bed in combination with the specified volume flow:

Vp

Rh &max

max, 2∆

= (6.21)

The factor 2 in this expression results from the fact that, in reality, the flow is not passing through the bed, but instead is generated or adsorbed uniformly in the bed so that the volume flow linearly increases towards the exit of the cell. A 0.5 mg/s ethylene mass flow at 1 bar

corresponds to V& = 0.42 ml/s, so that with ∆pmax = 103 Pa the maximum hydraulic resistance is found as: Rh,max = 4.5⋅103 Pa-s/ml.

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Figure 6.6 shows the stainless steel cylinder that was designed to measure the pressure drop over particle beds. It has the same length and diameter as the sorption compressor (l = 10 cm and Dinner = 0.94 cm). To measure the pressure drop over a particle bed, the cylinder was placed vertically with the filter at the bottom, it was filled with the activated carbon and closed with the cover at the top. Next, a controlled nitrogen mass flow was forced through the bed and the pressure drop was measured with a differential pressure transducer. Because the 2 µm filter has a significant flow resistance as well, this resistance was first characterized separately without particles in the tube. Figure 6.7 shows the pressure drop as a function of the volume flow, which was measured for a number of absolute gas pressures between 1 and 5 bar. From the measurements, a hydraulic flow resistance of 1.76⋅103 Pa-s/ml follows for the filter (which corresponds to a flow resistance of 1.01⋅103 Pa-s/ml for ethylene gas).

0

2000

4000

6000

8000

10000

0 0.2 0.4 0.6 0.8 1volume flow (ml/s)

pres

sure

dro

p (P

a)

filterMaxsorb, 17.4 micron (average)Maxsorb, 105-210 micronMaxsorb, >210 micron

Figure 6.7 Measurements of the pressure drop as a function of the volume flow for a stainless steel sintered filter, and three batches Maxsorb carbon with different particle sizes.

The hydraulic resistance was measured for the three batches of activated carbon that are

listed in table 6.1. The first batch consisted of very finely powdered Maxsorb carbon with an average particle diameter of 17.4 µm. The second and third batch were obtained from another stock of Maxsorb carbon, which originally had a very wide particle size distribution with an

sintered filter, 2 mµ

flow direction

Figure 6.6 Stainless steel cylinder that was made to measure the pressure drop over the sorption beds.

Table 6.1 Properties of the three batches Maxsorb carbon that were used to measure the flow resistance. Batch/experiment 1 2 3 type of activated carbon Maxsorb

(A, lot no. 92-11-B) Maxsorb (MSC-30, lot no. 98-05-61)

Maxsorb (MSC-30, lot no. 98-05-61)

particle size distribution unknown, fine powder 105-210 µm 210 µm ~ 1 mm apparent density 0.30 g/ml 0.27 g/ml 0.27 g/ml average particle diameter 17.4 µm 158 µm ~ 400 µm porosity 0.30 0.37 0.37 calculated resistance (Eq. (6.20)) 2.64⋅105 Pa-s/ml 1.38⋅103 Pa-s/ml 215 Pa-s/ml measured resistance (after correction for the filter)

1.87⋅105 Pa-s/ml 1.45⋅103 Pa-s/ml 419 Pa-s/ml

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average of 100 µm. It was filtered in the following size distributions: 0 – 20 µm, 20 – 32, 32 – 45, 45 – 63, 63 – 80, 80 – 105, 105 – 210 and particles larger than 210 µm (the largest particles were about 1 mm). The batches consisting of 105 – 210 µm and 210 ~ 1000 µm particles were used for the second and third measurement. The pressure drop was measured for a number of nitrogen flows between 0 and 1.25 mg/s, at absolute gas pressures between 1 and 5 bar; the results are included in figure 6.7. The hydraulic resistance of a particle bed is obtained by subtracting the hydraulic resistance of the filter from the measured total hydraulic resistance of the bed plus filter; the values are included in table 6.1.

To be able to compare the measured flow resistances with Eq. (6.20), the porosity of the three batches needs to be estimated. Table 4.2 lists for Maxsorb a volume fraction of 30% for a combination of the void volume (porosity) and macro pores, at an apparent density of 0.30 g/ml. According to Otawa [6.7], the macro pore density is very low for Maxsorb and it can, therefore, be neglected relative to the void volume. This results in ε ≈ 0.3 for the first batch with an apparent density of 0.30 g/ml. For the lower apparent density of the other two batches, the porosity can be calculated using the following expression:

poresmesoporesmicrosolid fff −−−= 1ε (6.22)

where the solid fraction can be calculated from the apparent density (fsolid = 0.27/2.2 = 0.123), and the micro and meso pore fractions from a downscaling of the original fractions with the ratio of the apparent densities (fmicro pores = 0.12⋅0.27/0.3 = 0.108 and fmeso pores = 0.444⋅0.27/0.3 = 0.400). This results in ε = 0.37 for the two batches.

Using the listed porosities and particle diameters, the flow resistances were calculated for the three sorption beds. From the results it can be concluded that the measured and calculated flow restrictions are very similar; a maximum deviation is found for the third batch. This could be caused by a somewhat smaller average particle size than the listed 400 µm. Anyhow, it was concluded that the model was accurate enough to estimate the minimum particle size for application in the sorption compressor to obtain a certain maximum flow resistance. To obtain Rh < 4.5⋅103 Pa-s/ml, it was found that dp > 100 µm for ε = 0.30 or dp > 70 µm for ε = 0.37. The filtered Maxsorb batch with particle sizes larger than 210 µm was selected for application in the sorption compressor.

From figure 6.5a it can furthermore be concluded that very large flow restrictions will be present in the solid Saran carbon (ε < 0.07) and composite carbons (ε < 0.15) that are mentioned in table 4.2, if these porosities are uniformly distributed through the solid (i.e. when a very small ‘particle size’ must be assumed in figure 6.5a). Because this is the case for these materials, special measures must be taken when these carbons are applied in sorption compressors. Such measures may consist of drilling holes in the longitudinal direction or the use of many small separated carbon parts that are assembled together with open spaces in between.

Eq. (6.20) can also be used to assess the influence of downscaling of the compressor cell on the pressure drop over the carbon bed. It follows that the hydraulic resistance scales with β -1 if the compressor length and diameter are both scaled with β and for a constant particle diameter. Alternatively, the minimum compressor dimensions can be estimated at which the hydraulic resistance equals the specified maximum resistance. For an ethylene flow of 0.5 mg/s, dp = 158 µm (batch 2) and a compressor length/diameter ratio of 10, this occurs at a

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compressor length of 1.6 cm and an (inner) diameter of 1.6 mm. In conclusion, for this mass flow the pressure drop over the carbon bed is not a limiting factor in downscaling of the compressor.

6.3.4 Heater

The heater of the sorption compressor can either be located on the wall of the inside container (in the gas-gap space), or somewhere inside this container. Heater requirements that are independent of this location are: 1) The heater should be resistant to temperatures of at least 600 K. 2) It should supply a heat load uniformly distributed along the length of the cylinder. 3) To prevent a reduction of the compressor COP, the heater thermal mass should be small compared to the total thermal mass of the inside container (see also Eq. (4.18)). If the heater is located inside the container, additional heater requirements are: 4) The heater resistance wire should be electrically isolated from the charcoal adsorption material, which is a good electrical conductor. 5) It should connect to the outside world via electrical feedthroughs in the inner cylinder, gas gap and outer cylinder. If the heater is located on the outside wall of the container, additional requirements are: 4) Since the heater is now operating in the vacuum of the gas gap, good thermal conduction must be guaranteed from the heater to the cylinder by proper clamping or adhesion of the heater to the cylinder wall. 5) Proper electrical isolation should be provided between the heater resistance material and the stainless steel cylinder. 6) The heater or the isolation material may not show significant outgassing since it is located in the closed vacuum space of the gas-gap heat switch. 7) It should connect to the outside world via feedthroughs in the gas gap and outer cylinder.

Based on these requirements, five different heater solutions were compared; three heaters for application on the outside wall and two heaters which can either be located inside or on the outside wall of the container. Each of the five solutions is briefly discussed below. In addition, experiments on three of the five heater concepts are presented; the other two heaters were commercially available.

Nickel-Chromium heater wire on top of an isolation layer. A thin NiCr heater wire can be

wrapped around the compressor cell, separated by some kind of isolation layer. Suitable thin isolation layers are mostly fabricated of a synthetic material (e.g. Kapton, Teflon, Polyimide) and will start to carbonize at 600 K and/or show significant outgassing behavior. For that reason, this type of heater is not suitable for application in combination with a closed gas-gap heat switch. It was only used as a temporarily heater solution in combination with the first prototype of the sorption compressor, which contained a gas gap that was not a closed system (but instead connected to a vacuum pump and gas supply). Figure 6.8 in section 6.4 shows a picture of this custom made heater. The following steps were made to fabricate it: 1) A thin film of liquid Polyimide [6.8] was applied using a brush, and subsequently cured in air at 600 K. 2) A second layer of Polyimide was applied in the same way and simultaneously a 0.8 x 0.1 mm NiCr heater wire was tightly wrapped around the cylinder. Again, the Polyimide was cured at 600 K. 3) In the same way, a third layer of Polyimide was applied. Electrical connections were made via a Teflon isolated copper wire, that was welded to the heater wire. Vacuum feedthroughs were sealed with Torr Seal. This heater was applied successfully in the compressor cells that were used in the experiments described in section 6.5.

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Kapton. Kapton insulated heaters are commercially available in a variety of shapes, and

typically consist of a 10 µm thick etched heater element encapsulated between two layers of 50 µm thick Kapton [6.9]. Such heaters could be fitted around the compressor cell. However, the foil needs to be clamped tightly on the wall, which is difficult or impossible to accomplish. Moreover, the required compressor temperatures exceed the specified maximum temperature of the heaters (~ 500 K). Also, outgassing of the Kapton will probably contaminate the gas gap. All together, flexible Kapton heaters were rejected as heater alternative for the compressor.

Thin film heater. A thin film heater can be fabricated by patterning a thin film metal layer,

with a thickness up to a few micrometers, that is deposited on top of a smooth isolation layer. Theoretically, such type of heater could be fabricated on the outside wall of the sorber container. If it can be fabricated, it will most likely fulfill all requirements. However, for proper fabrication a number of critical problems must be solved: 1) A uniform isolation layer must be deposited around the stainless steel cylinder that is able to survive repetitive thermal cycling of the compressor cell between 300 K and 600 K and that provides electrical isolation over the complete surface (to prevent electrical shorts of the heater). Possible isolation layers are: SiO2, Si3N4, AlO2, etc.; 2) A thin film metal layer must be deposited and patterned around the compressor cell; 3) Electrical connections must be made to the thin film. Most likely, mechanical clamping (or screwing) is required for this since soldering is difficult because of the high compressor operating temperatures and the requirement of repeated thermal cycling.

To investigate the feasibility of a thin film heater around the compressor cell, the problem was first investigated on a two-dimensional scale. Stainless steel ‘wafers’ were cut from chemically polished stainless steel plates using laser-cutting techniques [6.3]. The wafers measured 3” in diameter and had a thickness of 500 µm, and could thus be processed in the equipment of the MESA+ cleanroom as if they were standard 3” silicon wafers. A number of potential isolation layers were deposited using PECVD techniques: 500 nm SiO2, 500 nm Si3N4 and a stack of 100 nm SiO2 / 400 nm Si3N4 / 100 nm SiO2. All layers were deposited at 450 °C and showed proper adhesion after cooling of the substrate to ambient temperature. 400 nm platinum was sputtered on top of the isolation layers, with a 10 nm chromium adhesion layer in between. Heaters of 1 x 4 cm were patterned using lift-off techniques. Measurement of the heater resistances and the resistances between the heaters and the substrates showed that some heaters had one or more shorts to the substrate. The isolation layer consisting of the stack of SiO2/Si3N4/SiO2 gave the best results: 3 of the 5 produced heaters were isolated from the substrate and had a proper resistance. Both for the SiO2 and Si3N4 isolation layers, only one heater was isolated from the substrate. Eight small test structures with a surface area of 5 x 6 mm were included on the wafers; these structures were all isolated from the three substrates. Apparently, pinholes are present in the isolation layers, with the lowest density for the stack of SiO2/Si3N4/SiO2. These pinholes may be caused by local roughness of the stainless steel surface or by the PECVD process itself. The breakthrough voltage was characterized for the properly isolated heaters. For the SiO2 and Si3N4 isolation layers, voltage breakthrough started around 20 and 50 V. For the stack of SiO2/Si3N4/SiO2, no voltage breakthrough was observed for voltages up to 100 V. Repeated heating and cooling was done for the properly

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isolated heaters on the SiO2/Si3N4/SiO2 layer; no change in properties was observed. At this point, the experiment on the thin film heaters was stopped. It was concluded that a thin film heater on stainless steel substrates might be feasible, but much more development would be required to obtain a properly isolated thin film heater around the sorber container.

Thermocoax. This type of heater is commercially available [6.10] and consists of one or two

resistance wires encapsulated by a metal sheath, electrically isolated from one another and from the sheath by means of a highly compacted ceramic (MgO) powder. It is available with outer diameters ranging from 0.5 to several millimeters and can be brazed to other stainless steel components. If the 0.5 mm diameter heater is applied, then it fulfills all requirements for application inside or on the outer surface of the sorber container. It can be spiralled inside the compressor or spiralled and brazed on the outside of the cylinder. However, application on the outer surface makes it impossible to create a narrow gas gap of a few hundred micrometers anymore. Feedthroughs can be made by brazing.

Stainless steel sheathed thermocouple. Sheathed thermocouple wire is commercially

available [6.9] and is constructed in a similar way as the Thermocoax heaters: two thin (thermocouple) wires are contained in a metal sheath, and are electrically isolated from one another and the sheath by a ceramic powder. It is available as a type J, K, E, T and N thermocouple, with outer diameters ranging from a tiny 250 µm to several millimeters. Because it is available in a more suitable smaller diameter than the Thermocoax heater, it was proposed to more or less misuse such thermocouple as a heating element by supplying current through the thermocouple wires. Apart from satisfying all requirements, application of this type of heater inside the sorber container has two additional advantages: 1) With some simple electronics connected to it, the same element can also (sequentially in time) be used as a thermocouple to measure the temperature of the sorption cell; 2) The small diameter of the thermocouple facilitates a feedthrough through the gas supply tube of the compressor cell, if it is assumed that this tube is fabricated with an inner diameter larger than roughly 0.5 mm. In this way, the need of heater (and thermocouple) feedthroughs through the inner and outer cylinder is dropped, or in other words: the feedthrough of the gas tube now simultaneously performs three functions. Separation of the thermocouple and gas supply tube can be facilitated outside the compressor cell. A small disadvantage of this type of heater is that some heating power is dissipated outside the inner sorption container, since power is dissipated along the complete length of the sheathed thermocouple wire (i.e. starting from the point outside the compressor cell where the electrical connection is made to the sheathed thermocouple wire).

Initial experiments performed on a type E thermocouple showed that indeed very large powers could be dissipated in the thermocouple wires, without any significant degradation of the thermocouple calibration. Repeated thermal cycling, however, could result in metal fatigue and cracking of the thermocouple materials because of the repetitive straining of the thin wires in combination with the significant current densities that are present. Strain is induced in the wires because the wires and the sheath are made of different materials, resulting in thermal expansion differences upon thermal cycling. If it is assumed that the cross sectional area of the thermocouple wires is much smaller than the cross sectional area of the sheath and that the

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thermal expansion coefficients are constant over the temperature range, then the stress induced in one wire can be approximated by [6.11]:

wirewiresheathwirewirewire ETE ∆−≈≈ )( ααεσ (6.23)

where εwire is the strain induced in the wire, αsheath and αwire are the thermal expansion coefficients of the thermocouple sheath and wire, respectively, and Ewire is the Young’s modulus of the wire. Table 6.2 shows the mechanical properties of some thermocouple materials, as well as the calculated maximum stresses in the wires. In the last column these stresses are divided by the specified maximum tensile stresses.

Table 6.2 Mechanical properties of four materials that are used in thermocouples, as well as the maximum stresses induced in these materials if they are packaged in a stainless steel sheath (α = 1.67⋅10-5 K-1) and heated with ∆T = 300 K. All thermal expansion coefficients are taken at 450 K. Material properties for the N type thermocouple (Nicrosil and Nisil) could not be found.

material thermocouple type α (K-1) Ey (GPa) σt (MPa) σwire,max (MPa) σwire,max/σt

Alumel K- 1.44⋅10-5 180 550 124 0.23 Chromel K+, E+ 1.47⋅10-5 186 620 112 0.18

Constantan J-, E- 1.49⋅10-5 162 400 87 0.22 Iron J+ 1.37⋅10-5 170 180 153 0.85

To test the influence of repeated thermal cycling of the thermocouples, four different

thermocouples (type J, K, E and N) were tested in a long duration repeated thermal cycling experiment. The current through the four thermocouples was sequentially switched on and off, with a cycle period of 40 seconds. During the ‘ON’ state, the voltage over and the current through the four thermocouples was measured, and the associated powers and resistances were calculated. During the ‘OFF’ state, the thermocouple voltage was measured and the associated junction temperature was calculated. To be able to compare the four temperature measurements with each other, the four thermocouple junctions were thermally connected to each other. The length of the thermocouples was 50 cm (about the same length that would be applied in a compressor cell), and the initially measured resistances were as follows: RJ = 249 Ω, RK = 352 Ω, RE = 379 Ω and RN = 383 Ω. In the ‘ON’ state, a voltage of 70 V was supplied, resulting in input powers between 13 W and 20 W (which is significantly larger than the roughly 5 W of input power required for one compressor cell). These powers were sufficient to reach temperatures in air above 300 °C. During the experiment, the obtained maximum temperatures reduced slightly, which was attributed to an increased emissivity of the sheath due to oxidation of the outer surface. To compensate for this, the voltage was increased to 100 V, resulting in input powers between 26 W and 40 W. A PC with a National Instruments Data Acquisition Card [6.12] was used to measure and control the relevant parameters. A custom-written Labview [6.12] program was used to control, process, visualize and store the measurement data.

The type N thermocouple suddenly stopped operating after 3800 cycles; up to that moment all thermocouples performed properly and no significant changes were observed. An infinite resistance was measured for this thermocouple. The type J thermocouple started showing defects after 19000 cycles, which could be observed as short interruptions of the current. After a while, a permanent infinite resistance was measured for this thermocouple. From table 6.2, it can be concluded that the stress induced in the iron wire is close to the maximum tensile stress,

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which could explain the failure of the type J thermocouple. The rapid failure of the type N thermocouple was not expected, given the initial proper operation of the other thermocouples. Verification afterwards revealed an improper connection between the thermocouple and the connector. The type E and K thermocouples operated for 2⋅105 cycles, until the experiment was stopped. After the experiment, the temperature calibration was checked; for the type E thermocouple it was still accurate within 0.5% and for the type K thermocouple within 1.5%. This result shows that these thermocouples can simultaneously be used as heater and thermocouple without serious degradation of the thermocouple calibration.

The type E thermocouple was selected as a heater for application in the sorption compressor. Four type E thermocouples were subsequently tested in another long duration experiment to investigate the statistical chance of failure in more detail. After 2.5⋅105 cycles, all thermocouples were still operating properly, including the type E thermocouple that made already 2⋅105 cycles in the previous experiment.

6.4 Design and fabrication

Two versions of the sorption compressor were fabricated. The first version was designed for use with a heater around the compressor cell and is depicted in figure 6.8. Two of these compressor cells were used in the experiments described in section 6.5. Based on the experience obtained with this compressor cell and the introduction of the thermocouple-heater that was described in section 6.3.4, the second version depicted in figure 6.9 was designed and fabricated. This compressor has not yet been tested.

The fabrication sequence of the first cell was as follows: 1. All individual components were fabricated using precision engineering tools. 2. The stainless steel 2 µm sintered filter, the thermocouple feedthrough and the end-cap

were laser-welded. The thermocouple feedthrough is required because the sintered filter

1

1

Filter 2 micrometer

10 c

m

10 mm

cross section

sintered filter

thermocouple

activated carbon

gas supply tube

suspension of inner cell

inner cylinder (150 mwall thickness)

µ

gas-gap heat switch

= weld

(a)

Figure 6.8 (a) Cross sectional drawing of the first version of the sorption compressor cell. (b) Close-up photograph of the NiCr-heater. (c) Elements of the compressor cell prior to assembly.

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cannot be brazed and the thermocouple cannot be laser-welded. 3. The gas supply tube and the thermocouple were brazed to the end-cap assembly. 4. The end-cap assembly was laser-welded to the prepared compressor cylinder. 5. After thorough cleaning, the cylinder was filled with the adsorption material and the

bottom end-cap was laser-welded to the cylinder. 6. The Polyimide isolation layer with the NiCr heater was applied on the outer surface using

the procedure that is described in section 6.3.4. 7. The inner surface of the outer cylinder was milled and honed to obtain a smooth surface.

Next, a thin gold layer was plated on the surface to reduce the emissivity. This reduces the radiation heat losses during the heating phase of the sorption compressor to small values.

8. Finally, the inside container was positioned in the outer cylinder using the support structure, and the end-caps were glued to the outer cylinder. Glue was used instead of welding to enable disassembling of the cylinder in case of problems.

The fabrication sequence of the second cell is similar to that of the first cell. Apart from the thermocouple-heater, another change in the second design is that the gas supply tube now connects at the top side of the end-cap. There are two reasons for this. Firstly, sliding of the

sintered filter

thermocouple/heater

activated carbon

support for thermocouple

gas supply tube

suspension of inner cell

ZrNi thin-film hydrogenactuator

10

cm

10 mm

‘splitter’ of gas supply tubeand thermocouple

inner cylinder (150 mwall thickness)

µ

gas-gap heat switch

cro

ss s

ect

ion

(a)

Figure 6.9 (a) Cross sectional drawing of the second version of the sorption compressor cell. (b) Close-up photograph of the end-cap with sintered filter, thermocouple-heater, support, etc. (c) Elements of a sorption compressor cell. (d) Close-up photograph of the end-cap prior to the final welding.

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174

thermocouple through the tube was impossible in the first tightly coiled tube design. Secondly, a complete circular weld of the end-cap in the first design was impossible because of the presence of the gas supply tube at the side, which increased the chance of a bad weld. The 2 cm long extension of the top end-cap is required to reduce the thermal conduction losses through the longer gas supply tube. Furthermore, the lower end-cap of the outer cylinder can be supplied with the thin film ZrNi hydrogen actuator that was discussed in section 5.4.3, and that can be used to control the hydrogen gas pressure in the gas gap. An additional copper thin gas tube is required (not drawn) to evacuate the gap, fill it with hydrogen and permanently seal the gas gap by squeezing the tube.

With the introduction of the thermocouple heater and with the experience gained in the fabrication of these two versions of the cells, it seems possible to fabricate an even smaller compressor cell, for instance with a diameter of 5 mm and a length of 5 cm.

6.5 Experiments

To study the behavior of the sorption compressor cells and to compare it with the developed models, cycling experiments were carried out with a combination of two compressor cells. Figure 6.10 shows the experimental set-up that is designed to operate the two cells through ad- and desorption cycles as depicted in figure 6.3, where the two cells are 180 degrees out of phase. The metering valve was used to create the desired flow restriction and the active valve is used to start and stop the flow at the beginning and end of the flow period. The flow sensor is applied to measure the flow in one direction (from cell 1 to 2); in the opposite direction the flow can normally pass but no flow measurement can be taken. The gas-gap heat switch was operated with a combination of a nitrogen gas bottle and a vacuum pump that were connected to the gas gap via active valves. This system replaces the thin film ZrNi hydrogen actuator that was not yet available at the moment of testing. The ambient heat sink temperature was maintained by a small PC-fan mounted on top of a finned heat sink. A PC with a National Instruments Data Acquisition Card [6.12] was used to measure the following parameters: the electrical input powers, temperatures and pressures of the two sorption cells, the pressures in the two gas-gap heat switches, and the mass flow from cell one to two. To run the experiment automatically, the data acquisition system could control the following parameters: the input powers of the two cells, the active valve between the two cells that

mp2p1

gassupply

pump

compressor cell

valve

metering valve

safety valvepressure sensor

flow sensor T2T1

P2P1

Tambient

heater power

temp.

gas gap

gas-gapcontrol

Figure 6.10 Measurement set-up for flow tests between two sorption compressor cells.

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175

controls the mass flow period, and the active valves that control the pressure in the two gas-gap heat switches. A custom-written Labview [6.12] program was used to process, visualize and store the measurement data. An ethylene gas supply system and a vacuum pump were connected to the system via two valves; in this way the system could be pumped and purged before filling with ethylene gas. Care was taken in minimizing the dead volumes of the system because dead volumes deteriorate the compressor performance (see section 4.4.5). However, the active valve and the mass flow sensor still contributed significantly to the dead volume: 30% and 50% of the sorption cell volume, respectively. In a real sorption compressor these components are not present, and a much better performance can be expected.

Before conducting flow experiments, the behavior of the gas-gap heat switch was characterized. With a vacuum present in the gas gap, the residual thermal resistance was measured as 184.8 K/W (for TH = 523 K) and with 2 mbar nitrogen gas present, the thermal resistance was 13.7 K/W. This results in a limited ON-OFF ratio of 13.5. This low ON-OFF ratio is mainly caused by the limited ON-resistance that can be obtained with nitrogen gas, which was used in these initial experiments. Replacing nitrogen with hydrogen gas would reduce the ON-resistance with a factor of 7, and increase the ON-OFF ratio to 95. Anyhow, this ON-resistance was suitable to perform the initial flow-experiments. The rather low OFF-resistance causes approximately 30% extra input power losses for a compressor input power of 5.7 W (in four cells), see Eq. (6.14). Resistance values in between the minimum and maximum could be obtained by variation of the gas pressure, as described in section 5.3.

Figure 6.11 shows a typical measurement of the temperatures and pressures in the two cells. Also depicted are the state of the active valve between the cells and the mass flow from cell 1 to 2. The measurement clearly shows the alternating periods of the two cells. The phases A-D of figure 6.3 are indicated in figure 6.11 on the pressure-curve of cell 2. The Labview control software switches from phase A to B when the high pressure of cell 1 is reached and from phase B to C when the maximum temperature is reached; the same holds for the transitions C-D and D-A, but then the pressure and temperature of cell 2 are used. The constant high pressure during phase B and D was adjusted by controlling the input power of the accompanying sorption cell. Although a very simple ON/OFF controller was used with a time

Figure 6.11 Typical measurement results.

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176

constant of 1 second, the pressure could be controlled very accurately, within 20 mbar. This is explained by the rapid transfer of heat input to the desorption of gas. Also the low pressure is rather constant during adsorption of gas in the cell. This was obtained by a properly chosen gas-gap conduction during the adsorption phase, as was discussed in section 6.2. Furthermore, the sudden pressure drop and the pressure peak of cell 1 after opening of the active valve are caused by the dead volume of the active valve. This same dead volume is the reason that a mass flow is present in the period that the active valve is closed.

From the results in figure 6.11, it follows that the pressure was cycled between 2 and 15 bar instead of the required 1 and 20 bar. This limited pressure ratio is essentially caused by the influence of two parameters that were different in the experiment than was assumed in the model in section 4.4.5. Firstly, it was decided not to operate the NiCr heater above 200 °C (473 K) because there was a risk that the Polyimide layer would decompose or cause electrical breakthrough at higher temperatures, which would make it impossible to carry out the planned long-duration experiment. As can be seen from the plot in figure 4.8a, a reduction of the compressor high temperature from 600 K to below 500 K causes a dramatic reduction of the maximum pressures that can be reached (from 34 to below 18 bar). Secondly, the void volume of the components in the measurement set-up causes a further reduction of the high pressure that can be obtained. In fact, the obtained pressures and mass flows correspond closely to the modelled values, which is illustrated in the plot of figure 6.12. This plot is similar to figure 4.8a, but it is now calculated for the increased void volume of the system. To obtain a measurement point, the high pressure was controlled at the desired value and the total amount of gas that flowed from cell 1 to 2 was measured. It follows that the measured amount of gas that can be produced is about 10% smaller than the calculated. This difference is most likely caused by a difference between the adsorption data of ethylene and the used adsorption data of xenon. In a later experiment, where the compressor high temperature was increased to 300 °C (573 K), the pressure could be cycled from 1 to 15 bar. A further increase of the high temperature and a reduction of the void volume is expected to result in the required pressure cycling between 1 and 20 bar.

To investigate whether the repeated pressure and temperature variation of the compressor cells would result in possible malfunction, the described cycling experiment was continued for

0

0.05

0.1

0.15

0 5 10 15 20pH (bar)

x net

(g/

g)

Figure 6.12 Comparison between the calculated and measured values of the net amount of desorbed gas from the compressor cell, ∆xnet, as a function of the high pressure. This plot is calculated for the increased dead volume of the experimental set-up. Further assumptions: TL = 300 K, pL = 1 bar, TH = 500 K.

Sorption compressor

177

4.5 months, resulting in about 104 complete compressor cycles. No malfunction occurred, except for a temporary strong reduction of the flow after 2100 cycles, which lasted for about 200 cycles and after which normal flow values were observed again. This temporary flow reduction could only be explained by some kind of clogging mechanism between cell 2 and the metering valve. A possible explanation is clogging of the porous sintered filter with microscopic carbon particles – although the compressor cells were positioned vertically with the filter located at the topside. Moreover, no explanation was found for the fact that proper operation was obtained after this supposed clogging.

6.6 Conclusions

A sorption compressor cell with integrated gas-gap heat switch was developed, built and successfully tested. For proper operation, the sorption cell should be heated uniformly with an integrated heater, and be cooled uniformly and passively through the gas-gap to a fixed heat sink temperature. For a certain specified mass flow, the compressor cycle time scales proportionally with the compressor size. This size can be scaled down as long as: 1) no significant temperature profiles develop within the components; 2) no significant pressure drops develop within the adsorption material and 3) the cell can be fabricated without significantly increasing the ratio of the cylinder thermal mass to the adsorbent thermal mass. For the specified ethylene mass flow of 0.5 mg/s and compressor input power of 5.7 W, fabrication issues limited miniaturization to a cylinder diameter of 1 cm (and a length of 10 cm). Further miniaturization to a diameter of 5 mm (and a length of 5 cm) seems possible, but with some sacrifice of the compressor efficiency.

The required ON-state thermal resistance is determined by the need to cool the compressor cell within a certain part of the cycle period to the heat sink temperature. The required OFF-state thermal resistance is determined by the maximum thermal losses that are allowed when the compressor cell is heated to a high temperature. As a consequence, a sorption compressor cell can also be operated with a fixed thermal resistance between the inner compressor cell and the heat sink, with the penalty of a reduced compressor efficiency. Adding more cells to such a system reduces this penalty.

Different heater solutions were experimentally compared, leading to a solution in which a shielded thermocouple is simultaneously used as heater and as thermometer. This thermocouple is located inside the inner sorption compressor cylinder. Experiments showed that such a heater endures repetitive thermal cycling (>2.5⋅105 times) without significant deterioration of the thermocouple calibration.

Experiments on the fabricated compressor cells showed that pressure differences can be realized that are close to the modelled values. The required pressure ratio could not be reached because of extra dead volumes in the experimental set-up, but for a complete compressor with four cells these volumes are not present and it is expected that the required pressure ratio can be produced with a proper flow capacity. Two compressor cells were cyclically operated for 104 cycles, without an observed degradation of the performance. However, after 2100 cycles a temporary reduction of the flow occurred, which could not be explained properly. Further effort is required to finish the complete sorption compressor with four cells.

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6.7 References [6.1] S.A.J. Huinink, J.F. Burger, H.J. Holland, E.G. van der Sar, H.G.E. Gardeniers, H.J.M. ter Brake, H.

Rogalla, Experiments on a charcoal/nitrogen sorption compressor and model considerations, Cryocoolers 9, Plenum Press, New York (1996).

[6.2] G.D. Sandrock and E.L. Huston, How metals store hydrogen, CHEMTECH, dec. (1981), pp. 754. [6.3] Applied Physics Precision Engineering Workshop (FFW), University of Twente, The Netherlands,

www.tn.utwente.nl/ffw/Laser/Laser.htm. [6.4] J.M. Gere and S.P. Timoshenko, Mechanics of materials, PWS Publishers (1985). [6.5] Le Guellec, Zone Industrielle de Pouldavid, 29177 Douarnenez, Cedex, France, www.leguellec.com. [6.6] W.J. Beek and K.M.K. Muttzall, Transport Phenomena, John Wiley and Sons, London (1975). [6.7] T. Otowa, R. Tanibata and M. Itoh, Production and adsorption characteristics of MAXSORB: high-

surface-area active carbon, Gas separation & Purification, vol. 7, no. 7 (1993), pp. 241. [6.8] Supelco/Sigma-Aldrich Corp., Bellefonte, PA, USA. [6.9] Omega Engineering, Inc., One Omega Drive, Stamford, Connecticut 06907-0047, USA,

www.omega.com. [6.10] Thermocoax Snc, Bp 26 Athis de l'Orne, 61438 Flers Cedex, France, www.thermocoax.com. [6.11] J.F. Burger, Onderzoek naar de invloed van decoupling zones op stress van thermo-elastisch belaste

nitride membranen, 250-hours assignment, University of Twente, The Netherlands (1993). [6.12] National Instruments, Inc., 6504 Bridge Point Parkway, Austin, TX 78730-5039, USA,

www.natinst.com.

179

7 High pressure check valve unit

Chapter 7

High pressure check valve unit

This chapter presents the design and operation of a check valve with integrated filter that was tested for gas pressures up to 65 bar. In forward direction, the check valve has a very low pressure drop at low absolute gas pressures. An integrated unit of 10 valves is presented. Section 7.2 discusses first the requirements for the check valves, which are tailored on application in a miniature sorption compressor. The remainder of the chapter discusses the design, modelling, fabrication and characterization of the valves.

7.1 Introduction

A sorption compressor that must generate a constant DC flow of gas requires check valves to ‘rectify’ the intermittent flow of gas from the individual sorption cells; operation of such a continuous flow compressor is described in section 4.2. Check valves are passive valves and can be considered as the fluidic analogy of the electrical diode. In the forward direction a low hydraulic resistance is present, whereas in the closed direction a very high hydraulic resistance is present. Check valves exist in many different sizes and with a wide range of specifications. Typical applications for check valves include: (membrane) pumps, fluidic switching and applications in the chemical process industry (e.g. to prevent back-flow).

Figure 7.1 shows a cross section of a typical commercial stainless steel check valve [7.1]. It consists of a stainless steel housing that contains a moveable plate (‘poppet’) with bonded

Figure 7.1 Cross section of a typical commercial stainless steel check valve [7.1].

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180

elastomer seal. The spring facilitates a normal closed operation; the opening (‘cracking’) pressure can be chosen by inserting a spring with a certain spring constant. For this particular check valve, cracking pressures between 0.02 and 1.7 bar can be obtained.

Using MEMS technologies, in the last decade micro check valves have been developed for small fluid flows. Table 7.1 gives a schematic overview of different micro check valve principles that are described in the literature [7.2]. The check valves with moving parts make use of structures such as flaps, membranes, plates or balls to open or close a flow opening, depending on the flow direction. Valves without moving elements obtain their diode function from the difference in velocity profiles in the different directions. For a more detailed description of the different micro check valve principles, the reader is referred to the individual papers or to overviews given by Oosterbroek [7.2], Shoji [7.3], and van Cuyck [7.4].

Table 7.1 Different MEMS based check valve principles that are described in the literature [7.2].

schematic type

cantilever

V-shaped

membrane

bossed

ball

diffuser

nozzle

Tesla

Another class of valves is formed by the active valves. In contrast to passive check valves,

in active valves some kind of external actuation force is used to control the fluidic resistance. Active valves are more complicated systems then passive valves, but facilitate also more sophisticated fluid control. Applications for active valves are numerous and include: fluid flow and pressure controllers, fluid injection for chemical systems, injection systems for medical applications, etc. In cryocoolers active valves are used to create pulsating pressure waves in pulse tubes and GM coolers. In high pressure JT coolers, an active valve may be used to start or stop a cold stage that is connected to some high pressure supply (e.g. a gas bottle). In a continuous flow sorption compressor, however, active valves are not required because the pressure in the individual compressor cells can actively be controlled so that check valves can be applied that react passively to this pressure wave (in fact, in a similar way as check valves react passively on the pressure wave that is produced in a membrane compressor).

The check valves that are presented in this chapter were developed because no commercial valves could be found that fulfilled the requirements of the sorption compressor. MEMS techniques were chosen for the fabrication; it demonstrates the powerful opportunities of MEMS for developing cryocooler components. Moreover, for the production of check valves,


181

micromachining techniques offer some significant advantages compared to precision engineering techniques: • Very accurate construction of valve components is possible, for instance of small spring

elements. • A nearly perfect valve seal can be created using the flatness of a polished wafer surface. A

proper valve seal is required to obtain a small leakage flow when the valve is closed. Clean processing of the valves is also essential for a proper seal. Clean processing is inherent to MEMS techniques.

• Integration of eight valves in one unit becomes really straightforward. Dead volumes, which deteriorate the compressor performance, can thus be kept very small.

• Integration of micrometer-sized sieves in the design is possible to trap contamination that could cause leakage of the valve. In the next section, first the check valve requirements are discussed. Next, in section 7.3 the

design of the check valve is presented. In section 7.4 mechanical and fluidic modelling is applied to find proper dimensions for the valve so that it fulfills the requirements. The fabrication of the valve is presented in section 7.5 and, finally, experiments on the valve are discussed in section 7.6.

7.2 Check valve requirements

The requirements for the check valves are given in table 7.2. They are derived from the cooler specifications as described in section 4.7, and are discussed below.

Table 7.2 Check valve requirements. The numbers between brackets refer to the discussion in the text.

low pressure valve high pressure valve maximum pressure difference (1) 50 bar 50 bar closed direction maximum gas leakage (2) 0.01 mg/s 0.01 mg/s gas pressure (3) 1 bar 20 bar ethylene mass flow* (3) 1 mg/s 1 mg/s volume flow (3) 0.9 ml/s 0.04 ml/s

forward direction

maximum pressure drop (4) 0.02 bar 0.4 bar the valve should be normally closed (5) the valve should have some resistance against contamination (6) integration of eight to ten valves in one unit should be possible, including interconnection lines (7) *At the time that the check valves were designed, a mass flow of 1 mg/s was assumed. Later, the specified flow was adjusted to 0.5 mg/s. This change does not significantly affect the check valve design.

(1) The valves have to stand periodically pressure differences up to the maximum pressure difference of 20 bar; 50 bar is chosen as a safe limit. (2) Gas leakage in the closed direction is a loss factor and should be kept below a small fraction of the normal gas flow in forward direction (less than 1%, for instance). (3) In forward direction, the check valves connected to the high-pressure line of the cold stage have different requirements than the ones connected to the low-pressure line. The mass flows through the high- and low-pressure valves are the same but the absolute gas pressures, densities and volume flows are a factor of 20 different. (4) In both cases, the pressure drop should be a small fraction of the absolute pressure (less than 2%, for instance). By designing a check valve that fulfills this requirement for the low-pressure gas, the same valve will certainly also fulfill the requirements for the high-pressure gas. (5) The

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182

valve should close immediately as soon as the pressure difference reverses. Consequently, the valve should be normally closed, but without a significant spring force to reduce the pressure drop in forward direction. (6) From experiments with a large scale sorption cooler it appeared that leaking check valves (of a commercial type) were the major cause of malfunction of the system [7.5]. This was explained by contamination of the valve seat. From this we concluded that the valve seat should either have a certain resistance to contamination, or prevention of contamination of the valve seat should occur within the valve – for instance by integration of a particle filter. (7) Another requirement is that eight to ten valves (dependent on the compressor configuration) can be integrated into a single manifold, including the required interconnection lines. A schematic of a valve-unit is part of figure 4.15. Integration of the interconnection lines requires that high- and low-pressure lines can cross each other in the unit.

Because of the moving mass-spring systems, valves can be operated in a limited dynamic range and it is common to specify a dynamic range. However, dynamic properties are not really a design issue for this case because of the relatively long sorption compressor cycling period and slow switching times.

7.3 Design

The concept of a bossed valve with thin springs was chosen for the check valve design. The spring, the valve seal and the pressure resistant structure are separately implemented in different mechanical structures in this valve concept. This enables separate optimization of the different parts of the valve to the associated strict requirements (i.e. low pressure drop, proper sealing capability, large reverse pressure difference). In most other check valve concepts, the different functions are integrated in one structure, which makes requirement-matching more difficult, or even impossible in the case of extreme requirements such as given in section 7.2. For example, in the case of the flap-valve (see table 7.1), the spring, seal and pressure-resistant structure are all integrated in one flap. The required low pressure drop in forward direction demands a thin flexible flap but, on the other hand, the large pressure difference in reverse direction demands a thick and strong structure.

A design impression of the valve is given in figure 7.2. The valve consists of a thick plate (boss) suspended by four thin springs. The thin springs behave like single clamped beams, thus facilitating the high deflections that are required to obtain a low pressure drop in the forward direction [7.6]. When the valve is in the forward direction, the gas is able to flow through the holes surrounding the springs. On the other hand, this spring construction has a very high stiffness in the direction parallel to the plane. As a consequence, deflections parallel to the plane (for instance due to large g-forces on the boss) and associated dangerous stresses in the springs are limited. The entire valve construction, including the interfacing gas lines, is made out of two silicon wafers that are covered by two glass wafers, all bonded together. The design is such that the gas lines on both sides of the valve can cross in the upper and lower wafers. This is required for the construction of an integrated valve manifold that has only six connections to the outside world: four to the compressor cells and two to the cold stage. The valve seat is made out of the polished surface of the wafers, facilitating a perfect fit and alignment of both sides of the valve seat. Stiction of the fragile spring beams to the bottom wafer is prevented by etching a cavity in the bottom wafer under the beams. Stiction or bonding of the valve seat is prevented by application of a nitride coating [7.7]. The maximum


183

allowed deflection of the boss can be selected by choosing an appropriate thickness of the boss relative to the wafer thickness. A sieve with 4 µm openings is constructed in the inflow line of the valve to trap possible contamination. The sieve is made of a row of pillars standing in the channel.

7.4 Mechanical and fluidic modelling

Fluidic and mechanical modelling is required to find proper dimensions for the valve construction so that it fulfills the requirements. To facilitate a simple design procedure, first order analytical expressions are used to describe the expected important mechanical and fluidic effects in the check valve. After a discussion of these effects, a parameter study is done to find the proper dimensions for the valve.

The behavior of the valve can be described for the situation that the valve is closed and for the situation that it is in forward direction. For both situations, a sketch of the valve with relevant parameters is given in figure 7.3.

Closed valve. When the valve is closed and a large pressure difference is present, large stresses in the construction may develop and these have to be adjusted to safe values by a proper design. Three locations were identified where large stresses are expected: compressive stress in the valve seat; bending and shear stresses in the boss; and again bending and shear stresses in the closing glass wafer on top of the boss. These different stresses are described below.

Under the assumption that a uniform stress is present in the circular valve seat and that

Sieve

Boss

Wafer 1

Wafer 2

Wafer 3

Wafer 4

Input glass tube(glued)

Output glass tube(glued)

Spring

Top view Top view

Valve seat

glass

glass

silicon

Figure 7.2 Design impression of the high-pressure check valve. More details of the design are visible in the photographs of the realized valve, see figure 7.9.

hliftkspring

∆p =p -popen 1 2p2

p1

flowDseat

lseat

σc,seat

dboss

pL

pH

∆p =p -pclosed H L

bboss

Dboss

Figure 7.3 Sketch of valve in closed and forward situation.

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184

Dseat >> lseat, this compressive stress can be approximated by:

seat

seatclseatc l

Dp

⋅∆=

4,σ (7.1)

where ∆pcl = pH – pL, the pressure difference over the valve To describe the bending and shear stresses in the boss, it is assumed that the boss behaves

like a circular clamped membrane (worst-case assumption) with a uniform distributed pressure load. For such a configuration, the maximum bending stress is present at the boundary of the plate in the radial direction and equals [7.8]:

closed

boss

bossbossb p

d

D∆=

2

2

max,, 163

σ (7.2)

Also the shear stress is maximum at the boundary of the boss and it can be derived as:

closedboss

bossbosssh p

dD

∆=4max,,σ (7.3)

For the pressurized Pyrex glass wafers on top of the check valve, the failure mechanism is either related to cracking of the silicon or glass (A), or to failure of the silicon-glass bond (B) [7.9]. The two situations are illustrated in figure 7.4. For situation A, the bending and shear stresses in the glass or silicon cause cracking for a situation that the bond is still strong enough to hold the pressure. Obviously, cracking of Pyrex will occur since Pyrex is much weaker than silicon. For situation B, the pressure on the bond is large enough to open the bond before cracking of the Pyrex occurs. Once that happens, the pressure acts on an increased area and the interface will open further. During this process, the bending and shear stresses in the Pyrex will increase until it exceeds the maximum stress and a crack occurs due to mechanism A.

A B

Pyrex Pyrex

silicium siliciumcracks cracks

Figure 7.4 Two different failure mechanisms of the Pyrex wafer [7.9]. With mechanism A, only the Pyrex breaks because of excessive bending stresses. In mechanism B, first the bond between Pyrex and silicon opens before the Pyrex cracks because of excessive bending stresses.

To describe the bending and shear stresses in the Pyrex wafer for situation A, it is assumed

that a square-shaped clamped Pyrex plate is present above the boss with a uniformly distributed pressure load. For such a configuration, the maximum bending stress is present at the boundary of the plate in the middle of the edge, and it equals [7.10]:

H

pyrex

pyrexpyrexb p

d

b2

2

max,, 308.0=σ (7.4)

where bpyrex and dpyrex are the width and thickness of the unbonded square Pyrex plate above the valve. Also the shear stress is maximum at the boundary of the square plate and it can be derived as:


185

Hpyrex

pyrexpyrexsh p

d

b

4max,, =σ (7.5)

For situation B, Blom [7.9] derived an expression for the burst pressure of an infinite rectangular channel:

2

31

77

2048

channel

bpyrexpyrexburst

b

dEp

γ∆= (7.6)

where bchannel is the width of the channel and ∆γb is the effective bond energy of the anodic Pyrex-silicon bond. Eq. (7.6) can be used as a worst-case approximation for the burst pressure of a square plate with a width bchannel.

Valve in forward direction. When the valve is in the forward direction, a force equilibrium occurs between the pressure drop that is present over the valve seat and the valve spring - see figure 7.3. The pressure drop over the valve seat is caused by viscous forces in the fluid flow. If the flow is assumed to be incompressible and laminar and entrance effects are neglected, then the pressure drop can be described by Eq. (3.19). By using expressions for the friction factor, the Reynolds number, the gas velocity, and geometric factors, the pressure drop over the valve seat can be derived as:

3

12

liftseat

seatopen

hD

mlp

πρµ &

=∆ (7.7)

where µ is the dynamic viscosity and ρ the density of the gas, m& is the mass flow and the other parameters are as defined in figure 7.3. This pressure drop is balanced by the spring construction with spring constant:

lift

seatopen

lift

bosssopen

lift

bossspring h

Dp

h

Ap

hF

k4

2, π∆

=∆

== (7.8)

where As,boss is the surface area of the boss over which the pressure difference acts. By combining Equations (7.7) and (7.8), the pressure drop and the valve lift can be expressed as a function of the spring constant:

4/1

7

3

4

34

=∆ m

D

klp

seat

springseatopen &

ρµ

π (7.9)

4/1

3

= m

kDl

hspring

seatseatlift &

ρµ

(7.10)

The symmetrical spring construction can be modelled as four parallel double clamped beams that are loaded at one end [7.6]. For such configuration, the total spring constant equals:

3

3110,4

spring

springspringsispring

l

dbEk ><= (7.11)

where Esi,<110> is the Young’s modulus of silicon in the <110> direction and bspring, dspring and lspring are the width, thickness and length of one spring beam.

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186

An important additional parameter in forward direction of the valve is the bending stress that is present in the springs. The maximum bending stress occurs at both ends and at the surface of the beam, and it should be limited to a safe value. This maximum stress is given by [7.6]:

lift

spring

springsispringb h

l

dE2

110,max,,

3 ><=σ (7.12)

Parameter study. A large number of parameters are involved in the parameter study. They can be divided in specified system parameters (type of gas, gas pressures, mass flow), fixed material properties (gas properties, Young’s moduli, yield stresses, etc.), controllable dimensions (dimensions of the boss, valve seat, springs, etc.), and dependent parameters that should be kept within certain limits (pressure drop, valve lift, stresses at different locations, spring constant, etc.). Below, these dependent parameters will be calculated and plotted as a function of the relevant parameters. Table 7.3 gives an overview of the valve parameters; the obtained valve dimensions and resulting properties are included.

Table 7.3 Check valve parameters. Specified system parameters

gas ethylene pressure in forward flow, pL 1 bar maximum pressure difference in closed direction, ∆pclosed

50 bar (20 bar in normal use)

mass flow, m& 1 mg/s Material properties (at 300 K)

gas density @ 1 bar and 300 K, ρ [7.11] 1.131 kg/m3

gas viscosity @ 1 bar and 300 K, µ [7.11] 1.031⋅10-5 Pa⋅s Young’s modulus silicon, Esi [7.12] Esi,<100> = 134 GPa, Esi,<110> = 168 GPa yield strength silicon, σy,si [7.13] 7 GPa Young’s modulus Pyrex, Epyrex [7.14] 62.6 GPa yield strength Pyrex, σy,pyrex [7.15] 70 MPa bond energy anodic bond Pyrex-silicon, ebond [7.9] 1 J/m2 (estimated)

Chosen valve dimensions valve seat (diameter and length), Dseat and lseat Dseat = 0.98 mm, lseat = 60 µm boss (width and thickness), bboss and dboss bboss = 1.10 mm, dboss = 325 µm distance between boss and Pyrex (maximum lift of boss) 25 µm Pyrex cover wafer (width and thickness), bpyrex and dpyrex bpyrex = 1.93 mm, dpyrex = 500 µm spring (length x width x thickness), lspring, bspring, dspring lspring = 1.20 mm, bspring = 50 µm, dspring = 10 µm Calculated valve parameters, valve closed with 50 bar calculated required

compressive stress in valve seat, σc,seat 20 MPa < 250 MPa maximum bending stress in boss, σb,max,boss 8.5 MPa < 250 MPa boss deflection << 1 µm (≈ 1 nm) - maximum bending stress in Pyrex cover, σb,max,pyrex 23 MPa < 25 MPa burst pressure of Pyrex-silicon bond, pburst 39 bar > 50 bar Calculated valve paramters, valve in forward direction calculated required spring constant, kspring 19.4 N/m - pressure drop, ∆popen 4.4 mbar / 6.6 mbar* < 20 mbar valve lift, hlift 17 µm / 23 µm* - maximum bending stress in springs, σb,max,spring 60 MPa / 79 MPa* < 250 MPa *The first value is calculated for lseat = 60 µm, the second for lseat = 200 µm. This last value is a more realistic length over which the pressure drops. This value is obtained because the 60 µm long valve seat is part of a larger plateau, see photograph (c) in figure 7.9.


187

In order to minimize the pressure drop over the check valve, Eq. (7.9) shows that it is attractive to choose the length of the valve seat as short as possible – although the dependence is not so strong. The shortest length of the valve seat is limited by the maximum compressive stress that is allowed in the seat when the valve is closed and pressurized, see Eq. (7.1). By choosing a certain safe stress to be present in the seat when the valve is closed, lseat can be related to Dseat via Eq. (7.1). For pH = 50 bar and a safe σc,seat = 20 MPa, it follows that

seatseatseatseatc

Hseat DlD

pl

161

4 ,

=⇒=σ

(7.13)

This equation will be used in the rest of the parameter study to define the valve seat length. A short inspection of the shear stresses in Eq. (7.3) and (7.5) learns that, for this type of

construction with large span-widths, the shear stresses are much smaller than the bending stresses. Therefore, the shear stresses are neglected.

Figures 7.5 - 7.7 show the bending stress in the boss, the bending stress in the pyrex wafer, the burst pressure of the Pyrex wafer, the pressure drop and lift of the valve, the spring constant of the valve spring and the maximum bending stress in the spring as a function of the relevant parameters. The plots were calculated by application of Equations (7.1) - (7.13) and

1*109

0

5*108

0 10.5D (mm)boss

σb,

max

,bos

s (Pa

)

σ b,m

ax,p

yres

(Pa)d =10 mboss µ d =100 mpyrex µ

d =100 mpyrex µ

300 mµ300 mµ

500 mµ

500 mµ

700 mµ

700 mµ

1000 mµ

25 mµ

50 mµ

100 mµ300 mµ

2.0 2.01.5 1.51.0 1.00.5 0.50 0

6*107

4*107

2*107

0

b (mm)pyrex b (mm)pyrex

100

50

0

p (

bar)

burs

t

(a) (b) (c)

σmax,si

σmax,pyrex

Figure 7.5 (a) The maximum bending stress in the boss as a function of the boss diameter and for different values of the thickness of the boss, calculated with Eq. (7.2).(b) The maximum bending stress in the Pyrex wafer above the valve boss as a function of the width of the square plate and for different values of the thickness, calculated with Eq. (7.4) for situation A in figure 7.4. (c) The burst pressure of the Pyrex wafer as a function of the width of the Pyrex wafer and for different values of the thickness of the wafer, calculated with Eq. (7.6) for situation B in figure 7.4.

0

10

20

30

40

0 00.25 0.250.5 0.50.75 0.751.0 1.0D (mm)seat D (mm)seat

∆p

(m

bar)

open

∆popen,max

k =1 N/mspring

k =1 N/mspring

10 N/m

10 N/m

20 N/m

20 N/m

50 N/m 50 N/m

100 N/m

100 N/m

200 N/m

200 N/m

h (

m)

lift

µ

0

10

20

30

(a) (b)

Figure 7.6 The pressure drop (a) and lift (b) of the valve in forward direction as a function of the diameter of the valve seat and for different values of the spring constant, calculated with Equations (7.9) and (7.10).

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188

the system and material parameters as defined in table 7.3. The calculated stresses in silicon and Pyrex should be limited below a certain value. The

theoretical yield stress of silicon is about 7 GPa [7.13]. However, in a realistic construction silicon fractures at much smaller stresses because of crystal imperfections and surface irregularities that cause local stress concentrations. As a more realistic yield strength, σy = 1 GPa can be assumed, and (bending) stresses should be significantly smaller than this value to be sure that fracture does not occur, for instance a factor of four. This results in σmax,Si = 250 MPa. For Pyrex and other glasses, a yield stress of 70 – 100 MPa is reported for realistic constructions [7.15]; in practice a maximum tensile stress of about 30 MPa is allowed [7.16] and, therefore, σmax,pyrex = 25 MPa was assumed. These maximum allowed stresses are depicted in the figures.

An important design constraint is formed by the minimum spring dimensions that can be fabricated. The minimum thickness is limited by the fabrication scheme, which causes a non-uniformity of the spring thickness of several micrometers for springs on different locations on the wafer. A minimum spring thickness of 10 µm was assumed. Furthermore, a minimum beam width of 50 µm was assumed. From figure 7.7a it can now be concluded that for beams shorter than 1.5 mm, the obtained spring constant is larger than 10 N/m. Beams longer than 1.5 mm are unwanted because of the larger associated valve size. With this minimum spring constant, figure 7.6a shows that the diameter of the valve seat should be at least 250 µm to obtain ∆p < 20 mbar; a larger seat diameter results in a smaller pressure drop. For kspring = 10 N/m and Dseat > 250 µm, figure 7.6b shows that typical values for the valve lift are 10 – 15 µm. Larger values for kspring result in a slightly smaller valve lift, typically 5 – 15 µm. For such values of the valve lift, figure 7.7b shows that the length of the valve springs should be at least 0.5 mm to reduce the bending stresses in the beams below acceptable levels. With the chosen dimensions as given in table 7.3, all requirements are met - except for the opening/cracking pressure of the Pyrex-silicon bond. This parameter was not taken into account in the initial modelling of the valve and was added after the design and fabrication of the valve was finished. It is expected that the closing Pyrex wafer is the weakest part of the valve, and that the Pyrex will crack either by mechanism A or B in figure 7.4 when higher pressures are applied.

0 00.5 0.51.0 1.01.5 1.5l (mm)spring l (mm)spring

10

100

1000

k (

N/M

)sp

ring

1.0*109

5*108

0

σb,

max

,spr

ing (

Pa)

d =2 mspring µd =2 mspring µ

5 mµ5 mµ

10 mµ

10 mµ

20 mµ

20 mµ

30 mµ

30 mµ

(a)

(b)

σmax,si

Figure 7.7 The spring constant (a) and maximum bending stress (b) of the spring construction as a function of the length of the beams and for different values of the thickness calculated with Equations (7.11) and (7.12). To calculate the maximum bending stress, a valve lift (or beam deflection) of 17 µm was assumed.


189

7.5 Fabrication and results

7.5.1 Processing scheme

Figure 7.8 shows the essential processing steps for the check valve fabrication; more detailed steps as well as the mask sequence and the wafer lay-out are given in appendix A. The processing steps are such that the surfaces of the silicon wafers that are used for the direct silicon-silicon bond are covered with a protective nitride layer as much as possible to prevent degradation of the surface. Both wafers are double side polished wafers.

Wafer 2. (1) 1.0 µm LPCVD nitride is grown and etched back to 0.5 µm except at the backside of the boss that was patterned before. Next, the spring construction is patterned and etched to the desired thickness by means of RIE etching. (2) By means of 50% HF etching, 0.5 µm nitride is etched away without mask, leaving only 0.5 µm at the backside of the boss. Immediately after this step, 1.0 µm nitride is grown. (3) On the topside the KOH mask is etched in the nitride, and after that the 1.0 µm mask on top of the boss is thinned to 0.5 µm. This is a buried mask that can be freed after a period of KOH etching. The KOH mask includes a compensation structure. (4) KOH etching is done till approximately 25 µm silicon is left on top of the spring construction. (5) 0.5 µm nitride is etched away by means of 50% HF etching. After this, the KOH etching is continued till the spring construction is etched through. During this step, the boss is thinned to the desired thickness. (6) Just prior to the bonding step, the nitride mask is removed using 50% HF etching, leaving 0.5 µm nitride on the bottom of the boss.

Wafer 3. (7) 1.0 µm LPCVD nitride is grown. The valve seat is patterned and the nitride is

wafer 1, pyrex

wafer 4, pyrex

wafer 2

wafer 3

resist

polyimide

nitride

Wafer 2 Wafer 3

Cr

1) 7)

2) 8)

3) 9)

4) 10)

6) 12)

13)

5) 11)

Figure 7.8 Essential processing steps for the check valve fabrication.

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190

etched to 0.5 µm on both sides of the wafer. After that, the mask is made for the valve opening, the spring cavities and the connection tubes. (8) Cryogenic RIE etching is applied to etch 50 µm into the wafer [7.17]. Next, the nitride on the backside is patterned and covered with a second resist mask as given in the picture. (9) 230 µm cryogenic RIE etching is done at the backside of the wafer. (10) The resist is stripped and a polymer is applied on the frontside of the wafer to facilitate helium backside cooling during the last cryogenic RIE etching step (11) through the wafer. During this step the pillar structure of the sieve is etched. (12) The polymer is stripped and just prior to the bonding step the nitride is removed using 50% HF etching.

Bonding. (13) Wafers 2 and 3 are connected using aligned direct wafer bonding techniques. Cleaning and chemical activation prior to bonding is essential [7.18]. The two wafers are annealed at 1100 °C in nitrogen ambient to enhance the bond strength. Finally, the wafers are covered with anodically bonded Pyrex wafers. On wafer 1 a thin chromium layer is applied at the location of the boss to prevent bonding of the boss to the glass [7.19]. Due to the applied electric field for the bonding step, the boss is capacitively pulled to the top wafer.

Interfacing. Sawing of the samples is done through wafers 1, 2 and 4, leaving the connection tubes in wafer 3 intact. This was done to prevent contamination of the tubes during dicing. Breaking the samples from the wafers cleanly opened the tubes. Connections to the outside world are made by fused silica tubes, which were glued in the channels.

A number of process runs were done in which the critical steps were identified and, where possible, resolved. The most important topics are discussed in the next two sections. Figure 7.9 shows photographs of different parts of the valve, as well as a manifold containing 10 check valves.

7.5.2 KOH etching (wafer 2)

During KOH etching, convex corners in the mask must be ‘compensated’ to prevent underetch of the corners. This underetch is caused by the presence of crystal planes in convex corners that etch at a fast rate. A number of compensation techniques are described in the literature [7.20], all based on the addition of a mask pattern that is underetched during the KOH etching process, resulting in a more or less perfect convex corner at the end of the etching step. The KOH mask design for the check valve has many convex corners but limited space for compensation structures. For such a configuration, a suitable compensation method is to add beams at the corners in the <110> direction; these beams can be branched off to fit in the narrow space. The method works as follows: At the convex corner to be protected a concave corner is created, thus preventing direct undercutting. At the end of a <110> oriented beam there are two convex corners, which are laterally undercut by fast etching planes. The longer the <110> oriented beam is, the longer the convex corner is protected from undercutting. The best quality of the convex corner is obtained when the <110> beam is completely underetched. For this situation, the required beam length is given by [7.20]:

−⋅⋅−

⋅−⋅⋅=

⋅−−=

1)96.30tan(

1)96.30tan(2

2100

411

oo beambeam

etch

branchwidthetchbeam

bnb

R

Rd

LnLLL

(7.14)


191

where Letch is the underetching length in the <110> direction, and Lwidth and Lbranch are small correction factors for the influence of the beam width and the number of times, n, that the beam is splitted. In this expression, detch is the etched depth, R411 and R100 are the etch rates of the 411 and 100 crystal planes, and bbeam is the width of the beam. Based on this expression, with R411/R100 = 1.6 taken from the literature [7.21], a mask design was made

Figure 7.9 Photographs of the check valve. (a) The top silicon wafer with 4 KOH-etched bosses (part of a 10-valve manifold). (b) A single KOH-etched boss suspended by four springs. (c) The bottom silicon wafer with the valve seat. (d) The sieve at the edge of the inlet channel. (e) The backside of two manifolds with 10 valves, prior to separation (breaking) of the manifolds and integration with the glass-tubes. (f) The topside of two check valve manifolds; on the lower manifold four bosses are removed.

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192

and wafers were processed. Two problems emerged which are illustrated by the photographs of figure 7.10. Firstly, when the compensation beam is etched away completely at the end of the etch time, still a hillock remains at the bottom of the convex corner, formed by the 411 planes. The influence of this hillock was not taken into account in the design and, as can be seen from figure 7.10a, the springs were fixed to it. For some wafers the length of the hillock was a little shorter due to reasons that will be discussed later in this section, and the springs were not fixed. However, with these samples a second complication was observed that is illustrated in figure 7.10b. At the bottom of the etched cavity a rim is present, connecting to the end of the hillock. The height of this rim was measured: at the end of the hillock it is about 5 µm in height, levelling gradually to zero at a distance of 300 µm from the hillock. As a consequence, the springs must be over-etched to be freed and a non-uniformity of the spring thickness of a few micrometers will result, which is not a serious problem.

In a next process run, the KOH corner compensation structures were shortened to compensate for the hillock at the bottom of the convex corner. Some wafers were obtained with properly etched bosses such as depicted in figure 7.9b, but on some wafers still rather large hillocks were present. It was concluded that a variation of one or more parameters in this

Figure 7.10 (a) Hillocks at the bottom of the convex corners of the boss are fixed to the springs. Also visible are etch-pits, discussed later in this section. (b) A situation in which the hillocks are slightly shorter than in photograph a) and where the KOH etching just reached the springs. A rim of a few micrometers in height is present near the end of the hillock. (c) and (d). A situation where the nitride KOH-mask is still present on top of the boss, and where the compensation structure is almost completely under-etched. In photo c) the focus is on the mask and in photo d) on the bottom. Clearly visible are the hillocks, the rims at the bottom of the KOH etched well, and the asymmetry due to misalignment of the KOH mask with the crystal orientation.


193

process step was present, and a more detailed analysis was made of the situation. Three parameters were identified that varied between subsequent process runs and that influenced the underetching of the corner compensation structures: 1. The wafer thickness of different wafers varied from 360 µm with ±5 µm. Since the etched

spring thickness was taken constant, this variation directly translated into a variation of the etched depth, detch. This subsequently resulted in a maximum variation of the underetched length, Letch, between different wafers with ±16 µm.

2. The etch rate ratio R411/R100 was measured on five different wafers that were etched at different moments with similar process conditions. The etch rate ratio was determined by measuring the etched depth detch and the underetched length Letch of the corner compensation structure, and subsequent application of Eq. (7.14). It was found that R411/R100 varied from 1.62 to 1.72. No effort was made to investigate this variation, but possible explanations are: differences in the freshness and/or concentration of the KOH solution that influence R411/R100 or differences in wafer doping levels. For an etched depth of 350 µm, this variation of the etch rate ratio results in ±35 µm variation of the corner compensation underetch.

3. Misalignment of the KOH mask with respect to the crystal orientation of the wafer causes an asymmetry in underetch of the compensation structure on one boss. This is clearly visible in the photograph of figure 7.10c. From the experiments, a maximum variation of the underetch was estimated as ±30 µm (or 60 µm in total).

In the worst case, a total variation of 2⋅(16+35+30) = 162 µm may be present in the underetch of the compensation structure. This uncertainty in the underetch can now be compared with the required minimum and maximum (under)etch of the corners of the boss. The minimum underetch is limited by the requirement that the springs can be etched free; this is more or less the situation of figure 7.10b – provided that the rim at the bottom can be removed by overetching of the springs. The maximum underetch is limited by the requirement that the octagonal-shaped boss still fits adequately over the valve seat; this is more or less the situation of figure 7.9b. The difference between this minimum and maximum underetch is approximately 140 µm. If this number is compared with the maximum (worst-case) spreading of the underetch, 164 µm, it can be concluded that the present design in combination with the described process is quite critically. However, with an optimized length of the compensation structure, proper wafer selection and mask alignment, and a little luck, good results can be obtained as was shown in figure 7.9.

An important condition for this process step is that KOH etching is continued until the rim of a few µm is removed, see figure 7.10b. This overetching of the springs revealed another problem, which was already mentioned in the caption of figure 7.10a: etch pits appeared at some (but not all) concave corners of the springs. A close-up of these structures is shown in the photograph of figure 7.11a. These etch-pits were explained by local delamination of the silicon nitride in the concave corners of the beams. This nitride layer was deposited in processing step 2 (see figure 7.8) to protect the side walls of the beams during KOH etching. However, much built-in tensile stress is present in these layers (about 300 MPa, according to [7.22]), which leads to large normal stresses in the concave corners and apparently very localized delamination. As a consequence, KOH liquid can etch the silicon as soon as the bottom of the KOH-etched cavity reaches the beams. From figure 7.11a it can be seen that the

Chapter 7

194

etch-pits are bounded by 111 planes. The problem was solved by rounding off the corners of the beams, as is illustrated in figure 7.11b.

The processing scheme of wafer 2 can be simplified significantly by skipping some unnecessary processing steps. At the moment that the check valves were fabricated, maximum precaution was taken to protect the silicon wafer surface that was used in the direct bonding step. For that reason, processing was always started with the deposition of a protective nitride layer. Later, it was found that normal (but careful) processing of the wafers was possible without a protective nitride layer, without affecting the wafer bonding step. Another redundant step consisted of the nitride layers left on the valve seat and the boss to prevent bonding at that location. Later, it was found that a nitride layer on one of the surfaces is appropriate to prevent bonding. Consequently, the protection layer on the boss can be skipped. Altogether, the processing of wafer 2 can be simplified to the scheme depicted in figure 7.12, skipping 12 of the 31 original processing steps (see Appendix A).

nitride

Wafer 21)

2)

3)

4)

6)

5)

Figure 7.12 Simplified processing scheme of wafer 2.

7.5.3 Deep RIE etching (wafer 3)

A critical step was the etching of the sieves. In one and the same process step (step 11 in figure 7.8), the sieves are etched, the large open area next to the sieves is etched, and the wafer is etched through. An essential problem appeared to be that a different etch recipe was required for proper side wall passivation of the sieve-pillars with narrow trenches of 5 µm in between, compared to the recipe required for etching of the larger surface areas. This was attributed to the influence of the silicon etch-load on the etched profile; only limited research is

Figure 7.11 (a) Detail of the etch-pits in the concave corners of the springs. (b) Delamination of the silicon nitride on the side walls of the beams was prevented by rounding of the corners.


195

available on this topic [7.23]. Two extremes with different etch recipes are illustrated in figure 7.13 In figure 7.13a the pillars are properly etched at the topside, but spikes (‘grass’ or ‘black silicon’) can be seen on the large surface areas. This ‘grass’ is absolutely unwanted because the spikes can easily break off and contaminate the valve seat. The etched structure of figure 7.13b was obtained after careful tuning of the etching parameters. The ‘grass’ is not present anymore on the large surface areas, but the pillars are almost completely underetched at the topside.

Figure 7.13 (a) Wafer 3 etched with much side wall passivation during steps 9 and 11 (see figure 7.8). (b) Wafer 3 etched with less side wall passivation.

Another problem can be observed in figure 7.13a: an unexpected wall is present next to the

sieve. This was analyzed to be the passivation layer that was deposited during the deep vertical RIE step (step 9 in figure 7.8). During the successive etching of the sieves in step 11 (see figure 7.8), this passivation layer was apparently not removed and would thus block the entrance of the sieves. This problem was solved by reducing the passivation of the side walls during step 9. The drawback of this measure is more underetch of the mask, resulting in the sloping walls that can be seen in figure 7.9d. However, properly functioning sieves were obtained with the recipes used in figure 7.13b.

A number of measures can be taken to improve the fabrication of the sieves. Firstly, the aspect ratio of the sieve-structure can be reduced to make the process less critical (e.g. by reducing the etched depth). Secondly, the process and mask design can be changed to reduce the contrast between etch-loading of open spaces and narrow trenches. Thirdly, a different process can be applied with a better controlled side wall passivation. An example of such process is the Bosch-process [7.24], in which trench etching and side wall passivation is carried out sequentially in time with two different alternating processes, instead of simultaneously in time with one and the same process. Another improvement of the sieve performance consists of a reduction of the flow resistance by a better use of the wafer surface area. In the present design only one row of pillars is used, and this could be changed to a multiple-row arrangement that is placed between a comb-construction.

7.6 Experiments

A number of different experiments were done on the check valves: the burst pressure in closed direction was determined, the pressure drop in forward direction was measured, the influence of contamination on the leakage flow in closed direction was determined, and a long duration experiment involving many forward/closed switchings was done. For safety reasons,

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196

in all experiments nitrogen gas was used instead of ethylene. At room temperature the densities of these gases are almost the same, but the viscosity of nitrogen is a factor of 1.73 higher (at low pressures) than that of ethylene.

To measure the burst pressure, a sample was connected in closed direction to a gas bottle with pressure regulator. The pressure was increased in steps of 5 bar, and after each pressure increase a Bronkhorst flow sensor [7.25] was connected to the other side of the check valve to measure a possible leakage flow. The sensor had a resolution of about 0.25 µg/s. Before each pressure increase, the flow sensor was removed to prevent damage due to the possible cracking of the valve. Samples bonded with 500 µm Pyrex wafers could withstand pressures up to 65 bar in closed direction with a leakage flow that was not detectable with the used flow sensor. At higher pressures, the glass wafer burst but the boss of the valve stayed intact. Samples bonded with thicker Pyrex wafers were tested up to 125 bar and did not burst at all. Inspection of the crack in the glass wafer showed that an almost ‘perfect’ crack via mechanism A in figure 7.4 was present. Application of Eq. (7.4) shows that a maximum bending stress of about 30 MPa is present in the Pyrex wafer at pH = 65 bar. This is a reasonable value for the yield stress. Apparently, the worst-case estimation of the burst pressure via mechanism B in figure 7.4 (pburst = 39 bar) is not applicable. This can at least partly be explained by the difference between the square plate that is present on top of the check valve and the rectangular channel that was assumed for the calculation of Eq. (7.6). Also, the assumed value of the bond energy may not be accurate.

∆p

check valve

pH

gas supply withregulated pressure

(1.2 - 5 bar)

mass flowcontroller

vent at1 bar

Figure 7.14 Set-up to measure the pressure drop over the check valve as a function of the forward flow. Figure 7.14 shows the measurement set-up that was used to measure the pressure drop over

the valve as a function of the mass flow when the valve was placed in forward direction. The valve was connected to a pressure bottle with accurate pressure regulator that could regulate the pressure between 1.2 and 5 bar. A Bronkhorst flow controller [7.25] with a range of 1.25 mg/s nitrogen flow was connected at the exit of the valve; with this configuration the absolute gas pressure could be adjusted with the pressure regulator and at the same time the mass flow through the valve could be adjusted with the flow controller. The resulting pressure drop over the valve was measured with a differential pressure sensor with a range of 100 mbar, fabricated by Sensortechnics [7.26]. Because the connecting glass tubes and the filter caused a major part of the total pressure drop over the valve, separate measurements were done with complete check valve samples and with samples where the boss was removed. By subtracting these two measurements, an estimate of the net pressure drop over the valve seat could be obtained. Figure 7.15 shows typical results for an absolute gas pressure of 2 bar. The modelled pressure drop over the valve seat (see Eq. (7.9)) could be fitted to the measured values for a spring thickness of 11 µm. This thickness is close to the expected thickness. Measurements with other absolute gas pressures showed qualitatively similar results. The measured pressure drops for nitrogen gas flow at 2 bar can now be translated to pressure drops for the required ethylene


197

gas flow at 1 bar. This results in about 8 mbar pressure drop over the valve seat, 25 mbar over the glass tubes and a total pressure drop of 33 mbar. This value is larger than the required 20 mbar, although this value was chosen rather arbitrarily. However, a smaller pressure drop could be obtained by applying shorter glass tubes for the interfacing of the check valve.

0

5

10

15

20

25

30

35

40

45

0 0.2 0.4 0.6 0.8 1 1.2 1.4massflow (mg/s)

pres

sure

dro

p (m

bar)

sample without bossnormal samplenet valve seat pressure dropmodeled valve seat pressure drop

Figure 7.15 Pressure drops as a function of the mass flow through a check valve in forward direction at an absolute gas pressure of 2 bar. The modelled pressure drop is calculated for a spring thickness of 11 µm.

To test the influence of contamination on the closing behavior of the valve, small particles

of 1 – 10 µm were blown through a valve without integrated filter. At ∆p = 50 bar a leakage flow was measured of 1.2 mg/s, which is very significant (in the same range as the forward flow). This illustrates the importance to trap contaminant particles in a filter.

Finally, a long duration experiment was done, involving many forward/closed switchings. Figure 7.16 shows the set-up for this experiment. The check valve is placed between five active high-pressure valves that can switch the check valve between forward and closed direction. In forward direction, valves 2 and 4 are opened, a regulated low pressure is supplied, and the mass flow through the check valve is controlled. The pressure drop across the valve is measured, as well as the absolute pressure at the low pressure side. In closed direction, active valves 1 and 3 are opened, a regulated and measured high pressure is supplied to the check valve, and the leakage flow is measured with an accurate mass flow sensor. Active valve 5 is required to vent the high pressure gas that is present in the closed volume between the three active valves after closing active valve 1. The sequence of opening and closing of the five valves is as follows (start with all valves closed): 5 open, 5 closed, 3 open, 1 open, 1 closed, 3 closed, 5 open, 5 closed, 4 open, 2 open, 2 closed, 4 closed, 5 open, 5 closed, 3 open, 1 open, etc. A complete cycle of reverse/forward switching lasted 30 seconds.

high pressuresupply (20 bar)

∆pcheck valve

pH

low pressuresupply (1.25 bar)

mass flowcontroller

mass flowsensor

Closed direction: apply pressure and measure leakageForward direction: apply flow and measure pressure dropValves to control the gas flow

1

2

3

4

5

vent at1 bar

vent at 1 bar

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198

Figure 7.16 Set-up for a long duration experiment of the check valve, involving many forward/closed switchings.

The high pressure active valves are electromagnetic/pneumatic activated and of type HB

Series Air Actuated, manufactured by Nupro/Swagelok [7.27]. The mass flow controller and sensor are both from Bronkhorst [7.25]; the controller has a range of 1.25 mg/s nitrogen flow and the sensor a range of 0.0625 mg/s with a resolution of about 0.25 µg/s. The high pressure sensor is a 140 bar miniature sensor from Kulite [7.28], and the differential sensor from Sensortechnics with a range of 350 mbar [7.26]. A PC with a National Instruments Data Acquisition Card [7.29] was used to measure the relevant parameters and to control the active valves. A custom-written Labview program was used to process, visualize and store the measurement data.

At the time of the experiment, only a very limited number of properly fabricated and assembled valves were available. Two valves were characterized over a longer period of time, and showed an almost identical behavior. The forward flows were as expected and did not change after thousands of cycles. Both valves had a small leakage flow in the reverse direction; figure 7.17 shows for one of the valves that this leakage flow reduced from an initial 3% to 0.5% of the forward flow after a few thousand cycles. For the second valve the behavior was qualitatively similar, with a slightly smaller leakage flow. This behavior is probably caused by a small particle or irregularity in the valve seat, which is hammered into the seat during the repeated loading. Both valves were still operating properly and stable when the experiment was stopped after approximately 10000 and 25000 forward/closed cycles, respectively.

0

1

2

3

4

0 1000 2000 3000 4000 5000

number of forward-closed cycles

leak

age

flow

(%

of f

orw

ard

flow

)

nearly constant leakagefrom this point forward

short malfunction of set-up

first data point

Figure 7.17 Leakage flow as a function of the number of forward-closed cycles of a check valve.

7.7 Conclusions

For continuous operation of a sorption compressor, check valves are needed to rectify the slowly ‘pulsating’ pressure variation of the individual sorption compressor cells. Sorption compressors typically produce a very high pressure ratio, and this puts strict requirements on the check valves: they should stand pressures up to 50 bar, and have a low pressure drop at low absolute gas pressures in forward direction. The concept of a bossed valve suspended by thin springs was selected because the boss and the springs can individually be optimized to fit the requirements.


199

Analytical modelling of the pressure drop, spring constant, compressive and bending stresses as well as other parameters showed that proper valve dimensions could be found for which it could fulfill all requirements. An octagonal-shaped chopped cone of about 1 mm2 and 300 µm in height was chosen as a boss, suspended by four springs of 1.2 mm x 50 µm x 10 µm. The boss could fit on a circular valve seat. Fabrication was done by a combination of wet and dry etching in silicon, and subsequent waferbonding. Data from experiments on the valves agreed fairly well with the modelling. A long duration experiment involving many forward/closed switchings was done on two check valves. For both valves, proper operation was maintained until the experiment was stopped after 10000 and 25000 cycles, respectively. For both valves, a small leakage flow was observed in the reverse direction; it reduced during the first 1000 cycles to about 0.5% of the forward flow. Clearly, an opportunity exists to investigate this leakage in more detail. From the experiment, it was concluded that a particle or some kind of roughness was hammered into the valve seat upon cycling.

To prevent contamination of the valve seat, we proposed to integrate a sieve with the check valve to trap contaminant particles. However, the fabrication of the sieves required much of the current available etching technologies, and with a rather large sieve opening of 5 µm there is room to improve the sieve-concept.

7.8 References [7.1] CH Series Compact Check Valve, Nupro Company, 4800 E. 345th Street, Willoughby, OH 44094,

USA, www.swagelok.com. [7.2] R.E. Oosterbroek, Modelling, design and realization of microfluidic components, Ph.D. Thesis,

Twente University, The Netherlands (1999). [7.3] S. Shoji and M. Esashi, Microflow devices and systems, J. Micromech. Microeng., vol. 4 (1994), pp.

157-171. [7.4] J.C.C. van Kuijk, Numerical modelling of flows in micro mechanical devices, Ph.D. Thesis, Twente

University, The Netherlands (1997). [7.5] S. Bard, J. Wu, P. Karlmann, C. Mirate, L. Wade, Component reliability testing of long-life sorption

coolers, Proc. of the 6th Int. Cryocooler Conf. (1990). [7.6] J.F. Burger, Design and realisation of silicon slider suspension with integrated friction force sensors,

M.Sc. Thesis, Twente University, The Netherlands (1995). [7.7] C. Gui, R.E. Oosterbroek, J.W. Berenschot, S. Schlautman, T.S.J. Lammerink, A. van den Berg and

M. Elwenspoek, Selective fusion bonding by surface roughness control, Proc. 5th Int. Synp. on Semiconductor Wafer Bonding: Science, Technology and Applications, Hawaii, USA (1999).

[7.8] S. Timoshenko and S. Woinowsky-Krieger, Theory of plates and shells, McGraw-Hill book company, New York (1959), pp. 56.

[7.9] M.T. Blom, N.R. Tas, G. Pandraud, E. Chmela, J.G.E. Gardeniers, R. Tijssen, M. Elwenspoek and A. van den Berg, Failure mechanisms of pressurized microchannels, model and experiments, Proc. IEEE Workshop on MEMS, Japan (2000).

[7.10] S. Timoshenko and S. Woinowsky-Krieger, Theory of plates and shells, McGraw-Hill book company, New York (1959), pp. 202.

[7.11] Cryodata Inc., Niwot, Colorado, USA, www.sni.net/partners/index.html. [7.12] N. Ono, K. Kitamura, K. Nakajima and Y. Shimanuki, Measurement of Young's modulus of silicon

single crystal at high temperature and its dependency on boron concentration using the flexural vibration method, Jpn. J. Appl. Phys., vol. 39 (2000), pp. 368.

[7.13] K.E. Petersen, Silicon as a mechanical material, proc. of the IEEE, vol. 70 (1982). [7.14] S. Spinner, J. American Ceramic Society, vol. 39 (1956), pp. 113 and vol. 45 (1962), pp. 394. [7.15] J.M. Gere and S.P. Timoshenko, Mechanics of materials, 3rd ed., Chapman and Hall, London (1991).

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[7.16] P. Heller, J. Vervest, H. Wilbrink, Vademecum voor de glastechniek, Kluwer Technische Boeken B.V., Deventer, The Netherlands (1992).

[7.17] H. Wensink, M.J. de Boer, R.J. Wiegerink, R.A.F. Zwijze, M. Elwenspoek, First micromachined silicon load cell for loads up to 1000 kg, SPIE 98 (1998).

[7.18] C.Q. Gui, Direct wafer bonding with chemical mechanical polishing: applications in sensors and actuators, Ph.D. Thesis, University of Twente, The Netherlands (1998).

[7.19] R.E. Oosterbroek, J.W. Berenschot, S. Schlautmann, T.S.J Lammerink, A. vanden Berg, M. Elwenspoek, In-plane oriented fluid control components, fabricated withnewetching techniques, Actuator ’98, pp. 43-46.

[7.20] H. Sandmaier, H.L. Offereins, K. Kühl, W. Lang, Corner compensation techniques in anisotropic etching of (100)-silicon using aqueous KOH, Proc. 6th Int. Conf. Solid-State Sensors and Actuators (Transducers ’91), San Fransisco, USA (1991), pp. 456-459.

[7.21] G.K. Mayer, H.L. Offereins, H. Sandmaier and K. Kühl, Fabrication of non-underetched convex corners in anisotropic etching of <100> silicon in aqueous KOH with respect to novel micromechanic elements, J. Electrochem. Soc., vol. 137, no. 12 (1990), pp. 3947-3951.

[7.22] J.G.E. Gardeniers, H.A.C. Tilmans and C.C.G. Visser, LPCVD silicon-rich silicon nitride films for applications in micromechanics, studied with statistical experimental design, Journal of Vacuum Science and Technology A, vol. 14 (1996), pp. 2879-2892.

[7.23] H. Jansen, M. de Boer, J.F. Burger, R. Legtenberg and M. Elwenspoek, The black silicon method II: the effect of mask material and loading on the reactive ion etching of deep silicon trenches, Proc. Workshop on Micro and Nano Engineering, Davos, Switzerland (1994).

[7.24] M.A. Douglas, Trench etch process for a single-wafer RIE dry etch reactor, US Patent 4855017 (1989).

[7.25] Bronkhorst High-Tech B.V., Nijverheidsstraat 1A, Ruurlo, The Netherlands., www.bronkhorst.com. [7.26] Sensortechnics GmbH, Aubinger Weg 27, 82178 Puchheim, Germany, www.sensortechnics.com. [7.27] Nupro Company, 4800 E. 345th Street, Willoughby, OH 44094, USA, www.swagelok.com. [7.28] Kulite Semiconductor Products, Inc., One Willow Tree Road, Leonia, NJ 07605, USA.,

www.kulite.com. [7.29] National Instruments, Inc., 6504 Bridge Point Parkway, Austin, TX 78730-5039, USA,

www.natinst.com.

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8 Miniature Linde-Hampson cold stage

Chapter 8

Miniature Linde-Hampson cold stage

This chapter presents the design and operation of two different miniature cold stages, both employing JT expansion. In section 8.2, a simple but elegant cold stage is discussed that is fabricated of miniature glass tubes. The more sophisticated cold stage presented in section 8.3 employs such glass tubes in combination with MEMS based silicon components, and is designed to be used with a sorption compressor.

8.1 Introduction

As was discussed in section 3.5, MEMS techniques are suitable to fabricate passive fluidic components such as heat exchangers, flow restrictions, condensers and evaporators – components which are often used in cryocoolers. This chapter discusses the design, fabrication and characterization of two miniature cold stages employing such components. Section 8.2 presents a very simple Linde-Hampson cooler operating with pressurized nitrogen gas, in which miniature glass tubes are used as efficient counterflow heat exchangers. Based on the results of this work, a more sophisticated cold stage was designed, which applies a MEMS based silicon condenser, flow restriction and evaporator in combination with the previously described glass tube heat exchangers. In this way, a cold stage could be fabricated that employs the thermodynamic cycle with precooling of the high pressure gas that was proposed and discussed in section 4.6.2, and which can be applied in combination with a sorption compressor. This hybrid miniature cold stage is described in section 8.3.

8.2 Linde-Hampson cooler with glass tube heat exchanger

Miniature LH-coolers were constructed in a very simple manner by application of flexible glass tubes with a metallic wire inserted for the necessary JT flow impedance. The weight of the heat exchanger and the expansion valve (without high and low-pressure connections) is less than 0.2 gram. Furthermore, the glass tube heat exchanger is mechanically rather flexible. In this section two demonstrator versions are presented of these glass-tube coolers. The fabrication is described and experimental results are presented and discussed.

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8.2.1 Design and fabrication

The two coolers with glass tube heat exchangers are depicted in figure 8.1. In both coolers a tube-in-tube counterflow heat exchanger (CFHX) is used, one with a length of 270 mm, the other with a length of 105 mm. The high-pressure gas is fed through the inner tube and the expanded low-pressure gas is returned through the annulus. The tubes are made of fused silica glass with inner/outer diameters of 0.1/0.36 mm and 0.53/0.67 mm, respectively. They are commercially available and are normally used in gas chromatography [8.1]. They can stand high pressures: no problems were encountered in tests with pressures up to 160 bar. The tubes are coated with a Polyimide layer on the outside. The coating of the inner tube was removed to improve the radial heat conduction.

The tip of the outer tube is closed by a small plug of Torr Seal [8.2]. A short piece of NiCr wire, 0.08 mm in diameter and 15 mm in length, is placed at the tip in the inner tube forming the JT valve. The inlet of the glass tube CFHX is connected to a rigid high-pressure connector and the outlet to a metal outlet tube as shown in figure 8.2. The inner tube can be displaced

Figure 8.1 Photograph of the two glass tube-in-tube Linde-Hampson coolers.

Low pressureoutlet

High pressureinlet

TuningJT restriction

Vacuum flange

Wire insertGlue (TorrSeal)

CFHX

Cross-section CFHX

100

mµ

360

mµ53

0 mµ

670

mµ

105 mm

100 mµ1 mm

Inner glass tube 100/360 mµOuter glass tube 530/670 mµ

Scale :

Figure 8.2 Cross-section of the cooler with connectors and JT-valve tuning possibility. The close-up drawing of the tip is stretched in the radial direction.


203

with respect to the outer one by means of a screw construction at the room temperature side of the cooler. In this way the flow impedance of the JT valve can be tuned. All glue connections are made with Torr Seal. The cooler is equipped with a standard vacuum flange for simple connection to a vacuum space. Because of the thin-walled glass tubes the cooler is rather flexible (the minimum radius of curvature is roughly 15 cm).

8.2.2 Experiments and discussion

The cold tip temperature was measured by means of a DT 471-SD diode of LakeShore [8.3]. The cooling power was determined with the help of a little heater, a small SMD resistor of 10 kΩ. The temperature sensor and the electrical heater were glued onto separate thin silicon plates (3 x 8 x 0.3 mm3), which were then glued to the glass tube. Torr Seal glue was chosen except for the connection of the temperature sensor to the silicon plate which was done with GE varnish [8.4]. As electrical leads to the sensor and the heater, four Manganin wires with a diameter of 0.1 mm were used. They were thermally anchored on the heat exchanger with GE varnish to decrease the heat load on the tip. For thermal insulation, the cooler was placed in a vacuum space, which was pumped to below 10-4 mbar. About 10 layers of type NRC-2 superinsulation [8.4] were wrapped around the cooler to shield the cold tip from radiative heat flow from the room temperature wall. The cooler was supplied with nitrogen gas (99,999% purity) from a high-pressure cylinder and the input pressure of the cooler was measured at the pressure reducer of this cylinder. A zeolite filter was placed in the high-pressure line to trap water and other impurities. A Bronkhorst [8.5] mass flow meter was connected to the outlet tube which vents to the atmosphere.

For the cooler with a length of 270 mm, temperatures and mass flows are depicted in figure 8.3 as a function of the load supplied by the heater. Three different input pressures were applied: 70, 100 and 120 bar. These measurements show that virtually no temperature increase occurs with increasing heat load until a maximum load is reached. At this maximum load all the liquid produced is vaporized by the heat load corresponding to the enthalpy change 4-5 in figure 2.35b. The measured maximum loads are 13, 62 and 150 mW at mass flows of successively 6.7, 7.3 and 12.5 mg/s and temperatures of 88, 88 and 94 K, respectively. This

80

90

100

110

120

130

140

0 40 80 120 160Heat load (mW)

Tem

pera

ture

(K

)

0

2

4

6

8

10

12

14

16

Mas

s flo

w (

mg/

s)

Temp 70 barTemp 100 barTemp 120 barFlow 70 barFlow 100 barFlow 120 bar

Figure 8.3 Tip temperature and mass flow rate versus heat load supplied by the heater for the 270 mm glass-tube cooler. Measurements were done for 70 bar, 100 bar and 120 bar.

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higher temperature of 94 K is due to the higher pressure drop over the return line at higher flow rates; a higher pressure at the cold side of the return line means a higher boiling point. With a slightly higher flow impedance in the JT valve and, therefore, a lower flow rate, the 270 mm cooler was able to reach 82 K at a mass flow of 4.2 mg/s, a pressure of 100 bar and no heat load. The corresponding calculated pressure drop over the return line is 0.7 bar.

The mass flow rate also effects the efficiency of the CFHX; a lower flow rate gives a better efficiency. This effect was very striking in the experiments with the shorter cooler. At 100 bar and a flow of 11 mg/s, the minimum temperature which could be reached with the 105 mm cooler was 210 K. After replacing the restriction with dimensions 15 mm in length and 0.08 mm in diameter by a restriction with a length of 40 mm and a diameter of 0.09 mm the flow decreased to 3.8 mg/s and the temperature to about 120 K. These two temperatures are higher than the boiling temperature because at the boiling temperature no net refrigeration is available. In a follow-up experiment the gas was not filtered as it was supplied from the bottle to the high-pressure line in the cooler. As a result clogging occurred at the cold stage and the flow rate slowly decreased due to the increasing impedance of the JT valve. This effect made it possible to study the cooling performance as a function of the mass flow at constant pressure. At a flow of 2.3 mg/s the boiling point of 82 K was reached. Then, with a further decrease in flow, the temperature did not change until a minimum flow was reached. Below this minimum flow of about 1 mg/s the temperature of the cold tip increased.

This limited flow range with a cooling power large enough to reach the boiling temperature can be explained by means of a qualitative and schematic presentation of the relevant heat flows as a function of the mass flow, see figure 8.4. At high mass flow rates the CFHX is too small for the high radial heat transfer that is required for adequate heat exchange between the incoming high-pressure gas and the vented low-pressure gas. This non-ideal behavior of the CFHX causes a decrease in cooling power which can be expressed as a loss term. This CFHX loss, ql,CFHX, rapidly increases at high flow rates. Furthermore, the gross cooling power (qc,gross) scales with the mass flow rate. The losses due to radiation and conduction (ql,rad+cond) at the boiling temperature are flow independent. As a result, only a restricted range of flows yields a gross cooling power that is larger than the sum of the losses (Σql) . Only in that range a net cooling power (qc,net) at the boiling temperature is available.

He

at fl

ow

q c,gross

ql,rad +cond

ql,CFHX

qc,net

Mass flow mmin mmax

Σql

Figure 8.4 Schematic diagram of the net cooling power (qc,net), the gross cooling power (q,c,gross) and the sum of the losses (Σql) as function of the mass flow.


205

From the measurement of the minimum mass flow an indication of the total loss can be

calculated, resulting in a value of about 20 mW at 82 K and 100 bar for the 105 mm cooler. So, the loss of radiation and conduction at 82 K is less than 20 mW. For the 270 mm cooler this value is about 30 mW.

8.3 Miniature silicon/glass cold stage with TE precooling

This section discusses a miniature hybrid cold stage that can be used in combination with a sorption compressor. The thermodynamic cycle for this cold stage was proposed and discussed in sections 4.6.2 and 4.7.

8.3.1 Cold stage requirements

In section 4.6.2 it was shown that precooling of a LH cold stage with a TE cooler can improve the performance of the LH cold stage when it is used in combination with a sorption compressor. The requirements for such a cold stage are determined by the operating parameters of the complete cooling system, and are given in section 4.7. Additional requirements that will be discussed are: integration with TE-cooler, integration with a thermal load, temperature stability, size.

Integration with TE-cooler. It should be possible to mount a small thermo-electric cooler on the condenser that is located in the high pressure line, see figure 4.13. Proper heat transfer must be guaranteed from the condensing fluid to the surface area of the TE-cooler.

Integration with a thermal load at the cold end. A thermal load such as an IR-detector typically has a certain surface area that must be cooled uniformly. For that reason it is desired that the heat transfer from the liquid bath to the evaporator is high and that the evaporator itself is made of a material with a high thermal conductivity so that temperature gradients between the boiling liquid and the surface of the thermal load are minimized.

Temperature stability. Most applications of cryocoolers require a stable temperature at the cold end, preferably independent of the thermal load. A theoretical advantage of the LH-cycle is that the temperature of the boiling liquid is independent of the applied load, as long as the available cooling power is larger than the thermal load. However, the boiling temperature may vary due to a varying pressure drop over the low pressure return line and this should be minimized. Also, variation of the thermal load may cause temperature variations over the thermal resistance between the boiling liquid and the thermal load. For that reason, this thermal resistance should be minimized as well. If these intrinsic temperature variations cannot be minimized, a controlled heater can be added to the cold end of the cooler to maintain a stable temperature.

Size. Obviously, our goal is to construct a cooler of minimal size. The minimal size is limited by the mass flow and associated cooling power, which requires a certain size of the heat exchangers, condenser and evaporator.

Apart from these requirements, it is desired that the design and construction of the cold stage is simple and cheap. Another desired property is that the cold stage can be integrated with a vacuum housing on waferscale, see figure 1.2. In the next section, several design concepts will be compared shortly.

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8.3.2 Design considerations

Figure 8.5a shows a schematic of the cold stage with thermoelectric precooler and in figure 8.6 the cooling cycle is depicted in a T-s diagram for pH = 20 bar, pL = 1 bar, TA = 300 K, TTE = 240 K and TC = 168 K. This cycle combined with a sorption compressor gives an optimum overall cooler performance as was discussed in section 4.6.2. In the T-s diagram isobars and isenthalps are given, as well as the enthalpy changes that occur in the counterflow heat exchangers, condenser and evaporator if the cycle operates ideally in a situation where equilibrium exists between the supplied heat load and the cooling power.

Q


J-T restriction + evaporator

Refrigeration load



Condensor

TE-cooler

Heat-sink

(Sorption)Compressor

1 12 2

3 3

4 4

5

67

8 8

Q

Compressor

5

6a75a

(b)(a) Figure 8.5 (a) Schematic of the cold stage with thermoelectric precooling of the high pressure fluid; (b) Cold stage with an extra heat exchanger in the high pressure line at low temperature.

Figure 8.5b shows a configuration of the cold stage in which one heat exchanger is added in

the high pressure line. This heat exchanger reflects the situation that a large heat transfer occurs between the high pressure liquid in state 5 and the low pressure refrigeration temperature of the liquid bath. This situation will be discussed in more detail in section 8.3.3.

If all components of the system operate ideally, then the cooling power is given by 67hm ∆⋅& .

100

150

200

250

300

350

4 5 6 7 8s (J/gK)

T(K

)

12

34

5

65a/6a 7

820 bar

1 bar

-32 J/g-87 J/g

-358 J/g-93 J/g

0 J/g

+390 J/g

+93 J/g

+87 J/g

0.01 bar

0.1 bar

5 bar

10 bar

50 bar

100 bar

-200 J/g-100 J/g 0 J/g

-300 J/g 100 J/g

lines of constant enthalpy

Figure 8.6 T-s diagram for the cooling cycle depicted in figure 8.5.


207

To obtain the required cooling power of 200 mW, a mass flow of 0.5 mg/s is needed. The majority of the enthalpy change ∆h67 is created during condensation from state 3 to 4. A proper design of the condenser is, therefore, a major requirement so that the two-phase fluid reaches full condensation at state 4. The requirements on both counterflow heat exchangers, however, are less strict, especially when the requirements are compared with the requirements for the counterflow heat exchanger of a normal Linde-Hampson cycle without condenser (see section 2.4.3). If the first counterflow heat exchanger does not operate ideally, then the TE-cooler must supply more cooling power to compensate for the loss of enthalpy due to this non-ideal behavior. This increased cooling power corresponds to ∆h33’ = (1-εCFHX1)⋅∆h32 and is maximal if no counterflow heat exchanger is present at all, or ∆h33’ = ∆h32. For this situation the TE-cooler must supply 24% more cooling power. A similar situation holds for the second counterflow heat exchanger. If this one does not operate ideally, then the available enthalpy for cooling, ∆h67, is reduced by ∆h55’. This loss of cooling power is maximal if no counterflow heat exchanger is present at all, reducing the cooling power by 24% as well. Note that for a nitrogen LH-cycle operating from 300 K to 77 K the counterflow heat exchanger should operate with an efficiency of at least 92% to obtain a cooling power at all – see section 2.4.3.

Starting from the requirements given in section 8.3.1 and the cycle as described above, a number of different miniature design concepts can be compared. A comparison is shown in table 8.1; the design concepts are briefly discussed below.

Table 8.1 Qualitative comparison of different miniature cold stage concepts. glass tube glass

planar silicon planar

si/glass planar

si planar + glass tube

low thermal conduction losses

+ +/- -- +/- +

high transversal heat conduction to TE cooler and thermal load

- +/- + + +

integration with TE cooler - + + + + integration with thermal load

+/- + + + +

simple construction + +/- +/- - +/- vacuum house integration - + + + -

Glass tube. Despite the simple concept of the glass-tube cooler that was described in

section 8.2, a cold stage with integrated condenser is difficult to make from glass tubes alone. The high pressure gas that flows in the inner tube is difficult, if not impossible, to condense because of the limited heat transfer through the glass tubes and through the low pressure gas flowing through the annulus. Moreover, the described flow restriction is hard to control and an evaporator with good heat transfer is not available at all.

Glass planar. The coolers fabricated by MMR [8.6] and depicted in figure 2.37b could be classified as ‘glass planar’ coolers. Such coolers can relatively easily be fabricated by etching and bonding techniques and a TE cooler and thermal load can be integrated on the flat surface of the cooler. Furthermore, a vacuum housing such as depicted in figure 1.2 might be integrated on wafer-scale as well. Compared to glass tubes, glass planar coolers have a relatively large cross sectional area which will lead to larger conduction losses. Also, the transversal heat conduction to the TE cooler and thermal load is limited due to the use of glass.

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Silicon planar. The construction of silicon planar coolers could benefit of the wide range of MEMS technologies that are present. However, the thermal conduction of silicon is very high as was described in section 3.2.1. The required high transversal conduction to the TE cooler and to the low-temperature thermal load could benefit from this, but the thermal conduction losses through the cooler itself will be enormous as was explained in section 3.3.4.1, which makes this cooler concept impossible to be applied.

Silicon/glass planar. This cooler concept makes use of a combination of MEMS techniques for silicon and glass, such as described in section 3.2.2. It can, therefore, combine the attractive properties of the planar glass and silicon coolers such as described above, but it also makes the construction also more complicated.

Silicon planar + glass tubes. By combining silicon planar constructions for the condenser and evaporator with glass-tube counterflow heat exchangers, an interesting hybrid cooler may be constructed with attractive properties. However, the hybrid construction makes wafer-scale integration with a vacuum house impossible. This cooler concept will be worked out in more detail in the next sections.

8.3.3 Design

Figure 8.7 shows the design of a cold stage made of three silicon micromachined components with two glass-tube counterflow heat exchangers in between. All three silicon parts are constructed by fusion bonding of two 500 µm thick wafers in which channels and spaces are etched by KOH etching. After processing and separating of these silicon samples, the glass tube heat exchangers are manually glued into the samples, after which integration with a vacuum flange follows. This vacuum flange can be used to mount the cold stage into a vacuum chamber. Similar fused silica glass tubes were used as in the LH cooler that was described in section 8.2; the applied tubes have inner/outer diameters of 0.25/0.36 mm and 0.53/0.67 mm, respectively. Two glass support tubes are added parallel to the two counterflow heat exchangers to improve the stability of the system.

The left silicon part is called ‘splitter’, and makes it possible to supply separate connection lines to the high and low pressure channels of the first counterflow heat exchanger. In the condenser, the high pressure fluid that exits the first counterflow heat exchanger is able to condense in the long meandering channel that is etched in the silicon. This long channel ends in the high pressure tube of the second counterflow heat exchanger, which connects to the third silicon part, the restriction/evaporator. The high pressure fluid that enters the restriction/evaporator flows through an etched channel to the entrance of the flow restriction, which typically consists of a 4 mm wide, 1 µm shallow channel with a length of about 3 mm. Because the restriction/evaporator is made of a high conductivity material, the high pressure fluid that enters the silicon part easily cools to the low temperature of the evaporator before it enters the flow restriction. This is represented by the dotted extra heat exchanger in figure 8.5b and step 5-5a in the T-s diagram of figure 8.6. In this step, heat is exchanged with the liquid bath, corresponding to an enthalpy change from state 6a to 6. In this situation, the expansion occurs completely in the liquid state from state 5a to state 6a (these two states almost coincide in the T-s diagram of figure 8.6), whereas expansion from state 5 to 6 occurs partially in the vapor state. The low pressure liquid that exits the flow restriction (in state 6a in figure 8.6) is collected in the liquid bath of the evaporator, which connects at the top side to the low


209

pressure annulus of the second counterflow heat exchanger. In the present design, the orientation of the cold stage is important: the low pressure exit of the liquid bath should be oriented vertically upward so that gravity keeps the liquid in the bath and only vapor exits the liquid bath, except when the liquid bath is full. Both the flow restriction and the boiler structure are supported by pillars to prevent excessive bending stresses due to the high gas pressures of 20 bar that may be present. Notice that, in principle, in the boiler only (vapor) pressures of about 1 bar are present, except when the low pressure return line is blocked, for some reason. Finally, the low-pressure vapor returns through the annuli of the heat exchangers to the low pressure exit of the splitter.

The high pressure inner glass tubes are glued into the condenser and restriction/evaporator via a so-called ‘glue hole’, whereas the outer glass tube is glued at the entrance of the sample, see figure 8.7. This construction facilitates a robust separate connection of the high and low pressures. Furthermore, the condenser and the restriction/evaporator contain an etched channel that can be used to insert a 250 µm thick thermocouple to measure the temperature of these cooler parts.

The surface area of the condenser fits approximately to the surface of a two stage thermoelectric cooler, which is a MI2012T-type fabricated by Marlow Industries [8.7]. In the same way, a thermal load (some device) can be attached to the restriction/evaporator. In the current design, however, for test purposes a thin film heater is deposited on the restriction/evaporator and on the condenser. This heater can be used to study the behavior of

splitter condenser restriction/evaporator

restriction/evaporator

counterflow heat exchanger 1

counterflow heat exchanger 2

support tube

9 mm

phigh

plow

~2.5 cm

glue hole

channel for thermocouple

1.1 mm

restriction of 1.1 m highµevaporator

condenser

crosssection

cross section cross section

to compressor

thin fimheater

low

em

issi

vity

Au

laye

r

Figure 8.7 Design of a cold stage made of three silicon micromachined components with two glass-tube counterflow heat exchangers in between. Top: Overview of the design, bottom: details and cross sections of the condenser and restriction.

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210

the cold stage. To limit the radiation load on the cold stage, a gold layer is deposited on both sides of the cooler.

Because the glue hole connection was expected to be the major practical bottleneck of the cold stage, an additional backup-version of the cold stage was designed without counterflow heat exchangers. Instead, separate high and low-pressure glass tubes are applied, releasing the requirement to use glue hole connections, see figure 8.8.

In the next sections the designs of the different components are discussed more quantitatively. Different versions of the condenser, restriction and evaporator are presented.

8.3.3.1 Counterflow heat exchangers Important requirements for the two counterflow heat exchangers are: a small pressure

drop – especially for the low pressure return line, a low longitudinal heat conduction, and proper tube diameters so that the tubes can be integrated with the silicon elements as depicted in figure 8.7. Furthermore, a proper heat transfer and associated heat exchanger efficiency is desired (but not really required for a reasonable operation of the cooler, see section 8.3.2).

Capillary glass tubes are commercially available from Supelco [8.1] with the following outer and inner diameters (in millimeters): 0.36/0.10, 0.36/0.20, 0.36/0.25, 0.42/0.32, 0.67/0.53. Capillary tubes from other companies have similar diameters. Only the largest tube with an inner/outer diameter of 0.53/0.67 mm can be combined in a tube-in-tube configuration with one of the other smaller tubes. Fortunately, the 0.67 mm outer diameter of this tube can also be combined with the silicon elements by KOH-etching of a 0.35 mm deep channel in the two 0.5 mm thick opposite wafers; see figure 8.7.

Eq. (3.19) was used to calculate the pressure drop over the tubes for a mass flow of 0.5 mg/s; a parallel-plate approximation with C = 96 was applied to calculate the pressure drop over the annulus, resulting in a maximum error in the pressure drop of 5% for the depicted diameters of the annulus [8.8]. Figure 8.9 shows the pressure drop per cm of tube length as a function of the inner/outer diameter of the inner tube, for a constant inner diameter (0.53 mm) of the outer tube. The pressure drop is calculated for high pressure liquid and vapor in the inner tube, and low pressure liquid and vapor in the annulus. From the figure, it can be concluded that the pressure drop in the high pressure channel is relatively small, even for a diameter of 0.1 mm. The pressure drop over the low pressure annulus is more critical, but still rather small for an outer diameter of the inner tube of 0.36 mm and a length of a couple of centimeters. A combination of an outer tube with 0.67/0.53 mm diameter and an inner tube with 0.36/0.25 mm diameter was used in the design.

condenser restriction/evaporator

9 mm

phigh

plow

~2.5 cm

channel for thermocouple

Figure 8.8 Simplified design of a cold stage without counterflow heat exchangers, so that no glue holes and splitter are required.


211

The longitudinal heat conduction through the glass tube-in-tube configuration is very small. If it is assumed that ∆T = 60 K, it can be estimated by application of Eq. (3.27):

cmmWL

Pcond ⋅≈0.1

(8.1)

For a heat exchanger of one or two centimeters, the conduction heat losses through the heat exchanger can virtually be neglected compared to the radiation losses and conduction losses through the wires, which together are more than 10 mW (see section 8.3.5).

By application of the LMTD method that was described by Boersma [8.9], the required heat exchanger length can be calculated to reach a certain heat exchanger efficiency. For a mass flow of 0.5 mg/s and the temperatures and specific enthalpies in the cooler as described in figure 8.6, an efficiency of 75% is obtained for the first heat exchanger if the length is 1.3 cm and the tube diameters as given above. A similar length can be found for the second heat exchanger to operate with an efficiency of 75%. As a consequence, if 2.5 cm is taken for the length of both counterflow heat exchangers, then both heat exchangers operate with an efficiency close to 1 and the real cooling cycle should approximate the cycle as given in figure 8.6 – provided that the other components of the cycle operate properly.

8.3.3.2 Condenser In the condenser of the cooling cycle of figure 8.6, the vapor in state 3 must be transferred

to liquid in state 4 requiring a cooling power P34:

3434 hmP ∆⋅= & (8.2)

Route 3-4 consists, respectively, of cooling of superheated vapor from state 3 to the saturation temperature, condensation of vapor to liquid, and cooling of the condensed liquid to state 4 which is located somewhat below the saturation temperature. The temperature difference between the saturation temperature of the liquid-vapor interface in the condenser, Tsat, and the

20 bar, 270 K, vapor

20 bar, 205 K, liquid

Dhigh pressure

gas flow

D

0.53 mm

1 bar, 270 K, vapor

1 bar, 169 K, liquid

low pressuregas flow

0.25 0.361.0E-05

1.0E-04

1.0E-03

1.0E-02

1.0E-01

1.0E+00

0 0.1 0.2 0.3 0.4 0.5 0.6

Diameter (mm)

Pre

ssur

edr

op(b

ar)

Figure 8.9 Pressure drop per centimeter of tube length as a function of the inner and outer diameter of the inner tube of the counterflow heat exchanger. The inner diameter of the outer tube is taken constant (0.53 mm).

Chapter 8

212

surface temperature Ts is the rate-limiting parameter of the heat transfer in the condenser, which can be written as:

)(22 ssatspp TTAP −= α (8.3)

where the heat transfer coefficient α2p is given by Eq. (3.52) and As is the surface area of the condenser tube. For proper operation of the cycle, it is required that complete condensation is obtained for a given surface temperature Ts, or: P2p ≈ P34. This condition requires a proper condenser geometry (in fact: surface area) for a given (small) temperature difference between the saturation temperature and the surface temperature, (Tsat – Ts). For example, in order to reach complete condensation for the ethylene cycle that operates with a mass flow of 0.5 mg/s, (Tsat – Ts) = 1 K and a tube diameter of 100 µm, the tube should be longer than 5 cm.

200

220

240

260

280

300

0 0.5 1 1.5 2 2.5PTE (W)

TT

E (

K)

Pin = 6.5 W

smaller valuesof Pin

Figure 8.10 Temperature-load characteristic for the two-stage MI2012T TE-cooler from Marlow Ind. for an input power of 6.5 W. For smaller input powers, the load-line shifts to higher temperatures and smaller cooling powers.

For a given condenser configuration, the surface temperature of the condenser is fixed by

the interaction between the TE-cooler and the cooling cycle with its condenser. The behavior of the TE-cooler is characterized by its temperature-load characteristic, which is dependent on the input power of the TE-cooler, TTE = TTE(PTE, Pinput). Figure 8.10 shows a typical load-temperature diagram for the two-stage Marlow TE-cooler that was used. Dependent on the input power of the TE-cooler and the mass flow through the cooler, the condenser can be in one of two possible states: 1. The cooling power is large enough to reach complete condensation. For this situation, a

heat balance between Eq. (8.2) and the load-characteristics of the TE-cooler determines the state of the system, and supercooled liquid at some state 4 located on the liquid isobar exits the condenser at its surface temperature, or Ts = T4. More excess cooling power results in a lower Ts and thus a larger temperature difference (Tsat – Ts), which results in a larger heat transfer rate and more rapid complete condensation upon entrance of the vapor in the condenser.

2. The cooling power is too small to reach complete condensation. For this situation, a heat balance between Eq. (8.3) and the load-characteristics of the TE-cooler determines the state of the system. Dependent on the design (surface area) of the condenser, some temperature difference (Tsat – Ts) will be present between the saturation and surface


213

temperature. By designing a condenser with a large surface area (see above), this temperature difference can be made small so that Ts, that can be measured easily, is very close to Tsat.

Condensers were designed with a channel diameter of 100 µm and three different channel lengths: 1.2 cm, 7.5 cm and 14 cm. The longer channels could be applied for larger mass flows, but even the shortest length would yield complete condensation if the TE-cooler is adjusted to 240 K, as suggested in figure 8.6. In fact, the condenser should not be a critical component for proper operation of the cooling cycle.

8.3.3.3 Restriction/evaporator Operation and design of the Joule-Thomson flow restriction for a LH-cycle is dependent on

the type of flow that passes through the restriction. LH-coolers are often made of stainless steel components that have a low longitudinal thermal conduction so that the situation of figure 8.5a applies. As a consequence, during expansion the major part of the fluid is in the vapor phase and the large pressure drop creates sonic flow, which requires theory of compressible fluids for the design of the flow restriction. In our design of the cold stage, the large thermal conduction of silicon in the restriction/evaporator facilitates a large heat transfer between the high pressure liquid and the low pressure refrigeration temperature of the liquid bath, which is represented by the extra heat exchanger in figure 8.5b. The refrigerant is completely in the liquid state when it enters the restriction, and it stays in the liquid state until the low pressure is reached at the exit of the flow restriction. As a consequence, viscous flow with a very small density change causes the pressure drop and any type of (capillary) channel that gives the desired flow restriction can be applied as the JT restriction.

An important requirement for the flow restriction is that it should be resistant to clogging by contaminant gases in the refrigerant. Clogging occurs when contaminant gases such as water freeze on the walls of the narrow restriction. Obviously, clogging can be reduced by reducing the amount of contaminant gases in the refrigerant, for instance by making use of (sorption) filters. In large LH-coolers, the JT restriction can often actively or passively be controlled to compensate for possible clogging and to adjust the delivered cooling power to the load applied [8.10]. Unfortunately, not much information is available about the detailed mechanisms that enhance or delay clogging. One publication was found which experimentally investigates clogging in sonic flows [8.11]. In another publication porous materials are suggested and successfully tested as fixed JT flow restrictions instead of long small-diameter capillary tubes [8.12]. The idea behind this type of restriction is that clogging can be delayed by maximizing the cross sectional area of the flow restriction. Inspection of Eq. (3.23) shows that for viscous flow through a restriction of a certain length, the cross sectional area can be maximized by minimizing the hydraulic diameter of the flow restriction. This is the case in a porous material, which consists of many parallel channels with a very small hydraulic diameter. The same effect can be reached by making a narrow but very wide channel.

If viscous, laminar, incompressible and isothermal flow is assumed, the mass flow through such a narrow but wide channel can be calculated by application of Equations (3.17) to (3.20) and is given by:

∫=H

L

p

p

dpTpTp

lbd

Tm),(),(

121

)(3

µρ

& (8.4)

Chapter 8

214

The density and viscosity are both strongly dependent on temperature and pressure, and must, therefore, be integrated over the pressure range of interest. Figure 8.11a shows a plot of the ratio ρ/µ as a function of the temperature, for different values of the pressure; data was obtained from PROMIX [8.13]. The sharp increase of ρ/µ for reducing temperatures is caused by the vapor-liquid transition, which is accompanied by a strong increase of the fluid density. Figure 8.11b shows the calculated mass flow as a function of the temperature for a channel with the following dimensions: l = 2.85 mm, b = 4.9 mm and d = 1.1 µm; a correction was made for the support pillars in the channel (see figure 8.7). For T < 244 K, the fluid enters the restriction in the liquid state, causing an increase of the mass flow. For T < 203 K, the mass flow decreases again because of an increased viscosity for lower temperatures at a nearly constant density.

Figure 8.11b was derived under the assumption of viscous, incompressible flow. For T = 169 K, the equilibrium boiling temperature at 1 bar, this assumption is valid because the fluid stays in the liquid state until the low pressure is reached. However, at higher temperatures during the initial cool-down phase of the cooler, the fluid transfers into the vapor state at some intermediate pressure in the flow restriction, leading to additional compressible flow effects. For that reason, it is expected that during cool-down of the cold stage, the real flow will deviate somewhat from the calculated flow at higher temperatures in figure 8.11b. A rough estimation was made for the flow at ambient temperature using compressible flow-theory [8.14], which resulted in a roughly 50% smaller flow. Since the detailed behavior during cool-down is not of major interest, no more attention was given to these compressible flow effects.

The available surface area of the restriction/evaporator samples was divided between the flow restriction and the liquid bath. The size of the liquid bath was kept constant between different samples, but different values of the flow restriction were obtained by variation of the length and width of the flow restriction channel, see table 8.2. For one process run, the depth

0

1

2

3

4

5

6

7

160 180 200 220 240 260 280 300T (K)

dens

ity/v

isco

sity

(*1

06 s

/m2)

1 bar

5 bar

10 bar

15 bar

20 bar

(a)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

160 180 200 220 240 260 280 300T (K)

mas

sflo

w (

mg/

s)

(b)

Figure 8.11 (a) The ratio of the density and the viscosity as a function of the temperature, for different values of the pressure. (b) Calculated mass flow as a function of the temperature for a channel with: l = 2.85 mm, b = 4.9 mm and d = 1.1 µm.

Table 8.2 Dimensions and calculated mass flows for different flow restrictions. name l (µm) b (µm) d (µm) mass flow (mg/s) at 169 K, 20 bar

restr. 1.0 2845 4900 1.1 1.0 restr. 2.0 1472 4900 1.1 2.0

restr. 0.75 2845 3675 1.1 0.75 restr. 0.5 2845 2450 1.1 0.5

restr. 0.25 2845 1225 1.1 0.25 restr. 1.0_small 650 980 1.1 1.14


215

of the channel had to be fixed to one single value, as will be described in section 8.3.4. The flow restriction with smaller dimensions was included to investigate the influence of the flow restriction size on clogging.

The dimensions of the boiler are: l = 4.3 mm, b = 4.9 mm, d = 0.7 mm, which gives, after correction for the support structures, a volume of approximately 13 mm3. If this volume is filled with liquid ethylene, it corresponds to an heat of evaporation of 2.9 J at 1 bar vapor pressure. This liquid volume can be used to buffer variations in the cooling power or heat load.

8.3.4 Fabrication and results

8.3.4.1 Processing scheme Figure 8.12 shows the essential processing steps for the cold stage fabrication; more

detailed steps as well as the mask sequence and the wafer lay-out are given in appendix B. The processing steps are such that the surfaces of the wafers that are used for the direct silicon-silicon bond are covered with a protective nitride layer as much as possible to prevent degradation of the surfaces. Both wafers are double side polished wafers.

wafer 1 wafer 2

wafer 2

wafer 1

1) 6)

2) 7)

3) 8)

9)

4)

5)

Cr/Pt/AuCr/Au nitride

silicon nitride

Figure 8.12 Essential processing steps for the cold stage fabrication.

Wafer 1. (1) 1.0 µm LPCVD silicon nitride is grown on both sides and patterned by RIE

(Reactive Ion Etching) as a mask for KOH etching of the deep channels and the glue holes. Next, the mask for the flow restriction is prepared by etching (RIE) the nitride to 0.5 µm thickness. (2) The deep channels are made by KOH etching; for narrow channels the depth is fixed by the width of the V-shaped channel and for wide channels the depth is fixed by the etching time. (3) The mask for the flow restriction that was etched in step 1 is now activated by removing 0.5 µm nitride by means of 50% HF etching. (4) Next, the 1.1 µm deep flow restriction is etched by a very short KOH etching step. (5) Just prior to the bonding step, the nitride mask is removed using 50% HF etching.

Wafer 2. (6) 1.0 µm LPCVD nitride is grown on both sides of the wafer and subsequently etched back to 0.5 µm at the topside of the wafer by means of RIE. Next, the mask for KOH etching of the deep channels is patterned on the topside of the wafer by RIE. (7) The channels

Chapter 8

216

are etched by a KOH etching step similar to step 2. (8) Just prior to the bonding step, the 0.5 µm thick nitride mask is removed from the topside of the wafer using 50% HF etching, leaving 0.5 µm nitride on the backside of the wafer. This nitride layer will serve as an electrical isolation layer for the heater, which is deposited on top of the nitride in a later step.

Bonding and sample preparation. (9) Wafers 1 and 2 are connected using aligned direct wafer bonding techniques. Cleaning and chemical activation prior to bonding is essential [8.15]. The two wafers are annealed at 1100 °C in nitrogen atmosphere to enhance the bond strength. After this annealing step, a Cr/Au metal layer is sputtered on top of the two wafers to reduce the emissivity of the top surface; the 10 nm thick Cr layer serves as an adhesion layer. Next, a heater is made on the backside of the wafers by means of dry lift-off patterning. A stack of Cr/Pt/Au is used: 10 nm Cr is the adhesion layer, 400 nm Pt is the actual heater-resistance layer and the 50 nm Au layer reduces the emissivity of the backside surface. Finally, the wafers are sawed into strips of samples. Single samples are obtained by breaking the strips, thus freeing the heat exchanger entrance holes without contaminating the holes by sawing them.

Cold stage integration. Prior to gluing of the cold stage, the heater connection wires are soldered to the heater. Soldering after gluing is not possible because the high soldering temperature would destroy the glue. Next, the capillary glass tubes for the heat exchangers and

Figure 8.13 (a) Structured 4 inch silicon wafer after the first KOH etching step. (b) Close-up of splitter, condenser and restriction/evaporator samples. (c) Completely assembled cold stage connected to a vacuum flange with wiring to the thin film heaters. The coin (Dutch 25 cents) is 18 mm in diameter. (d) Opposite side of the condenser and evaporator with excess glue on the glue holes.


217

supports are accurately cut to the required length after which integration and gluing follows. Three subsequent process runs were done in which a number of critical steps were identified

and, where possible, resolved. The most important topics are discussed in the next sections. Figure 8.13a shows a structured 4 inch silicon wafer after the first KOH etching step (step 2 in figure 8.12); figure 8.13b shows some samples in more detail. An integrated cooler is shown in figures 8.13c and d.

8.3.4.2 KOH corner compensation. During KOH etching, convex corners in the mask must be ‘compensated’ to prevent

underetch of the corners. This underetch is caused by the presence of crystal planes in convex corners that etch at a fast rate. A number of compensation techniques are described in the literature [8.16], all based on the addition of a mask pattern that is underetched during the KOH etching process, resulting in a more or less perfect convex corner at the end of the etching step. The KOH mask design for the cold stage is characterized by small channels with many convex corners and limited space for compensation structures. For such a configuration, a suitable compensation method is to add beams at the corners in the <110> direction; these beams can be branched off to fit in the narrow space of the channels [8.16].

Figure 8.14a shows part of the initial mask design of a condenser, with corner compensation beams in the <110> direction. After successful processing of the wafers with the use of this mask, it appeared during integration of the samples with the glass tubes that the high pressure glass tubes were blocked from entering the high pressure channels in the samples, see figure 8.14a. This blocking was explained by the presence of remains of the corner compensation structure at the side wall and bottom of the channel. These remains are common for this type of compensation structure and can be divided into two types of remains. Firstly, the required length of the compensation structure is dependent on the etch rate ratio of the <411> and <100> planes, and this ratio is dependent on a number of process variables and may vary considerably from one run to another. As a consequence, if the length of the compensation structure is calculated for an average etch rate ratio of the <411> and <100> planes, then for some runs the calculated length of the compensation structure is too long and remains will be present. Secondly, etching of this type of compensation structure leaves a rim of several

(a)

(b)

compensation structure normalto the channel orientation

break-channel where the samples are separated

Figure 8.14 Detail of the initial (a) and final (b) version of the KOH-mask, showing the channels in which the tube-in-tube heat exchanger will be glued. Clearly visible are the KOH-compensation structures. Notice that, apart from the compensation structures, also the length-dimensions of the channels were adapted from the initial to the final design.

Chapter 8

218

micrometers in height at the bottom of the etched structure next to the compensation structure. These rims also caused problems in the fabrication of the check valves, and can be observed in figure 7.10. From these results it was concluded that, to prevent problems in KOH-etched channels which should be fitted with glass tubes, the compensation structures should always be aligned parallel to the channel orientation and not normal to the channel orientation. Figure 8.14b shows a part of the final mask design; samples fabricated with this design could be fitted successfully with the glass tubes.

8.3.4.3 Glue connections An essential but critical part of the cold stage design is the glue connection between the

glass tubes with Polyimide coating and the silicon components. Both the glue connection itself as well as the design of the glue hole connection for the high pressure tube were experimentally investigated.

The glue should fulfil two essential requirements. Firstly, the viscosity should be low enough for the glue to flow into the annular space between the glass tube and the silicon. Secondly, the glued connection should be resistant to repeated thermal cycling of the cold stage. Two different epoxy-based glues with the proper viscosity were selected and tested: Araldit from Ciba [8.17] and Varian’s Torr Seal [8.2]. In the experiments, a cold stage was assembled up to the second counterflow heat exchanger; the flow restriction/evaporator was not mounted but instead the end of the high pressure tube of the second counterflow heat exchanger was closed with glue. Next, a nitrogen gas pressure of 50 bar was applied to the high pressure inlet of the modified cold stage and the condenser was then thermally cycled by inserting it into a bath with liquid nitrogen. The sample glued with Araldit started leaking after the first thermal cycle. This was observed from gas bubbles emerging from the condenser when it was located below the liquid nitrogen surface. For the sample glued with Torr Seal no leakage could be observed by eye after 20 thermal cycles between room temperature and liquid nitrogen temperature. To verify if a small leakage would be present, the pressurized sample was inserted into a vacuum chamber and subsequently helium leak tested. No leakage was observed.

To check the glued connections after the experiments, the sample glued with Torr Seal was

Figure 8.15 SEM pictures of thermally cycled Torr Seal glue connections: (a) low pressure glass tube that enters a silicon condenser; (b) edge of a glue-hole.


219

sawed through and SEM-pictures were made of the cross section. Figure 8.15a shows a photo of the glued low pressure glass tube entering the silicon condenser. Clearly, a crack can be observed at the interface between the bulky excess glue (located at the outside of the silicon) and the silicon sample. However, the relatively thin layer of glue between the silicon and the glass tube stayed intact. An explanation for this difference may be that a larger tensile stress is induced at the interface of the bulky excess glue than at the interface of the thin layer of glue between the silicon and the glass tube. A similar difference can be observed in the photo of figure 8.15b, which shows a detail of the glued connection at the glue hole. Again, cracks can be seen but they stop when they enter the thin layer of glue between the silicon and glass. Similar cracking behavior was observed at other locations. It was concluded that Torr Seal can successfully be used to assemble the cold stage, although the observed cracks suggest a re-evaluation of this glue when it is considered for future long-term use.

Table 8.3 Five different configurations of the glue hole with increasing dimensions. configuration A B C D E glue hole (µm) 465 * 315 600 * 600 600 * 600 600 * 600 765 * 765 channel width at hole (µm)

465

600 * 600

700 * 700

765 * 765

765 * 765

mask design

top view after 300 µm etching

number of leaking samples (out of 14)

14

5

2

4#

0

#Three of the four leaking D-type connections were caused by too little applied glue. Initially, one type of glue hole connection was designed, with a rather small square hole of

465 x 315 µm (mask opening). Only a small fraction of the attempts resulted in a successful connection, and even then it was necessary to rotate the glass tube during gluing to spread the glue around the glass tube. This tube rotation easily led to shifting and glue-clogging of the glass tube, and it made the cooler integration a time-consuming job because the three glue-hole connections of a complete cooler had to be made one after the other. Moreover, the chance to produce a working cooler was very small. It was expected that widening of the glue holes and the channel below the glue hole would give better results. To investigate the influence of glue hole size and channel size, five different configurations were designed and fabricated – see table 8.3. Glass tubes were inserted in fourteen samples of each connection type and supplied with glue, without rotating the glass tubes. After curing, the samples were leak-tested; the results are depicted in table 8.3. For glue hole type D, three of the four leaking connections were caused by too little applied glue. From these total results it can be concluded that an increased channel width and glue hole size increased the chance of a successful connection significantly. Moreover, for the larger glue connections, rotation of the glass tube is not required anymore so that a complete cold stage can be integrated in one single glue-step. Figure 8.16a shows a cross section of a leaking type A connection, and figure 8.16b shows a cross section of a properly sealed type E connection. Figure 8.16c shows a longitudinal cross section of a glued high pressure tube (with a successful connection of type A, obtained by

Chapter 8

220

rotating the tube during gluing); on the left side of the picture the end of the low pressure tube can be seen.

8.3.4.4 Heater deposition To prevent liquid from entering the KOH-etched channels, dry lift-off with scotch tape was

applied to pattern the heater on the backside of the bonded wafers. For a number of wafers (but not all), the adhesion between Cr and nitride was bad and the heaters delaminated from the surface during the lift-off step. This can probably be explained by contamination of the nitride surface (by e.g. water), and back sputtering prior to the metal deposition should solve this problem. This facility, however, was not available on the used equipment. Samples with a destroyed heater were characterized by application of a separate heater that was connected to the evaporator.

8.3.5 Experiments

Different versions of the cold stage were characterized in a small vacuum chamber. Figure 8.17 shows a schematic drawing of the measurement set-up; photographs of the custom-made vacuum chamber with mounted cold stage are shown in figure 8.18.

Prior to mounting the cold stage, the TE-cooler (type MI2012T) from Marlow Ind. [8.7] was mounted to the backside of the vacuum chamber by means of Oral-B dental floss wire [8.18]. A thin layer of Glisseal vacuum grease [8.19] was applied in between to guarantee proper thermal contact. Next, a cold stage was inserted into the vacuum chamber and the condenser was tied to the TE-cooler with dental floss wire. Again, vacuum grease was applied

Figure 8.16 (a) Cross section of a leaking type A connection; (b) Cross section of a properly sealed type E connection; (c) Longitudinal cross section of a glued high pressure channel.


221

to guarantee thermal contact. Miniature stainless steel shielded thermocouples (type-E) with an outside diameter of 250 µm [8.20] were used to measure the temperature in the specially etched thermocouple-channels of the condenser and the evaporator. In addition, the temperature was monitored at the ambient side of the TE-cooler. Electrical connections were made with the TE-cooler and the thin film heaters; the vacuum feedthroughs of the wires and thermocouples were made by Torr Seal [8.2]. The design of the set-up facilitated easy exchange of the cold stage. A 1 cm thick glass plate was used to close the vacuum chamber; in this way visual inspection of the set-up was possible. The glass plate also facilitated observation of two-phase flow effects in the glass-tube heat exchangers, by making use of a video camera. To create a proper vacuum, the chamber was connected to a turbomolecular pump that was backed by a rotary pump.

The high pressure input of the cold stage was connected to an ethylene gas bottle (99.95% purity), with a zeolite filter in between to trap possible contaminant gases. Bronkhorst mass-flow sensors [8.5] were used to measure the mass flows going into and coming out of the cold stage. A miniature Kulite pressure transducer [8.21] was used to measure the pressure at the inlet of the cold stage. The gas-lines could be purged and evacuated by the vacuum pump, using valves and other plumbing.

A PC with a National Instruments Data Acquisition Card [8.22] was used to measure the following parameters: the temperatures of the condenser and evaporator, the input powers into the heaters and the TE-cooler, the input high pressure and the mass flow going into the system and coming out of the system. A custom-written Labview [8.22] program was used to process, visualize and store the measurement data. The input power of the TE-cooler as well as that of the heater on the evaporator could be adjusted via two PID controllers that were integrated in the Labview program. In this way, the temperatures of the condenser and the evaporator could be controlled accurately.

A typical measurement is depicted in figure 8.19. The cold stage that was used in this

experiment contained a condenser-sample with a channel length of 7.5 cm. The evaporator-sample contained a flow restriction with a width of 2.54 mm, a length of 2.75 mm and a depth

Q

filter min mout lab

bottleC H2 4

p

Tcondenser

Tevaporator

Pheater

PTE-cooler

pressureregulator

vacuumpump

Figure 8.17 Schematic picture of the cold stage characterization set-up.

Chapter 8

222

of 1.10 µm. Important steps of the measurement are numbered in the figure and are discussed below.

(1) The high pressure is supplied to the cooler and the evaporator cools to a temperature slightly below ambient. The cooling power corresponding to the enthalpy change produced at ambient temperature, ∆h12, is too small to overcome the thermal losses and reach lower temperatures. (2) The TE-cooler is started and temperature-controlled at 238 K, 6 K below the condensation temperature at 20 bar. As long as the condenser temperature is above 238 K, a maximum input power of 4.5 W is put in the TE-cooler. (3) The fluid starts to condense in the condenser. For a short period, the ingoing mass flow exceeds the outgoing mass flow to compensate for the liquid volume that is now being collected in the condenser. Also, the evaporator starts to cool more rapidly because of the increased cooling power of the liquid ethylene that now flows from the condenser to the evaporator. As long as the temperature of the evaporator is above the saturation temperature of ethylene at 20 bar (244 K), the produced liquid will evaporate upon reaching the silicon evaporator-sample – thus providing cooling

Figure 8.18 (a) Vacuum chamber with mounted cold stage, electrical connections, thermocouples and glass plate coverage. (b) Detail with the condenser and evaporator.


223

power to cool the sample. (4) The high pressure fluid now starts to enter the restriction as a liquid, which increases the mass flow because of changing fluid density and viscosity. This increase of mass flow requires more cooling power to condense the fluid in the condenser and, therefore, the input power of the TE-cooler increases. (5) The low pressure boiling temperature is reached and the boiler starts to fill with low pressure liquid. This explains why the ingoing mass flow exceeds the outgoing mass flow for a while. The outflow does not reach zero because of a partial evaporation of the produced liquid, caused by the heat load from the environment and cooling of the incoming high pressure liquid. Integration over time of the difference between the inflow and the outflow closely matches the amount of liquid that can be stored in the boiler, which is about 7 mg. (6) Because the cooling power exceeds the applied thermal load, two-phase fluid exits the evaporator. Capillary effects may explain the variations in the outgoing mass flow. The excess low pressure liquid that flows from the evaporator to the condenser will first exchange heat with the high pressure liquid in the second counterflow heat exchanger, and then evaporate upon entrance of the condenser. This gives cooling power, which is subtracted from the TE-cooler. This explains the reduction of the input power of the TE-cooler after t = 420 s.

In figure 8.20 the measured mass flow is plotted as a function of the temperature of the evaporator. In the picture, calculated mass flows are included, which were obtained by application of Eq. (8.4). The plotted experimental data is derived from the measurement depicted in figure 8.19; for temperatures below 240 K, the smooth data of the outflow is used and for temperatures above 240 K the smooth data of the inflow is used. From the figure it can be concluded that the measured flow is somewhat larger than the calculated flow, with a maximum deviation of about 25%. Some possible explanations for this deviation are as follows: 1. Eq. (8.4) is derived from Eq. (3.19), which gives the pressure drop for incompressible,

fully developed, viscous flow. In deriving Eq. (8.4), the friction factor f is used for laminar flow, f = C/Re, where C is a constant that can be analytically derived from the cross sectional shape of the tube and which is assumed to be independent of the scale. However, both Choi [8.23] and Pfahler [8.24] measured a reduced pressure drop in microchannels –

0

5

250 300 350 400 450

Pin

,TE (

W)

-110

-60

-10

250 300 350 400 450

T (

C)

T cond

T evap

0

0.5

1

250 300 350 400 450t (s)

flo

w (

mg

/s)

m flow in

m flow out

1

23 4

5 6

(a)

Figure 8.19 Typical measurement of a start-up of the cold stage.

Chapter 8

224

see the discussion in section 3.3.5. Pfahler measured a deviation of 19% for liquids flowing through channels with a width in the order of 1 µm. If such a deviation of the friction factor is taken into account in the calculated flow, then the corrected curve for f’ = f⋅0.81 is obtained.

2. Some deviation is possible in the etched depth of the flow restriction, because of non-uniformities over the wafer surface of the KOH etching step. The etched depth was only measured at one location. A variation of the depth of the flow restriction has a strong impact on the resulting flow, see Eq. (8.4).

3. As was discussed in section 8.3.3.3, compressible flow effects play a role at higher temperatures during cooling-down of the evaporator. Apparently, these compressible flow effects do not lead to very large deviations, but they may contribute to a deviating flow at higher and intermediate temperatures.

An important parameter of the cold stage is the net cooling power that can be withdrawn

from a thermal load, PC,net. This net cooling power can be measured with the use of the thin film heater. Two different methods were used that are described below. 1. A fixed heater power was applied to the heater on the evaporator, and slowly increased in

small steps, see figure 8.21. During the initial increase of the heat load, a small temperature increase of the evaporator can be observed, which may be explained by the temperature gradient that is present between the wall of the boiler and the boiling liquid. At a certain applied power, the liquid contents of the boiler started to evaporate and after complete evaporation a strong rise of the evaporator temperature was observed. Both effects indicated that Pheater > PC,net. The net cooling power lies in between the last and the fore-last applied heater power, for this case between 122 mW and 155 mW for a mass flow of 0.54 mg/s. The first two rapid temperature increases are probably caused by capillary forces at the exit of the boiler, which play an important role because of the small channel dimensions. Furthermore, integration of the difference between inflow and outflow over the period that the contents of the boiler evaporates shows that a complete boiler volume of liquid ethylene was evaporated.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

168 188 208 228 248 268 288T (K)

mas

sflo

w (

mg/

s)

measured flow

calculated flowcalculated flow,corrected withf ' = f * 0.81

Figure 8.20 Measured and calculated mass flows as a function of the evaporator temperature. The corrected calculated flow is based on a reduced friction factor in micrometer-sized channels, as was described by Pfahler [8.23].


225

2. By applying controlled heating power in the thin film heater, the temperature of the boiler was controlled at a fixed temperature, slightly above the boiling temperature of the low pressure liquid in the boiler. This situation is illustrated in figure 8.22. The average input power in the heater now equals the net cooling power. For this measurement at t = 400 s: m& = 0.285 mg/s and PC,net = 59 mW.

These measurements can now be compared with the expected net cooling power, which follows from:

lossesCgrossCnetC PPP ,,, −= (8.5)

where:

67, hmP grossC ∆⋅= & (8.6)

0

0.1

0.2

0.3

700 800 900 1000 1100 1200

P(W

) P heater

-110

-105

-100

-95

-90

700 800 900 1000 1100 1200

T(C

)

T evap

0

0.5

1

700 800 900 1000 1100 1200t (s)

flo

w (

mg

/s)

m flow in

m f low out

(b)

peak: 4 mg/s

due to capillary pres-

sure in return line

Figure 8.21 Step-by-step increase of the heater load on the evaporator. At Pheater = 155 mW, the boiler contents evaporates and the evaporator temperature starts to rise.

0

2

4

0 200 400 600 800

P (

W)

0.0

0.1P TE

Pheater

-110

-60

-10

0 200 400 600 800

T (

C)

T cond

T evap

0

0.4

0.8

0 200 400 600 800t (s)

flo

w (

mg

/s)

m flow in

m flow out

Figure 8.22 Measurement in which the temperature of the evaporator is controlled at 170 K by supplying controlled power to the heater. Notice that the mass flow is lower than expected (about 0.65 mg/s) and that it is still gradually decreasing in time. This is caused by partial clogging of the flow restriction.

Chapter 8

226

radcondwirescondvacuumcondCFHXidealnonCFHXlossesC PPPPPP ++++= − ,,,,, (8.7)

In Eq. (8.6),, ∆h67 is the available enthalpy for cooling (= 390 J/g, see figure 8.6). Furthermore, in Eq. (8.7) PCFHX,non-ideal are the efficiency-losses in the second counterflow heat exchanger, which can be neglected as was discussed in section 8.3.3.1. PCFHX,cond are the conduction heat losses through the second counterflow heat exchanger from the condenser to the evaporator. Since PCFHX,cond < 0.5 mW, these losses are also neglected for ease of calculation. Pvacuum,cond are the conduction losses through the residual gas in the vacuum chamber. These conduction losses are dependent on the vacuum pressure and can be estimated by application of the theory in chapter 5. If pvacuum < 10-3 mbar, then Pvacuum,cond < 1 mW and these conduction losses can be neglected. This situation applies for the described experiments. This reduces the losses on the evaporator to thermal conduction through the wires, Pwires,cond, and radiation from 300 K on the evaporator, Prad.

Thermal conduction occurs through the wires and through the thermocouple, and can be estimated by application of Eq. (3.27). To connect the heater on the evaporator, two copper (λCu = 390 W/mK) and to manganin (λMng = 22 W/mK) wires of 200 µm diameter and 15 cm length were used. In addition, a 12.5 cm long thermocouple with a 250 µm diameter was used. The averaged thermal conduction of the thermocouple materials and the stainless steel shield was estimated as 15 W/mK. In total, for TA – TC = 130 K, the conduction losses through the wires equal 23.1 mW.

Radiation occurs from the 300 K environment to the cold surface of the evaporator, and can be estimated by application of Eq. (3.37), where Aout >> Ain. The exposed surface area of the evaporator equals 200 mm2, and consists for 71% of a very low emissivity (≈ 0.02) gold surface, and for 29% of a very high emissivity (≈ 0.9) bare silicon and soldered surface. This results in a total radiation load on the evaporator of approximately 22.4 mW.

The total losses on the evaporator follow now as 55.5 mW. In table 8.4 these calculated losses are compared with the measured losses for the two described experiments; they agree well for both measurements.

If necessary, the thermal losses on this type of cold stage can be reduced drastically. This requires a reduction of the fraction surface area with a high emissivity and the use of a better wiring technique of the thermal load. In the case of the heater, for instance, a less thermally and electrically conductive wire can be used if the electrical resistance is chosen much higher than the 20 ohm that was used in the present design.

The measurement of figure 8.22 illustrates a problem that sometimes occurred: clogging of the flow restriction. The measurement was carried out with the same cold stage as the one used in the measurement of figure 8.19. As a consequence, at TC = 169 K a mass flow of 0.64 mg/s is expected instead of the measured 0.25 mg/s. Mostly, in the case that clogging occurred, the mass flow gradually decreased until no net cooling power was left and the evaporator temperature started to rise. The flow then suddenly increased again when the

Table 8.4 Overview of the measured and calculated data for the two experiments in which the cooling power was determined. experiment figure m

(mg/s) PC,gross (mW)

PC,net,measured (mW)

PC,losses,from meas. (mW)

PC,losses,calculated

(mW) 1, step-wise 8.21 0.54 211 122-155 56-89 55.5 2, controlled 8.22 0.285 111 59 52 55.5


227

evaporator temperature approached 0 °C, which indicates that water was frozen in the flow restriction. On some rare occasions, it was observed that also the condenser was clogged. The ethylene supplied from the gas bottle contained < 5 ppm water molecules. It is most likely that the zeolite filter was not able to adsorb this water content for long periods of time, which explains the observed clogging. Clogging could be prevented for several hours of operation when the cold stage and connecting lines were first evacuated. This pumping of the cold stage was facilitated by the set-up that is depicted in figure 8.17.

0

2

4

6

0 300 600 900 1200

PT

E (

W)

0.0

0.2

0.4P TE

Pheater

-110

-60

-10

0 300 600 900 1200

T (

C)

T cond

T evap

0

1

2

0 300 600 900 1200t (s)

flo

w (

mg

/s)

m flow in

m flow out

Figure 8.23 Measurement to determine the cooling power that is similar to the measurement depicted in figure 8.21. In the present experiment, a strong temperature rise of the evaporator can be observed before the liquid in the boiler is evaporated.

Another problem that was observed is illustrated in the measurement of figure 8.23. The

same step by step increase of heater power was applied that was described above for the measurement of figure 8.21. However, for the present experiment a strong temperature rise of the evaporator is observed for heater powers which are still smaller than the net cooling power (for a mass flow of 0.65 mg/s, the net cooling power is about 200 mW). At the same time, by eye another difference was observed between the two measurements. For the measurement of figure 8.21, the return flow through the annulus of the second counterflow heat exchanger was a kind of bubbly flow; liquid was present but at the same time it was obvious that vapor was passing as well. For the measurement of figure 8.23, it was observed that the annulus of the second counterflow heat exchanger was completely filled with liquid and no vapor was observed to pass. A liquid-vapor front was present somewhere halfway the heat exchanger. This situation was stable until t ≈ 1030 s and TC ≈ 200 K, the moment at which suddenly the liquid blew away from the annulus and the contents of the boiler started to evaporate. This can be observed from the sudden increase of the outflow; integration of the difference between the in- and outflow yields the liquid mass that was stored in the boiler. As a consequence, at t < 1030 s there was liquid present in the boiler at a much higher saturation pressure than atmospheric pressure since TC >> 169 K. At TC = 200 K, the temperature at which the liquid blew away from the annulus and the boiler-contents started to evaporate, the saturation pressure in the boiler was 4.6 bar! Apparently, some kind of capillary force is present when the

Chapter 8

228

annulus of the second counterflow heat exchanger is filled with liquid. Although no vapor was observed to leave the evaporator for t < 1030 s, there was still much cooling power available in the evaporator; this can be concluded from the very slow temperature rise (if no cooling power was available, the temperature rise would have occurred with a much larger rate). In addition, it was observed that this behavior especially occurred after the cold stage was evacuated to prevent clogging of the flow restriction. Since evacuation desorbs gas layers that were adsorbed or frozen on the surfaces, this observation suggests some influence of the surface condition of the walls of the evaporator and heat exchanger tubes; possibly a thin ice film on the walls prevents the capillary effects. At the time of this writing, no complete explanation was found for these effects.

Anyhow, by application of a controlled heater power as depicted in figure 8.22, a very stable low temperature of the evaporator could be maintained. For this situation, all produced liquid is evaporated before it can enter the low pressure annulus of the second counterflow heat exchanger.

8.4 Conclusions

In this chapter two cold stages were presented, and the realization and successful tests were described. With the first cold stage it was demonstrated that two miniature glass tubes placed concentrically around each other can successfully be used as counterflow heat exchangers in coolers operating with small gas flows and cooling powers. The conductive heat leakage from the warm to the cold side of these heat exchangers is very low as a result of the small cross sectional area and the low thermal conductivity of glass. Two coolers of 10 and 27 cm in length and with a diameter of 0.67 mm operating with nitrogen gas could closely reach liquid nitrogen temperatures. For the 10 cm cooler, a minimum temperature of 82 K was reached for a mass flow of 2 mg/s. For the 27 cm cooler, a net cooling power of 60 mW at 88 K was measured for a mass flow of 7.3 mg/s.

In the second cooler, these glass tube heat exchangers were combined with three silicon components that were fabricated by a combination of etching and waferbonding techniques. A novel glue connection was designed to facilitate a simple integration with the glass tube heat exchangers. One of the components was a condenser that was integrated in the heat exchanger to preliquefy the fluid, thus improving the thermodynamic performance of the cold stage. Also the flow restriction and the liquid bath were fabricated in silicon. The design of the flow restriction in silicon facilitates an accurate design of the required mass flow and accompanying cooling power of the cold stage. A number of measurements were performed on the cold stages; theory and experiments agreed well.

8.5 References [8.1] Supelco/Sigma-Aldrich Corp., Bellefonte, PA, USA. [8.2] Torr Seal is a vacuum sealing epoxy sold by Varian Vacuum Technologies, 121 Hartwell Avenue,

Lexington, MA 02421, USA., www.varianinc.com. [8.3] Lake Shore Cryotronics Inc., 64 East Walnut St., Westerville, OH 43081-9941, USA. [8.4] Oxford Instruments Limited, Eynsham, Oxford OX8 1TL, United Kingdom.,

www.oxfordinstruments.com. [8.5] Bronkhorst High-Tech B.V., Nijverheidsstraat 1A, Ruurlo, The Netherlands., www.bronkhorst.com.


229

[8.6] Little, W.A., Microminiature refrigeration, Rev. Sci. Instrum., 1984, 55, (5), 661-680; MMR Technologies Inc., 1400 North Shoreline Blvd., #5-A Mountain View, CA 94043-1312, USA, www.mmr.com.

[8.7] Marlow Ind. Inc., 10451 Vista Park Road, Dallas, Texas 75238-1645, USA, http://www.marlow.com. [8.8] W.M. Kays and A.L. London, Compact heat exchangers, McGraw-Hill Inc., New York (1984). [8.9] N. Boersma, A counter flow heat exchanger for microcooling: modelling & characterization set up,

M.Sc. thesis, University of Twente (1997). [8.10] G. Walker, Miniature refrigerators for cryogenic sensors and cold electronics, Oxford University

Press (1989), pp. 27-35. [8.11] L. Wade, C. Donnelly, E. Joham, K. Johnson, R. Phillips, E. Ryba, B. Self and R. Stanton, An

investigation into the mechanics of Joule-Thomson valve plug formation. [8.12] A.R. Levy and L.A. Wade, Characterization of porous metal flow restrictors for use as the J-T

expander in hydrogen sorption cryocoolers, Cryocoolers 10, Kluwer Academic/Plenum Publishers, New York (1999), pp. 545-552.

[8.13] PROMIX, Cryodata Inc., Niwot, Colorado, USA, www.sni.net/partners/index.html. [8.14] R.W. Fox, A.T. McDonald, Introduction to fluid mechanics, 4th ed., Wiley, New York (1992). [8.15] C.Q. Gui, Direct wafer bonding with chemical mechanical polishing: applications in sensors and

actuators, Ph.D. Thesis, University of Twente, The Netherlands (1998). [8.16] H. Sandmaier, H.L. Offereins, K. Kühl, W. Lang, Corner compensation techniques in anisotropic

etching of (100)-silicon using aqueous KOH, Proc. 6th Int. Conf. Solid-State Sensors and Actuators (Transducers ’91), San Fransisco, USA (1991), pp. 456-459.

[8.17] Ciba Specialty Chemicals N.V., Performance Polymers, Noordkustlaan 18, B-1702 Groot-Bijgaarden, België., www.cibasc.com.

[8.18] Johnson and Johnson, Inc., USA., www.johnsonandjohnson.com. [8.19] Glisseal from Borer Chemie AG, Switzerland, www.borerchemie.com. [8.20] Omega Engineering, Inc., One Omega Drive, Stamford, Connecticut 06907-0047, USA,

www.omega.com. [8.21] Kulite Semiconductor Products, Inc., One Willow Tree Road, Leonia, NJ 07605, USA.,

www.kulite.com. [8.22] National Instruments, Inc., 6504 Bridge Point Parkway, Austin, TX 78730-5039, USA,

www.natinst.com. [8.23] S.B. Choi, R.F. Barron and R.O. Warrington, Fluid flow and heat transfer in microtubes, ASME –

Micromechanical sensors, actuators and systems, DSC-32 (1991), pp. 123-134. [8.24] J. Pfahler, J. Harley, H. Bau and J.N. Zemel, Gas and liquid flow in small channels, ASME Dynamic

Systems and Control Division, vol. 32 (1991), pp. 49-60.

231

9 Conclusions and outlook

Chapter 9

Conclusions and outlook

9.1 Conclusions

Chapters 1-3. The development of a micromachined cryocooler is clearly a very challenging goal that could have many different applications. Integration of such a cooler with the cold electronics and vacuum housing would yield a small package that could be integrated easily with other systems. There appear to be a number of opportunities for miniaturization of conventional fluid cycles to small dimensions. In particular, operation of heat exchangers and regenerators could benefit of scaling to small dimensions. On the other hand, thermal conduction losses become more important at a smaller scale. Careful modelling and design is, therefore, required on system and component level to obtain a high cooler efficiency. An increase of the efficiency directly leads to a smaller compression power. However, even for an optimized system, the requirements for the fluid compression are very demanding and the development of a powerful and compact MEMS compressor is one of the major challenges in this new field.

A miniaturized planar regenerative cooler was discussed that illustrates the use of MEMS technologies. The cooler is based on the Twente-Stirling cycle, a new regenerative cooling cycle that was proposed in this thesis. This cycle seems particularly attractive for miniaturization because the cold displacer reacts passively and non-resonant on the generated pressure wave from the compressor.

Chapter 4. In this research project, the rather unknown but proved principle of (thermal) sorption compression was chosen for the compressor development. It was combined with a fluid cycle that employs Joule Thomson expansion to obtain refrigeration. The significant required compression power made the principle not suitable for application on a MEMS scale. Instead, small precision engineered compressor cells were developed. The characteristics of physical adsorption make it impossible for a single stage system to cool from ambient temperatures directly to below 100 K. However, a single stage system may have a number of

Chapter 9

232

applications in different temperature ranges (depending on the applied refrigerant), and a two stage cascaded system can be applied for cooling from ambient temperatures to below 100 K.

A sorption compressor can be considered as a thermodynamic engine that converts high temperature heat into low temperature heat and mechanical work that appears as compressed gas. The ideal behavior of this Carnot engine is strongly reduced by two loss mechanisms: much heat is lost in the periodical heating of the heat capacity of the sorption material and container, and much compressed gas is lost in the dead volume of the sorption material. By choosing proper operating parameters, a compressor efficiency of about 4% can be obtained.

Technology was developed for the construction of small compressor cells with integrated gas-gap heat switches. This includes the development of: fabrication techniques for the compressor cells with integrated gas-gap heat switch, a novel heater solution, a miniature hydrogen actuator for the gas-gap actuation, and a miniature check valve unit. The development of the hybrid cold stage shows that MEMS techniques can be used for the fabrication of cryogenic cooling systems.

Chapter 5. A gas-gap heat switch around a sorption cell is desired to isolate the cell during heating and to conduct away this heat during cooling of the cell. An ON-OFF ratio of about 50 is suitable for proper operation of the cells. The thermal conduction through a gas gap is varied by adjusting the gas pressure in the gap. Pressure adjustment in a gas gap can be realized with hydrogen gas that can reversibly be ab- and desorbed from a small amount of metal hydride. It was demonstrated that polycrystalline ZrNi thin films are feasible as a small scale hydrogen pressure actuator, both with respect to the pressure swing that can be obtained and the switching times that can be achieved. The pressure could reversibly be varied between 0.03 Pa and 125 Pa by variation of the temperature between 60 °C and 230 °C. The required switching times of 30 seconds and less could be achieved.

Chapter 6. A sorption compressor cell with integrated gas-gap heat switch was developed, built and successfully tested. For the specified ethylene mass flow of 0.5 mg/s and compressor input power of 10 W, fabrication issues limited miniaturization to a cylinder diameter of 1 cm (and a length of 10 cm). Further miniaturization to a 5 mm diameter (and a length of 5 cm) seems possible, but with some sacrifice of the compressor efficiency. Different heater solutions were experimentally compared, leading to a solution in which a shielded thermocouple is simultaneously used as heater and as thermocouple inside the sorption compressor cell. Experiments showed that such a heater endures repetitive thermal cycling (>2⋅105 times) without significant deterioration of the thermocouple calibration. Experiments on the fabricated compressor cells showed that pressure differences can be realized that are close to the modelled values. The required pressure ratio could not be reached because of extra dead volumes in the experimental set-up, but for a complete compressor with four cells these volumes are not present and it is expected that the required pressure ratio can be produced with significant flow capacity. Two compressor cells were cyclically operated for 104 cycles, without an observed degradation of the performance.

Chapter 7. For continuous operation of a sorption compressor, check valves are needed to rectify the slowly ‘pulsating’ pressure variation of the individual sorption compressor cells. Sorption compressors typically produce a very high pressure ratio, and this puts strict requirements on the check valves: they should stand pressures up to 50 bar, and have a low pressure drop at low absolute gas pressures in forward direction. A valve with a boss

Conclusions and outlook

233

suspended by thin springs was developed; the boss and the springs could individually be optimized to fit the requirements. Fabrication was done by a combination of wet and dry etching in silicon, and subsequent waferbonding. Data from experiments on the valves agreed fairly well with the modelling. A long duration experiment involving many forward/closed switchings was done on two check valves. For both valves, proper operation was maintained until the experiment was stopped after 10000 and 25000 cycles, respectively. For both valves, a small leakage flow was observed in the reverse direction; it reduced during the first 1000 cycles to about 0.5% of the forward flow.

Chapter 8. Two different cold stages were built and successfully tested. With the first cold stage it was demonstrated that two miniature glass tubes placed concentrically around each other can successfully be used as counterflow heat exchangers in coolers operating with small gas flows and cooling powers. The conductive heat leakage from the warm to the cold side of these heat exchangers is very low as a result of the small cross sectional area and the low thermal conductivity of glass. Two coolers of 10 and 27 cm in length and with a diameter of 0.67 mm operating with nitrogen gas could closely reach liquid nitrogen temperatures. In the second cooler, these glass tube heat exchangers were combined with three silicon components that were fabricated by a combination of etching and waferbonding techniques. A novel glue connection was designed to facilitate a simple integration with the glass tube heat exchangers. One of the components was a condenser that was integrated in the heat exchanger to preliquefy the fluid, thus improving the thermodynamic performance of the cold stage. Also the flow restriction and the liquid bath were fabricated in silicon. A number of measurements were performed on the cold stages; theory and experiments agreed well.

9.2 Opportunities for further research

Clearly, a lot of opportunities exist for further research to microcoolers and microcooler components. The most important topics are listed below. Regenerative cycles. 1. Careful thermodynamic modelling of MEMS-compatible regenerative cooler-designs to

investigate if and how losses can be reduced to acceptable levels. 2. Development of a MEMS gas compressor that can supply at least 200 mW of mechanical

compression power with a pressure ratio of more than two. 3. Development of a MEMS regenerator. 4. Experimental investigation of the feasibility of the Twente-Stirling cycle that was

presented in section 2.3.8. Sorption compressr. 5. Extension of the thermodynamic model of the sorption cooler so that the behavior can be

related to generalized fluid properties instead of specific fluid properties. 6. Numerical modelling of the sorption compressor dynamic behavior (for a combination of

more cells) and the subsequent development of proper cooler control algorithms and electronic hardware.

6. Alternative compressor configurations. 7. Further development and testing of the two stage sorption compressor that was presented

in section 4.6.1. 8. Further simplification of the design of the compressor cells.

Chapter 9

234

9. Further miniaturization of the compressor cells. 10. Demonstration of a closed gas-gap heat switch with integrated micromachined ZrNi

hydrogen pressure actuator. 11. Demonstration of the complete sorption compressor, including the integrated gas-gap heat

switch, check valves and proper control hardware. 12. Demonstration of a sorption compressors with more than four cells and a fixed gas-gap

thermal resistance (instead of the heat switch, see section 6.2). 13. Search and/or development of improved adsorption materials. Check valves. 14. Further characterization of the check valves. 15. Simplification of the fabrication scheme of the valves. Recuperative cold stage. 16. Investigation of the pressure drops that were observed in the low pressure return line of

the cold stage. 17. Investigation of clogging of the cold stage. 18. Development of a complete MEMS-based recuperative cold stage. 19. Integration of a cold stage with a vacuum house in one MEMS-package. System. 20. Cooler integration and testing.

235

Appendix A: Processing sequence of the check valves

Appendix A: Processing sequence of the check valves

Mask layout nr. name CLE layer non-invert mirror description mask 1 boss SiN 4 yes yes Mask for RIE of nitride on

the backside of the boss. For use with negative resist.

2 springs 1 yes yes Mask for cryo RIE of the

thin springs in silicon, as well as a hole for gas feedthrough through the wafer.

3 KOH 2 yes no Mask for KOH etching.

Compensating structure generates some corner overetch to be sure that silicon rim on bottom is removed.

4 boss

frontside 3 yes no Mask for RIE nitride

removal on the frontside of the boss. Also used to pattern a Cr layer on the backside of wafer 1.

5 valve seat 5 yes no Mask for RIE of nitride

valve seat on top of wafer 3.

6 spring

cavity 6 yes no Mask for cryo RIE of spring

cavities and top part of the wafer-through RIE etching.

7 sieve 7 yes yes Mask for second cryo RIE

on the backside of wafer 3. This is done with a buried nitride mask, that also contains the filter structure.

8 channels 8 yes yes Mask for first cryo RIE on

the backside of wafer 3. The fotoresist mask is located on top of the (buried) nitride mask 7.

Appendix A

236

Mask sequence wafer 1: mask nr. mask name proc. step

4

boss frontside

2a wafer 2:

4 3 1 2

boss frontside KOH

boss backside springs

10a 9a

4a 5a

wafer 3:

6 5 7 8

spring cavity valve seat

sieve channels

17a 15a

19a 20a

Processing scheme wafer 2:

nr. process step mask nr. 3 4 5 6 7 8 9

10

11

nitride depostion

nitride RIE

silicon RIE

nitride RIE

nitride 50% HF etching

nitride deposition

nitride RIE

nitride RIE

silicon KOH

-

1

2 - - -

3

4 -

wafer 2

Processing sequence of the check valves

237

12

13

nitride HF etching/

silicon KOH

nitride HF etching

- -

wafer 3:

nr. process step mask nr.

14

15

16

17

18

19

20

21

22

23

24

nitride depostion

nitride RIE

nitride RIE

nitride RIE

silicon RIE

nitride RIE

resist RIE

siliconRIE

polyimide deposition

silicon RIE

nitride HF etching

-

5 -

6 -

7

8 - - - -

wafer 3

Bonding:


26-28

Bonding

-

wafer 1, pyrex

wafer 4, pyrex

wafer 2

wafer 3

Appendix A

238

Processing steps wafer 1 nr. process step parameters remarks 1 Substrate material - Corning #7740 (Pyrex), 3”

- double side polished - 500 µm thickness

1a Glass wafer cleaning - 100% nitric acid 15 min. - quick dump rinse, DI, < 0.1 µS - spin drying

user made

2a Lithography-S&A-907/17-3”

- dehydration bake: 120 °C, 10 min - primer: HMDS (liquid), 4000 rpm, 20 s - resist: Olin 907/17, 4000rpm, 20 s - prebake: hotplate 95 °C, 90 s - maskaligner: Electronic Visions AL-6 - parameters: 4 No 20 µm 4.0 mm Hard contact 30 µm 3” Top 100/10 N 0.4 mm Yes 5.0 s 2 - after exposure bake 120 °C, 60 s - development: OPD 4262, 45 s - quick dump rinse, DI, < 0.1 µS - spin drying - visual microscopic inspection

backside mask 4: “boss frontside”

2b Cr sputter-deposition - UT-build sputter system (Sputterke) - pre-sputter vacuum pressure: 1.0E-6 mbar - Ar-flow: 90 sccm - pressure: 5.0e-3 mbar - DC power: 200 W - Cr sputter rate: 10 nm/min

backside The deposited layer should be more or less optically transparant. thickness: 15 nm time: 1 min 30 s

2c Lift-off - lift-off in acetone and ultrasonic bath - quick dump rinse, DI, < 0.1 µS - spin drying

Processing steps wafer 2 nr. Process step parameters remarks 3a Substrate material

- Silicon 3” <100> - double side polished - 360 µm thickness

Surfaces must be parallel within 3 µm (so that all springs are freed simultaneously in step 10).

3b Introduction cleaning

- fuming nitric acid (II), 5 min - quick dump rinse, DI, < 0.1 µS - boiling 70 % nitric acid (90°C), 15 min - quick dump rinse, DI, < 0.1 µS - spin drying

cleaning directly before LPCVD step

3c 1% HF dip - 1% HF etchant - t > 1 min or hydrofobic surface - quick dump rinse, DI, < 0.1 µS - spin drying

3d LPCVD SiRN-S&A - Tempress LPCVD Furnace program N4 - SiH2Cl2 flow: 70 sccm - NH3 flow: 18 sccm - temperature: 850 °C - pressure: 200mTorr - deposition rate: 8.3 nm/min

thickness: 1 µm time: 120 min

4a Lithography-S&A ICT-3

Negative resist: - dehydration bake: 120 °C, 10 min - primer: HMDS, 4000 rpm, 20 s - resist: ICT-3, 4000 rpm, 20 s

backside mask 1: “Boss SiN”


239

nr. Process step parameters remarks - prebake hotplate: 95 °C, 2 min

- maskaligner: Electronic Visions AL-6 - parameters: 4 No 20 µm 4.0 mm Hard contact 30 µm 3” Top 100/10 N 0.4 mm Yes 2.5 s 2 - N2–pressure: 1.5 bar - development: xylene, 20 s (beaker) xylene, 30 s (spray) - cleaning with IPA, 25 s (spray) - dry spinning - postbake: hotplate 120 °C, 30 min

Negative resist was chosen to reduce the chance of residual resist-spots after development. These could cause severe problems during bonding. Beaker partly filled

4b Plasma etching of SiRN

- Elektrotech PF 310/340 (Etske) - dirty chamber - styros electrode - electrode temperature: 10°C - CHF3 flow: 25 sccm - O2 flow: 5 sccm - pressure: 10 mTorr - power: 75 W - etchrate SiRN: 80 nm/min - etchrate Olin resist: 80 nm/min - SiN profile: slightly tapered for PR - SiN profile: directional for metal mask

backside depth: 500 nm time: ~ 7 min 30 s Make sure the nitride is etched halfway through. Check etch rate before with laser interferometer set-up, if required

4c Photoresist strip (Oxygen plasma)

- oxygen plasma Nanotech Plasmaprep 100 - O2 flow: 55 sccm - power: 120 W - electrode temperature: 150 °C - pressure: 2.00 mbar - time: 15min

backside

4d Short cleaning - fuming nitric acid (I), 5 min - fuming nitric acid (II), 5 min - quick dump rinse, DI, < 0.1 µS - spin drying

Standard procedure prior to lithography on SiN with Olin 907 resist


- dehydration bake: 120 °C, 10 min - primer: HMDS (liquid), 4000 rpm, 20 s - resist: Olin 907/17, 4000 rpm, 20 s - prebake: hotplate 95 °C, 90 s - maskaligner: Electronic Visions AL-6 - parameters: 4 No 20 µm 4.0 mm Hard contact 30 µm 3” Top 100/10 N 0.4 mm Yes 5.0 s 2 - after exposure bake 120 °C, 60 s - development: OPD 4262, 45 s - quick dump rinse, DI, < 0.1 µS - spin drying - visual microscopic inspection - postbake: hotplate 120 °C, 30 min

backside mask 2: “springs”

5b Annealing photoresist

- Heraeus convection furnace 155-165 °C, 15 min - cool-down to 30 °C

Step is required to prevent cracking of the resist during the cryogenic etching step.

5c Plasma etching of SiRN

- Elektrotech PF 310/340 (Etske) - dirty chamber - styros electrode - electrode temperature: 10 °C - CHF3 flow: 25 sccm

backside etch through nitride depth: 500 nm time: ~7 min 30 s

Appendix A

240

nr. Process step parameters remarks - O2 flow: 5 sccm - pressure: 10 mTorr - power: 75 W - etchrate SiRN: 80 nm/min - etchrate Olin resist: 80 nm/min - SiN profile: slightly tapered for PR - SiN profile: directional for metal mask

(60 s overetch)

5d Deep Plasma etching of Si

- Oxford Plasma lab 100 ICP (Katharina) - temperature: –110C° - SF6 flow: 125 sccm - O2 flow: 0 sccm - pressure: 10 mTorr - pressure (He): 20 mbar - ICP power: 600 W Si etching: - power: 1.8 W - Vdc: 19 V - etchrate: 4.8 µm/min (measure!)

backside depth: 21.5 µm time: 4 min 27 s

5e Photoresist strip (Oxygen plasma)

- oxygen plasma Nanotech Plasmaprep 100 - O2 flow: 55 sccm - power: 120 W - electrode temperature: 150 °C - pressure: 2.00 mbar - time: 15 min

backside

5f Short cleaning - fuming nitric acid (I), 5min - fuming nitric acid (II), 5min - quick dump rinse, DI, < 0.1 µS - spin drying

Because step 6 will be on the opposite side of the wafer, remove (“lift-off”) contamination by short cleaning

6 Plasma etching of SiRN

- Elektrotech PF 310/340 (Etske) - dirty chamber - styros electrode - electrode temperature: 10 °C - CHF3 flow: 25 sccm - O2 flow: 5 sccm - pressure: 10 mTorr - power: 75 W - etchrate SiRN: 80 nm/min - etchrate Olin resist: 80 nm/min - profile: slightly tapered for PR - mask - profile: directional for metal mask

backside depth: 500 nm time: ~7 min 30 s Make sure the nitride is etched halfway through. Check etch rate before with laser interferometer set-up, if required

7 50% HF etch SiRN - 50% HF solution - etch rate: ~ 5 nm/min - quick dump rinse, DI, < 0.1 µS - dry spinning

depth: 500 nm time: 105 min Do not overetch too long; this could destroy the wafer surface for bonding.

8 Online cleaning - fuming nitric acid (I), 5min - fuming nitric acid (II), 5min - quick dump rinse, DI, <0.1µS - boiling 70 % nitric acid (90°C), 15 min - quick dump rinse, DI, < 0.1 µS - spin drying

8b 1% HF dip - 1% HF etchant - t > 1 min or hydrofobic surface - quick dump rinse, DI, < 0.1 µS - spin drying

8c LPCVD SiRN-S&A - Tempress LPCVD Furnace program N4 - SiH2Cl2 flow: 70 sccm - NH3 flow: 18 sccm - temperature: 850 °C - pressure: 200 mTorr - deposition rate: 8.3 nm/min


9a Lithography-S&A- - dehydration bake: 120 °C, 10 min backside


241

nr. Process step parameters remarks 907/17-3” - primer: HMDS (liquid), 4000 rpm, 20 s

- resist: Olin 907/17, 4000 rpm, 20 s - prebake: hotplate 95 °C, 90 s - maskaligner: Electronic Visions AL-6 - parameters: 4 No 20 µm 4.0 mm Hard contact 30 µm 3” Top 100/10 N 0.4 mm Yes 5.0 s 2 - after exposure bake 120 °C, 60 s - development: OPD 4262, 45 s - quick dump rinse, DI, < 0.1 µS - spin drying - visual microscopic inspection - postbake: hotplate 120 °C, 30 min

mask 3: “KOH”


- Elektrotech PF 310/340 (Etske) - dirty chamber - styros electrode - electrode temperature: 10 °C - CHF3 flow: 25 sccm - O2 flow: 5 sccm - pressure: 10 mTorr - power: 75 W - etchrate SiRN: 80 nm/min - etchrate Olin resist: 80 nm/min - profile: slightly tapered for PR - mask - profile: directional for metal mask

frontside depth: 1000 nm time: ~ 15 min



frontside



frontside mask 4: “Boss Frontside”


- Elektrotech PF 310/340 (Etske) - dirty chamber - styros electrode - electrode temperature: 10 °C - CHF3 flow: 25 sccm - O2 flow: 5 sccm - pressure: 10 mTorr - power: 75 W - etchrate SiRN: 80 nm/min - etchrate Olin resist: 95 nm/min

frontside depth: 500 nm time: ~8 min 15 s Not so critical, because only for creating a buried mask and not for bonding

Appendix A

242

nr. Process step parameters remarks - profile: slightly tapered for PR - mask - profile: directional for metal mask


- oxygen plasma Nanotech Plasmaprep 100 - O2 flow: 55 sccm - power: 120W - electrode temperature: 150 °C - pressure: 2.00 mbar - time: 15 min

frontside

11a 1% HF dip - 1% HF etchant - t > 1 min or hydrofobic surface - quick dump rinse, DI, < 0.1 µS

NO spin drying, insert wafers wet in KOH vessel

11b KOH etching of Silicon

- 500 gr KOH - 1500 ml - temperature: 75 °C - stir with magnet - <100> etchrate: 1.06 µm/min (measure!!)

depth = waferthickness - depth(step 5e) + 25µm time = 308 min depth = 326 µm (contains an overetch margin compared to the above calculated depth)

11c RCA Cleaning H2SO4/H2O/H2O2

H2SO4/H2O/H2O2 5 : 1 : 1 procedure: - add H2SO4 to H2O (exothermic) - wait till temp. 80 °C, (switch on heater) - add H2O2 - time: 20 min - quick dump rinse, DI, < 0.1 µS - spin drying - store wafers in a cleaned wafer box

12a 50% HF etch SiRN - 50% HF solution - etch rate: ~ 4-5 nm/min - quick dump rinse, DI, < 0.1 µS - NO dry spinning - Keep wafers wet during transportation

depth 500 nm time = 140 min (~20 min overetch) This step should remove the nitride from the boss on the frontside.


- 500 gr KOH - 1500 ml - temperature: 75 °C - stir with magnet - <100> etchrate: 1.06 µm/min (measure!!)

Etch till the springs are (optically) etched through. time: 23 min beam thickness: 14 µm



13 50% HF etch SiRN - 50% HF solution - etch rate: ~ 4-5 nm/min - quick dump rinse, DI, < 0.1 µS - dry spinning

time: 76 min Strip the nitride, but leave ~500 nm on the boss on backside.

Processing steps wafer 3 nr. process step parameters Remarks 14a Substrate material

Silicon, double side polished, 3” <100>, thickness larger than 360 µm

The thickness of wafer 3 must be larger than 360 µm (for fused silica tubes).

14b Introduction cleaning

- fuming nitric acid (II), 5 min - quick dump rinse, DI, < 0.1 µS - boiling 70 % nitric acid (90 °C), 15 min



243

nr. process step parameters Remarks - quick dump rinse, DI, < 0.1 µS - spin drying


14d LPCVD SiRN-S&A - Tempress LPCVD Furnace program N4 - SiH2Cl2 flow: 70 sccm - NH3 flow: 18 sccm - temperature: 850 °C - pressure: 200 mTorr - deposition rate: 8.3 nm/min


15a Lithography-S&A ICT-3

Negative resist: - dehydration bake: 120 °C, 10 min - primer: HMDS, 4000 rpm, 20 s - resist: ICT-3, 4000 rpm, 20 s - prebake hotplate: 95 °C, 2 min - maskaligner: Electronic Visions AL-6 - parameters: 4 No 20 µm 4.0 mm Hard contact 30 µm 3” Top 100/10 N 0.4 mm Yes 2.5 s 2 - development: xylene, 20 s (beaker) xylene, 30 s (spray) - cleaning with IPA , 25 s (spray) - dry spinning - postbake: hotplate 120 °C, 30 min

frontside mask 5: “Valve seat” Negative resist was chosen to reduce the chance of residual resist-spots after development. These could cause severe problems during bonding. Beaker partly filled


- Elektrotech PF 310/340 (Etske) - dirty chamber - styros electrode - electrode temperature: 10°C - CHF3 flow: 25 sccm - O2 flow: 5 sccm - pressure: 10 mTorr - power: 75 W - etchrate SiRN: 80 nm/min - etchrate Olin resist: 80 nm/min - SiN profile: slightly tapered for PR - SiN profile: directional for metal mask

frontside depth: 500 nm time: ~7 min 45 s Make sure the nitride is etched halfway through. Check etch rate before with laser interferometer set-up, if required



frontside

15d Short cleaning - fuming nitric acid (I), 5min - fuming nitric acid (II), 5min - quick dump rinse, DI, < 0.1 µS - spin drying

Because step 16 will be on the opposite side of the wafer , remove (“lift-off”) contamination by short cleaning


- Elektrotech PF 310/340 (Etske) - dirty chamber - styros electrode - electrode temperature: 10 °C - CHF3 flow: 25 sccm - O2 flow: 5 sccm - pressure: 10 mTorr - power: 75 W - etchrate SiRN: 80 nm/min - etchrate Olin resist: 80 nm/min

backside depth: 500 nm time: ~ 7 min 30 s Make sure the nitride is etched halfway through. Check etch rate before with laser interferometer set-up, if required

Appendix A

244

nr. process step parameters Remarks - SiN profile: slightly tapered for PR - SiN profile: directional for metal mask



frontside mask 6: ”Spring cavity”

17b Annealing photoresist



17c Plasma etching of SiRN

- Elektrotech PF 310/340 (Etske) - dirty chamber - styros electrode - electrode temperature: 10 °C - CHF3 flow: 25 sccm - O2 flow: 5 sccm - pressure: 10 mTorr - power: 75 W - etchrate SiRN: 80 nm/min - etchrate Olin resist: 80 nm/min - SiN profile: slightly tapered for PR - SiN profile: directional for metal mask

frontside etch through nitride depth: 500 nm time: ~7 min 22 s

18a Deep Plasma etching of Si

- Oxford Plasma lab 100 ICP (Katharina) - temperature: –110 °C - SF6 flow: 125 sccm - O2 flow: 0 sccm - pressure: 10 mTorr - pressure (He): 20 mbar - ICP power: 600 W Native oxide removal: - power: 7.5 W - Vdc: 47 V Si etching: - power: 2.0 W - Vdc: 19 V - etchrate: 4.6 µm/min

frontside depth: 43 µm total time: 9 min 55 s (incl native oxide removal) time: 30 s time: 9 min 23 s



frontside


Because step 19a will be on the opposite side of the wafer, remove (“lift-off”) contamination by short cleaning


- dehydration bake: 120 °C, 10 min - primer: HMDS (liquid), 4000 rpm, 20 s - resist: Olin 907/17, 4000 rpm, 20 s

backside mask 7: “Sieve”


245

nr. process step parameters Remarks - prebake: hotplate 95 °C, 90 s - maskaligner: Electronic Visions AL-6 - parameters: 4 No 20 µm 4.0 mm Hard contact 30 µm 3” Top 100/10 N 0.4 mm Yes 5.0 s 2 - after exposure bake 120 °C, 60 s - development: OPD 4262, 45 s - quick dump rinse, DI, < 0.1 µS - spin drying - visual microscopic inspection - postbake: hotplate 120 °C, 30 min



backside etch through nitride depth: 500 nm time: ~ 7 min 30 s



backside

20 Lithography-S&A-907/17-3”

- dehydration bake: 120 °C, 10 min - primer: HMDS (liquid), 4000 rpm, 20 s - resist: Olin 907/17, 4000 rpm, 20 s - prebake: hotplate 95 °C, 90 s - maskaligner: Electronic Visions AL-6 - parameters: 4 No 20 µm 4.0 mm Hard contact 30 µm 3” Top 100/10 N 0.4 mm No 5.0 s 2 - after exposure bake 120 °C, 60 s - development: OPD 4262, 45 s - quick dump rinse, DI, < 0.1 µS - spin drying - visual microscopic inspection - postbake: hotplate 120 °C, 30 min

backside mask 8: “channels”

21a Annealing photoresist



21b Deep Plasma etching of Si

- Oxford Plasma lab 100 ICP (Katharina) - temperature: –110 °C - SF6 flow: 125 sccm - O2 flow: 0 sccm - pressure: 10 mTorr - pressure (He): 20 mbar - ICP power: 600 W Native oxide removal: - power: 7.5 W

backside mask resist depth: ~250 µm total time: 55 min (incl native oxide removal) time: 30 s

Appendix A

246

nr. process step parameters Remarks - Vdc: 44 V Si etching: - power: 3.2 W - Vdc: 22 V - etchrate: 4.5 µm/min

time: 54 min 30 s


- oxygen plasma Nanotech Plasmaprep 100 - O2 flow: 55 sccm - power: 120 W - electrode temperature: 150 °C - pressure: 2.00 mbar - time: 15min

backside

22 Polyimide deposition - dehydration bake: 120 °C, 5 min - primer: APS PI with 2 µm filter, 3000 rpm, 30 s - prebake: 90 °C, 10 s - polyimide: Probimide 7510 3000 rpm, 30 s - prebake: 90 °C, 25 min. - maskaligner: Electronic Visions AL-6, exposure without mask: menu: EXP. ONLY, 35 s - bake in vacuum oven: 150 °C, time 180 min incl. ramp-up

frontside Increase speed gradually but not too slowly; do not use tweezers to prevent stiction of polyimide Adjust N2-purge to a pressure of 1 mbar and remove wafer at temperature of max. 25 °C

23a Deep Plasma etching of Si

- Oxford Plasma lab 100 ICP (Katharina) - temperature: –100 °C - SF6 flow: 140 sccm - O2 flow: 0 sccm - pressure: 10 mTorr - pressure (He): 20 mbar - ICP power: 600 W Native oxide removal: - power: 7.5 W - Vdc: 44 V Si etching: - power: 2.6 W - Vdc: 22 V - etchrate Si: ~ 4.5 µm/min - etchrate SiN: ~ 12 nm/min

backside mask: 0.5 µm SiRN depth: ~ 100 µm total time: 22 min (incl native oxide removal) time: 30 s time: 21 min 30 s

23b Photoresist strip (Oxygen plasma)

- oxygen plasma Nanotech Plasmaprep 100 - O2 flow: 55 sccm - power: 120 W - electrode temperature: 150 °C - pressure: 2.00 mbar - time: 60 min + 30 + 30 + 30 min

backside Probimide 7510 not removable by oxygen plasma!!!

23c Online cleaning - fuming nitric acid (I), 5 min - fuming nitric acid (II), 5 min - quick dump rinse, DI, < 0.1 µS - boiling 70 % nitric acid (90°C), 15 min - quick dump rinse, DI, < 0.1 µS - spin drying

remove contamination Probimide 7510 not removable by oxygen plasma!!!

24 50% HF etch SiRN - 50% HF solution - etch rate: ~ 4-5 nm/min - quick dump rinse, DI, < 0.1 µS - dry spinning

Strip all the SiN, due to the problem in step 15 Also lift-off Probimide 7510 !!!!


247

Processing steps wafer 4 nr. process step parameters remarks 25 Substrate material - Pyrex 3”

- double side polished - 500 µm thickness

25a Glass wafer cleaning - 100% nitric acid 15 min - quick dump rinse, DI, < 0.1 µS - spin drying

user made

Aligned fusion bonding wafers 2 and 3 nr. process step parameters remarks 26a Introduction cleaning - fuming nitric acid (II), 5 min

- quick dump rinse, DI, < 0.1 µS - boiling nitric acid (95 °C), 15 min - quick dump rinse, DI, < 0.1 µS - spin drying

direct before bonding step


check hydrofobic

26c RCA “Piranha” cleaning for fusion bonding H2SO4/H2O2

procedure: - add H2O2 to H2SO4, 1:3 - exothermic process - wait till temp. 100 °C, switch on heater - time: 20 min - quick dump rinse, DI, < 0.1 µS - store and transport wafers under water - spin dry just before bonding in nearest bench - spin parameters: time 1.5 min, max speed

direct before bonding step

26d aligning and Pre-bonding

maskaligner: Electronic Visions AL-6, parameters: - mask: 0.6 mm - substrate: 0.6 mm - wedge error eq. 8 - separation: 60 µm - contact vaccuum, bottom bond - N2 purge: 5 - contact force: 100/10 [10] - manual correction: 0 µm - load top wafer with bondsurface down - set cross-hairs on alignment marks - load bottom wafer with bondsurface up - align alignment marks of backside of bottom wafer to crosshairs - adjust N2 pressure for center bending bottom wafer (~1.5 bar) - NO seal rise and NO purging pre-bonding

top wafer is wafer 2 bottom wafer is wafer 3 Problem: Design is in conflict with the vacuum lines in the bondholder!!! Solution: - Load first w2 - Apply sticker on the backside of w2 (the side that will not bond) to overcome vacuum problem - Follow now step 26d - remove sticker from waferpair

26e IR-inspection - use IR setup to check the pre-bond - use tweezers for additional pressure to promote bonding of not bonded spots

26f Annealing - diffusion oven - N2 ambient - temperature: 1100 °C - time: 120 min (excl. up and down ramp from and to 800 °C)

26g IR-inspection - use IR setup to check final bond

Appendix A

248

Aligned Anodic bonding of wafers 1, 2/3,4: nr. process step parameters Remarks 27a Cleaning

Wafer 1 - fuming nitric acid, 15 min - quick dump rinse, DI, < 0.1 µS - spin drying

NOT in standard wafer cleaning Standard procedure for glass prior to anodic bonding

27b Waferpair 2/3

Cleaning not necessary, because last step was done in a clean annealing tube!

27c Aligned Anodic Bonding wafers 1 and 2/3

- Use home-made chuck and align by using the probe-station microscope. Align metal pattern of glass-wafer 1 on structures of wafer 2 - Bonding setup on Floor 7 - temperature: 400 °C - bonding voltage: 500 V - waiting time: 20 min - bonding time: 60 min

To avoid contamination of the bottom wafer (wafer 3) put a clean wafer between (+) bottom electrode and this wafer

28a Cleaning Wafer 4

- fuming nitric acid, 15 min - quick dump rinse, DI, < 0.1 µS - spin drying

NOT in standard wafer cleaning Standard procedure for glass prior to anodic bonding

28b Waferpair 1/2/3 Cleaning not necessary, because of remark made in step 27 c)

28c Anodic bonding wafers 4 and 1/2/3

- Bonding setup on Floor 7 - temperature: 400 °C - bonding voltage: 500 V - waiting time: 20 min - bonding time: 60 min

To avoid contamination of the bottom glass wafer (wafer 1) put a clean wafer between (+) bottom electrode and this wafer

Sawing of wafers and packaging of samples: nr. process step Parameters Remarks 29a Apply dicing foil - Standard procedure. Laminate tape on

glasswafer 1 of waferstack 1/2/3/4 Check / remove the contamination on glass due to Na2O

29b Dicing two individual valves

- Dicing Saw Model 1006 of Micro Automation Inc. - blade type: Thermo Carbon TC300 Settings: - thickness: 2200 µm (safe thickness) - speed: 1 mm/sec - diameter of wafer: 80 mm Two step dicing procedure : - height 1: 1000 µm - height 2: 0.09 µm - remove samples from foil

Side to dice: Glass wafer 4 First separate 2 valves See mask layout max depth: 2500 µm blade width: 300 – 350 µm thickness waferstack1/2/3/4 ~ 1720µm. Foil: ~ 80 µm distance between blade and chuck during rest distance between blade and chuck during dicing

29c Apply dicing foil - Standard procedure. Laminate tape on glasswafer 1 of waferstack 1/2/3/4

New foil on valve units

29d Partly dicing of units

- Dicing Saw Model 1006 of Micro Automation Inc. - blade type: Thermo Carbon TC300 Settings: - thickness : 2200 µm (safe thickness) - Speed : 1 mm/sec - diameter of wafer : 80 mm Partly dicing procedure parallel to flat: - height : 1110 µm - remove waferstack from foil

Side to dice: Glass wafer1 Dice lines parallel to flat Units stay closed after this procedure max depth: 2500 µm blade width: 300 – 350 µm thickness waferstack1/2/3/4 ~ 1720µm. Foil ~ 80 µm waferstack + foil thickness – wafernr1 – 250 µm

29e Apply dicing foil - Standard procedure. Laminate tape on glasswafer 4 of waferstack 1/2/3/4

New foil on valve units

29f Dicing of units

- Dicing Saw Model 1006 of Micro Automation Inc. - blade type: Thermo Carbon TC300

Side to dice: Glass wafer1 Dice lines parallel to flat only partly


249

nr. process step Parameters Remarks Settings: - thickness : 2200 µm (safe thickness) - speed : 1 mm/sec - diameter of wafer : 80 mm Partly dicing procedure parallel to flat: - height : 1560 µm Dicing procedure perpendicular to flat: - two step dicing procedure : - height 1: 1000 µm - height 2: 0.09 µm - remove samples from foil

Dice lines perpendicular to flat completely through Units stay closed after this procedure Waferstack + foil thickness – 300 µm distance between blade and chuck during dicing

30 Breaking of samples - break samples on a sharp edge 31 Packaging using fused

silica tubes - measure required length of fused silica tubes to fit sample and brass connecting device - make scratch in tube and break it; use cutting tool or piece of silicon or aluminium oxide - insert both tubes in the sample; use 3D microscope - apply a small amount of expoxy glue (Araldide Rapid) around tube-silicon interface. Make sure the complete interface is wetted. - connect the brass device and seal with Araldite. Let it dry.

251

Appendix B: processing sequence of the cold stage

Appendix B: Processing sequence of the cold stage

Mask sequence Five different masks are used for the fabrication of the cold stage; the names and orientation are given in the figure

below. Masks 1 and 4 are identical but mirrored with respect to each other.

wafer 1: mask nr. mask name proc. step cross section

2 1 3

RIE JT channel KOH channels 1

KOH glue holes

3a 2a

4a wafer 2:

4 5

KOH channels 2

heaters

11a

16a

Processing scheme wafer 1:

step nr. process step mask nr. 1 2 3 4 5 6 7 8

nitride depostion

nitride RIE

nitride RIE

nitride RIE

KOH etching


silicon RIE


-

1

2

3 - - - -

Appendix B

252

wafer 2: step nr. process step mask nr.

9

10

11

12

13

nitride depostion

nitride RIE

nitride RIE

silicon KOH


- -

4 - -

Bonding:


14

15

16

Bonding

Cr/Au sputtering

Cr/Pt/Au sputtering + lift-off

- -

5

Processing steps of wafer 1 nr. process step parameters remarks 1a Substrate material Silicon, double side polished, 4” <100>,

525 µm thickness DSP is required because of the lower radiation emissivity of a polished (and coated) surface.

1b Introduction cleaning - fuming nitric acid (II), 5 min - quick dump rinse, DI, < 0.1 µS - boiling 70 % nitric acid (90°C), 15 min - quick dump rinse, DI, < 0.1 µS - spin drying



1d LPCVD SiRN-S&A - Tempress LPCVD Furnace program N4 - SiH2Cl2 flow: 70 sccm - NH3 flow: 18 sccm - temperature: 850 °C - pressure: 200 mTorr


Processing sequence of the cold stage

253

nr. process step parameters remarks - deposition rate: 8.3 nm/min


- dehydration bake: 120 °C, 10 min - primer: HMDS (liquid), 4000 rpm, 20 s - resist: Olin 907/17, 4000 rpm, 20 s - prebake: hotplate 95°C, 90 sec - maskaligner: Electronic Visions AL-6 - parameters: 4 No 20 µm 4.0 mm Hard contact 30 µm 3” Top 100/10 N 0.4 mm No 5.0 s 2 - after exposure bake: 120 °C, 60 sec - development: OPD 4262, 45 s - quick dump rinse, DI, < 0.1 µS - spin drying - visual microscopic inspection - postbake: hotplate 120 °C, 30 min

frontside mask 1: “KOH channels 1”


- Elektrotech PF 310/340 (Etske) - dirty chamber - styros electrode - electrode temperature: 10 °C - CHF3 flow: 25 sccm - O2 flow: 5 sccm - pressure: 10 mTorr - power: 75W - etchrate SiRN: 80 nm/min - etchrate Olin resist: 80 nm/min - SiN profile: slightly tapered for PR - SiN profile: directional for metal mask

frontside etch through nitride depth: 1000 nm time: ~15 min 30 s 5.25 periods on the interferometer set-up



frontside


- dehydration bake: 120 °C, 10 min - primer: HMDS (liquid), 4000 rpm, 20 s - resist: Olin 907/17, 4000 rpm, 20 s - prebake: hotplate 95 °C, 90 s - maskaligner: Electronic Visions AL-6 - parameters: 4 No 20 µm 4.0 mm Hard contact 30 µm 3” Top 100/10 N 0.4 mm No 5.0 s 2 - after exposure bake: 120 °C, 60 s - development: OPD 4262, 45 s - quick dump rinse, DI, < 0.1 µS - spin drying - visual microscopic inspection - postbake: hotplate 120 °C, 30 min

frontside mask 2: “RIE JT-channel”


- Elektrotech PF 310/340 (Etske) - dirty chamber - styros electrode - electrode temperature: 10 °C - CHF3 flow: 25 sccm - O2 flow: 5 sccm - pressure: 10 mTorr - power: 75 W

frontside etch halfway through nitride (layer of 1 µm), depth: 500 nm time: ~ 10 min (check with interferometer set-up)

Appendix B

254

nr. process step parameters remarks - etchrate SiRN: 80 nm/min - etchrate Olin resist: 80 nm/min - SiN profile: slightly tapered for PR - SiN profile: directional for metal mask



frontside


Because step 4 will be on the opposite side of the wafer, remove (“lift-off”) contamination by short cleaning


- dehydration bake: 120 °C, 10 min - primer: HMDS (liquid), 4000 rpm, 20 s - resist: Olin 907/17, 4000 rpm, 20 s - prebake: hotplate 95 °C, 90 s - maskaligner: Electronic Visions AL-6 - parameters: 4 No 20 µm 4.0 mm Hard contact 30 µm 3” Top 100/10 N 0.4 mm No 5.0 s 2 - after exposure bake: 120 °C, 60 s - development: OPD 4262, 45 s - quick dump rinse, DI, < 0.1 µS - spin drying - visual microscopic inspection - postbake: hotplate 120 °C, 30 min

backside mask 3: “KOH glue holes”



backside etch through nitride depth: 1000 nm time: ~15 min 30 s



backside

5a 1% HF dip - 1% HF etchant - t > 1 min or hydrofobic surface - quick dump rinse, DI, < 0.1 µS - spin drying


- 1000 gr KOH - 3000 ml DI-water - temperature: 75 °C - stir with magnet - <100> etchrate: ~ 1 µm/min

depth: 350 µm time: ~ [depth] min


H2SO4/H2O/H2O2 5 : 1 : 1 procedure: - add H2SO4 to H2O (exothermic)


255

nr. process step parameters remarks - wait till temp. 80 °C, (switch on heater) - add H2O2 - time: 20 min - quick dump rinse, DI, < 0.1 µS - spin drying - store wafers in a cleaned wafer box

6 50% HF etch SiRN - 50% HF solution - etch rate: ~ 5 nm/min - quick dump rinse, DI, < 0.1 µS - NO dry spinning, leave under water

strip 500 nm nitride, opening of mask 2 for the shallow JT channel

7 KOH etching of Silicon

- 1000 gr KOH - 3000 ml DI-water - temperature: 75°C - stir with magnet - <100> etchrate: ~ 1 µm/min

depth: 1.1 µm (!!) time: [depth] min à test required

7b RCA Cleaning H2SO4/H2O/H2O2


8a 50% HF etch SiRN - 50% HF solution - etch rate: ~ 5 nm/min - quick dump rinse, DI, < 0.1 µS - dry spinning

strip the nitride

Processing steps of wafer 2 nr. process step parameters remarks 9a Substrate material Silicon, double side polished, 4” <100>, 525

µm thickness DSP is required because of the lower radiation emissivity of a polished (and coated) surface.

9b Introduction cleaning - fuming nitric acid (II), 5 min - quick dump rinse, DI, < 0.1 µS - boiling 70 % nitric acid (90 °C), 15 min - quick dump rinse, DI, < 0.1 µS - spin drying



9d LPCVD SiRN-S&A - Tempress LPCVD Furnace program N4 - SiH2Cl2 flow: 70 sccm - NH3 flow: 18 sccm - temperature: 850°C - pressure: 200 mTorr - deposition rate: 8.3 nm/min



- Elektrotech PF 310/340 (Etske) - dirty chamber - styros electrode - electrode temperature: 10°C - CHF3 flow: 25 sccm - O2 flow: 5 sccm - pressure: 10 mTorr - power: 75 W - etchrate SiRN: 80 nm/min

frontside depth: 500 nm time: ~10 min Make sure the nitride is etched halfway through. Check etch rate before with laser interferometer set-up, if required.

Appendix B

256

nr. process step parameters remarks - etchrate Olin resist: 80 nm/min - SiN profile: slightly tapered for PR - SiN profile: directional for metal mask


- dehydration bake: 120 °C, 10 min - primer: HMDS (liquid), 4000 rpm, 20 s - resist: Olin 907/17, 4000 rpm, 20 s - prebake: hotplate 95°C, 90 s - maskaligner: Electronic Visions AL-6 - parameters: 4 No 20µm 4.0mm Hard contact 30µm 3” Top 100/10N 0.4mm No 5.0 s 2 - after exposure bake 120 °C, 60 s - development: OPD 4262, 45 s - quick dump rinse, DI, < 0.1 µS - spin drying - visual microscopic inspection - postbake: hotplate 120 °C, 30 min

frontside mask 4: “KOH channels 4”


- Elektrotech PF 310/340 (Etske) - dirty chamber - styros electrode - electrode temperature: 10 °C - CHF3 flow: 25 sccm - O2 flow: 5sccm - pressure: 10mTorr - power: 75W - etchrate SiRN: 80nm/min - etchrate Olin resist: 80nm/min - SiN profile: slightly tapered for PR - SiN profile: directional for metal mask

frontside etch through nitride depth: 500 nm time: ~ 8 min 30 s check with interferometer set-up



frontside

12a 1% HF dip - 1% HF etchant - t > 1 min or hydrofobic surface - quick dump rinse, DI, < 0.1 µS - spin drying


- 1000 gr KOH - 3000 ml DI-water - temperature: 75°C - stir with magnet - <100> etchrate: ~ 1 µm/min

depth: 350 µm time: ~ [depth] min



13a 50% HF etch SiRN - 50% HF solution - etch rate: ~ 5 nm/min - quick dump rinse, DI, < 0.1 µS - dry spinning

Strip the 500 nm nitride on the frontside, leaving 500 nm on the backside.


257

Aligned fusion bonding of wafers 1 and 2 nr. process step Parameters remarks 14a Introduction cleaning - fuming nitric acid (II), 5 min

- quick dump rinse, DI, < 0.1 µS - boiling nitric acid (90°C), 15 min - quick dump rinse, DI, < 0.1 µS - spin drying

cleaning direct before bonding step


check hydrofobic surface

14c “Piranha” cleaning for fusion bonding H2SO4/H2O2

procedure: - add H2O2 to H2SO4, 1:3 - exothermic process - wait till temp. 100°C, switch on heater - time 20 min - quick dump rinse, DI, < 0.1 µS - store and transport wafers under water - spin dry just before bonding in nearest bench - spin parameters: time 1.5 min, max speed

cleaning direct before bonding step

14d Aligning and Pre-bonding

maskaligner: Electronic Visions AL-6 parameters: - mask: 0.6 mm - substrate: 0.6 mm - wedge error eq. 8 - separation: 60 µm - contact: vaccuum, bottom bond - N2 purge: 5 - contact force: 100/10 [10] - manual correction: 0 µm - load top wafer with bondsurface down - set cross-hairs on alignment marks - load bottom wafer with bondsurface up - align alignment marks of backside of bottom wafer to crosshairs - adjust N2 pressure for center bending bottom wafer (~1.5 bar) - NO seal rise and NO purging pre-bonding

Use 4” bondtools top wafer is wafer 2 bottom wafer is wafer 1

14e IR-inspection - use IR setup to check the pre-bond - use tweezers for additional pressure to promote bonding of not bonded spots

14f Annealing - diffusion oven - nitrogen ambient - temperature: 1100 °C - time: 120 min (incl. up and down ramp from and to 800 °C)

14g IR-inspection - use IR setup to check final bond 15 Cr/Au sputter-

deposition on frontside (with glue holes)

- UT-build sputter system (Sputterke) - Ar flow: 90 sccm - pressure: 5.0e-3 mbar - DC power: 200 W - sputter rate Cr: 10 nm/min Au: 40 nm/min

This Au coating has a low emissivity and reduces the radiation load. thickness: 10/100 nm time: Cr - 1 min Au - 2 min 30 s

16a Lift-off Lithography-S&A-907/17-4”

- dehydration bake: 120 °C, 10 min - primer: HMDS (liquid), 4000 rpm, 20 s - resist: Olin 907/17, 4000 rpm, 20 s - prebake: hotplate 95°C, 90 s - maskaligner: Electronic Visions AL-6 - parameters: 4 No 20 µm

Backside (without holes) mask 5: “heaters” *) To prevent OPD 4262 from entering the channels, the development is done after applying double-sided dicing foil on the surfaces.

Appendix B

258

nr. process step Parameters remarks 4.0 mm Hard contact 30 µm 3” Top 100/10 N 0.4 mm No 5.0 s 2 - after exposure bake 120 °C, 60 s - development: OPD 4262, 45s *) - rinse with brush - visual microscopic inspection - remove foil on both sides

Method: - apply dicing foil to two frames - cut desired development area out of one foil for the backside - glue foil on both sides of the waferpair with open window on backside - remove wafer pair from the two frames

16b Cr/Pt/Au sputter-deposition

- UT-build sputter system (Sputterke) - Ar-flow: 90 sccm - pressure: 5.0e-3 mbar - DC power: 200 W - sputter rate Cr: 10 nm/min Pt: 20 nm/min Au: 40 nm/min

backside Pt serves as resistance material and the top Au layer as low emissivity coating. thickness: 10/500/50 nm time: 1/25/1,25 min

16c “Dry lift-off” - Apply Scotch tape to lift of the metal layers - After removing the metal, place wafer in spin dryer and flush with acetone during spinning

because of the stress in the metal layer sandwich, this method functions well

17a Apply dicing foil - Standard procedure. Laminate tape on wafer 1 of waferpair

holes are covered by dicing foil

17b Dicing

- Dicing Saw Model 1006 of Micro Automation Inc. - blade type: S 2035 settings: - thickness: 1300 µm - speed: 2 mm/sec - diameter of wafer: 80 mm - index: 8.80 mm two step dicing procedure : - height 1: 550 µm - height 2: 200 µm - remove samples from foil

- side to dice: wafer 2 - dice lines perpendicular to waferflat - max depth: 1000 µm - blade width: 50 - 70 µm - thickness waferpair 1/2: ~ 1050 µm. - foil thickness: ~ 80 µm - leave ~ 100 µm to overcome problems with water leakage through the holes of wafer 1 during dicing

17b Separation of samples Break samples parallel to flat

259

Summary

Summary Cryocoolers are refrigerators capable of reaching temperatures below roughly 120 kelvin.

Such coolers are used for cooling of, for instance, superconducting electronics and magnets, (infrared) detectors, and cryopumps. Low-temperature applications requiring very little cooling power, such as a single chip with a low noise amplifier or a superconducting magnetometer, would benefit from very small closed-cycle cryocoolers. Such coolers do not yet exist. This thesis is the result of a research project to investigate opportunities for such microcoolers. The project required a high degree of pioneering because the field of subjects and possibilities is vast and largely unexplored. As a result, the contents of this thesis is very divergent and cover various areas of science, such as (micro)mechanics, thermodynamics, fluid mechanics, heat transfer and material science. This divergence occurs especially in chapters 2 and 3, in which a number of cooling cycles are discussed, as well as opportunities for miniaturization of these coolers. The remainder of the thesis describes the development of miniature components for a sorption cooler. This cooling system was chosen because it is suitable to be applied on a small scale.

The motivation and project goals of the work, as discussed above, are presented in more detail in chapter 1.

In chapter 2, an overview is presented of a number of cooling cycles that can be applied in cryocoolers. Emphasis is put on thermodynamic theory, conceptual operation and possible loss mechanisms. The chapter serves as a conceptual framework on cryocooler theory which is referred to throughout this thesis. The following regenerative cooling cycles are discussed: Stirling, Gifford-McMahon, Vuillemier and pulse-tube. A new regenerative cooling cycle is proposed (and named the ‘Twente-Stirling’ cycle) which appears particularly suitable to be applied on a micro-scale because it reacts passively and non-resonant on a pressure wave from the compressor. Furthermore, the following recuperative cooling cycles are discussed: Vapor compression cycle, Linde-Hampson and Joule-Brayton cycle. Some alternative solid-state cooling cycles are also considered: thermoelectric cooling, magnetocaloric and optical cooling.

Chapter 3 discusses the opportunities and difficulties that appear when cryogenic coolers are miniaturized. First, a number of important micromachining techniques to structure silicon and glass are reviewed. These two materials exhibit, respectively, a very high and very low thermal conductivity which makes a combination of the two materials attractive to construct cryocooler components. Next, the theory and scaling behavior are discussed of a number of fields that play a role in coolers: structural mechanics, actuator theory, fluid mechanics and heat transfer. The results can be summarized as follows: active mechanical components as used in a number of cooling cycles are difficult to fabricate with MEMS techniques (MEMS stands for Micro Electro Mechanical Systems); most heat transfer mechanisms are enhanced upon downscaling, having both positive and negative effects on cryocooler operation; the development of a powerful, small and efficient MEMS compressor is an important condition for a complete integrated MEMS microcooler. Based on the discussed scaling theory, opportunities for downscaling of several cooling cycles are discussed. An example is given of a design of a micromachined regenerative cooler, based on the Twente-Stirling cycle. Finally, an

Summary

260

overview is presented of existing coolers and existing low-temperature applications, which is useful for determining potential applications of a microcooler.

In chapter 4, the operation and a thermodynamic analysis is presented of a sorption cooler, which consists of a sorption compressor and a Linde-Hampson cold stage. The cycle is promising because it has no moving parts. This facilitates scaling down to small sizes, it eliminates interferences, and it contributes to achieving a long life time. Operation of a sorption compressor is based on the principle that large amounts of gas can be adsorbed on certain solids such as highly porous carbon. If a pressure container is filled with a sorber material and gas is adsorbed at a low temperature and pressure, then a high pressure can be created inside the closed vessel by an increase of the temperature of the sorber material. Next, a controlled gas flow out of the vessel can be maintained at a high pressure by further increase of the temperature until most of the gas is desorbed. A sorption compressor can be considered as a thermodynamic engine that converts high temperature heat into low temperature heat and mechanical work that appears as compressed gas. The ideal behavior of this Carnot engine is strongly reduced by two loss mechanisms: much heat is lost in the periodical heating of the heat capacity of the sorption material and container, and a significant amount of the compressed gas is left in the dead volume of the sorption material. Detailed modelling of these losses showed a clear optimum in compressor performance at moderate high pressures of 10 – 30 bar, which appeared strongly dependent on the operating parameters such as compressor temperatures and the low pressure. Unfortunately, Linde-Hampson cold stages require relatively high pressures for proper operation. Two solutions were discussed to overcome this conflict: a novel two stage compressor and (thermoelectric) precooling of the gas in the cold stage. By precooling of the gas, a coefficient of performance of about 3 % can be obtained for a carbon/xenon cooler operating between 300 K and 165 K with a sorption compressor operating between 300 K and 600 K that compresses the gas between 1 and 20 bar.

In a sorption compressor, a thermal switch is required to isolate the sorption cell during heating, and to connect it thermally to a heat sink during cooling. An ON-OFF ratio of about 50 is suitable for proper operation of the cells. Chapter 5 discusses the operation of a gas-gap heat switch. The thermal conduction through a gas gap is varied by adjusting the gas pressure in the gap between two parallel surfaces. For low pressures, conduction occurs in the molecular regime and is independent of the gap-width; the lowest conduction is limited by thermal radiation through the gap. For hydrogen gas, this thermal radiation limit occurs for pressures below about 1 Pa. For high pressures, the maximum conduction is limited by the pressure-independent conduction through a continuum, and this conduction increases inversely proportional with the gap width. Typical maximum ON-OFF ratios that can be obtained for hydrogen gas are 150/d, where d is the width of the gas gap expressed in millimeters.

Pressure adjustment in a gas gap can be realized with hydrogen gas that can reversibly be ab- and desorbed from a small amount of metal hydride. From a comparison between different metal hydrides, it followed that ZrNi is a suitable candidate. The application of bulk ZrNi will inevitably result in a relatively oversized pressure regulation system which does not fit with the requirements of a relatively small sorption compressor. For that reason, the feasibility of thin film ZrNi was studied. It was demonstrated that polycrystalline ZrNi thin films are feasible as a small scale hydrogen pressure actuator, both with respect to the pressure swing that can be obtained and the switching times that can be achieved. The pressure could reversibly be varied

Summary

261

between 0.03 Pa and 125 Pa by variation of the temperature between 60 °C and 230 °C. The required switching times of 30 seconds could also be achieved. The pressure variation would result in an ON-OFF ratio of approximately 100 for a 300 µm wide gas-gap heat switch.

Chapter 6 describes the design, fabrication and testing of the individual sorption compressor cells with integrated gas-gap heat switches. One single compressor cell consists essentially of five elements: the inner stainless steel pressure cylinder with a diameter of 1 cm and a length of 10 cm, sorption material located inside this container, an electrical heater that is spiralled through the sorption material, a gas-gap heat switch between the inner and outer cylinders, and the outside container that is connected to a heat sink. In addition to these basic elements there are also: a support structure between the two containers and a gas tube through the outside container connecting to the inside pressure container. Different heater solutions were experimentally compared, leading to a solution in which a 250 µm thick stainless steel shielded thermocouple is simultaneously used as heater and as thermometer. Experiments showed that such heater endures repetitive thermal cycling (>2⋅105 times), without significant deterioration of the thermocouple calibration. Experiments on the fabricated compressor cells showed that pressure differences can be realized that are close to the modelled values.

For continuous operation of a sorption compressor, check valves are needed to rectify the slowly ‘pulsating’ pressure variation of the individual sorption compressor cells. Chapter 7 presents the design and operation of a micromachined check valve with integrated filter that was tested for gas pressures up to 65 bar. In forward direction, the check valve has a very low pressure drop at low absolute gas pressures. An integrated unit of 10 interconnected valves was developed as well. The valve design is based on the concept of a bossed valve suspended by thin springs; this concept was selected because the boss and the springs can individually be optimized to fit the requirements. The boss consists of an octagonal-shaped chopped cone of about 1 mm2 and 300 µm in height, which is suspended by four springs of 1.2 mm x 50 µm x 10 µm. The boss fits on a circular valve seal. Fabrication was done by a combination of wet and dry etching in silicon, and subsequent waferbonding. A long duration experiment involving many forward/closed switchings was done on two check valves. For both valves, proper operation was maintained until the experiment was stopped after 10000 and 25000 cycles, respectively.

Chapter 8 presents the design and operation of two different miniature cold stages, both employing Joule-Thomson (JT) expansion. The first cold stage consists of two miniature glass tubes with diameters of less than 1 mm, which are placed concentrically around each other and which operate as a counterflow heat exchanger. High pressure nitrogen gas flows through the inner glass tube from the warm to the cold end, where JT expansion occurs through a flow restriction that consists of a thin wire that is inserted in the inner tube. The expanded low pressure gas then flows back to the warm end of the counterflow heat exchanger through the annulus between the two glass tubes. A minimum temperature of 82 K was measured with the use of nitrogen gas as refrigerant.

In the second cooler, these glass tube heat exchangers are combined with three silicon components that were fabricated by a combination of etching and waferbonding techniques. A novel glue connection was designed to facilitate a simple integration with the glass tube heat exchangers. One of the components is a condenser that is integrated in the heat exchanger to preliquefy the fluid, thus improving the thermodynamic performance of the cold stage. Also the

Summary

262

flow restriction and the liquid bath are fabricated in silicon. The design of the flow restriction in silicon facilitates an accurate design of the required mass flow and accompanying cooling power of the cold stage. This cooler is specially designed for application with the described sorption compressor. A number of succesful measurements were performed on the cold stages; it was show that a stable temperature of 169 K could be obtained with ethylene as refrigerant and with cooling powers up to a few hundred milliwatts.

263

Samenvatting

Samenvatting Cryokoelers zijn koelers die temperaturen kunnen bereiken onder ongeveer 120 kelvin.

Zulke koelers worden gebruikt voor het koelen van bijvoorbeeld supergeleidende elektronica en magneten, (infrarood) detectoren en cryopompen. Lage-temperatuur toepassingen die weinig koelvermogen nodig hebben, zoals een enkele chip met een ruisarme versterker of een supergeleidende magnetometer, kunnen profiteren van miniatuur cryokoelers. Zulke koelers bestaan echter nog niet. Dit proefschrift is het resultaat van een onderzoeksproject waarin de mogelijkheden voor zulke microkoelers is onderzocht. Het project vereiste veel pionierswerk omdat het veld van onderwerpen en mogelijkheden enorm groot is, en tot nu toe nauwelijks verkend was. Dit heeft als gevolg dat de inhoud van dit proefschrift zeer divergent is en een aantal verschillende vakgebieden beslaat, waaronder (micro)mechanica, thermodynamica, vloeistofmechanica, warmteleer en materiaalkunde. Dit geldt vooral voor de hoofdstukken 2 en 3, waarin een aantal koelcycli worden besproken en de mogelijkheden worden geï nventariseerd om koelers gebaseerd op deze cycli te verkleinen. De rest van het proefschrift is gewijd aan de ontwikkeling van miniatuur componenten voor een sorptiekoeler. Dit koelsysteem is gekozen omdat het systeem geschikt is om te worden toegepast voor kleine afmetingen.

De motivatie en doelen van het project, zoals die hierboven zijn samengevat, worden uitgebreider beschreven in hoofdstuk 1.

In hoofdstuk 2 is een overzicht gepresenteerd van een aantal koelcycli die kunnen worden toegepast in cryokoelers. Nadruk is gelegd op de thermodynamica, de conceptuele werking en mogelijke verliezen van de cycli. Het hoofdstuk is bedoeld als een conceptueel raamwerk over cryokoeler theorie waar verderop in het proefschrift aan gerefereeerd kan worden. De volgende regeneratieve koelcycli worden besproken: Stirling, Gifford-McMahon, Vuillemier en pulsbuis. Tevens is er een nieuwe regeneratieve koelcyclus voorgesteld (de ‘Twente-Stirling’ cyclus) die speciaal geschikt lijkt om te worden toegepast op kleine afmetingen omdat hij passief en niet-resonant reageert op een drukvariatie van de compressor. Verder worden de volgende recuperatieve koelcycli besproken: vapor compression cyclus, Linde-Hampson en Joule-Brayton cyclus. Een aantal alternatieve solid-state koelcycli worden ook beschouwd: thermoelectrische koeling, magnetocalorische en optische koeling.

Hoofdstuk 3 bespreekt de kansen voor miniaturisatie van cryokoelers en de moeilijkheden die daarbij optreden. Allereerst wordt een kort overzicht gepresenteerd van belangrijke micromechanische technieken die beschikbaar zijn om silicium en glas te bewerken. Deze twee materialen vertonen, respectievelijk, een erg hoge en lage warmtegeleiding; dit maakt een combinatie van de twee materialen erg aantrekkelijk voor het fabriceren van cryokoeler onderdelen. Vervolgens worden de theorie en schalingseffecten bediscussierd van een aantal gebieden die een rol spelen in cryokoelers: mechanica, actuator theorie, vloeistofmechanica en warmteleer. De resultaten hiervan kunnen als volgt worden samengevat: aktieve mechanische componenten zoals die in een aantal koelcycli worden gebruikt zijn lastig te fabriceren met MEMS technieken (MEMS staat voor Micro Electro Mechanical Systems); de meeste warmte-overdracht mechanismen verbeteren bij schaling naar kleine afmetingen, wat zowel positieve

Samenvatting

264

als negatieve invloeden heeft op de werking van cryokoelers; de ontwikkeling van een krachtige, kleine en efficiënte MEMS compressor is een belangrijke voorwaarde voor een compleet geï ntegreerde MEMS microkoeler. Gebruikmakend van de gepresenteerde schalingstheorie worden de kansen voor miniaturisatie van een aantal koelcycli besproken. Een voorbeeld is gegeven van een ontwerp van een micromechanische regeneratieve koeler, gebaseerd op de Twente-Stirling cyclus. Tenslotte wordt er een overzicht gegeven van bestaande koelers en bestaande lage-temperatuur toepassingen; dit maakt duidelijk in welke hoek mogelijke toepassingen bestaan van een microkoeler.

In hoofdstuk 4 wordt de werking en een thermodynamische analyse gepresenteerd van een sorptiekoeler. Zo’n koeler bestaat uit een sorptiecompressor en een Linde-Hampson koude trap. De cyclus is aantrekkelijk omdat er geen bewegende delen aanwezig zijn. Dit maakt schaling naar kleine afmetingen mogelijk, het voorkomt interferenties en het draagt bij aan het bereiken van een lange levensduur. De werking van een sorptiecompressor is gebaseerd op het principe dat grote hoeveelheden gas kunnen worden geadsorbeerd op bepaalde materialen, zoals zeer poreuze koolsoorten. Als een drukvaatje gevuld wordt met zulk sorptiemateriaal, en gas is geadsorbeerd bij een lage temperatuur en druk, dan kan een hoge druk worden gegenereerd in het gesloten vaatje door de temperatuur van het sorptiemateriaal te verhogen. Vervolgens kan er een gecontroleerde gasflow bij een constante hoge druk uit het vaatje worden onderhouden door een verdere geleidelijke verhoging van de temperatuur van het sorptiemateriaal totdat het grootste deel van het gas is gedesorbeerd. Een sorptiecompressor kan worden beschouwd als een thermodynamische motor die warmte op een hoge temperatuur omzet naar warmte op een lagere temperatuur en mechanische arbeid, die beschikbaar komt in de vorm van gecomprimeerd gas. Het ideale gedrag van deze Carnot motor wordt sterk verslechterd door twee verliesmechanismen: veel warmte gaat verloren in het periodieke opwarmen van de warmtecapaciteit van het sorptiemateriaal en het drukvaatje, en een behoorlijke hoeveelheid van het gecomprimeerde gas blijft achter in het dode volume van het sorptiemateriaal. Gedetailleerde modelvorming van deze verliezen laat zien dat er een duidelijk optimum in de compressor werking bestaat bij gematigd hoge drukken van 10 – 30 bar. Dit optimum bleek tevens sterk afhankelijk van andere parameters, zoals de compressor temperaturen en de lage druk. Helaas heeft een Linde-Hampson koude trap een relatief hoge druk nodig om goed te werken. Twee oplossingen zijn aangedragen om dit conflict op te lossen: een nieuw soort tweetraps sorptiecompressor en (thermoelectrische) voorkoeling van het gas in de cold stage. Door het gas enigszins voor te koelen kan een Coefficient of Performance van 3% worden gehaald voor een carbon/xenon koeler die werkt tussen 300 K en 165 K, waarbij de sorptiecompressor werkt tussen 300 K en 600 K en het gas gecomprimeerd wordt tussen 1 en 20 bar.

In een sorptiecompressor is een thermische schakelaar nodig om de sorptiecel te isoleren tijdens het opwarmen, en om hem thermisch aan een heat sink te verbinden gedurende het afkoelen. Een AAN-UIT verhouding van ongeveer 50 is voldoende voor een goede werking van de cellen. Hoofdstuk 5 bespreekt de werking van een gas-gap warmteschakelaar. De thermische geleiding door een gas gap wordt gevarieerd door de druk van het gas in de ruimte tussen twee parallele vlakken in te stellen. Voor lage drukken vindt warmtegeleiding plaats in het moleculaire gebied, waar de geleiding onafhankelijk is van de breedte van de gap; de minimale geleiding is begrensd door de thermische straling door de spleet. Voor waterstofgas

Samenvatting

265

treedt deze stralingsgrens op bij drukken onder ongeveer 1 Pa. Voor hoge drukken wordt de maximale geleiding begrensd door de druk-onafhankelijke geleiding door een continu medium, en deze geleiding neemt omgekeerd evenredig toe met de breedte van de spleet. Typische maximale AAN-UIT verhoudingen die voor waterstof kunnen worden bereikt zijn 150/d, waar d de breedte van de gas gap is in millimeters.

Instelling van de druk in een gas gap kan worden gedaan met waterstofgas dat reversibel kan worden geabsorbeerd aan een kleine hoeveelheid metaalhydride. Uit een vergelijking van verschillende metaalhydrides is gebleken dat ZrNi een geschikte kandidaat is. De toepassing van bulk ZrNi zal zeker resulteren in een relatief overbemeten druk-regelsysteem, wat niet voldoet aan de eisen van een relatief kleine sorptiecompressor. Om die reden is de haalbaarheid van dunne-film ZrNi onderzocht. Het is aangetoond dat polycrystallijn dunne-film ZrNi geschikt is voor een miniatuur waterstof-drukactuator, zowel wat betreft de drukvariatie als de schakelsnelheid die kan worden bereikt. De druk kon reversibel worden gevarieerd tussen 0.03 Pa en 125 Pa door een variatie van de temperatuur tussen 60 °C en 230 °C. De benodigde schakelsnelheid van 30 seconden kon ook worden bereikt. De drukvariatie zou resulteren in een AAN-UIT verhouding van ongeveer 100 voor een 300 µm brede gas-gap heat switch.

Hoofdstuk 6 bespreekt het ontwerp, de fabricage en het testen van de individuele sorptie-compressorcellen met geï ntegreerde gas-gap warmteschakelaars. Eén enkele compressorcel bestaat in principe uit vijf onderdelen: de binnenste roestvrijstalen drukcilinder met een diameter van 1 cm en een lengte van 10 cm, sorptiemateriaal binnenin dit vaatje, een elektrische heater die door het sorptiemateriaal is gespiraliseerd, een gas-gap warmteschakelaar tussen de binnen- en buitencilinder, en de buitencilinder die verbonden is aan een heat sink. Behalve deze basiselementen bevat een compressorcel ook nog: een ophangingsconstructie tussen de twee cilinders en een aansluitbuis die door de buitencilinder aangesloten is aan het binnenvaatje. Verschillende heater-opties zijn experimenteel met elkaar vergeleken. Dit heeft geleid tot een oplossing waarin een thermokoppel met een roestvrijstalen mantel (250 µm buitendiameter) tegelijkertijd als heater en thermometer wordt gebruikt. Experimenten hebben aangetoond dat zo’n heater het herhaalde thermische cyclen kan doorstaan (>2⋅105 keer), zonder significant verloop van de thermokoppel callibratie. Experimenten aan de gefabriceerde cellen hebben aangetoond dat drukverschillen kunnen worden opgewekt die de gemodelleerde waardes goed benaderen.

Voor een continue werking van een sorptiecompressor zijn passieve kleppen (hydraulische diodes) nodig om de langzaam ‘pulserende’ drukvariatie van de individuele compressorcellen gelijk te richten. Hoofdstuk 7 presenteert het ontwerp, de realisatie en tests van een micromechanische passieve klep met geï ntegreerd filter die getest is voor gasdrukken tot 65 bar. De klep heeft bij lage absolute gasdrukken een zeer lage drukval in voorwaartse richting. Een geï ntegreerde unit met 10 onderling verbonden kleppen is ook ontwikkeld. Het ontwerp van de klep is gebaseerd op een verdikte plaat die is opgehangen aan dunne elastische veren; dit concept was geselecteerd omdat de plaat en de veren individueel kunnen worden geoptimaliseerd naar de eisen van de klep. De ‘plaat’ heeft de vorm van een achthoekige afgeknotte kegel met een basisoppervlakte van ongeveer 1 mm2 en een maximale dikte van 300 µm, en is opgehangen aan vier elastische veren van 1.2 mm x 50 µm x 10 µm. De plaat past op een ronde klepzitting. De fabricage is gedaan door een combinatie van nat en droog etsen in silicium, en daaropvolgende waferbonding. Met twee kleppen is een duurtest uitgevoerd

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waarin veel voorwaarts/sper omschakelingen werden opgelegd. Beide kleppen bleven goed functioneren totdat het experiment werd stopgezet na respectievelijk 10000 en 25000 cycli.

Hoofdstuk 8 presenteert het ontwerp en de werking van twee verschillende miniatuur koude trappen die beide gebruik maken van Joule-Thomson (JT) expansie. De eerste koude trap bestaat uit twee miniatuur glasbuisjes met een diameter van minder dan 1 mm, die concentrisch rondom elkaar geplaatst zijn en die werken als een tegenstroom-warmtewisselaar. Stikstof gas stroomt onder hoge druk door het binnenste glazen buisje van de warme naar de koude kant, waar JT expansie plaatsvindt door een flowrestrictie die gevormd wordt door een dun draadje dat in het uiteinde van het binnenste buisje is geschoven. Het geëxpandeerde gas onder lage druk stroomt vervolgens door de buitenste ring tussen de twee glazen buisjes terug naar de warme kant van de tegenstroom-warmtewisselaar. Een minimum temperatuur van 82 K is gemeten met gebruik van stikstof als koelmedium.

In de tweede koeler zijn deze glazen tegenstroom-warmtewisselaars gecombineerd met drie silicium onderdelen die gefabriceerd zijn door een combinatie van etsen waferbonding-technieken. Een nieuwe lijmtechniek is toegepast die een simpele integratie mogelijk maakt met de glazen tegenstroom-warmtewisselaars. Eén van de componenten is een condenser die is geï ntegreerd in de warmtewisselaar om condensatie van het gas mogelijk te maken, waardoor de thermodynamische werking van de koude trap verbetert. Ook de JT flowrestrictie en het vloeistofbad zijn gefabriceerd in silicium. Het ontwerp van de flowrestrictie in silicium maakt een precieze keuze mogelijk van de benodigde massaflow en het bijbehorende koelvermogen van de koude trap. Deze koeler is speciaal ontworpen voor toepassing met de eerder beschreven sorptiecompressor. Een aantal succesvolle metingen zijn uitgevoerd aan de koude trappen; hieruit bleek dat een stabiele temperatuur van 169 K bereikt kan worden met ethyleen als koelmiddel en met koelvermogens tot een paar honderd milliwatt.

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Dankwoord

Dankwoord Het is toch op z’n minst verwonderlijk dat er in een doorsnee proefschrift vrijwel niets

zichtbaar is van het gebeuren dat ten grondslag ligt aan het ontstaan van zo’n boekje. Dit wordt bereikt door de bovenmatige inspanning van de schrijver om een tekst te produceren waar iedere vorm van emotie is uitgebannen, met als curieus gevolg dat geen hond het meer wil lezen. Want de lezer wordt zo helaas het zicht onthouden op dat wat onderzoek juist zo interessant en leuk maakt. Dit proefschrift vormt daar zeker geen uitzondering op.

En nu ben ik dan aangeland bij het dankwoord, en daar kan eindelijk heel even afgeweken worden van deze regel. Mocht u nieuwsgierig geworden zijn hoe dit onderzoek werkelijk heeft plaatsgevonden, welke volstrekte chaos er achter de bertrekkelijke orde in dit boekje schuilgaat, schiet u dan even willekeurig één van de mensen aan die ik noem in dit dankwoord. Zij kunnen u meer vertellen. Zij waren op de één of andere manier belangrijk bij het onderzoeksgebeuren van de afgelopen vijf jaren, en zij hebben het verhaal van dit proefschrift mede geschreven. Een aantal van hen hebben veel van het eigenlijke werk gedaan. Mijn hartelijke dank daarvoor!

Allereerst wil ik mijn twee promotoren Horst Rogalla en Miko Elwenspoek bedanken. Jullie gaven me het vertrouwen om dit onderzoek te doen op het grensoverschrijdende gebied van de twee leerstoelen Lage Temperaturen en Micromechanica. Ik heb het als een voorrecht ervaren om in deze twee toch wel bijzondere groepen te mogen werken. Jullie weten op geheel eigen wijze in beide groepen een atmosfeer te creëren waarin in alle vrijheid onderzoek gedaan kan worden. Dubbele vrijheid dus voor mij, en die heb ik voluit gebruikt. Een idee kon niet gek genoeg zijn, of ik maakte er wel weer een projectje van. En zo mocht ik er spelenderwijs achterkomen dat de begrensde tijd soms een reële bedreiging vormt voor de vrijheid en creativiteit. Ik ben blij dat jullie me de kans hebben gegeven om de dingen af te maken waar ik in al m’n enthousiastme aan begonnen was. Miko, zowel je belangstelling voor de fysica als ook je belangstelling voor de mens achter de onderzoeker heb ik zeer gewaardeerd. Horst, ik vond het erg leuk en stimulerend om te merken dat je steeds weer enthousiast was voor het project.

Met heel veel plezier kijk ik terug op de nauwe samenwerking met Marcel ter Brake, mijn co-promotor. Marcel, jouw idee om te zoeken naar manieren om microkoelers te maken vormde de basis van dit onderzoek, en blijkt ook nu nog een eindeloze bron voor nieuwe ideeën. Ik heb veel steun gehad aan je vertrouwen in het onderzoek, je legendarische optimisme, daadkracht, humor en relativerende houding. Ik kan me maar één situatie herinneren dat het er voor ons even penibel uitzag. Dat was om één uur ’s nachts, in the middle of nowhere ergens in de VS, toen we na zes uur zoeken tot de conclusie waren gekomen dat je op Memorial Day toch echt een hotel moet reserveren om te kunnen overnachten. Maar ook dat probleem hebben we opgelost.

Harry Holland is in al die jaren mijn andere steun en toeverlaat geweest. Harry, jij hebt me als ongeletterde EL-er ingewijd in de geheimen van cryokoelers en cryogene technieken – ik herinner me onze eindeloze discussies voor het whiteboard in het eerste jaar van het onderzoek. Het perpetuum mobile hebben we daar weer regelmatig uitgevonden, en dat was

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geweldig! Ik ben na al die jaren ook nog steeds verwonderd hoe relaxed jij kunt blijven als er na weken noeste arbeid weer eens iets in rook opgaat of ander onheil onze microkoeler-in-wording overkomt. Terwijl er bij mij dan stoom uit mijn oren komt wandel jij rustig naar de werkplaats om met verbazingwekkende handigheid een nieuw onderdeeltje te fabriceren.

Han Gardeniers was als dagelijks begeleider vanuit de micromechanicagroep (‘Mbetrokken bij de micromechanische aspecten van het onderzoek. Han, bedankt! Met name voor je uitgebreide inzet bij het werk aan de ZrNi films en je heldere correcties van verschillende artikelen en dit proefschrift.

Zonder de inbreng van Erwin Berenschot weet ik niet of er veel micromechanische onderdelen werkend uit de cleanroom waren gekomen. Het was altijd een groot genoegen om met je samen te werken, Erwin! Erwin vormt samen met Meint de Boer het onderhand beroemde technologische duo van de MicMec. Door hun hoge van Kooten en de Bie gehalte blijft het altijd leuk om weer eens even op vloer 7 te buurten en de sociale strukturen in het EL-TN gebouw onder de loep te nemen. Meint, ook bedankt voor je ets-werk aan de kleppen!

Een flink aantal afstudeerders en stagaires hebben een belangrijke bijdrage geleverd aan het onderzoek. Elfried van der Sar, voordat ik begon had jij al een werkende sorptiecompressor gebouwd. Je maanlander staat nog steeds bij ons op de kast en heeft ons geï nspireerd tot veel nieuwe ideeën. Sander Huinink, als afstudeerder begeleidde jij mij als beginnende AIO en dat was leuk. Paragraaf 4.4.2 is ontstaan mede naar aanleiding van onze discussies over sorptiewarmte. Bedankt dus! Nienke Boersma, de heat exchangers van de cold stage doen het goed dankzij het voorwerk dat jij hebt gestopt in de modelvorming. Dank daarvoor! Michiel van der Wekken, zonder jou waren de kleppen er niet geweest en hadden we dus de lekken en explosies moeten missen. Dat was een leuke tijd. René Bosman, door jouw werk aan de gas gap doet-ie het, en snappen we ook waarom. Han van Egmond, het tweede deel van hoofdstuk 5 is in zijn geheel ontstaan dankzij jouw enorme inzet. Geweldig was dat! David Agar, you started the development of the cold stage by succesfully building the first micro-condensers. Thanks! Jan-Henry Seppenwoolde, jouw onderzoek aan de cold stage heeft geleid tot beter begrip en de mooie metingen uit hoofdstuk 8. Bedankt!

Alle andere LT-ers en MicMeccers wil ik hartelijk danken voor hun bijdrage in de afgelopen jaren. Het zal nog wel even touwtrekken blijven aan welk overbevolkt tafeltje ik ga lunchen in de pauze. Cheng-Qun Gui wil ik graag in het bijzonder noemen, met wie ik twee jaar met veel plezier de kamer deelde in T5. Ans, Inke en Judith: zonder jullie loopt alles in de soep en is het een stuk minder gezellig.

De staf van de MESA+ cleanroom houdt ondermeer de apparatuur daar draaiende, hartelijk dank daarvoor. Johnny Sanderink, bedankt dat je je hebt ingezet om de Cryo (en diens overige gebruikers) geschikt te maken voor het sputteren van ZrNi/Pd. Het is gelukt! Bert Otter, dankzij jou is semmen een zeer speciale gebeurtenis, niet in de laatste plaats door de mooie plaatjes die je weet te schieten. Verder een woord van dank aan de staf van de fijnmechanische werkplaats: Bernard Meinders, Klaas Smit, Joop Reijrink, Theo Punt en John Caspers. Nu weet ik wat erbij komt kijken om van een bouwtekening van een compressorcel een werkend exemplaar te maken.

Larry Wade gave me the opportunity to spend several times a shorter or a longer period in his sorption cooler group at NASA’s Jet Propulsion Laboratory. Larry, without your willingness to co-operate with us on sorption coolers, we would certainly have been stuck in

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the mud. I still consider it as a privilege that you let us steal your ideas, so that we could scale them down to make our own small sorption compressor. Thanks also for your hospitality and your willingness to listen to my stubborn arguments. Alan Levy, thanks to our discussions on sorption coolers I started to understand their operation in that first year of our project. Bob Bowman, our initial discussions on metal hydride operation finally led to chapter 5 of this thesis. Thanks! Pradeep Bhandari, Mauro Prina and Chris Lindensmith: thanks for your willingness to share your ideas with me.

En dan zijn er buiten het werk de vrienden en familie die belangrijk voor me zijn geweest gedurende de afgelopen jaren. Lianne, Sandra en Jenet, jullie waren geweldige huisgenotes die eerste twee jaar. Ik denk nog vaak terug aan de lol die we hadden in die tijd. Fred, bedankt dat je me hebt gestimuleerd om ook al die dingen te onderzoeken die dus niet in dit proefschrift staan. Jeroen, Janny, Joost Anne, Tiny, Jan, Margreet, Helmien, Jan, Janneke, Rinske, Wim, Trudy, Bea, Ton, Gijsbert, Janita, Petra, Elly, Anneloes, Niels, Dragana, Henri, Christina, Herman, Grietje, Floor, Eva – jullie allemaal bedankt voor je vriendschap en nabijheid in de afgelopen jaren, en het helpen zoeken naar het juiste perspectief. Dat blijft broodnodig om dit werk te kunnen doen. En natuurlijk: pa, ma, Wim, Arieneke, Rianne, Jos, Leon, Liesbeth, Leen, Gijs, Petra, Samuel, Martin Hans, Corry, Marjan, Else, Geert, Ika, Marc, Ellen - bedankt dat jullie steeds belangstelling en steun hebben getoond bij de dingen waar ik mee bezig was.

cryogenic microcooling ~ a micromachined cold stage ...by two coaxial glass-tube counterflow heat...

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