simon fraser universitysummit.sfu.ca/system/files/iritems1/19075/etd10748.pdf · ii approval name:...

Development of Capillary-assisted Low Pressure

Evaporator for Adsorption Chillers

by

Poovanna Cheppudira Thimmaiah

M.Sc., Coventry University, 2006

B.E., Visvesvaraya Technological University, 2004

Thesis Submitted in Partial Fulfillment of the

Requirements for the Degree of

Doctor of Philosophy

in the

School of Mechatronic Systems Engineering

Faculty of Applied Sciences

© Poovanna Cheppudira Thimmaiah

SIMON FRASER UNIVERSITY

Summer 2018

Copyright in this work rests with the author. Please ensure that any reproduction or re-use is done in accordance with the relevant national copyright legislation.

ii

Approval

Name: Poovanna Cheppudira Thimmaiah

Degree: Doctor of Philosophy

Title: Development of Capillary-assisted Low Pressure Evaporator for Adsorption Chillers

Examining Committee: Chair: Ahmad Rad Associate Director, School of Mechatronic Systems Engineering

Majid Bahrami Senior Supervisor Professor


Bonnie Gray Supervisor Professor

School of Engineering Science

Woo Soo Kim Supervisor Associate Professor


Neil Branda Internal Examiner Scientific Director – 4D LABS, Professor & Canada Research Chair in Materials Science Department of Chemistry

Jocelyn Bonjour External Examiner Professor & Director Center for Energy and Thermal Sciences (CETHIL)

The National Institute of Applied Sciences (INSA) of Lyon

Date Defended/Approved: June 07, 2018

iii

Abstract

The sales of air conditioners are poised to intensely increase over the next several years

as incomes and global temperatures rise around the world. Conventional air conditioning

systems use vapor-compression refrigeration (VCR) technology that has been the

dominant technology for close to a century. However, the environmental impact of VCR

systems, particularly their high energy consumption, around 36% of energy consumed in

the US building sector, is contrary to sustainable development. In addition to the

residential sector, VCR systems for vehicle air conditioning (A/C) applications can cause

a 20% increase in fuel consumption. Moreover, while the commonly used refrigerants in

VCR systems, hydrofluorocarbons (HFCs), are ozone-friendly, they still contribute to

global warming. Alternative, natural refrigerants, such as water, have no toxicity and

significantly lower global warming potential compared to HFCs. Furthermore, water is an

ideal refrigerant for systems driven by low-grade thermal energy. Solar-thermal and

waste-heat from industrial facilities and data centers are all abundant sources of low-

grade thermal energy, with a temperature less than 100°C. Low-grade thermal energy

can be used to run adsorption chillers for air conditioning of vehicle cabins and

residential units. When using water as an air conditioning refrigerant, evaporation occurs

at pressures below an atmosphere. In such a low pressure (LP) environment, the

performance of a flooded evaporator is negatively affected by the hydrostatic pressure.

This problem can be resolved by using a capillary-assisted low-pressure evaporator

(CALPE) that exploits thin film evaporation. The focus of this doctoral research is to

develop an effective CALPE for proof-of-concept demonstration of an adsorption chiller

for vehicle A/C applications. In this research, a low pressure evaporator testbed is

designed and built for the first time at Laboratory for Alternative Energy Conversion

(LAEC) to test CALPE. In addition, a mathematical model is developed to understand

detailed phenomena in capillary-assisted evaporation and to provide insight to design an

effective and compact CALPE. Several commercial tubes with different fin geometries

are tested. The results show that the capillary-assisted tubes provide two times greater

heat transfer rate compared to a plain tube. To further enhance the performance, the

outside surfaces of CALPE are coated with a thin film of porous copper to increase the

capillary action and the surface area available for thin film evaporation. The coating

increased the overall heat transfer coefficient by 30%. However, a significant amount of

the thermal resistance is from the inside of the evaporator tubes. Therefore, a new

µCALPE is designed with microchannels on the inside and rough capillary channels on

the outside is 3D printed by using direct metal laser sintering process. The internal

microchannels and external capillary channels led to enhanced heat transfer both

internally and externally. The µCALPE increased the overall heat transfer coefficient by a

factor of 2.5 when compared to the CALPE built with commercial Turbo Chil-40 FPI

tubes, which had footprint of four times larger than that of µCALPE. The developed

µCALPE is expandable to the entire low-grade thermal energy driven A/C systems in

vehicles as well as residential units.

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Keywords: Adsorption chiller; Flooded evaporator; Capillary; Evaporation; Thermal

resistance; Copper coating

v

Dedication

Throughout my life, two persons have always been there during the difficult and trying times. I would like

to dedicate this thesis and everything I do to my mother, Saroja and my grandmother, Late Amma. Also, I have always been supported by my strong father, Bose Thimmaiah. I would not be who I am today without the love and support of my brother Muthanna. To my sister-in-law Shilpa for always

standing by my side and helping me. To my niece Vanshikha and nephew Arjun, in the story of my life,

they have played their best part. To my Liya, although our time together was brief, her presence in my life will be felt forever. Finally, I would like to dedicate to the spirits of “JANA GANA MANA” and “O CANADA.”

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Acknowledgements

I would like to thank my supervisor, Prof. Majid Bahrami, for the patient guidance,

encouragement, and advice he has provided throughout my time as his student. I have

been incredibly lucky to have a supervisor who cared so much about my research, and

who responded to my questions and queries so promptly.

I am also thankful to my supervisory committee members, Dr. Woo Soo Kim and

Dr. Bonnie Gray, for their discussions and comments on my research project. I am also

grateful to Dr. Neil Branda and Dr. Jocelyn Bonjour for their time reading this thesis and

feedback. Also, I am grateful to Dr. Ahmad Rad, Associate Director, School of Mechatronic

Systems Engineering for being the defense committee chair.

I would like to thank my friends and colleagues at Laboratory for Alternative Energy

Conversion (LAEC) at Simon Fraser University for their support and contributions.

Especially, I thank Dr. Wendell Huttema, Dr. Claire McCague, Marius Haiducu, and, Dr.

Amir Sharafian, who supported this research project. I would like to offer my gratitude to

my co-op students Raaj Chatterjee, Chantal Osterman, and Ameer Ismail. Completing this

work would have been all the more difficult were it not for the support and friendship

provided by the other members of the School of Mechatronic Systems Engineering in

Surrey, School of Applied Science in Burnaby, SFU Public Square, and, SFU Renewable

Cities in Vancouver. I am indebted to them for their help.

I would like to place on record and acknowledge the Canadian Queen Elizabeth II

Diamond Jubilee Scholarship Program, not only for giving me the honor of the Queen

Elizabeth Advanced Scholar but also for the collaboration opportunity with the

Commonwealth partner institute, the Indian Institute of Science (IISc) and Fraser Basin

Council (FBC). I am very much thankful to Wolverine Tube Inc. and Wieland Thermal

Solutions for assisting our research by providing samples for our experiments. Finally, I

would like to express thanks to the Natural Sciences and Engineering Research Council

of Canada (NSERC) for funding my Ph.D. research.

vii

Table of Contents

Approval ............................................................................................................................... ii

Abstract ............................................................................................................................... iii

Dedication ............................................................................................................................v

Acknowledgements ............................................................................................................. vi

Table of Contents ............................................................................................................... vii

List of Tables ........................................................................................................................x

List of Figures...................................................................................................................... xi

List of Acronyms ................................................................................................................ xv

Nomenclature .................................................................................................................... xvi

Executive Summary ........................................................................................................ xviii

Chapter 1. Introduction ................................................................................................. 1

1.1. Research Importance and Background .................................................................... 1

1.2. State of the art .......................................................................................................... 5

1.2.1. Falling film evaporation..................................................................................... 5

1.2.2. Capillary-assisted evaporation ......................................................................... 6

1.3. Conclusion to the chapter ....................................................................................... 12

Chapter 2. Capillary-Assisted Low Pressure Evaporator [CALPE] ....................... 14

2.1. Theoretical description of capillary-assisted evaporation ...................................... 14

2.2. Experimental details ............................................................................................... 16

2.2.1. Operating conditions....................................................................................... 18

2.3. Data Analysis .......................................................................................................... 20

2.4. Tested commercial tubes ....................................................................................... 21

2.5. Base-case operating condition ............................................................................... 22

2.6. The Effect of the water height, dead volume, and flow rate .................................. 28

2.6.1. Effect of refrigerant water height .................................................................... 28

2.6.2. Effect of dead volume inside the evaporator ................................................. 31

2.6.3. Effect of chilled water mass flow rate ............................................................. 32


Chapter 3. Evaluation of Thermal Resistances of the CALPE ............................... 34

3.1. Measurement of the external heat transfer coefficient ........................................... 34

3.2. Deducing internal heat transfer coefficient ............................................................. 39

3.3. Thermal resistances ............................................................................................... 40

3.4. Effectiveness of the CALPE ................................................................................... 41


Chapter 4. Porous Copper Coated CALPE ............................................................... 44

4.1. Methods .................................................................................................................. 44

4.2. Uncoated CALPE .................................................................................................... 46

4.3. Porous coated CALPE ............................................................................................ 51

4.4. Surface area of the coating .................................................................................... 54

viii

4.5. Thermal resistances of porous coated CALPE ...................................................... 57


Chapter 5. Modeling of Capillary-Assisted Evaporation ......................................... 61

5.1. Background ............................................................................................................. 61

5.2. Assumptions ........................................................................................................... 62

5.3. CALPE sub-models ................................................................................................ 63

5.3.1. Natural convection pool model ....................................................................... 63

5.3.2. Liquid circumferential flow model ................................................................... 66

5.3.3. Evaporating thin film model ............................................................................ 68

5.3.4. Bulk model ...................................................................................................... 74

5.4. Heat transfer in the entire CALPE .......................................................................... 77

5.5. The solution implementation ................................................................................... 78

5.6. Details of the finned tube used in modelling .......................................................... 79

5.7. Model Results and Discussions.............................................................................. 80

5.7.1. Parametric study ............................................................................................. 84

Wall superheat ........................................................................................................... 84

Comparison with experiments ................................................................................... 85

Saturation temperature .............................................................................................. 86

Channel spacing ........................................................................................................ 86

Channel depth ........................................................................................................... 88


Chapter 6. Micro Capillary-Assisted Low Pressure Evaporator ............................ 91

6.1. Design of µCALPE .................................................................................................. 91

6.1.1. Pressure Drop................................................................................................. 93

6.1.2. Internal heat Transfer ..................................................................................... 94

6.1.3. Capillary channel height ................................................................................. 95

6.1.4. External heat transfer ..................................................................................... 96

6.1.5. Heat transfer in the entire µCALPE ................................................................ 97

6.2. 3D printed µCALPE ................................................................................................ 98

6.3. Experimental study ............................................................................................... 100

6.4. Results and discussion ......................................................................................... 101

6.5. Recommendations to reduce the pressure drop .................................................. 108

6.6. Conclusion to the chapter ..................................................................................... 111

Chapter 7. Summary and Future Work .................................................................... 112

7.1. General conclusions ............................................................................................. 112

7.2. Specific conclusions ............................................................................................. 113

7.3. Future Work .......................................................................................................... 115

References ..................................................................................................................... 116

Appendix A. Calculations of Fin Resistances ..................................................... 125

Appendix B. Uncertainity Analysis ....................................................................... 128

ix

Appendix C. Data Analysis .................................................................................... 129

Appendix D. Porosity and Surface Area of Porous Coatings ............................ 132

x

List of Tables

Table 1. Estimated fuel consumption and costs of using A/C [9] ............................. 3

Table 2 Performance of different LP evaporators with applications to adsorption chiller. .......................................................................................................... 9

Table 3. Base-case operating conditions for the experiments. .............................. 18

Table 4. Geometric details of the enhanced tubes used for the experiments. ...... 21

Table 5. Technical specifications of the enhanced tubes used for the experiments.................................................................................................................... 37

Table 6. Technical specifications of the uncoated tubes........................................ 46

Table 7. Technical specifications of the finned tubes used for the modelling........ 79

Table 8. Main dimensions of the serpentine flow µCALPE .................................... 98

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List of Figures

Figure 1. Primary energy consumption in U.S. residential building sector ............... 2

Figure 2. Energy split in an internal combustion engine............................................ 3

Figure 3. Schematic of the effect of hydrostatic pressure ......................................... 4

Figure 4. Schematic of the falling film evaporation .................................................... 6

Figure 5. Schematic of the capillary action and evaporation in a tree ...................... 6

Figure 6. Schematic of the capillary-assisted evaporation on a tube ........................ 7

Figure 7. Schematic of a finned tube with microchannels showing meniscus deformation ............................................................................................... 14

Figure 8. Schematic of an open rectangular microchannel ..................................... 15

Figure 9. An enlarged view of the micro region ....................................................... 16

Figure 10. Capillary-assisted evaporator built for testing different enhanced tubes: (a) top view, and (b) side view .................................................................. 17

Figure 11. Schematic of the LP evaporator experimental setup, (b) the actual experimental setup and the main components, and (c) custom-built heat exchangers prepared for the experiments ............................................... 19

Figure 12. The behavior of evaporator with 1.47 mm, 40 FPI tubes (Turbo Chil-40 FPI) at the thermal fluid (chilled water) inlet temperature of 15°C vs. time: (a) evaporator pressure operated from flooded to dry and (b) temperature at different locations in the evaporator ..................................................... 23

Figure 13. Heat transfer rate vs. time achieved by using 1.47 mm, 40 FPI tubes (Turbo Chil-40 FPI) ................................................................................... 24

Figure 14. Evaporator heat transfer coefficient vs. time achieved by using 1.47 mm, 40 FPI tubes (Turbo Chil-40 FPI). For the evaporator heat transfer coefficient, the plain tube surface area is A = 9.22 x 10-2 m2 ................... 25

Figure 15. Heat transfer rate vs. time achieved by using plain tubes ....................... 25

Figure 16. Evaporator heat transfer coefficient vs. time achieved by using plain tubes. For the evaporator heat transfer coefficient, the plain tube surface area is A = 9.22 x 10-2 m2 ......................................................................... 26

Figure 17. The total heat transfer rate (a) and the evaporator heat transfer coefficient (b) of evaporators with five different outer surface fin structure compared to plain tubes as function of thermal fluid (chilled water) temperature .... 27

Figure 18. Effect of water height variation on the performance of capillary-assisted evaporator with 1.47 mm, 40 FPI tubes (Turbo Chil-40 FPI) over time at chilled water inlet temperature of 15°C and mass flow rate of 2.53 kg/min, (b) Schematic of the evaporator filled with 2.4 kg of water to submerge the tubes by ~2 cm. Href =34.7 mm, Do =19.05 mm ................................. 29

Figure 19. Effect of water non-dimensional height, H*, on (a) total evaporation heat transfer rate and (b) evaporator heat transfer coefficient of capillary-assisted evaporator with 1.47 mm, 40 FPI tubes (Turbo Chil-40 FPI), Do =19.05 mm at thermal fluid (chilled water) inlet temperature of 15°C and mass flow rate of 2.53 kg/min. For the evaporator heat transfer coefficient, the plain tube surface area is A = 9.22 x 10-2 m2 ................... 30

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Figure 20. Schematic showing how dead volume inside the evaporator was changed using an acrylic block ................................................................................ 31

Figure 21. Effect of chilled water mass flow rate on (a) total evaporation heat transfer rate and (b) evaporator heat transfer coefficient for a capillary-assisted evaporator with 1.47 mm, 40 FPI tubes (Turbo Chil-40 FPI) at thermal fluid (chilled water) inlet temperature of 15°C. For the evaporator heat transfer coefficient, the plain tube surface area is A = 9.22 x 10-2 m2 ..... 32

Figure 22. Schematic of capillary-assisted evaporation. The red dots indicate the positions of thermocouples ....................................................................... 35

Figure 23. Capillary-assisted evaporator built for testing different enhanced tubes: (a) top view, and (b) side view. Red dots indicate the location of thermocouples .......................................................................................... 36

Figure 24. External heat transfer coefficient achieved by using (a) Wieland’s GEWA-KS-40 FPI tube, and (b) plain tube ........................................................... 38

Figure 25. The external heat transfer coefficient for three different enhanced tubes and one plain tube .................................................................................... 39

Figure 26. Comparison of thermal resistances for the LP evaporator built with a Turbo Chil-40 FPI tube ............................................................................. 40

Figure 27. Comparison of thermal resistances for three different enhanced tubes and one plain tube at chilled water inlet temperature of 20°C ........................ 41

Figure 28. Effectiveness, ε, of the LP evaporator with capillary-assisted tubes vs. NTU ........................................................................................................... 42

Figure 29. The schematic of the CALPE built with 7.9 mm ID tubes (a) Top view (b) Side view and (c) rectangular groove cross-section ................................ 45

Figure 30. Variation of overall heat transfer coefficient of the uncoated CALPE over

time, Tin =20°C, inm =2.5 kg/min ................................................................ 47

Figure 31. Comparison of thermal resistances for the uncoated CALPE ................. 47

Figure 32. Schematic of turbulent flow generators: (a) twisted tape and (b) Z-type. Geometrical details of (c) twisted tape and (d) Z-type turbulent flow generators ................................................................................................. 49

Figure 33. Comparison between tubes without turbulators, and with twisted tape and Z-type turbulators for the chilled water mass flow rate of 1.5 kg/min: (a) overall thermal resistance and (b) pressure drop .................................... 50

Figure 34. Photographs of uncoated and coated tubes and the CALPE .................. 51

Figure 35. (a) Evaporating meniscus inside an uncoated rectangular groove and (b) Evaporating meniscus inside a coated rectangular microchannel ........... 52

Figure 36. (a), (b), (c) and (d) SEM images of porous copper coatings .................... 53

Figure 37. (a), Wetting of uncoated CALPE, (b), (c) and (d) wetting at three random locations on the porous copper coated surface, (e) telescope-goniometer measurement setup .................................................................................. 56

Figure 38. Comparison of thermal resistances for the coated CALPE ..................... 57

Figure 39. Variation of overall heat transfer coefficient of the coated and uncoated

LP evaporator over time, Tin =20°C, inm =2.5 kg/min................................ 58

xiii

Figure 40. Comparison between standalone uncoated and coated CALPE (a)

average Q and (b) average U ................................................................... 59

Figure 41. The different sub-models considered in the modelling ............................ 63

Figure 42. Natural convection on the submerged portion of a finned tube ............... 64

Figure 43. Schematic describing circumferential flow model .................................... 66

Figure 44. Schematic of evaporating thin film............................................................ 69

Figure 45. Schematic of bulk region .......................................................................... 74

Figure 46. Flow chart for the solution implementation ............................................... 78

Figure 47. (a) CAD model of evaporator tube assembly and (b) CALPE placed in a evaporator chamber .................................................................................. 79

Figure 48. Variation of Pl and along ϕ -direction .................................................... 80

Figure 49. Variation of along ϕ-direction ................................................................. 81

Figure 50. The film thickness profile in the thin film region ....................................... 81

Figure 51. The evaporative heat flux in the thin film region....................................... 82

Figure 52. The heat transfer per unit length in the thin film region............................ 83

Figure 53. The heat transfer per unit length in the bulk region ................................. 83

Figure 54. Variation of bulk along the channel ........................................................... 84

Figure 55. Variation of hCALPE and Q̇ with the wall superheat .................................... 85

Figure 56. Variation of hCALPE with Tsat ...................................................................... 86

Figure 57. Variation of hCALPE and Q̇ with channel spacing W ................................... 87

Figure 58. Variation of hCALPE and Q̇ with channel spacing D.................................... 89

Figure 59. Schematic to explain the principle of µCALPE ......................................... 92

Figure 60. Schematic of (a) a serpentine flow µCALPE and (b) enlarged views of an inlet port and a capillary tube .................................................................... 94

Figure 61. (a) Capillary phenomenon in an open rectangular channel and (b) top view of the open channel .......................................................................... 96

Figure 62. An actual prototype showing (a) a µCALPE, (b) fins and (c) inlet port with microchannels ........................................................................................... 99

Figure 63. An actual prototype serpentine µCALPE (a) compared to a C$ 25 coin, (b) showing grainy surfaces ......................................................................... 100

Figure 64. Schematic of the µCALPE experimental setup ..................................... 101

Figure 65. The behavior of the µCALPE at Tin =15°C, inm =2.0 kg/min vs. time ..... 102

Figure 66. Variation of overall heat transfer coefficient of the µCALPE over time, Tin

=15°C, inm =2.0 kg/min ........................................................................... 102

Figure 67. Comparison of µCALPE with a CALPE built with Turbo Chil-40 FPI (Wolverine Tube Inc.) ............................................................................. 103

Figure 68. The total heat transfer rate (a), the overall heat transfer coefficient (b) of µCALPE and the CALPE built with Turbo Chil-40 FPI (Wolverine Tube Inc.) as function of chilled water mass flow rate..................................... 104

Figure 69. Effectiveness (ε) and a number of transfer units (NTU) of the µCALPE 105

xiv

Figure 70. Thermal resistance for the µCALPE ....................................................... 106

Figure 71. The pumping power (a), the cooing density and compactness (b) of µCALPE and the CALPE built with Turbo Chil-40 FPI (Wolverine Tube Inc.) ......................................................................................................... 107

Figure 72. Comparison of the measured and predicted pressure drop of serpentine type µCALPE .......................................................................................... 109

Figure 73. Schematic of a parallel flow type µCALPE ............................................. 109

Figure 74. Comparison between serpentine type and parallel type µCALPE ......... 110

xv

List of Acronyms

CALPE Capillary-assisted Low Pressure Evaporator

CFC chlorofluorocarbon refrigerants

COP Coefficient of performance

DMLS Direct Metal Laser Sintering

FPI Fins per inch

HCFC Hydro chlorofluorocarbon refrigerants

HVAC Heating, Ventilation, and Air Conditioning

LGTE Low Grade Thermal Energy

LGTE Low grade thermal energy

LP Low pressure

TCS temperature control system

VCR Vapor-Compression Refrigeration

μCALPE Micro Capillary-Assisted Low Pressure Evaporator

xvi

Nomenclature

A nominal surface area (m2), dispersion constant (J)

A/C air conditioning

α fluid/solid contact angle

pc heat capacity at constant pressure (J/kg∙K)

LMT log mean temperature difference (K)

lvh latent heat of vaporization (kJ/kg)

D diameter (m)

ε effectiveness (%)

β coefficient of cubic expansion in (1/K)

𝛿 film thickness (m)

f friction factor

Gr Grashof number

g gravity acceleration, m s-2

H height (m)

h heat transfer coefficient (W/m2 ∙ K)

k thermal conductivity (W/m ∙ K)

𝜅 curvature (m-1)

L length of the tube (m)

m mass (kg)

M molecular weight of water (kg/mol)

m mass flow rate (kg/s)

𝜇 dynamic viscosity (𝑁 ∙ 𝑠/𝑚2)

NTU number of transfer units

Nu Nusselt number

P pressure (Pa)

Pr Prandlt number

Q total heat transfer rate (W)

q heat transfer rate (W)

R thermal resistance (K/W), radius of curvature (m)

r radius (m)

Re Reynolds number

xvii

RO reverse osmosis desalination

R universal gas constant

ρ density (kg/m3)

𝜎 surface tension (N/m)

T temperature (°C)

t time (s)

θ dynamic contact angle

ν kinematic viscosity (m2/s), molar volume (m3/mol)

U overall heat transfer coefficient (W/m2∙K)

V velocity (m/s)

ν kinematic viscosity in (m2/s)

W Channel width (m)

Subscripts

copper copper tube

e evaporator

finned tube finned tube

in inlet chilled water

i inside/internal

l liquid

LM log mean

o outside/outer

out outlet chilled water

sat saturation

tube evaporator tube

v vapor-phase

wall/W tube wall

water evaporating water

xviii

Executive Summary

The sales of air conditioners are poised to intensely increase over the next several

years as incomes and global temperatures rise around the world. The growth is not only

driven by developed countries like the US, where almost 90% of homes have air

conditioning systems but also driven by developing countries. The leading example is

China, where sales of air conditioners have nearly doubled over the last five years. A

surge in use of air conditioning systems may put an unparalleled demand on the global

energy supply. Conventional air conditioning systems use vapor-compression

refrigeration (VCR) technology that has been the dominant technology for close to a

century, but their high energy consumption, around 40% of the consumption in the US

building sector, and environmental impact are contrary to sustainable development. In

addition to the residential sector, VCR systems for vehicle air conditioning (A/C)

applications can cause a 20% increase in fuel consumption. Moreover, while the

commonly used refrigerants in VCR systems, hydrofluorocarbons (HFCs), are ozone-

friendly, they still contribute to global warming. Therefore, using natural refrigerant such

as water as an alternative refrigerant provides substantial environmental benefits over

HFCs, including no toxicity and significantly lower global warming potential. Furthermore,

water is an ideal refrigerant for systems driven by low-grade thermal energy (LGTE).

LGTE, with a temperature less than 100°C, is available from many sources such as solar-

thermal, geothermal, and waste-heat from industrial facilities and data centers. LGTE can

be used to run adsorption chillers for air conditioning of vehicle cabins and residential

units. Due to the environmental benefits and energy savings, an LGTE-driven adsorption

chiller is a promising technology. However, low specific cooling capacity (SCP) and low

coefficient of performance (COP) are the main technical challenges facing

commercialization of adsorption chillers and lead to its large size and mass compared to

a VCR system. To this end, designing a highly efficient and compact evaporator will help

to reduce the mass and size of adsorption chillers.

Most LGTE technologies use conventional flooded low pressure (LP) evaporators.

The performance of a flooded LP evaporator is negatively affected by the saturation

pressure difference along the height of the water column. This is particularly the case in a

system that operates below atmospheric pressure, such as an adsorption chiller. Under

such low evaporation pressures (~1 kPa), the height of the water column in the evaporator

xix

affects the water saturation pressure and, thus, its saturation temperature. This

temperature gradient inside the evaporator severely reduces the performance of an

adsorption chiller. Despite this limitation, water is still an attractive choice of refrigerant

due to its non-toxicity and high enthalpy of evaporation. This has motivated researchers

to develop LP evaporators that optimize heat transfer by exploiting the evaporation of

water in a thin film. Therefore, falling film evaporators that utilize pumps to spray a thin

film of water on the external surface of the evaporator tubes are used. The benefit of falling

film evaporators is a high overall heat transfer coefficient. However, there are drawbacks

due to system complexity and added power consumption for the internal pumps.

One practical solution in LP evaporators is to use a capillary-assisted low pressure

evaporator (CALPE). A CALPE draws water from a pool into the grooves between fins

and covers the external surface of the evaporator tube. Capillary forces draw the water

along the grooves without the use of external power and uniformly distribute the water

along the tubes, leading to thin film evaporation.

In this PhD research project, a modular CALPE testbed is designed and built for

the first time at the Laboratory for Alternative Energy Conversion (LAEC) to test different

CALPEs under a range of operating conditions. Also, a semi-analytical model is developed

to an in-depth understanding of the phenomena in capillary-assisted evaporation and to

provide insight to design an effective and compact CALPE.

Potential Impact, Security, Environment, and Economy:

If successful, the proposed CALPE technology has the potential to transform on-

demand cooling in vehicles, while increasing their fuel economy. Greater use of adsorption

chillers in vehicles would reduce greenhouse gas emissions, 30% of which come from the

transportation sector. Increased use of adsorption chillers in other applications would

decrease Canada’s dependence on electricity. The present CALPE technology would

increase the marketability of adsorption chillers, helping to sustainably meet the additional

demand on the global energy supply due to the increased use of air conditioning systems.

Research objectives

The objectives of this research project are to understand heat transfer in a CALPE, and

consequently, build an evaporator with a cooling capacity of 1 kW and effectiveness of

xx

above 80%. This evaporator will be installed in the waste heat-driven adsorption chiller,

currently available at LAEC, which serves as a proof-of-concept demonstration of an

adsorption chiller for vehicle A/C applications. The following steps are considered during

this research to meet the objectives:

• Measurement of heat transfer performance of capillary-assisted tubes to achieve

maximum performance, and determine the most suited evaporator tube for a

CALPE,

• Development of a mathematical model to understand and predict the LP

evaporator performance under different operating conditions,

• Building a proof-of-concept CALPE with a cooling power of 1 kW for LGTE-driven

adsorption chillers for vehicle A/C applications.

Research Roadmap and Contributions

The research roadmap for accomplishing the objectives is shown at the end of this

section. The contributions of this research project were designing an experimental setup

and developing a conceptual mathematical model to support the knowledge of the

capillary-assisted low pressure evaporation. The outcome of this research has resulted in

an invention of a novel micro capillary-assisted low pressure evaporator (μCALPE), and

SFU-industry engagement has agreed to support the invention (US Provisional Patent

Application #: US 62/623,406) and commercialize the technology. A technology

assignment to SFU and revenue sharing agreement (TARSA) has been already executed.

The detailed outcomes of this research project are listed below:

1. Capillary-assisted tube characterization to determine the most suitable tube for

use in an LP evaporator (Published in Applied Energy, 2016)

In this experimental study, the effects of capillary-assisted tubes with different fin

geometries on the performance of a low-pressure evaporator were investigated. A new

capillary-assisted evaporator test bed was designed and built. The test showed that

parallel fins, fin height, and external surface area were the main features of capillary-

assisted tubes. The results indicated that the height of water column in the evaporator

has detrimental effect on the cooling power of the evaporator and it should be

maintained below the tube diameter.

xxi

2. Determination of main factors affecting the performance of a capillary-assisted

evaporator (Selected for publication in a special issue of Heat Pipe Science and

Technology, An International Journal, 2016)

Here in this experimental study, three enhanced tubes with parallel fin geometries

(with different fin spacing and fin height) and a plain tube were tested. The results

showed that enhanced tubes provide ~2 times higher total evaporation heat transfer

rate compared to the plain tube. Under equal inner and outer heat transfer surface

areas, the results also show that the enhanced tube with parallel continuous fins and

higher fin height has 13% higher evaporation heat transfer coefficient than that of a

tube with lower fin height.

3. Experimental evaluation of thermal resistances of low-pressure capillary-assisted

tubes (Published, Applied Thermal Engineering, 2016)

This experimental study investigated the thermal resistances of the finned tubes

used in CALPE. The study showed that external heat transfer coefficient had a positive

correlation to chilled water inlet temperature. The tests indicated that the internal heat

transfer coefficient was the bottleneck of the CALPE. The major finding of this study

was that up to 89% of the overall thermal resistance is due to the internal heat transfer

resistance. This clearly indicated that the main bottleneck in the performance of a LP

evaporator was the convective heat resistance inside the tube. Therefore, the internal

heat transfer coefficient and internal surface area of enhanced tubes should be

increased to enhance the performance of the CALPE.

4. Evaluating the performance of low-pressure evaporator inserted with turbulent

flow generators (Published, Energy, 2016)

Here, the performance of a low-pressure evaporator was experimentally studied.

To reduce the internal thermal resistance, small diameter commercial tubes were

sourced. In addition, twisted and Z-type turbulent flow generators were incorporated

into the evaporator tubes. The evaporator cooling power showed an increase by 12%

and 58% when twisted tape and Z-type turbulators were used at the cost of an increase

in the internal pressure drop by 2.5 and 14.5 times, respectively. However, there was

inadequate capillary performance leading to higher external thermal resistance due to

low fin density of the sourced small diameter tubes. To reduce the external thermal

resistance, the outside surface of the evaporator tubes was coated with porous copper.

xxii

5. Assessment of effects of porous copper coatings on capillary-assisted low

pressure evaporation (under review, International Journal of Thermal Sciences,

2018)

To reduce the external thermal resistance, the outside surfaces of the evaporator

tubes of a CALPE were coated with copper metal foam. This led to enhanced capillary

action and increased surface area for thin film evaporation. The coating increased the

overall heat transfer coefficient by a factor of 1.3 and the cooling power by a factor of

2. By applying a thin film of porous coating, the bottleneck in heat transfer was shifted

from external convective thermal resistance to internal convective thermal resistance.

6. Determination of surface roughness and porosity of porous coated capillary-

assisted low pressure evaporators (Revised, Nature Scientific Reports, 2018)

In this study, the porosity and surface area of porous metal films utilizing a helium

pycnometer and computed micro-tomography (CMT) were determined. The surface

roughness was defined based on Wenzel method using a telescope-goniometer.

Experiments were conducted on four varieties of thin film samples coated with copper

powder using wire flame and plasma thermal spray coating methods. The test results

showed that the wire flame and plasma thermal spray methods produced highly porous

thin films with porosities between 39-43%. The tests revealed that the thermal spray

coating increased the hydrophobicity of the surface and the plasma coating led to a

super-hydrophobic surface. The new approach established that the porosity of thin

films can be non-invasively determined and may also be applied to a wide variety of

coated surfaces.

7. Development of a Mathematical model for predicting the CALPE performance

(manuscript ready to be submitted)

In this analytical study, a model was developed to understand and predict the

CALPE performance and support an in-depth understanding of the phenomena in

capillary-assisted evaporation and to provide insight to design an effective and

compact CALPE. To capture the physics of capillary-assisted evaporation in an open

rectangular microchannel, the four sub-models are considered: (1) the natural

convection model; (2) the liquid circumferential flow model; (3) the evaporating thin

film model; and, (4) the bulk model. Using this model, menisci curvatures in an

evaporating flow were attained; the length and thickness of the thin film region were

xxiii

determined; bulk region and thin film region were demarcated, and heat transfer

coefficient for capillary-assisted evaporation in open rectangular microchannels was

computed. Finally, the heat transfer rate (cooling power) in the entire CALPE was

estimated.

8. Development of a novel µCALPE for an onboard vehicle cabin air-conditioning (US

Provisional Patent filed, application #: US 62/623,406)

Based on the experiences and learning from the above studies, in this invention

the main bottleneck was overcome by designing and building a new Micro Capillary-

Assisted Low Pressure Evaporator (μCALPE). A new μCALPE was 3D printed using

direct metal laser sintering (DMLS). The general idea of the proposed invention is to

run chilled water through mini/microchannels and transfer the thermal energy to

evaporate water through capillary action at low pressure. The capillary action was

achieved by creating narrow channels, with an optimal gap for capillary effect, using

high-density fins. The fins have a grainy surface to provide additional heat transfer

surface, which was achieved through laser sintering process. The experimental

results showed that the of the 3D printed μCALPE provided ten times higher cooling

power density when compared to the CALPE.

In summary, the contributions of this research have resulted in seven peer-

reviewed high impact journal papers, six conferences papers published/presented

and one US provisional patent filed:

Journal Publications

1. P. C. Thimmaiah, A. Sharafian, W. Huttema, and M. Bahrami, (2015) “Effects of

fin spacing and fin height of capillary-assisted tubes on the performance of a low

operating pressure evaporator for an adsorption cooling system”, Heat Pipe

Science and Technology, An International Journal, 6, pp 195-204

2. P. C. Thimmaiah, A. Sharafian, C. McCague, W. Huttema, and M. Bahrami, (2016)

“Effects of capillary-assisted tubes with different fin geometries on the performance

of a low-operating pressure evaporator for adsorption cooling system

applications”, Applied Energy, 171, pp 256–265

https://www.researchgate.net/profile/Claire_Mccague

xxiv

3. P. C. Thimmaiah, A. Sharafian, W. Huttema, and M. Bahrami, (2016) “Performance

of finned tubes used in low-pressure capillary-assisted evaporator of adsorption

cooling system”, Applied Thermal Engineering, 106, pp 371-380

4. P. C. Thimmaiah, C M. Rouhani, W. Huttema, and M. Bahrami, (2017) "Evaluation

of low-pressure flooded evaporator for adsorption chillers", Energy, 122, pp 144-

58

5. P. C. Thimmaiah, R. Chatterjee, W. Huttema, and M. Bahrami, (2018) “Capillary-

Assisted Low Pressure Evaporator for Low Grade Energy Driven Systems: Effects

of a Porous Copper Coating”, International Journal of Thermal Sciences, under

review

6. P. C. Thimmaiah, A. K. Panda , U. K. Pandey , Dr. C. McCague, , P. Dutta , M.

Bahrami, (2018) “A New Approach to Compute the Porosity and Surface

Roughness of Porous Coated Capillary-Assisted Low Pressure Evaporators”,

Nature Scientific Reports, Revised

7. A. Sharafian, S. M. N. Mehr, P. C. Thimmaiah, W. Huttema, and M. Bahrami,

(2016) “Effects of adsorbent mass and number of adsorber beds on the

performance of a waste-heat driven adsorption cooling system for vehicle air

conditioning applications”, Energy, 112, pp 481-493

Conference Publications

1. P. C. Thimmaiah, A. Fradin, W. Huttema and M. Bahrami, (2018) “Porous copper

coated low pressure condenser/evaporator for sorption chillers” Heat Powered

Cycles Conference (HPC 2018), Bayreuth, Germany

2. P. C. Thimmaiah, W. Huttema, and M. Bahrami, (2017) “Impact of Porous Copper

Coating on Capillary-Assisted Low Pressure Evaporator for an Adsorption Chiller”

International Sorption Heat Pump Conference (ISHPC 2017), Aug. 7-10, 2017,

Tokyo, Japan

3. P. C. Thimmaiah, W. Huttema, and M. Bahrami, (2017) “Putting Waste-Heat to

Work: The Future of Air-Conditioning” Researching the Globe, SFU Public

Square’s community Summit-Who Needs Canada? March 8, 2017, Vancouver,

Canada

https://www.researchgate.net/profile/Claire_Mccague

xxv

4. P. C. Thimmaiah, W. Huttema, and M. Bahrami, (2017) “Putting Waste-Heat to

Work: The Future of Air-Conditioning” Global Learning Forum, Renewable Cities,

May 17-19, 2017, Vancouver, Canada

5. P. C. Thimmaiah, A. Sharafian, W. Huttema, and M. Bahrami, (2016) “Performance

evaluation of low pressure evaporator with low-finned tubes for an adsorption

cooling system”, IVth International Symposium on Innovative Materials for

Processes in Energy Systems (IMPRES 2016), Taormina, Sicily, Italy

6. P. C. Thimmaiah, A. Sharafian, W. Huttema, and M. Bahrami, (2015), “Effects of

fin spacing and fin height of capillary-assisted on the performance of low-operating

pressure evaporator in adsorption cooling system”, 9th International Seminar: Heat

Pipes, Heat Pumps, Refrigerators, Power Sources, Minsk, Belarus

Patent Application

• US provisional patent 62/623406, filed January 29, 2018: MICRO CAPILLARY

ASSISTED LOW-PRESSURE EVAPORATOR (µCALPE)

xxvi

Scope and deliverables of the present research project.

1

Chapter 1. Introduction

1.1. Research Importance and Background

As the world moves to meet its greenhouse gas (GHG) emissions targets, novel

refrigerants must be developed to replace the existing refrigerants that have high global

warming potential (GWP) [1,2]. The motivation to develop non-toxic refrigerants with low

GWP is supported by international agreements, such as the Montreal Protocol, ratified in

1989, which was a major step by nations to phase out ozone layer-depleting CFCs and

HCFCs [3,4]. While the commonly used replacements [2], hydrofluorocarbons (HFCs), are

ozone-friendly, they still contribute to global warming [2] and are specified as GHGs under

the Kyoto Protocol [5]. The Paris Agreement of 2016 requires countries to significantly

reduce their GHG emissions to limit global warming to 2°C above pre-industrial levels [6].

Therefore, using water as an alternative refrigerant provides substantial environmental

benefits over HFCs, including no toxicity and significantly lower GWP. Furthermore, water

is an ideal refrigerant for systems driven by low-grade thermal energy (LGTE). LGTE, with

a temperature less than 100°C, is available from many sources such as solar-thermal,

geothermal, and waste-heat from industrial facilities and data centers.

Using conventional vapor-compression refrigeration (VCR) technology for air-

conditioning in vehicles contribute to significantly to greenhouse gas emissions, 30%

of which come from the transportation sector. VCR technology has been the dominant

technology of air conditioning systems for close to a century [7], but their environmental

impact and high energy consumption [8] are contrary to sustainable development.

Synthetic refrigerants used in VCR systems contribute strongly to climate change and

the energy consumption of heating, ventilation, and air conditioning (HVAC) equipment

(including VCR systems) is considerable. For example, HVAC equipment contributed

to over 36% of the total primary energy consumption in the U.S. buildings sector [1] in

2013, as shown in Figure 1

2

Figure 1. Primary energy consumption in U.S. residential building sector

In the transportation sector, VCR systems of vehicles cause a 20% increase in the

fuel consumption [9]. In Table 1, the estimated fuel consumption, costs, and CO2

emissions from A/C systems of vehicles are listed [9]. With more than 20 million passenger

vehicles on the road in Canada, the potential for savings is substantial. Figure 2 shows

the typical energy split in an internal combustion engine (ICE). About 70% of the total fuel

energy released in an ICE of a light-duty vehicle is dissipated as a waste heat through the

engine coolant and the exhaust gas [10]. Foreseen management of this waste heat energy

and the anticipated commitment to phase out hydrofluorocarbon (HFC) refrigerants have

stimulated interest in alternative HVAC systems such as waste heat-driven adsorption

chillers. A portion of the waste heat of an ICE is sufficient to run an adsorption chiller and

generate the cooling power required for the vehicle A/C applications (about 2-3.5 kW [11]).

HVAC 36%

Water heating

14%Lighting 9%

Electronics

9%

Cleaning 6%

Computers

4%

Refrigeration

6%

Cooking 3%

Others 12%

3

Table 1. Estimated fuel consumption and costs of using A/C [9]

Annual distance drove using A/C

Annual increase in fuel consumption with A/C use

Fuel cost of A/C use over 10 years

CO2 emissions from fuel used for A/C over 10 years

If your A/C uses 1 L/100 km






14,000 km 140 L 280 L $1,820 $3,640 3,220 kg 6,440 kg

12,000 km 120 L 240 L $1,560 $3,120 2,760 kg 5,520 kg

10,000 km 100 L 200 L $1,300 $2,600 2,300 kg 4,600 kg

8,000 km 80 L 160 L $1040 $2,080 1,840 kg 3,680 kg

6,000 km 60 L 120 L $780 $1,560 1,380 kg 2,760 kg Note: For illustrative purposes, savings are based on a fuel price of $1.30/L and a CO2 emissions factor of 2.3 kg/L of gasoline.

Figure 2. Energy split in an internal combustion engine

Furthermore, an adsorption chiller has the benefits of simple construction, no

moving parts (except valves), no vibration, quiet operation, and low operating cost [12–

14]. However, high vacuum operating pressure, low specific cooling capacity, and low

coefficient of performance (COP) are technical challenges facing commercialization of

adsorption chillers. These drawbacks increase the size and mass of adsorption chillers

compared to those of VCR systems [15–17]

Adsorption chillers have four main components: adsorber beds, condenser,

expansion valve, and evaporator. The lowest pressure in any A/C systems, including

HVAC49%

25-40%Effectivepower(mobilityandaccessories)

5%Frictionandparasiticpowerconsumption

Enginecoolant

Exhaustgas

60-70%wasteheat

4

adsorption chillers, happen in their evaporator. The performance of a flooded LP

evaporator is negatively affected by the saturation pressure difference along the height of

the water column [18,19]. For example, as shown in Figure 3, having a liquid water column

of 5 cm in an evaporator creates a hydrostatic pressure of 0.49 kPa. For an evaporator

operating at 1.0 kPa, this additional hydrostatic pressure increases the saturation

temperature of water from 6.9°C at the surface to 13.0°C at a depth of 5 cm, where the

pressure is 1.49 kPa (1.0 + 0.49 kPa). This temperature variation in the evaporator can

drastically reduce the cooling power. Despite this limitation, water is still an attractive

choice of refrigerant due to its non-toxicity and high enthalpy of evaporation [3]. This has

motivated research to develop LP evaporators that optimize heat transfer by exploiting the

evaporation of water in a thin film [20,21].

Figure 3. Schematic of the effect of hydrostatic pressure

1.0 kPa

Vacuum chamber

Vacuum pump 1.49 kPa

5 cm

6.97oC

13oC

5

1.2. State of the art

Low pressure (LP) evaporator technologies are classified as: i) falling film, and ii) capillary-

assisted. Figure 4 shows the schematic of LP evaporator technology

Falling film evaporation

Several studies are investigating falling film evaporation from the outside surface

of plain and enhanced (structured) tubes for refrigeration applications. Enhanced tubes

refer to tubes with fins (or regular patterns) on their other surface and high surface area

compared to a plain tube. Ribatski and Jacobi [22] reviewed experimental and theoretical

studies of falling film evaporation and concluded that the heat transfer coefficient of

enhanced tubes was up to 10 times greater than that of a plain tube. Yang et al. [23]

investigated the variation of heat transfer coefficient of falling film evaporation as a function

of flow density, evaporation temperatures, and the temperature difference between the

wall and the saturated water. They showed that when the flow density was increased from

0.013 kg/(ms) to 0.062 kg/(ms), the heat transfer coefficient was increased from 5,000

W/(m2K) to 30,000 W/(m2K). Li et al. [24] measured the average heat transfer coefficients

of water falling films on five types of enhanced tubes, with plain tubes as a benchmark.

The tests were conducted at one kPa, and the results showed that tubes with enhanced

outer and inner surfaces were required to achieve high heat transfer flux (22 kW/m2). Li et

al. [25] tested commercialized enhanced tubes with 19 and 26 fins per inch (FPI) (Turbo

CAB®, Wolverine Tube Inc.). They found that tested tubes provided overall heat transfer

coefficients of 3,000-4,000 W/(m2K) at a falling film flow rate of 1 m3/h and temperature

of 15°C. Their work confirmed that tubes with enhanced inner surfaces provided better

heat transfer performance. While falling film evaporators can provide large cooling

capacities in a small footprint, the uniform distribution of refrigerant, the parasitic power

consumption of internal pump and circulator, and liquid spray equipment make falling film

evaporators impractical for an adsorption chiller installed in a light-duty vehicle A/C system

[26]. Also, non-uniform thin films can cause dry-out on sections of the evaporator tubes,

which has a detrimental effect on the performance [25].

6

Figure 4. Schematic of the falling film evaporation

Capillary-assisted evaporation

Figure 5. Schematic of the capillary action and evaporation in a tree

A simpler alternative is to mimic the evaporation process in trees. Trees are natural

hydraulic pumps. As shown in Figure 5 trees and plants absorb water through their roots

and pump the water using capillary action to the leaves where it evaporates. Inspired by

capillary assisted evaporation in trees, we attained efficient LP evaporation using a

capillary-assisted low-pressure evaporator (CALPE). As shown in Figure 6 a CALPE

draws water from a pool into the grooves between fins and covers the external surface of

the evaporator tube. Capillary forces draw the water along the grooves without the use of

Side view Front view

Tube bundle

Distributor

CapillaryEvaporation

Water absorbed

7

external power and uniformly distribute the water along the tubes, leading to thin film

evaporation[27].

Figure 6. Schematic of the capillary-assisted evaporation on a tube

Low pressure capillary-assisted evaporation for adsorption chiller applications is

relatively novel, and there are limited studies available in the literature. Capillary-assisted

flow and evaporation inside a circumferential rectangular micro groove were studied by

Xia et al. [27,28] for a silica gel-water adsorption chiller. A heat transfer tube with outside

circumferential micro-grooves was immersed in a pool of liquid. The fluid flowing inside

the tube heated the thin liquid film located on the outer micro-grooves where the liquid

water rose along the micro-grooves by capillary action and was evaporated. Xia et al. also

investigated the factors influencing the capillary-assisted evaporation performance, such

as the immersion depth, evaporation pressure, and superheating degree. Their

experimental results showed that there was a positive correlation between the evaporation

heat transfer coefficient and the evaporation pressure, and negative correlation for the

superheating and immersion depth. For water at saturation temperature of 5°C, wall

superheat of 4°C and dimensionless liquid level (ratio of the immersion depth to tube

diameter) of 0.5, the evaporation heat transfer coefficient was 3,500 W/(m2K). And when

the liquid level to tube diameter ratio was 0.25 (i.e., the height of water column was up to

a quarter of the tube diameter), the film side heat transfer coefficient was 5,500 W/(m2K)

[27].

Chen et al. [29] used a capillary-assisted evaporator in the experimental study of

a compact silica gel-water adsorption chiller. The evaporator consisted of five trays, and

x

y

Capillary water

Pooled water

Fins

8

each tray contained nine copper tubes with outside micro-grooves. Capillary-assisted

evaporation was employed in these evaporators based on Ref. [27,28]. They achieved an

overall heat transfer coefficient (U) of about 5,000 W/ (m2K). Lanzerath et al. [30] studied

a combination of finned tubes and thermal coating for capillary-assisted evaporation at

low pressures. Their investigation showed a strong dependency of the evaporation heat

transfer coefficient on the filling level. Their study also established that a combination of

macroscopic fin structures and micro porous coatings yielded evaporation heat transfer

coefficient of 5,500 W/(m2K) compared with ordinary plain tubes with the evaporation heat

transfer coefficient of 500 W/(m2K). Sabir et al. [31] observed that an internally powder

coated evaporator had a greater overall heat transfer coefficient compared to evaporators

with deep and shallow internal grooves. Schnabel et al. [32] evaluated different evaporator

concepts for adsorption systems, and capillary-assisted evaporation was one among

them. They achieved a maximum cooling power of 1.2 kW while maintaining the operating

pressure of 1.1-1.7 kPa. The tubes in their study involved both outer and inner structures,

but Schnabel et al. did not distinguish the effect of inner and outer heat transfer. The

performances of different LP evaporators are compared in Table 2.

9

Table 2 Performance of different LP evaporators with applications to adsorption chiller.

Ref. Evaporator Technology

Max. cooling power (kW)

Tube details

Operating pressure (kPa)

material Refrigerant Thermal fluid

Castro et al. [33]

Falling film 2.0 Length - 1.3 m OD - 0.63" # of tubes - 36

1.0 steel LiBr/Water Water

Florides et al. [34]

Falling film/ Vertical tube

1.0 Length - 1.0 m OD - 0.375" ID - 0.32" # of tubes - 11

0.9 Copper LiBr/Water Water

Sabir et al. [31,35,36]

Capillary-assisted on the inner surface of the tube

0.7-1.6 Length - 0.3 m OD - 1 ⅛" # of tubes - 9

1.5 Copper Water Air

Schnabel et al. [32]

Capillary-assisted on the outer surface of the tube

1.2 Length - 0.4 m OD - 0.71" # of tubes - 4

1.1-1.7 Copper Water Water

Xia et al. [27]




Lanzerath et al. [21]


0.3-0.6 Total length - 2.00 m OD - 0.74" ID - 0.52"


Thimmaiah et al.[37]


0.3-0.4 Length - 0.39 m OD - ¾." # of tubes - 4


Castro et al. [38]

Flooded type


1.1 Copper Water Water

10

In a compact LP evaporator, there must be a high 𝑈 between the evaporating water

and thermal fluid (chilled water) flowing inside the evaporator tubes. Using commercially-

available tubes with high fin density in the CALPE has been shown to increase 𝑈 by two

times as compared to plain tubes [37]. 𝑈 can be further doubled by applying a thin porous

coating to the surface of the grooves [21]. However, a major bottleneck comes from the

internal heat transfer resistance of the liquid chilled water flowing inside the evaporator

tubes [39].

Since most publications on LP evaporation focus in detail on boiling regimes or

fundamental studies in heat transfer, data on application-oriented LP evaporators is rare.

There is a lack of experimental data on LP evaporators that address challenges in both

internal and external heat transfer. 𝑈 was recorded at high chilled water flow rates (16

kg/min) in Lanzerath et al.’s experiment for both uncoated and porous coated finned tube

evaporators [21]. In practical situations, the chilled water often exchanges heat with an air

handling unit (AHU) [40]. While large flow rates remove the limiting factor of internal heat

transfer resistance, pressure drop increases significantly with higher velocities through the

evaporator, piping, and AHU, requires powerful pumps. This underscores the need to

study CALPE at lower mass flow rates (1-3 kg/min) with a sizable temperature difference

between the inlet and outlet ports. Such evaporators will have a greater effectiveness.

Driving temperature for CALPE

In flooded evaporators, the primary limitation on the performance of low pressure

evaporator is the effect of the operating pressure. At common evaporation temperatures

of 5 –10°C water vapor pressures are very low and therefore the favorable mechanism of

nucleate boiling requires high wall superheat of up to 20°C [41]. At low saturation

pressures, the heat transfer due to natural convection results in low heat transfer

coefficients. For which, the driving temperature is the temperature difference between wall

temperature and saturation temperature. This “driving” temperature difference is directly

connected to the evaporation and therefore the liquid water temperature.

One way to improve the flooded evaporator performance is to vary the hydrostatic

pressure by varying the filling level. Giraud et al. [42] and Lanzerath et al. [21] showed

that the filling level strongly influences the evaporation rate of the low pressure evaporator.

Another way to improve the performance of the low pressure evaporator is to

optimize the evaporation through a thin film evaporation in capillary-assisted evaporators.

11

Since the thickness of the film is very small, the film temperature is almost equal to the

wall temperature. Therefore, the driving temperature is the temperature difference

between film temperature and vapor temperature, which has been explained in the work

of Xia et al. [27] and Lanzerath et al. [21]. Accordingly, in this study, driving temperatures

are measured by placing thermocouples outside the tube wall (or the thin film) and the

vapor space. There is also a small portion of the tube submerged under the liquid pool,

which receives heat from the thermal fluid. In this region, the evaporation takes place from

the free surface of the liquid pool due to natural convection. In addition to the capillary

evaporation and natural convective evaporation, there is a natural convection heat transfer

between the liquid bulk and the vapor that cools the liquid bulk.

Capillarity in heat pipes

The heat pipe has been extensively used for cooling high power density devices.

The working fluid absorbs the heat from the heat source at the evaporation section via

evaporation. The vapor then condenses at the distant section, where the latent heat is

released to the environment. The condensed fluid is drawn to the evaporator through the

wick by the capillary force to complete the cycle [43]. Wick material eliminates the need

for active pumping of the fluid [44]. The high capillary force is created in the evaporator

due to fine porous wicks (primary wicks), such as sintered metal powder with an effective

pore radius of 0.7–15 m and a porosity of 55–75% [45].

A low heat transfer resistance characterizes a right heat pipe. The evaporator

resistance is the critical part of the overall thermal resistance of a heat pipe [46]. It is

influenced by many parameters, including the heat load, porosity, and permeability of the

wick, suitable working fluid, and the wick capillarity. Quiescent surface evaporation

prevails for sintered-mesh or sintered-powder wicks working with water [43]. Fine pores

at the wick help sustain a thin water film under large heat loads. Smaller evaporator

resistances, as well as large maximum heat loads, could be reached [43].

In previous studies, the microgrooves with triangular cross-sections have obtained

most considerations due to ease of groove machining[47–49], Lately, a lot of

microfabrication technologies have been used to produce wick structures that provide a

better capillary suction. It has been experimentally proved that it is possible to produce a

metal capillary structure with the significant capillary action using selective laser melting

12

[9,10]. The heat and mass transfer in rectangular micro-grooves have gained much of

interest recently [52].

1.3. Conclusion to the chapter

In brief, the lack of information about the CALPE in the available literature can be listed

as follows. Previous studies:

• did not determine the external features of enhanced tubes required to achieve the

highest capillary evaporation,

• focused on enhancing the external heat transfer coefficient and they did not reflect

the importance of the overall heat transfer coefficient (including both internal and

external heat transfer coefficients),

• did not report the importance of the effects of tube wall thermal resistance to the

heat transfer,

• did not give clear path for performance improvement of capillary-assisted tubes

• did not evaluate low-pressure flooded evaporator performance for adsorption

chillers (another type of LP evaporators)

According to the above discussion, to design and build a LP evaporator for an

adsorption chiller with high overall thermal conductance (UA) and effectiveness, this

research project is divided into three parts: (i) capillary-assisted tube assesment, (ii) low

pressure capillary-assisted evaporator design, and (iii) enhancement of the LP evaporator

performance. To this end, a modular experimental LP evaporator testbed is designed and

built for the first time at Laboratory for Alternative Energy Conversion (LAEC) to test

different capillary-assisted tubes under different operating conditions. In addition, a

mathematical model is developed to understand detailed phenomena in capillary-assisted

evaporation.

Thesis structure

This introductory chapter (Chapter I) develops the motivation for the research and reviews

the work developed in the study of the low-pressure evaporator technology to enhance

heat transfer for LGTE driven applications.

Chapter II presents a concise theoretical description of capillary-assisted evaporation and

13

deliberates the capillary-assisted tube characterization to determine the most suitable tube

for use in an LP evaporator. Furthermore, Chapter II identifies the main factors affecting

the performance of a capillary-assisted low pressure evaporator (CALPE). A significant

part of the work presented in chapter II is already published in two scientific peer-reviewed

international journals: Applied Energy and Heat Pipe Science and Technology.

Experimental evaluation of thermal resistances of low-pressure capillary-assisted tubes is

presented in Chapter III. The main bottleneck in the CALPE performance is identified and

presented here. The corresponding research work is also published in a scientific peer-

reviewed international journal: Applied Thermal Engineering.

In Chapter IV, the evaluation of the performance of CALPE with turbulent flow generators

is presented. It also describes the assessment of effects of porous copper coatings on

capillary-assisted low pressure evaporation. A significant part of the work performed in

chapter IV is already published/submitted for publication in the Energy Journal, Nature

Scientific Reports and in the Int. Journal of Heat and Mass Transfer.

The development of a mathematical model for predicting the CALPE performance begins

with Chapter V. The corresponding work is developed into a manuscript and has been

internally reviewed and ready to be submitted to a scientific journal.

Chapter VI describes the development of a novel micro capillary-assisted low pressure

evaporator (µCALPE) for an onboard vehicle cabin air-conditioning. A US Provisional

Patent has been filed on this technology.

Chapter VII, where the relevant conclusions of this work are drawn and some

recommendations for future work are proposed.

14

Chapter 2. Capillary-Assisted Low Pressure Evaporator [CALPE]

2.1. Theoretical description of capillary-assisted evaporation

As discussed in the Chapter 1 subsection 1.2.2, a simpler alternative to attain

efficient low pressure (LP) evaporation is capillary-assisted low-pressure evaporator

(CALPE). As shown in Figure 6, a CALPE draws water from a pool into the channel

between fins and covers the external surface of the evaporator tube.

Figure 7. Schematic of a finned tube with microchannels showing meniscus deformation

Figure 7 shows a sketch of an open rectangular channel on the outside surface of

a finned tube. Capillary forces draw the water along the channel against gravity and

viscous force and uniformly distribute the water along the tubes, leading to thin film

evaporation [27]. Due to surface tension inside a rectangular-groove, the liquid–vapor

interface forms a curved surface, which leads to a pressure jump across the interface.

This pressure jump can be calculated by the augmented Young–Laplace equation [52].

15

− = +3v l

AP P (1)

where and 3

A

represents the pressure jump caused by surface tension and disjoining

pressure, respectively. is the capillary pressure that represents the pressure

difference across the liquid/vapor interface. Since the channel length is greater than the

channel width, the liquid-vapor interface curvature ( ) is assumed as constant for any

cross-section of the channel. This is because is mainly controlled by the curvature of

the meniscus [52].

At a given cross section (φ) along the channel, the change in may occur as the

circular meniscus merges into a micron level thin film that occupies a very small portion of

the channel wall. At a macroscopic level, the contact angle is defined as the angle between

the circular meniscus and the channel wall.

At the channel liquid entry (o = ) the dynamic contact angle is assumed to be

90o and curvature is assumed to be zero. The curvature gradually increases along

the channel’s circumferential direction ( -direction), which creates a pressure gradient to

drive the liquid along the channel. The resulting deformation of gradually reduces the

contact angle, causing the circumferential decrease in as depicted in Figure 7 A

schematic of a cross section of an open rectangular channel is shown in Figure 8.

Figure 8. Schematic of an open rectangular microchannel

16

As the liquid moves towards the apex of the channel, the liquid film thickness

between the vapor and the channel wall starts to decrease and becomes thinner and

thinner. The disjoining pressure

3

Ain Eq.(1), increases rapidly. The increase of

3

A term

creates a pressure gradient that drives the liquid to flow towards the apex of the channel

wall. Where δ in in Eq.(1) is the thickness of the film.

Figure 9. An enlarged view of the micro region

As schematically shown in Figure 9, the extended meniscus region can be divided

into three sub-regions (I) the non-evaporating region, (II) the evaporating thin film region,

and (III) the bulk region. The most heat is transferred in region II, where the liquid film is

extremely thin, and the thermal resistance is extremely low. As the heat flux imposed on

the thin film region increases, the evaporation and heat transfer rates through the

evaporating thin film also increase [53]. Since the evaporation occurs only in region II,

therefore is not constant in this region. The evaporating thin film region II and the bulk

region III are separated at the point where thin film= bulk. As becomes very small at the

apex and the film is adsorbed to the channel wall, and the liquid film is superheated.

Therefore, there is no heat transfer through region III. More information on the

mechanisms of heat transfer in capillary-assisted grooved tubes can be found elsewhere

[28,52,54–56].

2.2. Experimental details

A capillary-assisted LP evaporator was designed and built in Laboratory for

Alternative Energy Conversion (LAEC) as shown in Figure 10a. Evaporator tube consisted

of a four-pass arrangement with a total length of 1.54 m. Capillary evaporation took place

at the free surface of the tube that helps to maintain the evaporation heat transfer rate as

the water height decreases. The tube was placed horizontally at the bottom of the box to

I - Non evaporating region

II - Thin film region

III – Bulk region

evaporation

17

minimize the water height as shown in Figure 10b. Type T thermocouples (Omega, model

#5SRTC-TT-T-36-36) with an accuracy of 0.75% of reading reading were used to monitor

and record the temperature variations in the evaporator over time. A pressure transducer

with 0-34.5 kPa operating range (Omega, model #PX309-005AI) and ±0.4 kPa accuracy

was used to monitor and record the pressure variations in the evaporator over time. A

positive displacement flow meter (FLOMEC, Model # OM015S001-222) with the accuracy

of 0.5% of reading was used to monitor and record chilled water flow rate variations in the

evaporator over time.

a

b

Figure 10. Capillary-assisted evaporator built for testing different enhanced tubes: (a) top view, and (b) side view

A schematic diagram of the experimental setup is shown in Figure 11a. The

experimental test bed is designed to measure the cooling capacity and overall heat

21.6 cm

8.5”

Ti

To

Tsat Tsat

Twall, 2

Twall, 1

38.10 cm

15”

Pv

7.6 cm

3”

18

transfer coefficient of the evaporator. The setup consisted of a temperature control system

(TCS) and a variable speed pump to provide a constant temperature chilled water to the

evaporator at different mass flow rates. Control valves are employed to regulate the

pressure inside the evaporator. To protect the vacuum pump from the water vapor coming

from the evaporator, a cold trap was installed before the vacuum pump to deposit (direct

transition from gas to solid) water vapor. In the cold trap, a solution of dry ice and isopropyl

alcohol (IPA) was used to produce a cold temperature of -78°C. The vacuum pump and

cold trap in this setup mimicked the adsorber bed of adsorption chiller. The actual test

setup and custom-built heat exchanger with enhanced tube are shown in Figure 11b and

c.

Operating conditions

Once the evaporator was evacuated using the vacuum pump, the evaporator was

filled with the makeup water (1,200 g) to immerse the evaporator tube in the water. When

all the temperatures and pressure inside the evaporator became constant, the control

valve was opened and adjusted until the evaporator pressure reached the specific value

given in Table 3. No water was added during the experiment, so the water level dropped

until all of the water in the chamber evaporated. The operating conditions during the

experiments are summarized in Table 3.

Table 3. Base-case operating conditions for the experiments.

Parameter Values

Chilled water inlet temperatures 10°C/ 15°C/ 20°C

Chilled water flow rate 2.4-2.7 kg/min

Evaporator pressure 0.5 kPa @ chilled water inlet temperature of 10°C

0.6 kPa @ chilled water inlet temperature of 15°C

0.8 kPa @ chilled water inlet temperature of 20°C

Amount of water filled inside the evaporator for each experiment

1200 g

19

a

b

c

Figure 11. Schematic of the LP evaporator experimental setup, (b) the actual experimental setup and the main components, and (c) custom-built heat exchangers prepared for the experiments

TCS

T

F

T

Camera &

LED

P

Makeup

waterControl

valveVacuum pump

Cold trap

dry ice and IPA, -

78 C

Ti

To

Tsat Tsat

Twall

Twall

Evaporator

Chilled water inletChilled water outletMakeup waterFlow

meterVariable speed pump

Cold traps

20

2.3. Data Analysis

The chilled water inlet and outlet temperatures, Tin and Tout, and the mass flow rate

inm were used to calculate the heat transfer rate from the chilled water flowing inside the

tubes [57]:

= −in in out( )e pq m c T T (2)

The mean specific heat capacity at constant pressure from chilled water stream is

considered. The total evaporation rate eQ is calculated by time averaging the heat flow

rate:

=−

2

1

e

e

2 1

[ ]

t

t

q dt

Q Wt t

(3)

Where t1 and t2 are the beginning and the end of the time when the temperatures in the

evaporator remain constant. Finally, the overall evaporator heat transfer conductance,

UA, is given by:

=

e

LMTD

QUA

T (4)

Where A is the nominal surface area of the tubes and LMTDT is the logarithmic mean

temperature difference between the chilled water and the liquid refrigerant:

− =

−

−

in outLMTD

in sat

out sat

ln

T TT

T T

T T

(5)

=−

2

1

LMTD

2 1

t

t

LMTD

T dt

Tt t

(6)

With Tsat being the refrigerant saturation temperature.

21

2.4. Tested commercial tubes

The tests are conducted for five types of enhanced heat transfer tubes with

different fin structures and a plain tube as a benchmark as listed in Table 4.

Table 4. Geometric details of the enhanced tubes used for the experiments.

Tube name and details Fin structure 5x zoom view

Turbo Chil-26 FPI (Wolverine Tube Inc.)

Copper Alloys C12200

OD: 3/4″ (19.05 mm)

Fin Height: 1.422 mm

Min. wall under fins: 0.737 mm

Inside surface area: 0.049 m2/m

Outside surface area: 0.193 m2/m



OD: 3/4″ (19.05 mm)





Turbo ELP (Wolverine Tube Inc.)


OD: 3/4″ (19.05 mm)

Min. wall under fins: 0.889



22

Turbo CLF-40 FPI (Wolverine Tube Inc.)


OD: 3/4″ (19.05 mm)





GEWA-KS-40 FPI (Wieland Thermal Solutions)


OD: 3/4″ 19.05 mm)

Fin Height: 0.9 mm




Plain Tube


OD: 3/4″ (19.05 mm)



2.5. Base-case operating condition

Figure 12a shows the operating pressure and temperatures of the evaporator with

a fin height of 1.473 mm and 40 FPI (Turbo Chil-40 FPI) for a constant 15°C thermal fluid

inlet temperature. As shown in Figure 12a, when the control valve between the evaporator

and the cold trap is opened, the evaporator pressure decreases and then remains

constant until the evaporator runs out of the water. The six thermocouples read 15°C at

the start of the experiment. After the valve is opened, the temperature of the tubes and

refrigerant drop as shown in Figure 12b. The total heat transfer rate and the evaporator

23

heat transfer coefficient are calculated from the steady state data from the region

demarcated in grey in Figure 12

a

b

Figure 12. The behavior of evaporator with 1.47 mm, 40 FPI tubes (Turbo Chil-40 FPI) at the thermal fluid (chilled water) inlet temperature of 15°C vs. time: (a) evaporator pressure operated from flooded to dry and (b) temperature at different locations in the evaporator

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 2000 4000 6000 8000 10000

Evapo

rato

r pre

ssure

(kP

a)

Time (s)

7

9

11

13

15

17

0 2000 4000 6000 8000 10000

Te

mp

era

ture

( C

)

Time (s)

Tsat

Ti

To

Twall, 1,2

24

In the following section, the performance of this evaporator is compared with one

built from plain tubes. The Turbo Chil-40 FPI tube has a heat transfer coefficient of 767

W/(m2K) compared to 308 W/(m2K) for the plain tube. As shown in Figure 13 and Figure

14, the capillary phenomenon on the finned tubes results in an almost constant total heat

transfer rate and, consequently, constant overall heat transfer coefficient over time (U).

As the height of the liquid water decreases, the capillary action continues to cover the

entire outside surface of the tube.

Figure 13. Heat transfer rate vs. time achieved by using 1.47 mm, 40 FPI tubes (Turbo Chil-40 FPI)

300

305

310

315

320

325

330

2500 3500 4500 5500 6500 7500

Evapora

tion h

eat tr

ansfe

r ra

te, (W

)

Time (s)

Turbo Chil-40 FPI

25

Figure 14. Evaporator heat transfer coefficient vs. time achieved by using 1.47 mm, 40 FPI tubes (Turbo Chil-40 FPI). For the evaporator heat transfer coefficient, the plain tube surface area is A = 9.22 x 10-2 m2

Figure 15 and Figure 16 show that the heat transfer rate and the heat transfer

coefficient for the plain tube drop as a function of time. With the plain tube, as the height

of the liquid water inside the evaporator decreases, the area of the tube surface in contact

with the water decreases, and this result in a decrease in the heat transfer rate and heat

transfer coefficient.

Figure 15. Heat transfer rate vs. time achieved by using plain tubes

700

720

740

760

780

800

2500 3500 4500 5500 6500 7500

Evapora

tor

heat tr

ansfe

r coeffic

ient, U

, (W

/m2K

)

Time (s)

Plain tube surface area, Aevap = 9.22 x 10-2 m2

90

110

130

150

170

190

210

0 5000 10000 15000

Evapora

tion h

eat tr

ansfe

r ra

te, (W

)

Time (s)

26

Figure 16. Evaporator heat transfer coefficient vs. time achieved by using plain tubes. For the evaporator heat transfer coefficient, the plain tube surface area is A = 9.22 x 10-2 m2

280

300

320

340

360

380

400

420

0 5000 10000 15000

Evapora

tor

heat tr

ansfe

r coeffic

ient, U

, (W

/m2K

)

Time (s)

27

a

b

Figure 17. The total heat transfer rate (a) and the evaporator heat transfer coefficient (b) of evaporators with five different outer surface fin structure compared to plain tubes as function of thermal fluid (chilled water) temperature

To evaluate the performance of tubes with the five distinct fin types listed in Table

4, each tube type was tested with thermal fluid inlet temperatures of 10, 15, and 20°C

under the operating conditions summarized in Table 3. The total heat transfer rates and

the heat transfer coefficients of the evaporator with each fin type are shown in Figure 17.

The enhanced tubes had heat transfer rates significantly greater than that of the plain

tube. The evaporator with fin height of 1.473 mm and 40 FPI (Turbo Chil-40 FPI) provided

the highest total heat transfer rate, 422 W when operated at 20°C, followed by Turbo Chil-

26 FPI and Turbo ELP-42 FPI. The evaporator with Turbo Chil-40 FPI tubes had an overall

heat transfer coefficient ranging from 596 to 888 W/(m2K) when operated at inlet

temperatures of 10-20°C, as shown in Figure 17b. While for the plain tube evaporator the

heat transfer coefficient varies from 285 to 365 W/(m2K).

0

50

100

150

200

250

300

350

400

450

8 10 12 14 16 18 20 22

Tota

l evapora

tion h

eat

transfe

r ra

te, (W

)

Chilled water inlet temperature, T chilled, i ( C)

Plain tube

Turbo CLF-40 FPI

Turbo ELP-42 FPI

Turbo Chil-40 FPI

Turbo Chil-26 FPI

GEWA-KS-40 FPI

200

300

400

500

600

700

800

900

8 10 12 14 16 18 20 22

Eva

po

rato

r h

eat tr

an

fer

co

effic

ien

t, U

evap,

(W/m

2K

)

Chilled water inlet temperature, T chilled, i ( C)

Plain tube surface area, Aevap = 9.22 x 10-2 m2

Plain tube

Turbo CLF-40 FPI

Turbo ELP-42 FPI

Turbo Chil-40 FPI

Turbo Chil-26 FPI

GEWA-KS-40 FPI

200

300

400

500

600

700

800

900

0.7 0.9 1.1 1.3 1.5 1.7 1.9

Evapora

tor

heat tr

ansfe

r coeffic

ient, U

, (W

/m2K

)

H* = Href / Dtube

Turbo Chil-40 FPI

28

Comparing the evaporator heat transfer coefficients of the enhanced tubes, as

shown in Figure 17b, indicates that having continuous parallel fins, such as Turbo Chil-40

FPI and Turbo Chil-26 FPI, and high heat transfer surface area, such as Turbo ELP, are

the two most important parameters in the design of capillary-assisted evaporators. The

evaporator with 1.422 mm fin height and 26 FPI tubes (Turbo Chil-26 FPI) had a greater

heat transfer coefficient than the one with 0.9 mm fin height and 40 FPI (GEWA-KS-40

FPI) despite having identical internal and external heat transfer surface areas, indicating

the importance of fin height to capillary action. Thus, the main features of an enhanced

tube designed for capillary-assisted evaporator are i) continuous parallel fins, ii) high fin

height, and iii) high heat transfer surface area.

As a result, it can be concluded that the evaporator built with Turbo Chil-40 FPI

provides the highest cooling power compared with the other enhanced tubes.

2.6. The Effect of the water height, dead volume, and flow

rate

In the above section, it was noticed that the Turbo Chil-40 FPI with continuous

parallel fins outperformed other tested tubes. In this section, the effects of water height,

the dead volume inside the evaporator, and thermal fluid (chilled water) mass flow rate on

the performance of the evaporator built with Turbo Chil-40 FPI are studied.

Effect of refrigerant water height

To test the effect of water height on the performance, the evaporator was filled with

2.4 kg of water to submerge the tubes by ~2 cm as shown in Figure 18b. Figure 18a

shows the variations of heat transfer rate as a function of water height versus time during

operation with Tin of 15°C and a mass flow rate of 2.53 kg/min.

29

a

b

Figure 18. Effect of water height variation on the performance of capillary-assisted evaporator with 1.47 mm, 40 FPI tubes (Turbo Chil-40 FPI) over time at chilled water inlet temperature of 15°C and mass flow rate of 2.53 kg/min, (b) Schematic of the evaporator filled with 2.4 kg of water to submerge the tubes by ~2 cm. Href =34.7 mm, Do =19.05 mm

The evaporation heat transfer rate is divided into three regions: region I (tube is

fully submerged), region II (transition region), and region III (water height is lower than the

tube diameter, and the capillary evaporation is in effect). In region I, the evaporation heat

transfer rate is about 200 W. In this region, the hydrostatic pressure creates a pressure

gradient between the liquid water-vapor interface and the bottom of the evaporator. As a

result, the saturation temperature of water increases at the bottom of the evaporator

decreases the temperature difference between the chilled water circulated inside the tube

and the water (refrigerant) located outside the tube, reducing the cooling power.

180

200

220

240

260

280

300

320

5500 7500 9500 11500 13500 15500 17500 19500

Evapora

tion h

eat tr

ansfe

r ra

te, (W

)

Time (s)

Region I

Region II

Region III

Turbo Chil-40 FPI

Href

30

a

b

Figure 19. Effect of water non-dimensional height, H*, on (a) total evaporation heat transfer rate and (b) evaporator heat transfer coefficient of capillary-assisted evaporator with 1.47 mm, 40 FPI tubes (Turbo Chil-40 FPI), Do =19.05 mm at thermal fluid (chilled water) inlet temperature of 15°C and mass flow rate of 2.53 kg/min. For the evaporator heat transfer coefficient, the plain tube surface area is A = 9.22 x 10-2 m2

When evaporation lowers the water level to the height of the tube diameter, the

hydrostatic pressure is reduced and the heat transfer rate increases from 220 to 300 W

(region II). In region III, the heat transfer rate remains high as the water level decreases

further due to thin film capillary evaporation. The heat transfer coefficient of the

evaporation was 568 W/ (m2K) in the region I, and increased to 767 W/ (m2K) in region

III.

200

240

280

320

360

0.8 1.0 1.2 1.4 1.6 1.8 2.0

To

tal e

va

po

ratio

n h

ea

t tr

an

sfe

r ra

te, (W

)

H* = Href / Dtube

Turbo Chil-40 FPI

200

300

400

500

600

700

800

900

0.7 0.9 1.1 1.3 1.5 1.7 1.9

Eva

po

rato

r h

eat tr

an

sfe

r co

effic

ien

t, U

, (W

/m2K

)

H* = Href / Dtube

Turbo Chil-40 FPI

31

The effect of water non-dimensional height, H*, inside the evaporator on the total

evaporation heat transfer rate and evaporator heat transfer coefficient is shown Figure 19.

H* represents the ratio of water (refrigerant) height to the tube diameter. Figure 19a shows

that by increasing H* from one to 1.8 (80% increase), the total evaporation heat transfer

rate reduces by 25% from 313 W to 250 W. Accordingly, the evaporator heat transfer

coefficient reduced by 33% as shown in Figure 19b.

Effect of dead volume inside the evaporator

To determine whether the dead volume inside the evaporator affects the

performance, an acrylic block was placed above the tubes to reduce the interior volume

of the evaporator by 25% as schematically shown in Figure 20.

Figure 20. Schematic showing how dead volume inside the evaporator was changed using an acrylic block

The evaporator was tested with and without the filler block, operating with thermal

fluid Tin of 15°C and ṁin of 2.53 kg/min, and starting with 1.2 kg of water.

Calculating from steady state operating temperatures (i.e., after the initial period in

which the thermal inertia of the evaporator affects refrigerant temperature), it was found

that reducing the interior volume of the evaporator decreased the heat transfer rate by

2.3% and the heat transfer coefficient by 10%. The slight change observed in the heat

transfer rate was within the uncertainty of the test and may reflect a small increase, due

to the filler block, in the mass transfer resistance for water vapor leaving the evaporator.

Acrylic filled block

32

Effect of chilled water mass flow rate

a

b

Figure 21. Effect of chilled water mass flow rate on (a) total evaporation heat transfer rate and (b) evaporator heat transfer coefficient for a capillary-assisted evaporator with 1.47 mm, 40 FPI tubes (Turbo Chil-40 FPI) at thermal fluid (chilled water) inlet temperature of 15°C. For the evaporator heat transfer coefficient, the plain tube surface area is A = 9.22 x 10-2 m2

Xia et al. measured heat transfer coefficients ranging from 4,000 to 8,000 W/(m2K)

for capillary evaporation of water on finned tubes around the circumference of the tubes

[27,28]. However, the single-phase heat transfer from the thermal fluid inside the tube to

the refrigerant on the surface of the tube, where heat transfer with phase-change occurs,

is always limited by the heat transfer conductance of the thermal fluid (chilled water, hiAi).

280

300

320

340

360

380

400

0 2 4 6 8 10 12 14 16

To

tal e

va

po

ratio

n h

ea

t tr

an

sfe

r ra

te, (W

)

Chilled water mass flow rate, ṁin (kg/min)

Turbo Chil-40 FPI

400

600

800

1000

1200

1400

1600

1800

0 2 4 6 8 10 12 14 16

Evapora

tor

heat tr

ansfe

r coeffic

ient, U

, (W

/m2K

)

Chilled water mass flow rate, ṁin (kg/min)

33

The evaporator heat transfer coefficient (U) can be increased by increasing the flow rate

inside the tube.

The effect of thermal fluid mass flow rate on the total heat transfer rate and

evaporator heat transfer coefficient was measured using the evaporator with Turbo Chil-

40 FPI tube. It can be seen in Figure 21 that increasing the mass flow rate from 2.5 kg/min

to 15.3 kg/min (6.1 times) increases the total evaporation heat transfer rate by from 313

W to 373 W (20%). Also the evaporator heat transfer coefficient increases from 767

W/(m2K) to 1,613 W/(m2K) (110%). However, higher thermal fluid mass flow rates require

higher water pump power consumption, which is a consideration for overall adsorption

chiller designs.


• Five types of capillary-assisted tubes were evaluated for a low-pressure

evaporator.

• The evaporator consisted of horizontal capillary-assisted tubes that were in contact

with a pool of water while the pressure in the evaporator was maintained at 0.5,

0.6 or 0.8 kPa for tests with thermal fluid inlet temperatures of 10, 15 and 20°C,

respectively.

• The total heat transfer rate and heat transfer coefficient of evaporators with a plain

tube and five different enhanced tubes with various surface geometries were

experimentally investigated.

• The experimental results indicated that Turbo Chil-40 FPI provided the highest

heat transfer rate and evaporator heat transfer coefficient.

• Tubes with continuous parallel fins on their outer surfaces had significantly higher

heat transfer rate and heat transfer coefficients relative to plain tubes.

• To achieve the highest heat transfer rate, the refrigerant (water) height in the

evaporator had to be less than the tube diameter.

• The interior volume above the enhanced tubes of the capillary-assisted evaporator

did not have a significant effect on evaporator performance.

• Increasing the thermal fluid (chilled water) mass flow rate of 2.5 kg/min to 15.3

kg/min (6.1 times) increased the total evaporation heat transfer rate and

evaporator heat transfer coefficient by 20% and 110%, respectively.

34

Chapter 3. Evaluation of Thermal Resistances of the CALPE

Previous studies focused mainly on enhancing the external heat transfer

coefficient, and used commercially available tubes. Knowledge of all thermal resistances

is needed to understand the overall heat transfer coefficient and provide a clear path for

performance improvement of CALPE.

To generate cooling, the heat has to be transferred from the chilled liquid water

flowing inside the tube, to the tube wall, and finally, to the refrigerant. To evaluate the

thermal resistance to the heat flow when transferring heat from the chilled water to the

refrigerant, the external heat transfer coefficient (ho) and overall heat transfer coefficient

(U) of LP evaporator tubes need to be measured. The conductive resistance due to tube

wall is also calculated. Finally, the internal heat transfer coefficient (hi) is deduced. The

importance of the thermal resistances has never been assessed before for low-operating

pressure capillary-assisted evaporation in adsorption chiller applications.

3.1. Measurement of the external heat transfer coefficient

A schematic of capillary-assisted evaporation is shown in Figure 6, where an

enhanced tube with external fins and small fin spacing is in contact with a pool of liquid.

The thermocouples used to measure the outside wall temperature of the tubes were

placed at 90° apart at two different cross sections as shown in Figure 22. The positions of

the thermocouples are also shown in the top view (Figure 23a), and side view (Figure 23b)

Details of the experimental procedure and operating conditions are described in section

2.2. The tests were conducted for three types of commercially available enhanced tubes

with different fin structures and one plain tube, as a benchmark, as listed in Table 5. The

data analysis is also presented in section 2.3, and the only difference is the wall

temperature and the saturation temperature equations.

35

Figure 22. Schematic of capillary-assisted evaporation. The red dots indicate the positions of thermocouples

=

= 8

wall i

i 1

1

8T T (7)

( )= + +sat sat,1 sat,2 sat,3

1

2T T T T (8)

Eq. (9) gives the external heat transfer coefficient (ho):

( )=

evap

o

o

Qh

A T (9)

WhereT is the difference between tube wall temperature, wallT and saturation

temperature Tsat,

36

a

b

Figure 23. Capillary-assisted evaporator built for testing different enhanced tubes: (a) top view, and (b) side view. Red dots indicate the location of thermocouples

21.6 cm

8.5”

Ti

To

Tsat Tsat

T1, 2,3,4

T4,5,6,8

38.10 cm

15”

Pv

7.6 cm

3”

Tsat,1 Tsat,2 Tsat,3

37

Table 5. Technical specifications of the enhanced tubes used for the experiments.



OD: 19.05 mm (3/4”)






OD: 19.05 mm (3/4”)





GEWA-KS-40 FPI (Wieland Thermal Solutions)

OD: 19.05 mm (3/4”)

Fin Height: 0.9 mm




Plain Tube

OD: 19.05 mm (3/4”)



Figure 24 shows the effect of the capillary phenomenon on the performance of an

evaporator built with a GEWA-KS-40 FPI tube at chilled water inlet temperature of 15°C

compared with the one built with plain tubes. As shown in Figure 24a, the GEWA-KS-40

FPI tube results in an increasing ho over time. Even as the height of the liquid decreases,

38

the capillary action ensures that, the entire outside surface of the tube remains covered

and the external heat transfer is characterized by the thin film evaporation. Figure 24b

shows that the plain tube fails to maintain the external heat transfer rate and,

consequently, ho drop as the height of the liquid water inside the evaporator drops.

a

b Figure 24. External heat transfer coefficient achieved by using (a) Wieland’s

GEWA-KS-40 FPI tube, and (b) plain tube

Figure 25 shows the comparisons of both ho for all tubes. As shown in Figure 25,

the enhanced tubes result in an average ho increase of 3.9, 4.2, and 3.9 times compared

39

to the plain tube at chilled water inlet temperatures of 10, 15, and 20°C, respectively. The

Turbo Chil-40 FPI tube provides the highest ho of 5,030 W/(m2·K) at the chilled water inlet

temperature of 20°C, followed by Turbo Chil-26 FPI.

Figure 25. The external heat transfer coefficient for three different enhanced

tubes and one plain tube

3.2. Deducing internal heat transfer coefficient

The internal heat transfer coefficient (hi) of enhanced tubes is deduced using Eq.(10) [58]:

= + +

,

1 1 1o finned tube

o o i i

RUA h A h A

(10)

The first term on the right hand side of Eq. (10) describes the external convective heat

resistance due to evaporation on the external surface of the tube, the second term is the

internal convective heat resistance due to single-phase flow inside the tube, and the third

term is the conductive heat resistance of the tube wall. From the analysis shown in

Appendix A, the internal convective heat resistance is calculated. The internal heat

transfer coefficient (hi) of the plain tube is calculated using the following relation

ln( / )1 1 1

2

o i

o o i i

r r

UA h A h A kL= + + (11)

0

1000

2000

3000

4000

5000

6000

7000

8000

8 10 12 14 16 18 20 22

Exte

rna

l h

ea

t tr

an

sfe

r co

effic

ient,

h

o[W

/m2K

]

Chilled water inlet temperature, Tin [ C]

Plain tube

Turbo Chil-40 FPI

Turbo Chil-26 FPI

GEWA KS-40 FPI

40

The detailed calculations of the total uncertainties for U and ho are shown in Appendix B.

3.3. Thermal resistances

Figure 26 shows the comparison of different thermal resistances in a Turbo Chil-

40 FPI tube. The internal thermal resistances are 15, 17, and 18 times higher than the

external thermal resistances at the chilled water inlet temperatures of 10, 15, and 20°C,

respectively. One can notice from Figure 26 that the internal heat transfer resistance

(1/hiAi) controls the overall heat transfer resistance (1/UA).

Figure 26. Comparison of thermal resistances for the LP evaporator built with a

Turbo Chil-40 FPI tube

The comparison of thermal resistances for different tubes at chilled water inlet

temperature of 20°C is shown in Figure 27. For the plain tube, both internal and external

convective resistances contribute to the overall heat transfer resistance almost equally.

For the enhanced tubes, the external convective resistance is much smaller than the

internal convective resistance due to enhancement on the outside surface of the tube and

the capillary evaporation. For the enhanced tubes, an average of 85% of the overall

thermal resistance is due to the internal convective resistance, while the conductive and

external convective resistances contribute to only 8% and 7% of the overall thermal

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

10°C 15°C 20°C

Th

erm

al re

sis

tan

ce

, [

K/W

]

Chilled water inlet temperature, Ti [°C]

Ext. convection resistance

Int. convection resistance

Overall thermal resistance

41

resistance, respectively. Therefore, one can conclude that the internal heat transfer

resistance controls the overall heat transfer resistance and is the main hindrance to the

heat transfer. The overall thermal resistance in both Figure 26 and Figure 27 suggests

that to improve the thermal performance of an LP evaporator, the internal convective

resistance should reduce by increasing both hi and Ai. Therefore, there is need for smaller

diameter tubes in a CALPE.

Figure 27. Comparison of thermal resistances for three different enhanced tubes and one plain tube at chilled water inlet temperature of 20°C

3.4. Effectiveness of the CALPE

The effectiveness (ε) and a number of transfer units (NTU) of the LP evaporator are

calculated by Eq. (12) and Eq.(13), respectively.

− −

= = =− −

in

in satmax

( )

( )

p in out in out

p in in sat

m c T T T TQ

m c T T T TQ (12)

0

0.003

0.006

0.009

0.012

0.015

0.018

0.021

0.024

Ext. convectionresistance

Conductiveresistance

Int. convectionresistance

Overall thermalresistance

Th

erm

al re

sis

tan

ce

, [

K/W

]

Turbo Chil-40 FPI

Turbo Chil-26 FPI

GEWA KS-40 FPI

Plain tube

Plain tube-

2.7E-05 K/W

42

=in p

UANTU

m c (13)

Figure 28. Effectiveness, ε, of the LP evaporator with capillary-assisted tubes vs. NTU

The -NTU shown in Figure 28 can be of great practical utility in designing an LP

evaporator. Using Turbo Chil-40 FPI yields the highest and NTU of 45% and 0.6 at the

chilled water inlet temperature of 20°C, respectively. For higher , one must increase the

UA value by increasing the overall heat transfer coefficient and the length of the tube.

Increasing the length of the tubes increases the size (and cost) of the LP evaporator.

Therefore, for a constant tube length and diameter, one should employ heat transfer

augmentation techniques at the inside of the tube to decrease the internal convective

resistance (1/hiAi), and consequently, increase the effectiveness.


In this study, three different tubes with various surface geometries were

experimentally investigated and their effects on the external and overall heat transfer

coefficients examined.

• Turbo Chil-40 FPI showed the lowest overall thermal resistance under

different operating conditions.

43

• For the enhanced tubes, up to 85% of the overall thermal resistance was

due to the internal convective resistance.

• For the plain tube, 49% and 51% of the overall thermal resistance was due

to the external and internal convective resistances, respectively

• The maximum effectiveness and NTU achieved were 45% and 0.6,

respectively, for Turbo Chil-40 FPI at chilled water inlet temperature of

20°C.

• The main bottleneck in the performance of an LP evaporator was the

internal heat transfer.

44

Chapter 4. Porous Copper Coated CALPE

In previous chapters it has been discussed that the development of the CALPE in

our lab started with an assembly made from 14.45 mm inner diameter (ID) uncoated tubes

with a high fin density (40 fins per inch), corresponding to a 0.635 mm fin spacing. The

high fin density (increased surface area) enables capillary action leading to increased

external heat transfer coefficient (ℎ𝑜), thus increasing the external thermal conductance

(ℎ𝑜𝐴𝑜). However, the large diameter caused a poor internal heat transfer coefficient (ℎ𝑖).

To overcome the bottleneck in internal heat transfer, a smaller tube with 7.9 mm ID was

sourced. The commercially available finned tubes at 7.9 mm ID had a maximum fin density

of 26 fins per inch, which resulted in a weakened capillary effect, causing ℎ𝑜 to suffer.

Finally, the finned 7.9 mm ID tubes were coated with a porous copper coating that

effectively reduced fin spacing and increased the area for thin film evaporation to occur,

leading to improved ℎ𝑖 and ℎ𝑜𝐴𝑜.

4.1. Methods

The experimental setup shown in Figure 11a utilizes a temperature control system (TCS)

and a variable speed pump to provide a constant temperature thermal fluid (chilled water)

to the evaporator at different mass flow rates. The new CALPE was designed and built as

shown Figure 29. A vacuum pump was used to lower the system pressure, and control

valves were employed to regulate the pressure inside the evaporator. To protect the

vacuum pump from the water vapor produced by the evaporator, two cold traps (dry ice

and isopropyl alcohol) were installed before the vacuum pump. Experiments began with

the evaporator tubes submerged in a pool of water and continued as continuous

evaporation decreased the height of the water, and ended when the evaporator chamber

was dry. The evaporator tubes were in contact with a pool of water while the pressure in

the evaporator was maintained at ~1 kPa for tests with thermal fluid inlet temperatures of

10, 15 and 20°C, and a thermal fluid flow rate of 2.5 kg/min. The section 2.2 in Chapter 2

contains the detailed procedure of the test, along with the types of thermocouples,

pressure transducers, and flowmeters used and the details of the vacuum pump, cold trap,

and other components. The detailed data analysis is presented in 2.3. The tests were

45

conducted on a set of Wieland GEWA®-K-2615 tubes. The geometry and dimensions of

this evaporator are summarized in Table 6. Figure 29c shows the schematic of the

rectangular groove cross-section and applied coatings on the fins. The detailed data

analysis is presented in Appendix C.

a

b

c

Figure 29. The schematic of the CALPE built with 7.9 mm ID tubes (a) Top view (b) Side view and (c) rectangular groove cross-section

Tout

Tin

42.0 cm (16.5")

34.3 cm

(13.5" )dP1

Pevap

38.1 cm (15.0" )

11.4 cm

(4.5")

CALPE finned tube, side viewside view

Rectangular groovesCoating

46

Table 6. Technical specifications of the uncoated tubes.

Evaporator name and details

GEWA®-K-2615 (Wieland Thermal Solutions) Copper Alloys C12200 Fin type: continuous and parallel fins OD: 1/2″ (12.7 mm) Fin height: 1.5 mm Root wall thickness under fins: 0.8 mm Inside surface area: 0.024 m2/m Outside surface area: 0.124 m2/m Number of tubes-12 Number of passes-12

5x zoom view Photograph of the evapoartor

4.2. Uncoated CALPE

To test the effect of water height on the heat transfer performance, the evaporator

was initially filled with water so that the tubes sit ~10 mm below the water’s surface. Figure

30 shows the variations in 𝑈 as a function of water height (water height decreases with

time). In region I (tube is fully submerged), 𝑈 is about 780 W/ (m2K). In this region, the

hydrostatic pressure creates a pressure gradient between the liquid water-vapor interface

and the bottom of the evaporator. As a result, the saturation temperature of the water is

higher at the bottom of the evaporator. This decreases the temperature difference

between the chilled water circulated inside the tube and the pool of water (refrigerant)

located outside the tube, and consequently reduces �̇�. In region II, evaporation has

decreased the water level to below the height of the tube diameter. Capillary action begins

in this region and the hydrostatic pressure is reduced and the 𝑈 is increased by 90% from

780 to 1,480 W/ (m2K). Though the height of the liquid water decreases, partial capillarity

allows water to cover the entire outside surface of the tube. As the water level drops further

(region III), the capillary force fails to cover the entire surface. Due to loss of heat transfer

surface area, 𝑈 in region III shows a decreasing trend. After region III, once liquid level

falls below the tubes, there is a sudden drop in 𝑈. One solution to improve 𝑈 at lower

water levels is to coat a porous copper layer on the external surface of the tubes. Then it

47

can draw water through enhanced capillary action to cover the entire outer surface. Due

to the subsequent increase in heat transfer surface area between the refrigerant and the

coated surface, ℎ𝑜𝐴𝑜 would increase significantly.

Figure 30. Variation of overall heat transfer coefficient of the uncoated CALPE

over time, Tin =20°C, inm =2.5 kg/min

Figure 31. Comparison of thermal resistances for the uncoated CALPE

Figure 31 shows the comparison of thermal resistances in the uncoated CALPE.

An average of 38% of the overall thermal resistance is due to the internal convective

resistance. The internal thermal resistance dominates the overall thermal resistance,

mainly due to the small internal heat transfer surface area of the tubes. To reduce the

0

500

1000

1500

2000

2500

3000

650 1200 1750 2300 2850 3400 3950 4500 5050 5600

Ove

rall

he

at tr

an

sfe

r co

effic

ien

t, U

[W

/(m

2.K

)]

Time [s]

Region I

Region II Region III

Region I

Region II

Region III

Pooled water

48

overall thermal resistance for any chilled water temperature, the internal resistance of the

evaporator should be reduced. This can be achieved by incorporating turbulators,

enhancing the internal heat transfer surface area, Ai, or increasing the mass flow rate.

Increasing Ai for 7.9 mm ID tubes is not practical and increasing the mass flow rate results

in a higher pressure drop and higher pumping power. Also, increasing the mass flow rate

results in a lower temperature difference between the inlet and outlet of the evaporator.

Therefore, to improve the thermal performance of the evaporator, two types of turbulent

flow generators (twisted-tape [59] and Z-type) were tested.

Effect of turbulent flow generators

Twisted tape turbulent flow generators were chosen based on the work of

Piriyarungrod [59]. The incorporation of turbulent flow generators disrupts the flow and

thermal boundary layer of the thermal fluid and produces vortices. A schematic of a twisted

tape turbulent flow generators is shown in Figure 32a with geometric details shown in

Figure 32c. The Z-type turbulent flow generator and its detailed geometry, designed with

the help of Voss Manufacturing Inc. [60], are shown in Figure 32b and d. Z-type turbulent

flow generators further enhance the chaotic flow, particularly at low Re numbers. However,

introducing inserts significantly increased the pressure drop in the evaporator tubes to the

extent that the pump could no longer maintain the flow rate of 2.5 kg/min. Therefore, the

following experiments were conducted at a mass flow rate of 1.5 kg/min.

49

a b

c

d

Figure 32. Schematic of turbulent flow generators: (a) twisted tape and (b) Z-type. Geometrical details of (c) twisted tape and (d) Z-type turbulent flow generators

A comparison of the thermal resistances and pressure drops of evaporators using

twisted tape and Z-type turbulent flow generators are shown in Figure 33. Twisted tape

provides a 12% reduction in the overall thermal resistance and results in a 2.5 times higher

pressure drop than that of tubes with no turbulators. Z-type inserts caused a 58% reduction

in the overall thermal resistance while they resulted in a 14.5 times higher pressure drop.

This significant pressure drop and more pump power must be considered in the overall

design of a CALPE.

Conductive and external thermal resistances contributed, on average, 31% each.

Combined, conductive and external heat transfers are a major hindrance to overall heat

y=27.65 mm

W=7.9 mm

y = 12.7 mm

4.06 mm

W = 6.35 mm

50

transfer. The conductive resistance of the enhanced tubes depends on the overall fin

efficiency (𝜂𝑜,𝑓𝑖𝑛) and external thermal conductance (ℎ𝑜𝐴𝑜). In Eq. (A6), ℎ𝑜𝐴𝑜 appears in

both external convective thermal resistance and conductive thermal resistance due to the

fins. Applying a thin porous copper coating on the surface increases ℎ𝑜𝐴𝑜 of the CALPE

tubes, this improves both the conductive resistance and the external resistance. This

effect reduces the overall thermal resistance of the CALPE. The calculation of different

thermal resistances of the finned tube is explained in Appendix A.

a

b

Figure 33. Comparison between tubes without turbulators, and with twisted tape and Z-type turbulators for the chilled water mass flow rate of 1.5 kg/min: (a) overall thermal resistance and (b) pressure drop

0

0.005

0.01

0.015

0.02

0.025

5 10 15

Overa

ll th

erm

al re

sis

tan

ce

[K

/W]

Chilled water inlet temperature [oC]

W/o turbulator

Twisted tape

Z-type

8.1 7.6 8.019.6 20.3 19.8

115.0 115.2 115.1

0

45

90

135

180

5 10 15

Pre

ssure

dro

p [

kP

a]


W/o turbulator

Twisted tape

Z-type

51

Figure 34. Photographs of uncoated and coated tubes and the CALPE

4.3. Porous coated CALPE

Figure 34 compares the uncoated and coated surfaces. The metal foam coating is

applied by a thermal spray process using a Metco 12 E wire flame spray gun with 1/8”

diameter copper wire. The spray gun was positioned 10″ from the tubes, and burned

acetylene and oxygen to heat the wire and deposit the atomized copper particles [61]. The

coating increases the external surface area of the CALPE and reduces the effective fin

spacing, which aids capillary action. The coating consists of open cell porous structures

applied uniformly on all external faces of the tubes.

Due to surface tension inside the rectangular grooves between the fins, the liquid–

vapor interface forms a curved surface, which leads to a pressure jump across the

interface. This pressure jump can be calculated by the augmented Young–Laplace

equation [52]. The curvature increases gradually along the circumferential direction of the

groove, creating a pressure gradient due to meniscus deformation [52], which is

responsible for the upward flow of the liquid. As schematically shown in Figure 35a, the

extended meniscus region can be divided into three sub-regions: 1) the bulk region, 2) the

thin film region, and 3) the non-evaporating region. In region 1, heat transfer is low due to

the large thickness of the liquid layer. In region 2, the highest heat transfer and evaporation

Uncoated finned tube Coated finned tube

Coated CALPE

https://en.wikipedia.org/wiki/Prime_(symbol)

52

rate occur. However, once the liquid film becomes very thin, the surface interaction forces

between the film and surface increase leading to zone 3, where virtually no evaporation

occurs.

In an uncoated evaporator, the area of region 2 is limited but as Figure 35b shows,

a porous metal coating can draw a uniform thin film of water through its pores, wetting the

surface of the fin and increasing the effective area of thin film evaporation several times

[62]. Heat transfer within the coated surface has two mechanisms: 1) evaporation from the

small liquid menisci in the porous coating [49], and 2) the formation of vapor bubbles

(boiling) which travel through the porous coating into the larger, open pores [62]. With both

mechanisms working on a uniformly wetted surface, the effective ℎ𝑜𝐴𝑜 of a coated CALPE

is higher that an uncoated CALPE. These mechanisms have been verified experimentally

in the work of Wang et al [49].

a

b

Figure 35. (a) Evaporating meniscus inside an uncoated rectangular groove and (b) Evaporating meniscus inside a coated rectangular microchannel

Water vapor

Water vapor Small liquid menisci in

pores of coating

53

In Figure 36a SEM imagery of the porous copper coating is shown from a top view

at a scale range of 200 µm. Zooming in to the 50 µm scale range shows the open cell

pores (Figure 36b). Zooming in further shows a standard pore opening at 12.1 µm wide

(Figure 36c). The thickness of the coated layer is approximately 250 µm, and the side view

shows the small channels that are formed through connections between pores that allow

water and vapor to flow through (Figure 36d).

a

b

c

d

Figure 36. (a), (b), (c) and (d) SEM images of porous copper coatings

18

Coating

Substrate

54

The fundamental characteristics of metal coatings that influence the heat transfer are: i)

enhanced surface area (surface roughness), and ii) the porosity, particularly the open pore

porosity. It is a significant challenge to nondestructively analyze open porosity, closed

porosity and surface roughness due to the meager amount of copper per coated area.

Appendix D, discusses the new approach to non-invasively determine the porosity of metal

films utilizing a helium pycnometer and computed micro-tomography (CMT. Obtaining the

effective surface area due to coating is very important to find the breakdown of thermal

resistances for the coated CALPE.

4.4. Surface area of the coating

One method to calculate the surface area of the applied coating is the Wenzel

method, which requires measuring the contact angle of a water droplet on representative

samples of uncoated and coated CALPE surfaces. The wetted surface area under a

droplet can be approximated using the Wenzel model [63–65]. The scale condition of the

model is satisfied: the diameter of the droplet (~5mm) is three orders of magnitude larger

than the surface pores (~12m as shown in Figure 36c.) [66]. The surface roughness r is

the ratio between the effective surface area due to roughness and the projected surface

area. The Wenzel relation states that r is equal to the ratio of cosines of the contact angles

of a liquid on the rough surface (𝜃∗) and the contact angle of the same liquid on and ideal,

flat surface (𝜃) [67]:

cos 𝜃∗ = 𝑟𝑐𝑜𝑠𝜃 (14)

In Figure 37, the contact angles on an uncoated and coated copper substrate have

been measured with a telescope-goniometer with precision of ±2°deg (Figure 37e) [68].

The contact angle of water on the uncoated copper sample is 94 while the average

contact angle of water at various locations (Figure 37b to Figure 37d) on the coated

surface is 126. As predicted in the Wenzel model, the surface roughness enhances the

hydrophobicity of the coated surface [66,69] due to lotus effect [70–73]. By Wenzel’s

relation, the wetted surface area of the porous copper coated surface is 8.5 times the

wetted surface area of the uncoated surface.

55

Lotus effect

The lotus leaf is well-known for having a super hydrophobic, surface, therefore giving the

name to the lotus effect [74]. The lotus leaf is attributed it to the double-roughness

structure of the surface with micro- and nanostructures[75]. The wettability of such

surfaces and these effects were fundamentally described by Wenzel [67] and Cassie−

Baxter [76]. They found that the wettability was strongly dependent on the free energy of

the surfaces and on the surface structures as well. The Wenzel state is a model that allows

intrusion of water droplets, and the Cassie state is a model that prevents intrusion of water

droplets by taking in air pockets. On a lotus leaf, water is prevented from penetrating the

air pockets of the leaf by the nano-microstructure (Cassie state).

56

a

b

c

d

e

f

Figure 37. (a), Wetting of uncoated CALPE, (b), (c) and (d) wetting at three random locations on the porous copper coated surface, (e) telescope-goniometer measurement setup

57

4.5. Thermal resistances of porous coated CALPE

Using the outer effective surface area of the porous copper coating found from

contact angle goniometry, the thermal resistances can also be shown in the coated

CALPE (Figure 38). Due to significant reductions in the external and conductive

resistances, the overall thermal resistance, on average, is 32% lower than the uncoated

CALPE. The external and conductive resistances as a proportion of total thermal

resistance decreased from 31% each in the uncoated CALPE to 22% and 23%,

respectively in the coated CALPE. Both external and conductive heat transfer benefit from

a doubling of ℎ𝑜𝐴𝑜 from the coating.

Internal resistance is now the major bottleneck in heat transfer of the coated CALPE,

contributing 55% of the total thermal resistance. Internal thermal resistance can be

decreased by using microchannel finned tubes. However, these come with the challenge

of increased pressure drop of the chilled water through the CALPE.

Figure 38. Comparison of thermal resistances for the coated CALPE

Due to an increase in ℎ𝑜𝐴𝑜 and according to Eq. (A6), 𝑈 for the coated CALPE

should increase. As shown in Figure 39, maximum 𝑈 is 30% higher in the coated CALPE.

Due to enhanced capillary action and increased external thermal conductance in the

coated CALPE, evaporation time decreased by 43%. Since the coating provides a more

uniform wetting due to enhanced capillary action, there is no sudden drop in 𝑈 (as

0.000

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

10 15 20

Th

erm

al re

sis

tan

ce

[K

/W]


External resistance

Conductive resistance

Internal resistance

58

compared to uncoated) once liquid level falls below the bottom of the tubes. The beginning

of the experiment is not shown due to high uncertainty in 𝑈, because the inlet and outlet

temperatures take time to reach steady state.

The performance of both the coated and uncoated CALPEs was tested over a

range of chilled water inlet temperatures: 10, 15, and 20°C. After the valve between the

cold trap and evaporator is opened, both the pressure in the evaporator and the

temperature of tubes and refrigerant drop initially then maintain a constant level

throughout the experiment. Heat transfer rate, �̇�, and 𝑈 are calculated from the steady

state data in the region of constant temperature and pressure. The average �̇� and 𝑈 over

the duration of steady state conditions are presented in Figure 40. �̇� in the coated CALPE

increases from 495 W to 867 W between 10°C and 20°C as shown in Figure 40a. As

explained in the previous chapter, both �̇� and 𝑈 increase as a function of chilled water

inlet temperature (𝑇in)[18]. At 𝑇in = 15°C, 𝑈 increased by 1.25 times and �̇� increased by

91%. The log mean temperature difference (Δ𝑇𝐿𝑀) increased by 1°C from 1.9°C to 2.9°C.

The coated CALPE was again tested after seven months to check its durability. The tests

resulted in consistent performance, indicating that there is no degradation of the coating

when exposed to air for significant periods of time.

Figure 39. Variation of overall heat transfer coefficient of the coated and

uncoated LP evaporator over time, Tin =20°C, inm =2.5 kg/min

0

500

1000

1500

2000

650 1200 1750 2300 2850 3400 3950 4500 5050 5600

Ove

rall

he

at tr

an

sfe

r co

effcie

nt

[W/(

m2.K

)]

Time [s]

Uncoated

Coated

59

a

b

Figure 40. Comparison between standalone uncoated and coated CALPE (a)

average Q and (b) average U


This chapter evaluated the performance enhancement of a thin porous copper coating

sprayed on the external surface of capillary-assisted low pressure evaporator tubes. A

significant bottleneck was the external convective heat transfer conductance (ℎ𝑜𝐴𝑜). The

0

200

400

600

800

1000

1200

5 10 15 20 25

Co

olin

g P

ow

er

[W]


Coated Uncoated

500

1000

1500

2000

2500

5 10 15 20 25

Ove

rall

he

at tr

an

sfe

r co

effic

ien

t [W

/m2•K

]


Coated Uncoated

60

porous copper coating enhanced the capillary effect by reducing effective distance

between fins and significantly increased the external surface area of the evaporator. This

increased the amount of thin film evaporation and thus ℎ𝑜𝐴𝑜 increased leading to a

considerable improvement in the overall heat transfer coefficient (𝑈). This nearly doubled

�̇� of the CALPE. By coating, the bottleneck in heat transfer has shifted from external

convective resistance to internal convective resistance. The primary findings of this study

are summarized as follows:

• The external, conductive, and internal thermal resistances were 22%, 23%, and

55%, respectively in the coated CALPE. This compares to 31%, 31%, and 38%,

respectively in the uncoated CALPE.

• Overall thermal resistance of the coated CALPE is 32% lower than the uncoated

CALPE.

• 𝑈 of the coated CALPE is, on average, 28% higher than the uncoated CALPE;

• Heat transfer rate, �̇�, of the coated CALPE is, on average, 90% higher than the

uncoated CALPE;

61

Chapter 5. Modeling of Capillary-Assisted Evaporation

5.1. Background

Capillary-assisted evaporation has been widely used in cooling of electronic

components [77]. These components generally use heat pipes to remove large amounts

of heat [78]. In the microchannels of a heat pipe, liquid–vapor phase change creates a

large heat flux due to capillary-assisted evaporation from the thin film formed in the

microchannel. Recently, capillary-assisted evaporation has found its place in low pressure

evaporation systems as well, including LGTE-driven adsorption chillers [3,26,79,80]. Most

previous research on capillary-assisted evaporation focused on triangular grooves

[48,49,53,81–85]. Although triangular grooves can be easily manufactured, the V shape

provides only half the cross sectional area of a rectangular channel and has higher viscous

friction, thereby reducing the bulk flow rate [52,86]. Therefore, utilizing open rectangular

microchannels for capillary-assisted evaporation can increase the performance of CALPE.

The flow in a microchannel is driven by the gradient of capillary pressure [87]. The

meniscus is flat in the entry region and progressively deforms with the curvature gradually

increasing along the circumferential direction of the channel. This deformation of the

meniscus creates a pressure gradient [52], which is responsible for the upward flow of the

liquid. Most studies report the heat transfer in the extended meniscus as schematically

shown in Figure 9. The extended meniscus region can be divided into three sub-regions

(I) the non-evaporating region, (II) the evaporating thin film region, and (III) the bulk region.

The most heat is transferred in region II, where the liquid film is extremely thin, and the

thermal resistance is extremely low. As the heat flux imposed on the thin film region

increases, the evaporation and heat transfer rates through the evaporating thin film also

increase [53]. The detailed physics is presented in section 2.1.

Due to recent advances in the 3D printing, direct metal laser sintering, and electrical

discharge machining (EDM) [88], creating open rectangular microchannels has become

much easier. Thus, the focus of the present model is on capillary-assisted evaporation in

open rectangular microchannels, a field with very few existing studies [27,28]. The attempt

62

here is to understand the existing models and apply them to capture the behavior of the

CALPE. Therefore, this chapter focuses mainly on how to

i) attain menisci curvatures in an open evaporating flow,

ii) determine the length and thickness of the thin film region,

iii) demarcate between bulk curvature and thin film curvature, and

iv) attain heat transfer coefficients for capillary-assisted evaporation in open

rectangular microchannels.

5.2. Assumptions

Based on the explanation in section 2.1, the following assumptions are made in the

modelling of capillary-assisted evaporation:

• the vapor pressure (Pv) is constant,

• the microchannel wall temperature (Tw) is constant,

• in bulk region III, is assumed as constant for any cross-section (φ) of the

microchannel and the 3

Aterm is neglected,

• the evaporating thin film region II and the bulk region III are separated at the point

when thin film= bulk,

• in the non-evaporating region I, is very small, so the liquid film is attached to the

channel wall and is superheated. (Therefore, in region I the heat transfer is

neglected.),

• the liquid circumferential flow is confined to the bulk region III,

• the evaporating thin film region II and the non-evaporating region I meet at the

apex of the channel wall, where the liquid film thickness gradient

d

dz reduces

to zero and z-coordinate is zero, and

• the dynamic contact angle (θ) is defined in a macroscopic sense and is assumed

constant for any circumferential cross-section of the channel.

63

5.3. CALPE sub-models

To capture the physics of capillary-assisted evaporation in an open rectangular

microchannel, the following sub-models are considered: (1) the natural convection model;

(2) the liquid circumferential flow model; (3) the evaporating thin film model; and, (4) the

bulk model. Figure 41 shows the schematic of the different sub-models and their details

are presented in the following sections

Natural convection pool model

Figure 42 shows a schematic of a submerged portion of a finned tube, where

natural convection governs the heat transfer. At evaporation temperatures between 5 to

10 °C, nucleate boiling does not occur as it requires a high wall superheat of up to 20 °C

[19,41,89]. At low pressure, natural convection determines the heat transfer, which results

in low heat transfer coefficients. The saturation temperature of the refrigerant is a function

of the hydrostatic pressure gradient that exists along the height of the liquid column (Hwater).

To establish an accurate model, the evolution of the saturation temperature according to

"q

1. Natural convection pool model

4. Bulk region model

2. Liquid circumferential flow model

3. Evaporating thin film model

D

W

Figure 41. The different sub-models considered in the modelling

64

the filling level should be included. The saturation temperature of water, Tsat, in °C is

calculated using Antoine’s equation:

= −

− +sat

10 vap waterlog ( )

BT C

A P gH, (15)

where constants are A=10.1962, B=1730.63, and C=233.426. P, ρ, g and Hwater in Eq. (15)

are the pressure (Pa), the density of liquid water (kg/m3), the acceleration of gravity (m/s2),

and the height of the refrigerant (m), respectively. For a wall superheat less than 5°C,

boiling is characterized by natural convection. Schnabel et al. [90] showed that at low

evaporation pressure, natural convection is the dominant phenomenon in the evaporation

process. In this case, the flow can be described with the Grashof number [91]:

=

3

o,tube

2o

g TDGr (16)

where β is the coefficient of cubic expansion in 1/K, ν is the kinematic viscosity in m2/s,

and ΔT is the difference between the wall temperature (Twall) and the water saturation

temperature (Tsat). As β, ν and the dynamic viscosity of water, , vary with temperature

the following fits were used to determine their values:

γ

Ao , active heat transfer surface area

Figure 42. Natural convection on the submerged portion of a finned tube

65

= −

10.0138 [ ] 0.0595T C

K (17)

− −= − +8 6[ ² / ] 4.10 [ ] 2.10m s T C (18)

−= − +5[ ] 4.10 [ ] 0.0017Pa s T C (19)

For Gro < 109, the flow field is laminar and the Nusselt number on the outer surface of the

tube, Nuo, is calculated by [90]:

( )= 0.25

o o oNu 0.60 Gr Pr (20)

where Pro is the Prandtl number for water [92]:

=

Prp

o

water

c

k. (21)

Finally, the external heat transfer coefficient and the total heat transfer rate are calculated

by

=,

o watero

o tube

Nu kh

D (22)

where kwater and Ao are the water thermal conductivity and the active heat transfer

surface area of the tubes:

= −

1o finnedA A (23)

where

−

=* 0.5

cos0.5

H (24)

and

=* water

tube

HH

D (25)

66

Liquid circumferential flow model

The liquid circumferential flow model is used to find the deformation in (or change

in θ) as water rises from o to π. The circumferential flow is in the -direction as indicated

in Figure 43. The conservation of mass describing the evaporating flow along the

rectangular open channel in the one-dimensional form:

" 2 ( )lv

dmq p h

D d

= − (26)

where " q the heat flux applied, p is the pitch between two fins and lvh is the latent heat

of vaporization. The liquid mass flow rate ( )lm in the channel is given by

=( ) ( )l l l lm u A , (27)

where lA is the liquid area, given by

=l cA A s , (28)

where Ac is the cross-sectional area of a channel of uniform width W and height H. The

parameter s is the volume fraction of the channel containing the liquid which, is given by

− + − += − −

+2 2

2( ) sin(2( ))1

2 2 8cos cos ( )

W Ws

D D, (29)

π

φo

Fc (gradient of liquid pressure)

"q

lm•

CV

Fg (gravity force)

Fg (viscous force)

CV

Figure 43. Schematic describing circumferential flow model

67

where and θ are given by

=

−

2cos ))

1 sin ) (30)

=

2tan (31)

The circumferential liquid velocity ( )lu is determined by the balance between the

gradient of capillary pressure Fc, gravity force Fg and viscous force Fv. Therefore, the force

balance equation for flow in direction is :

+ + =

2

( )2sin 0l lf u dP

gD dW

(32)

The viscosity is assumed uniform, and the gravitational force opposes the

pressure driven flow. The friction coefficient f for rectangular open channel flow of this type

has been determined by Xia et al. [28]. Therefore, the circumferential liquid velocity ( )lu

is can be written as:

= − +

2 ( )2sinl

l

dPWu g

f D d (33)

Substituting Eq. (33) into Eq. (27) and incorporating •

( )lm into Eq.(26), a second

order differential equation is obtained.

− = −

2

2 2

( ) coslP abd Qc

a b (34)

Where,

=

2

2

b= WHs

c=

l

aD

f

W

(35)

68

The following boundary conditions apply:

( )

( )

= =

= =

0 0

0

l

l

P

P (36)

The liquid pressure (Pl) is determined as a function of . Using the Young-Laplace

equation and neglecting the disjoining forces, can be obtained using:

− =v lP P (37)

Finally, the contact angle θ is obtained by:

=cos

2

W (38)

Evaporating thin film model

The evaporation thin film model is based on the work of Schonberg et al. [93] and

Wayner et al. [48]. Consider a stationary thin film at the leading edge of a thicker bulk

liquid on a stationary vertical substrate (channel wall), as shown in Figure 44. The film is

sufficiently thin that the hydrodynamics are governed by lubrication theory [93]. Therefore,

the pressure in the liquid does not vary in the direction perpendicular to the channel wall.

Since only the disjoining pressure affects the extended thin-film region, the pressure jump

is given by

− =

3v l

AP P (39)

69

The pressure gradient in the direction of the flow is obtained by differentiating Eq. (39):

= −

4

3ldP A d

dz dz (40)

The velocity distribution at any point in the thin film is obtained from momentum

conservation:

=2

2

ldP d u

dz dy (41)

By applying the traditional no-slip condition at the liquid-solid interface and no-shear at the

liquid-vapor interface, the velocity distribution in the film is obtained:

= −

21( )

2ldP y

u y ydz

(42)

The mass flow rate per unit width of the thin film is:

= = −

3

0( )

3l

l

dPu y dy

dz (43)

Figure 44. Schematic of evaporating thin film

70

Therefore, the mass flow rate is given by

=

1A d

dz (44)

The local evaporative mass flux leaving the film surface is:

= − = −

1e

d A d dm

dz dz dz (45)

By defining dimensionless coordinate z* as:

=*

0

zz

z (46)

where

id

2

0

Az

m= (47)

a non-dimensional local evaporative flux is defined:

• =

*

* * *

1d dM

dz dz (48)

Following Schonberg et al. [93], the mass flux of vapor leaving the liquid interphase is

modeled as,

( ) ( )= − − −e lv v l vm a T T b P P (49)

where lvT is the temperature of the liquid-vapor interface. The first part of the right-hand

side of the above equation is the mass flux due to the temperature difference and the

second part is the mass flux due to the pressure difference. The coefficients a and b are

functions of the properties of the liquid. For low temperature differences, they are given

by

=

1/2

2

wall wall

22

v lvP M hMa

RT RT (50)

71

and

=

1/2

wall wall

22

l vV PMb

RT RT (51)

where M is the molecular weight of water, R is the universal gas constant, and lV is the

molar volume of the liquid.

The evaporative heat flux [W/m²] only depends on the mass flux of vapor leaving

the interface

= e lvq m h (52)

The temperature of the liquid at the liquid vapor interface is related to the

temperature of the substrate, wallT through the one dimensional conduction heat transfer

model for the liquid film.

( )lv

le wall lv

km T T

h= −

(53)

where lk is the thermal conductivity of the liquid. Therefore, Eqs (53) and(49), may be

combined to eliminate lvT and obtain

( )

= − −

+3

0

1

1wall v

bAm a T T (54)

where 0 is the film thickness for zero mass flux,

( )

= −

1/3

0

wall sat

bA

a T T (55)

and is the dimensionless group, defined as

= lv oa h

k (56)

72

Equation (54) is made dimensionless by defining a reference flux that would occur in the

absence of pressure effects

wall sat 3( )id

o

bAm a T T

= − = (57)

By defining a non-dimensional film thickness term

=*

o

(58)

we obtain,

• = = −

+ * *3

1 11

1id

mM

m (59)

Finally, a non-dimensional differential equation for the thickness of the thin film, based on

mass balance, is obtained:

− = +

+

22 * *

* *2 *2 * * *3

1 1 1 11

1

d d

dz dz (60)

Equation (60) can be written as a pair of differential equations:

( )

=

= + + +

**

*

2 * *2

*

*2 * * *3

1 11

1

dG

dz

dG

dz

(61)

This set of equations are solved by a fourth order Runge-Kutta method, subject to the

following boundary conditions:

( )

( )

= =

= =

* *

**

*

0 1

0 0

z

dz

dz

(62)

The curvature of the interface in the evaporating thin film is related to the film thickness

by

73

= +

3/22

²/ 1

²z z (63)

Equation (63) can be written as a pair of differential equations:

=

= +

32 2(1 )

dG

dz

dGG

dz

(64)

This set of equation is solved by a fourth order Runge-Kutta method, subject to the

following boundary conditions

( )

( )

= =

= =

0

0 0

oz

G z (65)

The local heat transfer coefficient in the evaporating thin film is calculated by

( )=

−local

wall sat

qh

T T (66)

The cumulative evaporating heat flux [W/m] along the interface of the half meniscus is

given by:

= bulk

thinfilm

0

' ( )

z

q q z dz (67)

The opposite side of the meniscus is treated by symmetry. Therefore, for the entire

evaporator, the heat transfer rate [W] is given by

= 2thinfilm thinfilm fin tube2 ' 2

2

DQ q n n (68)

where D2 is the external diameter of the tubes, nfin the number of fins, and ntube the number

of tubes in the evaporator.

74

Bulk model

Figure 45. Schematic of bulk region

Figure 45 shows the parameters considered for the heat transfer in the bulk region.

The surface tension dominates the shape of the liquid–vapor interface, which results in

negligible convective heat transfer. Therefore, the heat transfer through the bulk region is

assumed to be purely conduction. The liquid temperature distribution in the bulk region

can be determined by solving the two-dimensional, steady-state energy equation:

+ =

2 2

2 20

T T

x y (69)

Since the thermal conductivity of the material is higher, the wall temperature is assumed

as constant.

=

=

=

=

0,

0

W x W

W y

T T

T T (70)

( ) = − −*

cos cosH D r (71)

where α and θ are defined as

75

=

=

arcsin

arcsin

x

r

W

r

(72)

Eq. (72) is made non-dimensional by defining,

=

=

=

x

W

y

D

WK

D

(73)

where W is the width and D is the depth of the microchannel. The dimensionless

temperature can be defined as

( )( ) ( )

− −

= =− −

wall wall

wall lv wall lv

, ,,

T T x y T T

T T T T (74)

where Twall is the wall temperature, and Tlv is the interface temperature. The non-

dimensional energy equation is given by

+ =

2 22

2 20K (75)

Equation (75) is subject to the following boundary conditions:

= =

=

=

= *

1, 00

1

(76)

Using the separation of variables method ϕ can be expressed as

( )

=

− − =

1

2 1 2 1, cos sinh

2 2n

n

n nC

K (77)

76

To solve Eq.(77), the rectangular channel is meshed into i x j nodes and the coordinate of

each node is ( ) ;i j. For each i the meniscus height as well as the Cn,i are calculated.

The height of the meniscus ( ) =*

i if is calculated by

( )( ) ( )( )( ) = − −*

bulk bulk

bulk

11 cos asin cos asini iWK WK

DK (78)

Therefore, the Cn,i can be determined by solving the following matrix problem:

−= 1

,n iC A B (79)

Once the temperature distribution is solved using the Galerkin method, the heat flux from

the sidewalls and the bottom wall is determined by

( )( )

− = = −

wall lv"( ) 1

k T Tq

W (80)

where

=

− − − = −

1

2 1 2 1 2 1sin sinh

2 2 2n

n

n n nC

K (81)

Therefore,

( )

=

− − − − = − −

wall lv

1

2 1 2 1 2 1"( ) sin sinh

2 2 2n

n

k T T n n nq C

W K (82)

The integral heat transfer rate 'q [W/m] along the sidewall can be obtained by

( )

=

− − − − = = − −

1 1wall lv

sidewall

10 0

1 2 1 2 1 2 1"( ) sin sinh

2 2 2n

n

k T T n n nq q d C d

D DW K (83)

The integral heat transfer rate 'q [W/m] along the bottom wall can be obtained in a

similar way.

For the bulk region III, the total heat transfer rate per unit length is

77

= +bulk sidewall bottomwall2 2q q q (84)

The heat transfer rate from the bottom wall is negligible compared to the sidewall.

Therefore, for the entire bulk region of the evaporator, the heat transfer rate [W] is given

by

= 2fin tube2 2

2bulk bulk

DQ q n n (85)

5.4. Heat transfer in the entire CALPE

The heat transfer rate [W] for the entire CALPE is the contribution coming from the

natural convection model, the evaporating thin film model, and the bulk model. Therefore,

the heat transfer rate [W] for the entire CALPE is given by

= + +CALPE pool thinfilm bulkQ Q Q Q (86)

The heat transfer coefficient [W/m2∙K] for the entire CALPE is given by

=−

CALPECALPE

finned wall sat( )

Qh

A T T (87)

78

5.5. The solution implementation

Figure 46. Flow chart for the solution implementation

The parameter to be solved for is κ, the dynamic contact at different φ. As shown in

Figure 46, a new numerical model is developed to solve the set of equations

describing the evaporation in CALPE. The following is a brief description of the solution

steps. The rectangle open channel from =0 to π is divided into n elements. Along with

the known parameters, such as the geometric parameters, liquid properties, channel liquid

entry (o), saturation pressure and wall superheat, the initial guess for the q are given as

the input. The κ’s and ’s are obtained for the n elements along φ. Then, for each of the

elements, the thin film and the bulk models are evaluated. The total heat transfer rate per

unit meter thinfilmq and bulkq are then obtained. Then new heat flux q is obtained and

compared to the initial guess. If the difference is within the permitted values the iteration

START

Input: Twall, ΔT , φo, liquid

properties and geometric

properties

Initial guess: q,, and θ

Calculate bulk κ and θ

Calculate z and δ (z)

Calculate q,

thinfilm and q,

bulk

End

No Yesis Δκ and Δθ

acceptable

Calculate new κ and θ

Calculate

CALPEQ

Calculate new q,,

CALPEh

is new q,,

acceptable

Yes

No

79

stops, or else the above steps are repeated. Then the natural convection pool model is

evaluated to obtainpoolQ . Finally,

CALPEQ for the entire evaporator is obtained.

5.6. Details of the finned tube used in modelling

Table 7. Technical specifications of the finned tubes used for the modelling.


Turbo Chil-40 FPI (Wolverine Tube Inc.) Copper Alloys C12200 OD: 3/4″ (19.05 mm) Fin Height: 1.473 mm Min. wall under fins: 0.635 mm Inside surface area: 0.051 m2/m Outside surface area: 0.263 m2/m

Number of tubes: 12 Design: Serpentine Length of the tube : 14″ (355.6 mm) OD D2: 19.05 mm Plain diameter D1=16.10 mm ID Di: 13.30 mm Thickness of the tube =(D1-Di)/2 Spacing between fins W=0.474 mm Fin pitch P=0.635 mm

a b

Figure 47. (a) CAD model of evaporator tube assembly and (b) CALPE placed in a evaporator chamber

Finned tubes with the geometric parameters listed in Table 7 were used in the

modelling. A CALPE was also built as shown in Figure 47 and the CALPE consisted of a

12-pass arrangement with a total length of 4.27 m. This CALPE was tested according the

procedure described in section 2.2. The results of the measurements were used to

compare with models results.

80

5.7. Model Results and Discussions

Figure 48. Variation of Pl and along ϕ -direction

Figure 48 shows the distribution of the liquid pressure (Pl) and the curvature ( )

along ϕ-direction predicted by the present model. At the channel entry point ( o =0), Pl is

equal to the saturation pressure (Psat). As the liquid rises along -direction, there is a drop

in Pl ,which creates a pressure difference for the circumferential movement of the liquid.

At o =0 (i.e. channel liquid entry point), there is no curvature (i.e. =0), which results in

dynamic contact angle =90°. Along the ϕ-direction the curvature increases. This

change in indicates that the shape of meniscus is changing in the circumferential

direction as indicated in Figure 7. Capillary pressure plays an important role in determining

the film profile throughout the extended meniscus. The changes in Pl and along the

open channel is observed because of the opposing forces caused by friction and gravity.

At =, both liquid pressure and curvature plateaus because of the symmetry boundary

condition. The variation in along the -direction is shown in Figure 49.

0

500

1000

1500

2000

2500

880

900

920

940

960

980

1000

1020

1040

1060

1080

0.00 0.79 1.57 2.36 3.14

Cu

rvat

ure

κ[1

/m]

Liq

uid

pre

ssure

Pl [P

a]

ϕ [radians]

Liquid pressure

Curvature

π

0

81

Figure 49. Variation of along ϕ-direction

Figure 50. The film thickness profile in the thin film region

In Figure 9, a thin film region is sketched and the detailed schematic is shown

Figure 44. In a rectangular open microchannel, the channel length is several orders of

magnitude larger than the thin film region. As shown in Figure 50, the film thickness

remains at the initial value ( 0 ) to mark the non-evaporating region I before it increases

sharply to meet the bulk region III. The profile of thin film curvature can be found by using

Eq. (63). When curvature of the thin film region meets bulk curvature, the length of the thin

40

50

60

70

80

90

100

0.00 0.79 1.57 2.36 3.14

θ [deg]

ϕ [radians]

Dynamic contactangle

Tsat= 8oC, ΔT= 0.3 K

π

0

0

0.0005

0.001

0.0015

0.002

0.0025

0.00E+00 5.00E-06 1.00E-05 1.50E-05 2.00E-05

Th

in film

th

ickn

ess δ

[m]

z [m]


82

film region is determined. The thin film region also corresponds to the region with a high

evaporative heat flux as shown Figure 51. In the extended meniscus, the thin film region

is seen to be the major contributor to the overall heat transfer.

Figure 51. The evaporative heat flux in the thin film region

The evaporation rate increases from zero (at the non-evaporating region) to a

maximum in the thin film region and then decreases to zero (at the bulk region). Also, from

Figure 50 and Figure 51, it can be seen that the evaporative heat flux rises in

correspondence with the decreasing film thickness. The heat transfer per unit length is

shown in Figure 52. The heat transfer contribution from bulk region along the depth of the

channel is shown in Figure 53. The heat transfer is almost negligible up to a channel depth

of 1 mm and it increases sharply close the apex of the channel. This is due to a huge

resistance to the heat transfer coming from the thick film below the bulk curvature. The

contribution from the bottom wall is negligible due to the large resistance and therefore it

is neglected.

0 E+00

2 E+04

4 E+04

6 E+04

8 E+04

1 E+05

1 E+05

0.00E+00 5.00E-06 1.00E-05 1.50E-05 2.00E-05

Heat tr

ansfe

r flux [

W/m

2]

z [m]


83

Figure 52. The heat transfer per unit length in the thin film region

Figure 53. The heat transfer per unit length in the bulk region

In Figure 54 it can be seen that bulk decreases along channel. This is because

bulk is also increasing along the ϕ-direction. The higher bulk results in a smaller contact

angle, which results in the thinner film along the channel.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.00E+00 5.00E-06 1.00E-05 1.50E-05 2.00E-05

Th

e h

eat tr

ansfe

r p

er

un

it le

ngth

[W

/m]

z [m]


0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

10.0

0.00E+00 5.00E-04 1.00E-03 1.50E-03 2.00E-03

Heat tr

ansfe

r per

unit length

[W

/m]

y [m]


84

Figure 54. Variation of bulk along the channel

It is necessary to understand the collective effect of the heat transfers from all the

regions on the heat transfer coefficient and total heat transfer rate of the CALPE.

Therefore, parametric studies are conducted in the next section by varying the wall

superheat, evaporation temperature, spacing and depth of the rectangular microchannel.

Parametric study

Wall superheat

Here, all the geometrical properties, initial filling level (o ) and the liquid thermo-

physical properties are kept constant to see the effect of ΔT on the heat transfer coefficient

and the total heat transfer rate of the CALPE. Figure 55a shows the effect of the wall

superheat (ΔT) on the heat transfer coefficient of the CALPE ( CALPEh ). CALPEh decreases

from 4500 to 3100 W/m2∙K, when ΔT increases from 0.1 to 0.5 K. Figure 55b shows the

effect of the wall superheat (ΔT) on the total heat transfer rate of the CALPE (CALPEQ ).

CALPEQ increases from 545 to 1200 W when ΔT increases from 0.1 to 0.5K. The ΔT

increases the film temperature resulting in a thinner film. The thinner film reduces the

resistance to heat transfer. The wall superheat increases the liquid temperature and

reduces its viscosity and increases the thermal conductivity. Therefore, when the

superheat is increased, evaporation is strengthened and CALPEQ increases.

0.0E+00

1.0E-04

2.0E-04

3.0E-04

4.0E-04

5.0E-04

6.0E-04

7.0E-04

0.00 0.79 1.57 2.36 3.14

δbulk

[m]

ϕ [radians]


π

0

85

a

b

Figure 55. Variation of hCALPE and Q̇ with the wall superheat

Comparison with experiments

The CALPEQ computed from the present CALPE model has been compared with

the experiments. The experiments were conducted using the CALPE, whose details are

shown in Table 7. The comparison of the results is shown in Figure 55b. It can be

concluded that the present model captures the experimental trend and compares very

2,000

2,500

3,000

3,500

4,000

4,500

5,000

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35

hC

ALP

E[W

/m2

∙K]

ΔT [K]

0

300

600

900

1,200

1,500

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35

To

tal h

ea

t tr

an

sfe

r ra

te [W

]

ΔT [K]

86

close the experimental values. It can be noticed that at higher ΔT, the model slightly

underestimates the experimental data and at lower ΔT it slightly overestimates the

experimental data. However, the model results fall well within the range of uncertainty of

the experiments. Since the present model captures trend of the experiments, it can be

used to an in-depth understanding of the phenomena in capillary-assisted evaporation

and to provide insight to design an effective CALPE.

Saturation temperature

The effect of saturation temperature (Tsat) is shown in Figure 56. When the wall

superheat is kept constant and Tsat is increased from 4 K to 10 K, CALPEh increases from

2700 to 3100 W/m2∙K. The higher Tsat reduces the liquid viscosity and increases the liquid

thermal conductivity. The other geometrical parameters considered are shown in Table 7.

Channel spacing

Figure 57a shows the effect of the channel spacing (W) on the heat transfer

coefficient of the CALPE ( CALPEh ). Higher W affects the capillarity in the channel since

more liquid has to be raised. bulk under larger W is also higher, which increases the .

Therefore, under constant Tsat and T when the W is increased from 0.1 to 0.6 mm, CALPEh

falls from 3350 to 2850 W/m2∙K. Higher W increases the surface area for heat transfer.

2,000

2,200

2,400

2,600

2,800

3,000

3,200

3,400

3,600

2.00 4.00 6.00 8.00 10.00 12.00

hC

ALP

E[W

/m2∙K

]

Tsat [K]

Figure 56. Variation of hCALPE with Tsat

87

However, higher W also increase the bulk resulting in thicker films. The thicker film

increases the resistance to the heat transfer which negatively affects the total heat transfer

rate of the CALPE (CALPEQ ). The influence of CALPEh will have a significant impact on

CALPEQ as well. Under constant Tsat and T and when the W is increased, CALPEQ decrease

as shown in Figure 57b. It is shown that when W is increased from 0.1 to 0.6 mm, CALPEQ

decreases from 2855 W to 1010 W.

Figure 57. Variation of hCALPE and Q̇ with channel spacing W

a

b

2,800

2,900

3,000

3,100

3,200

3,300

3,400

3,500

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

hC

ALP

E[W

/m2

∙K]

W [m]


0

500

1,000

1,500

2,000

2,500

3,000

3,500

0 0.1 0.2 0.3 0.4 0.5 0.6

To

tal h

ea

t tr

an

sfe

r ra

te [W

]

W [m]


88

Channel depth

The effect of channel depth (D) on the heat transfer coefficient of the CALPE (

CALPEh ) is shown in Figure 58a. Higher D affects the capillarity in the channel since more

driving force is required to raise the liquid. Therefore, CALPEh decreases from 6100 to 1000

W/m2∙K when D is increased from 1mm to 4.5mm. Under constant Tsat and T the CALPEQ

increases when the channel depth is increased. This increase could be mainly attributed

to the significant rise in the heat transfer surface coming from deeper fins. Figure 58b

shows the effect of the D on theCALPEQ . Under constant Tsat and T and when the D is

increased, CALPEQ increases as shown in Figure 58b. It is shown that when D is increased

from 1mm to 4.5mm, CALPEQ increases from 1045 W to 1686 W.

89

a

b

Figure 58. Variation of hCALPE and Q̇ with channel spacing D


In this chapter, an attempt was made to capture the physics of capillary-assisted

evaporation in an open rectangular microchannel using various submodels: (1) the natural

convection model; (2) the liquid circumferential flow model; (3) the evaporating thin film

model; and, (4) the bulk model. Using the present model, menisci curvatures along the

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

0 0.001 0.002 0.003 0.004 0.005

hC

ALP

E[W

/m2∙K

]

D [m]


800

1,000

1,200

1,400

1,600

1,800

2,000

0 0.001 0.002 0.003 0.004 0.005

Tota

l heat tr

ansfe

r ra

te [W

]

D [m]


90

circumferential micro channel for an open evaporating flow were obtained. From the thin

film model, the length and thickness of the thin film were attained. Using the liquid

circumferential flow model, the bulk curvature and thin film curvature were demarcated.

Finally, the heat transfer coefficients for capillary-assisted evaporation in open rectangular

microchannels were determined. In addition, the results of the model were compared with

the experimental results. The model captured the experimental trend and compared very

close to the experimental values. Moreover, the model can be used to in-depth

understanding of the phenomena in capillary-assisted evaporation and to provide insight

to design an effective CALPE.

By solving the present model under the assumptions described in the chapter, the

following conclusions can be made:

• As the liquid raised along -direction, there was a drop in liquid pressure

(Pl), which creates a pressure difference for the circumferential movement

of the liquid.

• Capillary pressure played an important role in determining the film profile

throughout the extended meniscus.

• In the extended meniscus, the thin film region is the major contributor to

the overall heat transfer.

• The heat transfer coefficient of the CALPE ( CALPEh ) decreased from 4500

to 3100 W/m2∙K, when ΔT increases from 0.1 to 0.5 K.

• The total heat transfer rate of the CALPE (CALPEQ )

increased from 545 to 1200 W when ΔT increases from 0.1 to 0.5K.

• The saturation temperature (Tsat) had a positive effect on CALPEh

• Under constant Tsat and the wall superheat (T), when the W was increased

from 0.1 to 0.6 mm, CALPEh decreased from 3350 to 2850 W/m2∙K. When W

is increased from 0.1 to 0.6 mm, CALPEQ decreased from 2855 W to 1010

W.

• CALPEh decreased from 6100 to 1000 W/m2∙K when D is increased from 1

mm to 4.5 mm and when D is increased from 1mm to 4.5mm, CALPEQ

increases from 1045 W to 1686 W.

91

Chapter 6. Micro Capillary-Assisted Low Pressure Evaporator

The Chapter 2 and 3 presents the development and performance of the CALPE

using commercial finned tubes. Following the detailed evaluation of thermal performance,

a CALPE with smaller tube diameters was designed to overcome the internal thermal

resistance and maximize overall heat transfer conductance. In Chapter 4, the availability

of commercially available small diameter tubes was discussed and it was shown that how

the available tube sizes led to weakened capillary effect, causing the outer heat transfer

to suffer due to low fin density. Chapter 4 also presents how applying a thin film of porous

copper coating that effectively reduced fin spacing and increased the area for thin film

evaporation to occur, leading to improved internal and external heat transfer coefficients.

However, the internal heat transfer was still the main bottleneck to heat transfer and

became the hindrance to the performance. Based on the experiences and learning from

the experimental results (Chapter 2, Chapter 3 and Chapter 4 ) and the modeling exercise

(Chapter 5), the present chapter attempts to overcome this bottleneck by designing and

building a new Micro Capillary-Assisted Low Pressure Evaporator (µCALPE).

6.1. Design of µCALPE

The general idea of the proposed design is to run chilled water through mini/micro

channels and transfer the thermal energy to evaporate water through capillary action at

low pressure (see Figure 59). The capillary action is achieved by creating narrow

channels, with an optimal gap for capillary effect, using high density fins. These fins will

have a grainy surface to provide additional heat transfer surface area and further

enhances the performance of the evaporator. The advantage of evaporation through

capillary action is to draw the refrigerant from the pool to cover the outside surface of the

tube and to produce a uniform distribution of refrigerant along the tubes. Drawing water

through capillary action avoids the negative hydrostatic pressure impacts in the LP

evaporator without using additional power for pumping.

92

a

b

Figure 59. Schematic to explain the principle of µCALPE

The advantage of utilizing mini/micro channels is to achieve internally high

Reynolds number flow and to overcome the major bottleneck of internal heat transfer

resistance.

Figure 59b shows the capillary tubes are arranged in a serpentine fashion with multiple

passes. As mentioned earlier, compact CALPE will find an application in LGTE systems

like waste heat-driven adsorption chillers, which are beleaguered with technical limitations,

(0) 0cP =

min2 cos( )( )cP L

W

=

)(2 xr

)(1 xrx

Vacuum chamber

Vapour outlet

Inlet port Outlet port

Microchannel tube

93

including the low SCP and low COP of these systems. These limitations lead to large sizes

compared to incumbent conventional VCR systems. When designing a microchannel

based µCALPE, the main goal is to enhancing heat transfer while minimizing pressure

drops and reducing the size and increasing the compactness of heat exchangers.

Following sections explains necessary steps considered for the design of serpentine flow

µCALPE.

Pressure Drop

The utilization of microchannels result in more compact CALPE and higher

internal heat transfer coefficients through high surface area density. However, the main

challenges of integrating microchannels in CALPE are: i) the manufacturing complications,

and ii) high pressure drop which leads to higher pumping power required to flow the chilled

water through the microchannels [94]. Therefore, the channel (port) diameter and the

header must be carefully designed.

Figure 60 shows a schematic of serpentine flow µCALPE. The single-

phase chilled water follows through the inlet header and is distributed into a row of

microchannels of a capillary tube and flows through the intermediate headers (elbow) and

finally exits through the outlet port. The pressure drop for the entire µCALPE is the sum of

pressure drops in the inlet header (part of the inlet port for serpentine flow type µCALPE),

port inlet contraction, along the port, port exit expansion, exit header, and the outlet port.

The pressure drop equations are taken from the work of Yin et.al [95]. The total pressure

drop for serpentine flow µCALPE can be expressed as:

2 2 2 222 2

exp

(inlet header) (inlet port contraction) (along port) (outlet port expa

( 1 ) ( 1 )2 2 2 2 2

ip ip p p op opt tin out ip con t op

ip ip p t t p op op

L G G G L GL GP P f f f

D D D

− = + + − + + − + +

nsion) (outlet header)

(88)

where, Pin is the chilled water pressure at the inlet, Pout is the pressure at the outlet of

µCALPE, G is the mass flux, f is the friction factor, and γ is the area ratio of the header

tube to the cross section area to a single microchannel port’s cross sectional area.

Equation (88) is used to predict the pressure drop of a serpentine flow µCALPE.

94

a

b

Figure 60. Schematic of (a) a serpentine flow µCALPE and (b) enlarged views of an inlet port and a capillary tube

Internal heat Transfer

To evaluate the internal convective heat transfer coefficient, hi, for port diameters above

1mm Gnielinski correlation [58] is used. The flow of chilled water inside the tube is

characterized by the Reynolds number, Rei:

Inlet header

Outlet header

Inlet port

Outlet port

Intermediate header

Intermediate header

Microchannel tube

95

i,tube

iReVD

= (89)

where, V is the chilled water velocity. For Reynolds numbers higher than 2,300 (2,300 <

Rei < 5x106 ) Gnielinski correlation [58] can be used to calculate the Nusselt number:

( )

i i

i 0.52

3i

(Re 1000)Pr2

1 12.7 Pr 12

f

Nuf

−

=

+ −

(90)

With

1

4i0.078Ref−

= (91)

Finally, the internal heat transfer coefficient, hi, is calculated as follows:

i wateri

i,tube

Nu kh

D= (92)

Capillary channel height

The capillary channel height is computed as given by the literature [96]. As shown in Figure

61, an open channel with a rectangular cross-sectional area draws water in vertical

direction when its bottom end is inserted in the liquid. For a capillary channel of width W

and depth of the groove L, the capillary height (H) is given by:

[(2 )cos ]

[ ]l

L W WH

LW g

+ −= (93)

where σ (σlv) is the surface tension between the liquid-vapor interface, θ is the contact

angle and ρl is the liquid density.

96

a b

Figure 61. (a) Capillary phenomenon in an open rectangular channel and (b) top view of the open channel

External heat transfer

The external heat transfer is modeled as described in Chapter 5 and the physics

of capillary-assisted evaporation in an open rectangular microchannel is captured by

solving the following sub-models: (1) the natural convection model (section 5.3.1); (2) the

liquid axial flow model, section 5.3.2 is solved in Cartesian coordinates; (3) and the

evaporating thin film model (section 5.3.3). The capillary pressure (Pc) is determined as a

function of x.

2

2

1( )

2

= +c

Q xP x Ax

AsW (94)

where, constant A is obtained by solving the Eq. (94) and applying following boundary

conditions apply:

( )

( )

0

min

0

2cos

c

c

P x x

Px L

x W

= =

= =

(95)

Using Young-Laplace equation [x] and neglecting the disjoining forces, can be

obtained:

cP = (96)

g

x

dx

L

W

lv

sv

sl

Top view

97

Finally, the contact angle θ is obtained by:

=cos

2

W (97)

The evaporating thin film model explained in section 5.3.3 is used to calculate the external

heat transfer coefficient.

Therefore, for the entire µCALPE, the heat transfer rate [W] is given by

�̇� = 2 𝑞𝑡ℎ𝑖𝑛𝑓𝑖𝑙𝑚′ 𝐿 𝑛𝑓𝑖𝑛𝑛𝑡𝑢𝑏𝑒 (98)

where L is the fin length, nfin the number of fins, and ntube the number of tubes in the

µCALPE.

Heat transfer in the entire µCALPE

The heat transfer rate [W] for the entire µCALPE is the contribution coming from

the natural convection model and the evaporating thin film model. Therefore, the heat

transfer rate [W] for the entire µCALPE is estimated by

CALPE pool thinfilmQ Q Q = + (99)

The obtained main dimensions of the serpentine flow type evaporator used in the 3D

printing of µCALPE are given in Table 8.

98

Table 8. Main dimensions of the serpentine flow µCALPE

Capillary tube geometry parameters

Number of ports in a capillary tube 12

Diameter of ports (mm) 2

Diameter of inlet header (inches) 1.27

Effective length of the capillary tube (inches)

47.25

Capillary channel parameters

Capillary tube thickness (mm) 2.8

Fin length (inches) 1.25

Fin height (mm) 2

Fin thickness (mm) 0.5

Fin spacing (mm) 0.4

Distance from wall to port (mm) 0.35

6.2. 3D printed µCALPE

To build an economically viable prototype of µCALPE, a serpentine flow µCALPE with

dimensions given in Table 8 is 3D printed by using direct metal laser sintering process

(DMLS).

99

a

b c

Figure 62. An actual prototype showing (a) a µCALPE, (b) fins and (c) inlet port with microchannels

A micro capillary-assisted low-pressure evaporator (µCALPE) consists of the following

components:

a. a vacuum chamber to hold capillary tubes placed in a pool of refrigerant (e.g.

water) and to produce vapor,

b. capillary tubes with high density fins on the outside of the tubes and row(s) of

mini/micro channels on the inside of the tube,

c. designed heat exchanger (CALPE) with optimized number, arrangements, cross-

sectional shape, and diameter of mini-/micro-channels,

d. manifold(s) (or header) to distribute the chilled water into the micro-channels, and

e. an inlet port and an outlet port.

The actual prototype is shown in Figure 62a. Figure 62b shows the fins (capillary

channels) and Figure 62c shows the inlet port with microchannels. In Figure 63a,

images of actual prototype of serpentine µCALPE is compared to a C$ 25 coin. In

addition, the grainy surface due to laser sintering is shown in Figure 63b.

100

a

b

Figure 63. An actual prototype serpentine µCALPE (a) compared to a C$ 25 coin, (b) showing grainy surfaces

6.3. Experimental study

The custom-build experimental setup is shown in Figure 64, and is consisted of a

temperature control system (TCS) and a variable speed pump to provide a constant

temperature thermal fluid (chilled water) to the μCALPE at different mass flow rates.

The vacuum pump was used to lower the system pressure and control valves were

employed to regulate the pressure inside the evaporator. To protect the vacuum pump

from the water vapor produced by the evaporator, two cold traps (dry ice and isopropyl

alcohol) were installed before the vacuum pump. Experiments began with the evaporator

tubes submerged in a pool of water and continued as continuous evaporation decreased

the height of the water, and ended when the evaporator chamber was dry. The evaporator

tubes were in contact with a pool of water while the pressure in the evaporator was

maintained at ~1 kPa for duration of the tests with chilled water inlet temperatures of 10,

15 and 20°C, and a thermal fluid flow rate of 2.0 kg/min. Section 2.2 in Chapter 2 contains

the detailed procedure of the test, along with the types of thermocouples, pressure

transducers, and flowmeters used and the details of the vacuum pump, cold trap, and

other components. The detailed data analysis is presented in Appendix C.

101

Figure 64. Schematic of the µCALPE experimental setup

6.4. Results and discussion

Figure 65 shows the operating pressure of the tested µCALPE for a constant 15°C

chilled water inlet temperature and mass flow rate 2 kg/min. As shown in Figure 65, when

the control valve between the evaporator and the cold trap was opened, the evaporator

pressure decreases and then remains ~1.0 kPa until the evaporator runs out of the water.

TCS

P

T T

F

Evaporator

T

Makeup waterControl

valveVacuum pump

Cold trapdry ice and IPA, -77°C

102

Figure 65. The behavior of the µCALPE at Tin =15°C, inm =2.0 kg/min vs. time

Figure 66. Variation of overall heat transfer coefficient of the µCALPE over

time, Tin =15°C, inm =2.0 kg/min

To test the effect of water height on the heat transfer performance, the evaporator

was initially filled with water so that the µCALPE sit ~5 mm below the water’s surface.

Figure 66 shows the variations in 𝑈 as a function of water height (water height decreases

with time). As shown in Figure 66, the capillary phenomenon on the finned tubes results

in increasing overall heat transfer coefficient over time (U). As the height of the liquid

water decreases and the hydrostatic pressure is reduced, the capillary action continues to

cover the entire outside surface of the tube. This behavior is contrary to the U from CALPE

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 2000 4000 6000 8000

Evapora

tor

pre

ssure

(kP

a)

Time (s)

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 2000 4000 6000 8000

Ove

rall

he

at tr

an

sfe

r co

effic

ien

t, [W

/m2∙K

]

Time (s)

103

built with Turbo Chil-40 FPI (Wolverine Tube Inc.) where U is constant with decreasing

height of water, which is shown in Figure 14. This proves that the internal heat transfer is

no longer a bottleneck in µCALPE.

In the following section, the performance of this µCALPE is compared with the one

built from Turbo Chil-40 FPI (Wolverine Tube Inc.) tubes. In Figure 67, an actual µCALPE

porotype is compared with the CALPE built from Turbo Chil-40 FPI (Wolverine Tube Inc.)

tubes and compared to a C$ 25 coin.

Figure 67. Comparison of µCALPE with a CALPE built with Turbo Chil-40 FPI (Wolverine Tube Inc.)

To evaluate the performance of µCALPE, it was tested with the chilled water inlet

mass flow rate of 1, 1.5, and 2.0 kg/min (Re based on inlet port diameter of 1100, 1650

and 2200, respectively) at 15°C chilled water inlet temperature. The comparison of total

heat transfer rates and the heat transfer coefficients of the µCALPE and the CALPE are

shown in Figure 68. The µCALPE has heat transfer rates significantly greater than that of

the CALPE. The µCALPE provided the almost similar total heat transfer rate, 630 W

(maximum value) when operated at 2.0 kg/min (Re= 2200) at 15°C against 792 W for

CALPE However, it is important to note that the footprint of CALPE is four times than that

of the proposed µCALPE.

104

a

b

Figure 68. The total heat transfer rate (a), the overall heat transfer coefficient (b) of µCALPE and the CALPE built with Turbo Chil-40 FPI (Wolverine Tube Inc.) as function of chilled water mass flow rate

Before checking the ε and NTU, it is essential to compare the maximum overall

heat transfer coefficient. The µCALPE has a maximum U of 3,174 W/ (m2K) compared to

1,350 W/ (m2K) for the Turbo Chil-40 FPI tube. The U of µCALPE is ~2.4 times higher

than that of CALPE built from Wolverine Tube Inc. tubes. However, the improvement

comes at the cost of huge pressure drop. The effectiveness (ε) and a number of transfer

units (NTU) of the µCALPE are calculated based on Eq. (12) and Eq.(13). Using µCALPE

yields the highest ε and NTU (shown in Figure 69) of 88.6% and 2.16 at the chilled water

0

200

400

600

800

1000

1200

1.0, [Re=1100] 1.5, [Re=1650] 2.0, [Re=2200]

To

tal e

va

pora

tio

n h

eat tr

ansfe

r ra

te,

(W)

Chilled water mass flow rate, ṁ in (kg/min)

µCALPE

CALPE

0

500

1000

1500

2000

2500

3000

3500

4000

1.0, [Re=1100] 1.5, [Re=1650] 2.0, [Re=2200]

Ove

rall

he

at

transfe

r co

eff

icie

nt,

[W/m

2∙K

]

Chilled water mass flow rate, ṁ in (kg/min)

µCALPE

CALPE

105

inlet temperature of 15°C, respectively. The ε and NTU of CALPE are not presented

directly here because the CALPE built using Turbo Chil-40 FPI (Wolverine Tube Inc.)

tubes are oversized and the effective length of the CALPE tubes is 3.5 times longer than

the length of capillary tubes of µCALPE. To make a reasonable comparison, ε and NTU

of CAPLE with similar length is calculated and presented in Figure 69.

Figure 69. Effectiveness (ε) and a number of transfer units (NTU) of the µCALPE

The actual breakdown of internal, external, and conductive heat transfer

resistances cannot be shown for the µCALPE. This is because the external surface area

of the tubes (Ao) must be accurately determined to calculate external convective thermal

resistance, which is not available for the sintered surface of our µCALPE. Due to laser

sintering process of the 3D printing, a grainy surface is formed as shown in Figure 63b.

An accurate surface area measurement of the µCALPE is not in the scope of this research,

but quantifying the effective surface area of the µCALPE surface could be a valuable future

study. However, to demonstrate how the proposed µCALPE overcame the bottleneck of

internal heat transfer resistance, the breakdown of thermal resistances is computed

(Appendix C) by assuming Ao as plain surface area without surface roughness. The

external heat transfer coefficient ho can be assumed 2,000-4,000 W/ (m2K) for capillary-

assisted evaporation based on Xia et al.[27] and Thimmaiah et al [97]. To be on the safe

side, ho =1,000 W/ (m2K) is taken from model assuming plain surface without any

0.0

20.0

40.0

60.0

80.0

100.0

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5

Effe

ctive

ne

ss, [%

]

Number of transfer units

µCALPE

CALPE

106

roughness for the breakdown of internal, external, and conductive heat transfer

resistances.

As shown in Figure 70, there is a significant reduction in the internal resistance due

the utilization of microchannels, which is attributed to the high Reynolds number flow.

When compared to the CALPE built using Turbo Chil-40 FPI (Wolverine Tube Inc.) in

which up to 85% of the overall thermal resistance, was due to the internal convective

resistance, µCALPE has a very negligible internal convective resistance.

Figure 70. Thermal resistance for the µCALPE

Internal resistance is no longer a major bottleneck in heat transfer of the µCALPE.

However, this heat transfer enhancement comes with the challenge of the increased

pressure drop of the chilled water through the µCALPE, and thus higher pumping power.

The pressure drop for µCALPE working at 2.0 kg/min at 15°C chilled water inlet

temperature is 175 kPa, which is 140 times higher compared to CALPE built using Turbo

Chil-40 FPI (Wolverine Tube Inc.).

0

0.001

0.002

0.003

0.004

0.005

0.006

External thermalresistance

Conductivethermal

resistance

Internal thermalresistance

Overall thermalresistance

Therm

al re

sis

tance (

K/W

)

2.0E-06 K/W

107

Figure 71. The pumping power (a), the cooing density and compactness (b) of µCALPE and the CALPE built with Turbo Chil-40 FPI (Wolverine Tube Inc.)

Table 9 shows the comparison of the power consumption, the cooling power and

the cooling density of CALPE and µCALPE. Also, Figure 71a, compares the power

a

b

0.04

5.83

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

CALPE µCALPE

Pu

mpin

g p

ow

er

(W)

789 W/m3

7,706 W/m3

77 m2/m3

4,084 m2/m3

0

1000

2000

3000

4000

5000

6000

7000

8000

CALPE µCALPE

Cooling density (ϳ)

Compactness (β)

108

consumption (pumping power) of the pump to deliver a volumetric flow of 3.33 E-05 m3/s.

The pumping power required by the µCALPE is 145 times higher than compared to

CALPE.

However, the disadvantage of higher pumping power is compensated by the area

density or compactness (β) of the µCALPE. A two phase heat exchanger is compact when

it has a heat transfer area to volume ratio greater than 400 m2/ m3 [98]. Figure 71b shows

the compactness (β) for µCALPE is 4084 m2/ m3, which is 5223% compared to CALPE.

The higher β is a good indication of performance, the higher the compactness generally,

the higher the effectiveness for given pumping power.

As discussed in Chapter 1, the main technical challenges facing commercialization

of adsorption chillers are its large size and mass compared to a VCR system. Hence, a

compact evaporator with a high cooling density (j) is essential, which will help to reduce

the mass and size of adsorption chillers. In Figure 71b, the cooling densities of CALPE

and µCALPE are compared. When operated at 2.0 kg/min at 15°C chilled water inlet

temperature, µCALPE provides 7,706 W/m3 of cooling density, which is ten times higher

compared to CALPE. Thus, the higher j of µCALPE will transform on-demand cooling in

vehicles, while increasing their fuel economy. Therefore, the issue of pressure drop should

not blind side entirely the benefits of cooling density and compactness particularly when

the µCALPE is best suited when space and weight are a major concern.

6.5. Recommendations to reduce the pressure drop

There are various ways to reduce the pumping power (or pressure drop) of a µCALPE.

One way is to consider parallel type µCALPE, which can have several tubes on a single

pass or multiple passes. Another way is slightly increasing the micro port diameter.

However, an accurate modelling of the tradeoff between pressure drop and heat transfer

of the µCALPE is necessary.

109

Figure 72. Comparison of the measured and predicted pressure drop of serpentine type µCALPE

Figure 73. Schematic of a parallel flow type µCALPE

0

20

40

60

80

100

120

140

160

180

200

Re=1100 Re=1650 Re=2000

Pre

ssure

dro

p (kP

a) Measured

Predicted

Inlet port

Outlet port

Microchannel tube

Intermediate header

Header

110

Figure 74. Comparison between serpentine type and parallel type µCALPE

The pressure drop due to parallel type configuration can be predicted using the

model shown in Equation. (88). The validity of the pressure drop model applied on

serpentine µCALPE is shown in Figure 72. The schematic of a parallel type µCALPE is in

Figure 73 with dimensions similar to serpentine type µCALPE. The parallel type µCALPE

has six tubes with one parallel pass with an inlet header and an outlet header. The

Equation (88) is used to account for the pressure drop in parallel type configuration similar

to the work of Yin et al. [95].

Figure 74 shows the effect of choosing parallel type configuration on the pressure

drop. In addition, the effect of the port diameter is presented in Figure 74. For same

dimensions and operating conditions, the parallel type configuration gives thirty times

lower pressure drop than the serpentine type configuration. Furthermore, if we increase

the port diameter from 2 mm to 2.5 mm. It is predicted that the pressure drop serpentine

type µCALPE falls by 73%. In this study, prototyping and testing of parallel flow type

µCALPE were not chosen because of the significant material cost associated with the 3D

printing of headers.

175

47

61

0.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

160.0

180.0

200.0

2.0 2.5

Pre

ssure

dro

p (kP

a)

Port diameter (mm)

Serpentine type

Parallel type

111


• The internal heat transfer was no longer a bottleneck in µCALPE.

• The µCALPE provided the similar total heat transfer rate as CALPE from Turbo

Chil-40 FPI (Wolverine Tube Inc.) tubes, which had footprint of 4 times higher than

that of µCALPE.

• The overall heat transfer coefficient (U) of µCALPE working at 2.0 kg/min at 15°C

chilled water inlet temperature was ~2.4 times higher than that of CALPE built from

Wolverine Tube Inc. tubes.

• µCALPE yielded the highest effectiveness (ε) of 88.6%.

• The pressure drop for µCALPE working at 2.0 kg/min at 15°C chilled water inlet

temperature was 175 kPa, which is 140 times higher compared to CALPE built

using Turbo Chil-40 FPI (Wolverine Tube Inc.).

• When operated at 2.0 kg/min at 15°C chilled water inlet temperature, µCALPE

provided 7,706 W/m3 of cooling density, which is ten times higher compared to

CALPE.

112

Chapter 7. Summary and Future Work

In this chapter, an overall synopsis of the main results is presented, along with the

most pertinent conclusions. In addition, proposals for future work are recommended.

7.1. General conclusions

This Ph.D. research began with identifying the major gaps in the literature

pertaining to low-pressure evaporator technology. An experimental investigation was

conducted to determine the most suitable tube for use in the capillary-assisted low

pressure evaporator (CALPE) and the main factors affecting the performance of a CALPE

were identified. Furthermore, an experimental evaluation of thermal resistances of low-

pressure capillary-assisted tubes was conducted and the main bottleneck in the CALPE

performance was recognized. To overcome the bottleneck, which was the internal transfer

in the CALPE tubes, smaller diameter commercial tubes were sourced. Moreover, The

CALPE was inserted with turbulent flow generators and its performance was

experimentally evaluated. Thereafter, to improve the capillary performance the external

surfaces of the CALPE were coated with thin film of porous coating and the porous coated

CALPE was evaluated. In addition, a mathematical model for predicting the CALPE

performance was developed. Finally, novel micro capillary-assisted low pressure

evaporator (µCALPE), which was suitable for an adsorption chiller was developed.

The development of the µCALPE started with an assembly made from 14.45 mm

inner diameter (ID) commercial tubes with a high fin density (40 fins per inch)

corresponding to a 0.635 mm fin spacing. The high fin density increased the area of the

thin film region due to capillary action and increased the external heat transfer coefficient.

However, the large diameter caused a poor internal heat transfer coefficient. To overcome

the bottleneck in the internal heat transfer, a smaller tube with 7.9 mm ID was sourced.

The commercially available finned tubes at 7.9 mm ID had a maximum fin density of 26

fins per inch, which resulted in a weakened capillary effect, causing the outer heat transfer

coefficient to suffer. Finally, the finned 7.9 mm ID were coated with a porous copper

coating that effectively reduced fin spacing and increased the area for thin film evaporation

to occur, leading to improved internal and external heat transfer coefficients. However,

while the internal heat transfer was still the main bottleneck to heat transfer and became

the hindrance to the performance. To overcome this bottleneck, µCALPE was designed

113

and built using 3D printing technology. Our µCALPE had significantly higher heat transfer

performance compared to CALPE’s built with industrial tubes and coated tubes.

7.2. Specific conclusions

The followings are the specific conclusions of this research:

➢ Capillary-assisted tube characterization to determine the most suitable tube for

use in an LP evaporator

• Five types of capillary-assisted tubes were evaluated for a low pressure

evaporator.

• The experimental results indicated that Turbo Chil-40 FPI provided the

highest heat transfer rate and overall heat transfer coefficient.

• Tubes with continuous parallel fins on their outer surfaces had significantly

higher heat transfer rate and heat transfer coefficients relative to plain tubes.

• To achieve the highest heat transfer rate, the refrigerant (water) height in

the evaporator had to be less than the tube diameter.

• The interior volume above the enhanced tubes of the capillary-assisted

evaporator did not have a significant effect on evaporator performance.

• Increasing the thermal fluid (chilled water) mass flow rate of 2.5 kg/min to

15.3 kg/min (6.1 times) increased the total evaporation heat transfer rate and

evaporator heat transfer coefficient by 20% and 110%, respectively.

➢ Experimental evaluation of thermal resistances of commercially available low-

pressure capillary-assisted tubes

• Turbo Chil-40 FPI showed the lowest overall thermal resistance under

different operating conditions.

• For the enhanced tubes, up to 85% of the overall thermal resistance was due

to the internal convective resistance.

• For the plain tube, 48.8% and 51% of the overall thermal resistance was due

to the external and internal convective resistances, respectively

• The maximum effectiveness and NTU achieved were 45% and 0.6,

respectively, for Turbo Chil-40 FPI at chilled water inlet temperature of 20°C.

• The main bottleneck in the performance of an LP evaporator was the internal

heat transfer.

114

➢ Assessment of effects of porous copper coatings on capillary-assisted low

pressure evaporation

• The porous copper coating enhanced the capillary effect by reducing

effective distance between fins and significantly increased the external

surface area of the evaporator.

• The porous copper coating increased the amount of thin film evaporation and

thus hoAo increased leading to a considerable improvement in the overall

heat transfer coefficient (U).

• Overall thermal resistance of the coated CALPE is 32% lower than the

uncoated CALPE.

• U of the coated CALPE is, on average, 28% higher than the uncoated

CALPE;

• Heat transfer rate, �̇�, of the coated CALPE is, on average, 90% higher than

the uncoated CALPE.

➢ Development of a mathematical model for predicting the CALPE performance

• The model showed, as the liquid raised along channel, there was a drop in

liquid pressure (Pl), which created a pressure difference for the

circumferential movement of the liquid.

• The model showed, the thin film region was the major contributor to the

overall heat transfer.

• The model predicted, the heat transfer coefficient of the CALPE ( CALPEh )

decreased 45% W/m2∙K, when ΔT increases from 0.1 to 0.5 K.

• The saturation temperature (Tsat) had a positive effect on CALPEh

• The model predicted, under constant Tsat and the wall superheat (T), the W

had negative effect on CALPEh and CALPEQ .

• The model showed that under the assumptions considered, CALPEh

decreased from 6100 to 1000 W/m2∙K when D is increased from 1 mm to 4.5

mm and when D is increased from 1mm to 4.5mm, CALPEQ increases from

1045 W to 1686 W.

➢ Development of a novel µCALPE

• The internal heat transfer was no longer a bottleneck in µCALPE.

115

• The µCALPE provided the similar total heat transfer rate as CALPE from

Turbo Chil-40 FPI (Wolverine Tube Inc.) tubes, which had footprint of 4 times

higher than that of µCALPE.

• The overall heat transfer coeffcient (U) of µCALPE was ~2.4 times higher

than that of CALPE built from Wolverine Tube Inc. tubes.

• µCALPE yielded the highest effectiveness (ε) of 88.6%.

• The pressure drop for µCALPE working at 2.0 kg/min at 15°C chilled water

inlet temperature was 175 kPa, which is 140 times higher compared to

CALPE built using Turbo Chil-40 FPI (Wolverine Tube Inc.).

• When operated at 2.0 kg/min at 15°C chilled water inlet temperature,

µCALPE provided 7,706 W/m3 of cooling density, which is ten times higher

compared to CALPE.

Thus, it is possible to defend that the proposed goal and objectives were achieved.

From this thesis it was evident to emphasize that the CALPE has a great potential in thin

film evaporation in low grade thermal energy driven systems.

7.3. Future Work

The following research directions can be considered as the continuation of this

study:

• Experimental data can be collected as function of water level height.

• The effect of CALPE due to vibration and inclination needs to be exploited.

• The mathematical model can be upgraded to a more advanced model by

adding impact of dry-out and corner flows in capillary channels.

• More accurate and non-invasive measurement to quantify the surface area

of thin film porous coating can be performed.

• The trade-off between pressure drop and heat transfer in µCALPE can be

performed.

116

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125

Appendix A. Calculations of Fin Resistances

To calculate the internal convective resistance due to a fluid circulated in a finned

tube, the following steps should be taken. The tubes of interest in this study have

circumferential, rectangular cross-section fins. The efficiency of a fin located on the

surface of the tube with circumferential, rectangular cross-section fins can be calculated

from Eqs. (A1-A5) [58]:

−

= +

1 1 1 2 1 1 1 2

0 1 1 2 0 1 1 2

( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

c cf

c c

K mr I mr I mr K mrC

I mr K mr K mr I mr (A1)

( )

( )=

−

1

2 2

2 1

2 /

c

r mC

r r (A2)

2

f

hm

kt

=

(A3)

( )2 2 / 2c fr r t= + (A4)

2 2

2 12 ( )f cA r r= − (A5)

Where 1r and 2r are the distances from the center of the tube to the fin base and fin tip,

respectively. I0, and K0 in Eq. (A1) are modified, zero-order Bessel functions of the first

and second kinds, respectively. I1, and K1 in Eq. (A1) are modified, first-order Bessel

functions of the first and second kinds, respectively. ft in Eq. (A3) is the fin thickness and

Af in Eq. (A5) is the fin heat transfer surface area. The total external heat transfer surface

area of the finned tube is calculated as follows:

( )t f bA N A A= + (A6)

126

12b bA rt= (A7)

Where N is the total number of fins, and bA and bt are the prime (plain) heat transfer

surface area of the finned tube and the space between two fins, respectively. Using Eqs.

(A1), (A5), and (A6), the overall efficiency of the finned tube can be calculated [58]:

, 1 (1 )f

o fin f

f b

A

A A = − −

+ (A8)

Consequently, the conductive heat transfer resistance due to the fins of the finned tube

can be estimated.

,

1fin

o fin o t

Rh A

= (A9)

Where the convection coefficient ho is measured in the experiment. Also, the conductive

resistance of wall located under the fins can be calculated as follows:

( )1 0ln /

2wall

r rR

kL= (A10)

where 0r and L are the internal radius and length of the finned tube, respectively. Rfin

and Rwall are thermal resistances in series. Therefore, the overall conductive resistance

of the finned tube is calculated by Eq. (A11).

,o finned tube fin wallR R R= + (A11)

Finally, Eq. (A12) gives the internal convective heat transfer resistance of the finned tube.

,

1 1 1o finned tube

i i o o

Rh A UA h A

= − +

(A12)

From the experimental data measurements, the capillary evaporation coefficient on the

external surface of a finned tube can be calculated. Information required to calculate the

internal convective resistances of enhanced tubes at 20ºC chilled water inlet temperature

are listed in Table A1.

127

Table A1. Detailed geometry of Turbo Chil-40 FPI tubes.

Parameter value

L 1.54 m

r0 7.417 10-3 m

r1 8.052 10-3 m

r2 9.525 10-3 m

tf 1.59 10-4 m

tb 4.76 10-4 m

ho 5,000 W/m2·K

k 340 W/m·K

At 0.41 m2

A 0.0922 m2

Ai 0.0796 m2

128

Appendix B. Uncertainity Analysis

e systematic uncertainty [99] in the evaporator heat transfer rate calculation is:

( ) − = + −

22

i oe in

e in i osystematic

T Tq m

q m T T (B1)

where,

( ) − = +

−

22

i o oi

i o i o

T T TT

T T T T (B2)

Thus, the maximum systematic uncertainty in the calculation of evaporator heat transfer

rate is:

100e

e systematic

q

q (B3)

Also, the standard deviation for eq due to the random uncertainty is calculated from the

data. Eq. (B4) gives the systematic uncertainty of the overall heat transfer coefficient:

= +

2 2

e LMTD

LMTDe systematicsystematic

QU T

U TQ (B4)

From the random uncertainty in the measurement for Uevap over time, the maximum

uncertainty of overall heat transfer coefficient is calculated. Eq. (B5) gives the systematic

uncertainty of the external heat transfer coefficient:

= +

2 2

o e

o esystematic systematic

h Q T

h TQ (B5)

129

Appendix C. Data Analysis

The chilled water inlet and outlet temperatures, Tin and Tout, and the mass flow rate inm

were used to calculate the heat transfer rate from the chilled water flowing inside the tubes:

in in out( )e pq m c T T= − (C1)

The mean specific heat capacity at constant pressure from chilled water stream is

considered. The total evaporation rate, eQ , is calculated by time averaging the heat flow

rate:

2

1

e

e

2 1

[ ]

t

t

q dt

Q Wt t

=−

(C2)

where t1 and t2 are the beginning and the end of the time when the temperatures in the

evaporator remain constant. Finally, the overall evaporator heat transfer conductance, UA,

is given by:

e

LM

QUA

T=

(C3)

where A is the nominal surface area of the tubes and LMT is the logarithmic mean

temperature difference between the chilled water and the liquid refrigerant:

in outLM

in sat

out sat

ln

T TT

T T

T T

− =

−

−

(C4)

130

2

1

LMTD

2 1

t

t

LM

T dt

Tt t

=−

(C5)

with Tsat the refrigerant saturation temperature.

The overall heat transfer conductance UA can also be expressed as [58]:

o,finned tube

o o i i

1 1 1R

UA h A h A

= + +

(C6)

The first term on the right hand side of Eq. (6) describes the external convective thermal

resistance due to evaporation on the external surface of the tube, the second term is the

internal convective thermal resistance due to single-phase flow inside the tube, and the

third term is the conductive thermal resistance of the tube wall. To evaluate the internal

convective resistance, hi, needs to be calculated. The flow of chilled water inside the tube

is characterized by the Reynolds number, Rei:

i,tube

iReVD

= (C7)

where, V is the chilled water velocity. For Reynolds numbers higher than 2300 (2300 <

Rei < 5x106 ) Gnielinski correlation [58] can be used to calculate the Nusselt number:

( )

i i

i 0.52

3i

(Re 1000) Pr2

1 12.7 Pr 12

f

Nuf

−

=

+ −

(C8)

with

1

4i0.078Ref−

= (C9)

Finally, the internal heat transfer coefficient, hi, is calculated as follows:

131

i wateri

i,tube

Nu kh

D=

(C10)

Then the conductive thermal resistance of the tube wall due to the fin resistance is

calculated as explained in Appendix A and Eq. (A6) is rewritten in order to obtain the

external heat transfer coefficient (ho) of the uncoated finned tubes:

o,finned tube o

i i

1

1 1oh

R AUA h A

=

− +

(C11)

However, the resistance of the finned tube Ro,finned tube depends on the external heat

transfer coefficient. Therefore, an iterative process is implemented to calculate ho.

132

Appendix D. Porosity and Surface Area of Porous Coatings

In a low-pressure (LP) evaporator, the operating pressure of the refrigerant (water)

is quite low (~1 kPa) and the cooling power generation in a flooded evaporator is

negatively affected by the saturation pressure difference along the height of the water

column [18,19]. At evaporation temperatures between 5 to 10 °C, nucleate boiling does

not occur as it requires a high wall superheat of up to 20 K [19,41,89]. At low pressure,

natural convection determines the heat transfer, which results in low heat transfer

coefficients. As a result, large surface areas are required to achieve high thermal

conductance. To achieve high heat transfer coefficients, several researchers have studied

thin-film evaporation, such as capillary-assisted evaporation, including applying porous

metal coatings to fins to increase capillary action and enhance heat transfer

[37,90,100,101]. While the narrow channels between high-density fins provide necessary

wicking to wet the outside surface of the tube, the thin film porous coating lead to double

wicking of the water into the pores leading to high external heat transfer coefficient ho.

The fundamental characteristics of metal coatings that influence the heat transfer

are: i) surface roughness, and ii) the porosity, particularly the open pore porosity. It is a

significant challenge to nondestructively analyze open porosity, closed porosity and

surface roughness due to the meager amount of copper per coated area. The porosity (P)

is defined as the ratio of pore volume (Vpore) to the total volume (Vtotal).

𝑃 =𝑉𝑝𝑜𝑟𝑒

𝑉𝑡𝑜𝑡𝑎𝑙 (D1)

Gas adsorption measurements are often used to quantify open porosity [102,103].

However, for thin films adhered to the surface of a substrate such as copper, the small

amount of coated mass relative to the substrate mass creates experimental challenges

and leads to high uncertainties [17]. Besides, gas adsorption experiments need grinding

of the material to access the closed pores and quantify the total porosity. However,

grinding the thin film material is not advisable because of the small amount of material per

coated area.

133

A broad range of direct imaging methods can be used to analyze the porosity of

thin films, including scanning electron microscopy (SEM) with energy dispersive X-ray

spectroscopy (EDX), wavelength dispersive X-ray spectroscopy [104], focused ion beam

SEM (FIB-SEM) and transmission electron microscopy (TEM). Imaging methods allow for

quantification of the porosity via visualization and reconstruction of the pore geometry from

2-D projections of thin films cross sections [105]. However, they require elaborate sample

modification, which can result in morphological changes to pore. Therefore, a direct

imaging process that can visualize non-invasively and nondestructively is desirable.

Mercury intrusion porosimetry (MIP) is another method for characterizing open

pores and interconnected pores [106]. However, mercury can react with copper in a

process called amalgamation [107]. Therefore, methods involving inert fluids should be

considered.

Gas expansion methods that employ Boyle’s law, most notably helium pycnometry,

are considered among the most accurate techniques for measuring porosity [106,108]. An

inert gas, rather than a liquid, is used because it penetrates even the finest pores and

minimizes the influence of surface chemistry [109]. Helium has a high diffusivity, and

therefore affords a useful means for determining the porosity of thin films. However, the

pycnometer can only measure the volume of pores accessible to the helium, therefore it

can only measure the open porosity of a sample. Therefore, pycnometry has to be

combined with another non-invasive method for complete analysis of both open and

closed pores.

X-ray computed micro-tomography (CMT) [110] has become a valued tool for non-

destructive 3D visualization and characterization of porous material [111] [112]. However,

CMT is a relatively expensive technique due to the complexity of the instrument and the

required image processing software.

There are several methods to measure the roughness of the coated surface.

Atomic force microscopy (AFM) is commonly used for surface roughness measurements,

although the measurement area for AFM is usually limited to few micrometers. Stylus

based profilometres are also used to measure the surface roughness. Usually for

thermally coated surfaces, the roughness is usually a few micrometers and stylus

134

profilometres cannot provide accurate roughness measurement. The stylus is usually few

microns in diameter which makes it impossible to penetrate into smaller structures.

The Wenzel method [63–65] is a simpler, alternative approach, in which the

contact angle of the liquid droplet measured on the coated film surface is used to establish

the surface roughness. The scale condition of the Wenzel model should be satisfied, that

is, the diameter of the droplet (~5 mm) should be three orders of magnitude larger than

the surface pores [66].

In this appendix, a new approach to determine the film porosity by utilizing both

helium pycnometer and computed micro-tomography (CMT) is presented. The typical

approach here is based on measuring the open pore volume (pycnometer), mass

deposition of the film and the thickness of coated films (CMT). The mass of the film

deposition is converted into film density by dividing the measured thickness (thickness x

area) of the film. Ultimately, the film porosity is calculated from the measured porous film

density and the density of bulk, non-porous material. Unlike traditional methods and

imaging methods, by using this approach, the open, closed and total porosity of the copper

thin films can be distinctly measured without grinding the sample or changing the

morphology of pores. To our knowledge, the quantification of porosity of thin films

employing pycnometer and CMT has never been reported in the literature. Therefore, vital

contributions of this work are the quantification of porosity of copper thin films using

pycnometer and CMT. To determine surface roughness, contact angles are measured

using a telescope-goniometer and the Wenzel method is used for analysis.

Methodology

The new approach to determine the thin film porosity and surface roughness is

illustrated in Figure D1. The procedure to quantify the porosity is demonstrated on thin-

film of copper coated on to a copper substrate. The copper powder was coated using

state-of the –art thermal spray coating techniques [113], which provide uniform coating

thickness. The overall method involves the following steps: the quantification of open

porosity by helium pycnometry, the determination of mass deposition by weighing the

uncoated and coated samples, and the determination of film thickness non-invasively by

CMT. The average density of the film is calculated from the mass deposition of the coated

film and measured film thickness. The film porosity is calculated according to Eq.1 from

135

the measured density of the uncoated sample and the calculated film density. The contact

angles on an uncoated and coated copper substrate are measured with a telescope-

goniometer and the surface roughness is measured by applying the Wenzel model.

Figure D1. The proposed approach to determine porosity and surface roughness.

Sample Preparation

Experiments were conducted on five varieties of samples. Two kinds of thermal

spray techniques were employed, namely wire flame and plasma spray technology [113].

Two samples were prepared from each techniques. Samples from wire flame coating is

named as W1 and W2, samples prepared from plasma spray coating is named as P1 and

P2 and the uncoated sample is named as UC. Figure D2 illustrates the samples prepared

from the different thermal spray techniques.

136

Figure D2. Schematic of wire flame thermal spray coated (W1, W2), plasma

thermal spray coated (P1, P2) and uncoated (UC) samples

Copper (Cu) powder was thermally sprayed onto a 99.9% pure copper sheet of 20

mm x 20 mm and a thickness of 0.7 mm. The standoff distance between the sample and

the gun was 5 inches. The process gases were acetylene and oxygen. Two samples

were prepared using a flame spray wire gun (Metco 12E) and two samples were prepared

using a plasma thermal spray gun (Metco). One uncoated sample was also prepared

which serves as reference material to determine the bulk density.

Helium Pycnometry

Figure D3. Schematic of the helium pycnometer

The volumes of samples were calculated using helium pycnometry (Ultrapyc

1200e, Quantachrome Instruments [109]) shown schematically in Figure D3.

137

(a)

(b)

(c)

(d)

Figure D4. Schematic of sample volumes treated in a helium pycnometer with the measured sample volume shaded. a) an open pore; b) connected pores; c) an open pore and an isolated closed pore; and d) an isolated closed pore.

The method consists of placing a dry sample of known bulk volume, Vbulk, in a

sample chamber of known volume, Va, which is connected to an evacuated chamber of

known volume, Vb. Helium is introduced into Va and the pressure, P1, set to an arbitrary

value typically around 19 psi. The helium is released into Vb and allowed to equilibrate

throughout both chambers, decreasing to a new stable level (P2). Using the ideal gas law,

the volume of the sample, Vs, can be calculated from Eq. 2 [108]

138

𝑉s = 𝑉a + 𝑉b(𝑃2

𝑃2−𝑃1) (D2)

The density of the sample is determined from the sample weight and sample volume, Vs.

The pores inside the samples that are inaccessible to the helium are included in the Vs,

as schematically shown in Figure D4.

The volume of the pores that are accessible to helium gas (open pores) can be calculated

from

𝑉o = 𝑉bulk − 𝑉s (D3)

The open porosity, Po, based on the bulk volume is computed as

𝑃o =𝑉o

𝑉bulk (D4)

The bulk volume, Vbulk, of the sample is much greater than the coating volume, therefore

the Po is a small fraction. The open pore volume can also be calculated as a fraction of

the film volume, Vf. It should be noted that the copper substrate will also contain pores

because of the manufacturing process [114]. Therefore, the open pore volume of the

substrate, Vos, should be deducted. The open film porosity, Pof, based on the film volume

is computed as

𝑃of =𝑉o−𝑉os

𝑉f (D5)

To calculate the closed porosity, the mass of the deposited film, mf, is converted into film

density, film, by dividing the measured film thickness, tf (volume based on thickness and

area). mf can be calculated by measuring the coated and uncoated samples. For the

measurement of tf, computed micro tomography (CMT) is employed.

To calculate the closed porosity, the mass of the deposited film, mf, is converted into

film density, film, by dividing the measured film thickness, tf (volume based on thickness

and area). mf can be calculated by measuring the coated and uncoated samples. For the

measurement of tf, computed micro tomography (CMT) is employed.

139

Computed Micro Tomography (CMT)

Thin film thickness of coated samples was measured by CMT (VersaXRM-500,

Xradia, Zeiss, Jena, Germany). The coated sample mounted in the instrument for micro-

tomography, whose schematic is shown in Figure D5. The X-ray source energy was

140 kV, and a 4x objective with 3s exposure time and HE3 filter for single image

acquisition with 25–35% transmission. Several 2D transmission images were captured

with sample rotation of 360°. The collected 2D images were reconstructed into a 3D

tomogram in XMReconstructor software (Xradia, Zeiss, Jena, Germany) using standard

beam hardening correction with 0.7 kernal size. From the 3D tomogram, the exact

thickness of the coating is extracted from slices taken at various locations. Thickness

measurement by CMT has the advantage over SEM or other imaging techniques as the

former provides the film thickness at various locations without fracturing the sample and

changing the morphology of pores.

Figure D5. A schematic of computed micro-tomography

From the measured thickness and the mass deposition, the film density is calculated

from:

𝜌𝑓𝑖𝑙𝑚 =𝑚𝑓

𝑡𝑓 (D6)

To calculate the film porosity (total porosity), the density of the uncoated sample was

evaluated as bulk density, bulk. Consequently, the film porosity is calculated as

𝑃𝑓𝑖𝑙𝑚 = 1 −𝜌𝑓𝑖𝑙𝑚

𝜌𝑏𝑢𝑙𝑘 (D7)

140

Finally, the closed porosity is evaluated by taking the difference between film porosity

and open porosity:

𝑃𝑐 = 𝑃𝑓𝑖𝑙𝑚 − 𝑃o (D8)

Telescope-goniometer

Contact angles are measured on three varieties of samples namely W1, P1, and

UC. The telescope-goniometer consists of a flat stage to mount the sample, a micrometer

pipette to form a water drop, an illumination source, and a telescope equipped with a

protractor eyepiece. The measurement was achieved by merely aligning the tangent of

the water drop profile at the contact point with the surface and reading the protractor

through the eyepiece. An integrated camera is used to take photographs of the drop profile

so as to measure the contact angle.

Figure D6. (a) a schematic of telescope-goniometer showing a liquid

sessile drop formed on a coated surface

The surface roughness, r, is the ratio of the effective surface area due to roughness

and the projected surface area. The Wenzel relation states that r is equal to the ratio of

cosines of the contact angles of a liquid droplet on the rough surface (𝜃∗) and the contact

angle of the same liquid on and ideal, flat surface (𝜃)[67]:

cos 𝜃∗ = 𝑟𝑐𝑜𝑠𝜃 (D9)

141

Film thickness

a

b

Figure D7. Images from computed micro tomography (CMT) showing (a) 3D tomogram and (b) thickness of the coating

Figure D7 shows the images from computed micro tomography (CMT). The 3D X-

ray tomogram pictured in Figure D7a shows the 3D image of porous thin film applied on a

copper substrate, which is constructed from CMT. The sliced film of the coating in Figure

D7b indicates that the pores are present beneath the surface as well. It also suggests that

the pores are not homogenous throughout the depth of the film.

142

a

b

Figure D8. (a) a schematic showing the procedure to obtain the average thickness, and (b) orthogonal slices generated from image processing software AVIZO 9.4.0

Using XMReconstructor software of Xradia, a TXM format of 3D tomogram is

generated. This file is read in an imaging software called AVIZO 9.4.0. The orthogonal

slices are created from AVIZO as shown in Figure D8. The thickness (t) is calculated from

taking the average of m slices in x direction and n slices in y direction as depicted in Figure

D8a. The average thickness of wire flame coating is ~200-230 m, while plasma coating

is ~175-201 m thick. Table D1 shows the measured thickness, standard deviation and

percentage of error for all coated samples.

143

Table D1. Details of thickness measure from CMT

Sample name

W1 W2 P1 P2

m,n number of slices in x and y

direction m,n=4 m,n=4 m,n=4 m,n=4

t, film thickness

(m) 200 230 180 201

, standard

deviation 5.6 6.3 5.9 4.9

E, Percentage of error (%)

E=[/t]x100 2.8 2.7 3.3 2.5

Mass deposition, film density and porosity

The mass deposited on the samples was calculated from the difference in the weight

between the UC and coated samples. Based on the mass of the deposited film and the

measured thickness by CMT, the densities of the thin film samples were calculated using

the Eq.D6. To calculate the film porosity (total porosity), the density of the uncoated

sample was evaluated as bulk density, bulk. Consequently, the film porosity (Eq.D7) is:

144

Table D2. Measured parameters of all coated samples

Sample name

W1 W2 P1 P2

Substrate volume (cc)

0.295 0.295 0.295 0.295

Mass deposition (g) 0.391 0.430 0.355 0.407

Film thickness (m)

from CMT 200 230 180 201

Helium pycnometer measurements

Open pore volume of the substrate,

Vos (cc) 0.007 0.007 0.007 0.007

Sample volume, Vs (cc)

0.352 0.356 0.348 0.356

Open pore volume, Vo (cc)

0.023 0.030 0.018 0.022

Film density, 𝝆𝒇𝒊𝒍𝒎(g/cc)

5.036 4.742 5.007 4.917

Table D2 shows the measured data for all coated samples and Figure D9 shows

open porosity, closed porosity as well as film porosity (total porosity). For the sample W1,

which is coated with wire flame thermal spray method, the mass of the film deposited is

0.3971 g, and the measured thickness is 200 m (standard deviation =5.6), the density of

the film amounts to 5.04 g/cc. The film porosity is arrived by using Eq.D7 and taking

percentage value, which is 39.77%. Consequently, the open porosity and closed porosity

amounts to 19.89% and 19.88% respectively.

For the sample W2, there is 8.3% more film deposited which corresponds to 15 %

increase in the thickness of the coating. Therefore, it resulted in 10% increase in the film

porosity. The wire flame and plasma thermal spray methods produce highly porous thin

films of porosity between 39-43%.

145

Figure D9. Open porosity and closed porosity for W1, W2, P1 and P2

Surface roughness

In Table D3, the contact angles on an uncoated and coated copper substrate have

been measured with a telescope-goniometer with precision of ± 2°. The average contact

angle of water droplets on the uncoated copper was 94, while the average contact angle

on the wire flame coated surface and the plasma coated surface were 126 and 150,

respectively. The contact angles increased due the applied thin film. Therefore, the

surface roughness enhances the hydrophobicity of the uncoated surface [66,69]. For the

case of plasma coating, the surface has become super-hydrophobic [66]. By Wenzel’s

relation, the wetted surface area of the porous copper coated thin film surface is 8.5 times

and 12.4 times the wetted surface area of the uncoated surface for wire flame and plasma

spray methods, respectively.

19.9

25.2

15.4 14.4

19.9

18.6

24.8 26.6

0

5

10

15

20

25

30

35

40

45

50

W1 W2 P1 P2

Po

rosit

y [

%]

Sample name

Open porosity

Closed porosity

146

Table D3. Wetting at three random locations on the porous copper coated surface

Sample Images of the contact angle at three locations Average

contact

angle

Surface

Roughness

UC

94

W1

126 8.49

P1

150 12.41

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