EMD 442 System DesignProposal

Four Power Piston HTD Gamma Stirling Engine

Group 3Name Matric no.

Yiauw Diing Shenq 111585

Muhamad Khairil Hafizi Bin Mohd Zorkipli 111549

Mohammad Fareez Bin Jaaffar 113606

Mohammad Nizar Bin Mohamed Zukri 111544

Lee Jin Liang 113605

School of Mechanical EngineeringLecturer: Dr. Mohamad Yusof Idroas

Date of Submission: 10th October 2014

Table of Contents

1.0 Problem Description...........................................................................................................1

2.0 Introduction.........................................................................................................................1

3.0 Objective..............................................................................................................................8

4.0 Design Methodology...........................................................................................................8

4.1 Heat Source.......................................................................................................................8

4.2 Displacer Cylinder............................................................................................................8

4.3 Power Piston Cylinder....................................................................................................10

4.4 Flywheel.........................................................................................................................10

4.5 Cooler.............................................................................................................................11

4.6 Heat Regenerator............................................................................................................12

4.7 Polyphase Generator.......................................................................................................14

4.8 Working Fluid.................................................................................................................15

5.0 Appendix............................................................................................................................17

6.0 References..........................................................................................................................19

1.0 Problem Description

The Stirling engine has attracted much attention over the years. Its potential for high

efficiency and the ability to use a wide variety of fuels has made it a serious contender for

alternative power sources, especially in automotive applications. The potential for Stirling

engines to replace the Internal Combustion Engine (ICE) in automobiles was explored in the

late 1970’s and 1980’s.

Kongtragool and Wongwises [1] built and presented the performance of a four

power-piston, gamma-configuration, low-temperature differential Stirling engine. Fig. 1

shows the schematics of the engine built by them. With an energy input of 1378 W and heater

temperature of 439 K, the engine produced a torque of 2.91 N m, 6.1 W maximum shaft

power, and a maximum brake efficiency of 0.44 % at 20 rpm. The four power-piston Stirling

engine gave rise to a question: Will more power piston give more power output and higher

efficiency?

In this project, we will investigate the correlation between number of power piston

and Stirling engine efficiency, the feasibility of four-power-piston configuration on High

Temperature Difference (HTD) Stirling engine, the engine layout, components design, and

components interaction to produce an electric output power of 1 kW. Calculations, graphs and

simulations using computer softwares will be used to verify and validate the proposed Stirling

engine system design.

2.0 Introduction

The Stirling engine were invented in 1816 by Robert Stirling [2] in Scotland, some 80

years ago before the invention of diesel engine. A Stirling cycle machine is a device, which

operates on a closed regenerative thermodynamic cycle, with cyclic compression and

expansion of the working fluid at different temperature levels. The flow is controlled by

volume changes so that there is a net conversion of heat to work or vice versa. In the

beginning of 19th century, due to the rapid development of internal combustion engines and

electrical machine, further development of Stirling engines was severely hampered.

High heat efficiency, low noise operation and ability of Stirling engines to use many

fuels meet the demand of the effective use of energy and environmental security [3]. Stirling

engine-based units are considered best among the most effective low-power range solar

thermal conversion units [4]. In 1980, with fuel crises, Stirling engines become a viable

proposition with rapid advances in material technology. This was the second stage of

transformation for the Stirling engines.

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Kontragool and Wongwises [5] theoretically investigated the power output of a

gamma-configuration Low Temperature Difference (LTD) Stirling engine. Former works on

Stirling engine power output calculations were studied and discussed. They pointed out that

the mean-pressure power formula was the most appropriate for LTD Stirling engine power

output estimation. However, the hot-space and cold-space working fluid temperatures were

needed in the mean-pressure power formula.

Fig. 1 Four power-piston, gamma-configuration, low-temperature differential Stirling engine

schematics by Kontragool and Wongwises

Franco Normani [6] made a computer simulator based on FORTRAN language to

estimate the power output and efficiency of alpha, beta and gamma type Stirling engines. He

pointed out some design considerations in designing the heater, cooler, heat regenerator,

displacer cylinder, power piston cylinder, working fluid, and flywheel of Stirling engines.

Some calculations and optimised values for various parameters were presented in his work

based on the experimental work of previous researchers.

D. G. Thombare and S.K. Verma [7] presented the thermodynamics of Stirling engine

cycle. Fig. 2 shows the Stirling cycle. The work output of a Stirling cycle is defined by the

area of the cycle in the PV diagram.

2

(a) PV and TS diagram for Stirling engine

(b) Engine arrangement and piston

(c) Time displacement diagram

Fig. 2 The Stirling cycle

The efficiency of a Stirling cycle can be written as

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ηt=mRT 3 ln (rv )−mRT 1 ln ( rv )

mRT 3 ln (rv )

ηt=1−T 1

T 3=1−

T min

Tmax=1−τ

D. G. Thombare and S.K. Verma [7] also presented the isothermal analysis of Stirling engine,

which is modelled by Urieli, Berchowitz consisting of compression space c, cooler k,

regenerator r, heater h, and expansion space e as shown in Fig. 3. The analysis assumed that

the total mass of working gas in the machine is constant.

Fig. 3 Ideal isothermal model

Where the work done by the engine over a complete cycle is the algebraic sum of the work

done by compression and expansion spaces.

W =W c+W e

W =∮ pd V c+∮ p d V e

W =∮ p ( d V c

dϕ+

d V e

dϕ )dϕ

Where ϕ is the crank angle.

After 55 years of Stirling cycle engine invention, Schmidt [8] made an analysis of the

engine cycle in 1871 called as classical analysis. The analysis was made for three types of

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practical Stirling engine configuration wise alpha, beta and gamma. Schmidt obtained close

theory, which provides sinusoidal volume variation of working space in the reciprocating

engines. The engine configurations considered for classical analysis of operation of Stirling

engine are shown in Figs 4-7.

Fig. 4 Alpha configuration

Fig. 5 Piston-displacer type – beta configuration

Fig. 6 Piston-displacer in separate cylinder – gamma configuration

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Fig. 7 Schmidt’s analysis of a gamma-type Stirling engine

However in Schmidt’s theory, there are some principal assumptions in the analysis of Stirling

cycle engines:

1. All processes are reversible.

2. The regeneration process is perfect.

3. The working fluid obeys perfect gas law, pV=mRT .

4. The mass of air in the system remains constant, no leakage in the system.

5. The volume variation in the working space is sinusoidal.

6. There is no temperature gradient in the heat exchanger.

7. The cylinder wall and piston temperature are constant.

8. The speed of the machine is constant.

9. Steady state conditions are established.

10. There are no flow losses and hence no spatial pressure loss.

11. No leakage of working gas.

12. The temperature in heater and expansion space is isothermal at T E.

13. The temperature in cooler and compression space is isothermal at T C.

14. The temperature in the dead space and hence in regenerator space is isothermal.

William Beale [9] presented that in practice the maximum power output of well-

developed engine is roughly proportional to pressure, volume and speed. The Beale number is

BN=P i

PM V se N

However, one important factor that is not taken in to account by Beale correlation is the

temperature at which the engine is operated. Iwamoto [10] shows that Beale number is about

0.15 in case of high temperature differential Stirling engine whose heater wall temperature is

about 650 ° C. The effect of temperature is later considered by West, which the number is

defined as

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W S=Pi

PM V SC N (T E−T C

T E+TC)

The West number is about 0.25 in case of 5-150 kW Stirling engines and is about 0.35 in case

of smaller power engines.

This proposal will present the design methodology to design a four-power-piston,

gamma configuration, high temperature difference Stirling engine which can produce 1 kW of

electrical power output. The proposed system will consist of the design of the heat source,

displacer cylinder, power piston cylinder, flywheel, cooler, heat regenerator, polyphase

electric generator, and the working fluid to fulfil the required specifications. Calculations and

analysis of the Stirling cycle engine will be made based on Schmidt’s analysis, as provided in

the Appendix section. The expected outcome from the design will be the Beale and West

numbers, along with calculations to support the concept of a 1 kW Stirling engine.

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3.0 Objective

The objective of this project is to design a system which will be powered using a

four-power-piston, gamma-configuration, HTD Stirling engine to produce 1 kW of electrical

power output.

4.0 Design Methodology

4.1 Heat Source

4.1.1 Introduction

External heat is needed by the Stirling engine to generate electrical power. External

combustion is the example of the external heat supply to the engine. The biomass is needed in

the combustion to supply heat to the engine. The heat conductive mechanism needed in the

heat supply system.

4.1.2 Methodology

The group have done some research on designing the heat combustion chamber and

the heat sources which are the biomass. The sites and journals on the design the heat

combustion chamber and the heat sources have been gone through. For this design, the group

will use biomass as external burning fuels to generate heat for the Stirling engine. There are 2

main parameters that need to consider in designing the heat transfer system which are the

external combustion chamber and the mechanism of inner tube to transfer the heat to the roof.

There also have to include the heat transfer coefficient and the friction factor.

The group will find some example of the biomass that can be used in this project. The

biomass examples are rise husks, bagasse, rice straw, wood and coconut shell. The mass

needed to generate more than 1 kW electricity, the mass flow rate to maintain the temperature

and heat supply during the combustion process will be calculated. For the combustion

chamber, material that has high melting point and can stand the high temperature will be used.

The suggested material for the chamber is titanium aluminides.

4.2 Displacer Cylinder

4.2.1 Introduction

The displacer is used to displace, or move the working fluid in the Stirling engine

between the heater and cooler to enable the working fluid to absorb heat from the heater side,

and release heat to the cooler side. The displacer is required to allow the compression and

expansion process to occur in the engine, and thus to give power to the power piston.

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4.2.2 Methodology

The annular gap between the displacer and cylinder wall is typically sealed, using

seals on the cold end (compression space side). This will help reduce pumping losses

resulting from working fluid “squeezing” through the gap.

The difference between the cylinder internal diameter and displacer outer diameter

will be less than 1mm. The annular gap must be small to minimize dead volume. In addition

the gap must be long enough to allow the hot working fluid from the expansion space to cool

sufficiently by the time it reaches the seal. This is important as seals generally cannot

withstand high temperature. Franco Normani [6] suggested that the displacer length should be

about 1.5 times the diameter.

However having a long gap will result in a loss in thermal efficiency of the engine.

This is due to the heat loss that occurs when hot gas flows into the gap and loses heat to the

colder displacer and cylinder wall. Thus, a metal ring, or also called a “hot ring” will be

added around the displacer at the hot end. This helps prevent hot working gas from flowing

into the gap during the displacer motion. The ring will be made of a wear resistant alloy

which will be able to operate well without lubrication at high temperatures. Fig. 8 shows the

cross sectional view of the proposed displacer cylinder.

Fig. 8 Cross sectional view of the proposed displacer cylinder

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4.3 Power Piston Cylinder

4.3.1 Introduction

The power piston is the power producer for the engine, where it is connected in 90°

difference in phase angle with respect to the displacer rod on the flywheel. The compressed

working fluid from the displacer creates a pressure on the power piston, which creates a force

on the piston and piston rod. The force is the transmitted to the flywheel of the Stirling engine

to turn the flywheel, thus producing power with similar concept as the power stroke of an

internal combustion engine.

4.3.2 Methodology

In theory, the larger the power piston (hence the larger the swept volume), the more

power will be generated by the Stirling engine. However in practical cases, it is not true due

to the following reasons.

First, there will be more friction with the larger piston or longer stroke. As the

Stirling engine revs up, the effect of friction becomes more significant, and this may lead to a

lower net power as we plot the power curve for the engine.

Second, the higher the compression, the more likely the engine will experience power

loss due to gas leaks past the piston. Gas leaks past the piston reduce the pressure ratio and

will reduce engine power even at low compression. The losses become greater as the

compression increases.

Therefore, the four power pistons will be designed to maximize power output while

keeping the surface area in contact between the pistons and the cylinder wall at minimum.

Also, oil sealing will be used to prevent the working fluid from escaping the piston cylinder,

thus reducing gas leaks and enhancing engine efficiency.

4.4 Flywheel

4.4.1 Introduction

Selecting a flywheel of suitable size and mass is an important aspect of the design of

Stirling engines. It has to be “heavy” enough to absorb energy from the engine during the

power stroke (without speeding up too much) and then use that energy to “push” through the

compression stroke (without slowing down too much). A proper flywheel will minimize

fluctuations in rotational speed. This is necessary to ensure “smooth” engine operation. If the

flywheel is not heavy enough the engine rotation will be “jerky” and engine performance will

be poor.

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4.4.2 Methodology

The goal is the design a flywheel that is heavy enough to do the job but is not too big

and heavy. The “heaviness” of a flywheel is referring to its rotational inertia about its center

of rotation. Therefore, the flywheel needs to have high rotational inertia while keeping the

mass as low as possible. This will be accomplished by using a flywheel with a solid outer rim,

in which most of the mass will be concentrated around the outside. Fig. 9 shows the basic

flywheel design for Stirling engines.

Fig. 9 Basic flywheel design for Stirling engines

Mathematically, the rotational inertia of the flywheel is given by:

I=m r2

Where m is the mass of the outer rim. So from the equation, to achieve a light-weight

flywheel, the flywheel will have a large radius with 90% of its total mass in the outer rim, and

only 10% of its mass in the inside hub for support.

4.5 Cooler

4.5.1 Introduction

Cooler part is essential part in Stirling engines to provides a sufficiently low temperature

consistently and remove heat from the system to keep the cycle running. To obtain the highest

temperature difference, cooler is designed as external system [12]. There is elevation on the

temperature so that the thermal efficiency is should be considered. Hence, the coolant’s

temperature need to be designed as minimum as possible beside to obtain the high

temperature difference [13]. The flow condition is similar as a heater but at the lower

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temperature. The main concept is heat exchanger. To cool down the fluid in cooler part,

coolant (air, water and etc.) passing through the compression space where it is absorbs heat.

Heat is removed in one medium and transferred to another medium [8]. By the previous

researcher, it was found that in purpose to design 1kw Stirling gamma type engine, the

temperature difference is 590 °C whereas the working fluid at heater part around 650 °C and

working fluid in cooler part is around 60 °C [14].

4.5.2 Methodology

1. Study on heat exchanger and heat transfer;

2. Design flow process of cooler (coolant absorb heat > inlet of radiator tank > heat

distribute to core (copper-fins and brass-tube) > coolant go to another tank (cool

again) > coolant fed back (cycle repeat));

3. Equipment: tube, tank, water (coolant), core and fan (convection mechanism), and

water pump;

4. Analyze heat that is absorbed by coolant (water), total heat transfer coefficient

(parameter: water thermal conductivity, diameter of tube and etc.);

5. Summarize and get the temperature difference.

4.6 Heat Regenerator

4.6.1 Introduction

A regenerator is typically made of a dense matrix consisting of stacked metal screens,

or metal felt, woven from fine wires. This provides the high heat transfer capability needed to

“store” and “release” heat. It separates both sources of heat and operate as a thermal sponge

which accepts and rejects heat from the working fluid. The way the regenerator works is by

storing some of the heat energy of the working gas as it moves from the heater to the cooler.

From the studies, Stirling engine efficiency and heat input are affected by both regenerator

effectiveness and dead volumes.

Fig. 4: Example of regenerator design that commonly used in Stirling engine.

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From Fig. 4, it shows void volume and regenerator matrix. These two parameters are

very important in determined the efficiency of the Stirling engine. The “regenerator void

volume is simply the volume of empty space inside the regenerator housing. This is the space

is not “filled” with matrix material. Regenerator matrix is choose from material that have high

thermal conductivity which mean the materials can absorbs heat as much as possible.

Besides, there are also tubes inside the regenerator housing. The purpose of these

tubes is to transfer the working fluids. The main benefits using a large number of tubes is that

it “splits” up the flow and reduces pumping (flow) losses.

4.6.2 Methodology

The group has done some researches on designing of the regenerator for Stirling

engine. Many journals that are related to regenerator were found at directscience.com website.

Based on the studies, regenerator is a must component in the Stirling engine, since the

working principle of this engine operates from the external burning of fuels.

First of all, to design regenerator the components or parameters inside the regenerator

housing must be known. There are basically 4 main parameters we need to consider in

designing a good regenerator named as void volume, number of tube, matrix material and

regenerator housing.

Regenerator are linked between cooler and heater. Most of the formula used in

finding values are related to the heater and cooler. Calculations for energy and work done that

have regenerator void volume and imperfect regeneration considered are the most practical

way in designing this part. By finding energy and work done at each transition we can find

the efficiency of the engine.

Fig. 5: Thermodynamics cycles for Stirling engine

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From researches, the efficiency of the Stirling engine is between 32.9% and 33.2%.

The group will try to design regenerator that can increase the efficiency or exactly the same as

stated in most journals. By knowing the efficiency, the next step we can calculate the size or

dimension of the housing regenerator and void volume that are related to some of the work

done and energy formula. A spreadsheet calculator is created for regenerator to achieve our

target values to get the highest efficiency. Among the parameters that need to be changed in

order to achieve highest efficiency possible is void volume, regenerator housing, volume of

matrix materials and number of tubes.

The group also takes account the type of materials that will be used for matrix.

Stainless steel is the most common material used for matrix material due to its high heat

capacity and thermal exchange rate. The most suitable materials that have high thermal

conductivity will be used. The higher the thermal conductivity of the material the more heat

can be transferred per second. The regenerator housing will be insulated with low thermal

conductivity materials so that heat cannot escape to surrounding. Nickel-copper alloy is one

the materials that will be taken into considerations for matrix material because of its good

material properties.

4.7 Polyphase Generator

4.7.1 Introduction

Based on the study on a website [14], the working principle of a polyphase motor is

being reversed to become a polyphase generator to generate electrical energy from

mechanical energy by rotating permanent magnet rotor. In the documentation, there are a lot

of details information about the phase coil connections, phase arrangements and mechanical-

to-electrical energy conversion, which include all associated calculations for the critical

parameters and conflicting factors in determining the most appropriate specifications and

structure design of polyphase generator with optimum performance in conjunction with the

gamma Stirling engine system design.

Reverse motor requires a commutator and brushes in order periodically to reverse the

current through each armature coil. However, the brushes have to be periodically changed and

the commutator resurfaced due to wear as a consequence of the sliding contacts between the

brushes and commutator. To avoid such problem brushless permanent magnet generator is

preferred. With the brushless permanent magnet generator, the current-carrying inductive

coils are fixed and the permanent magnet rotor rotates.

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A generator is basically a device that converts mechanical energy to electrical energy.

Polyphase generator allows us to decide the number of phases required, number of poles of

permanent magnet needed and the associated number of coils as well based on the specific

ratio of mechanical-to-electrical energy conversion.

Besides, phase arrangements also play an important role in the performance of a

polyphase generator. There are multiple ways to arrange the wiring of a polyphase generator,

but mostly based on two basic configurations, the delta and Y circuit arrangements. What

mainly differentiates delta and Y system is the connection of their phase coil groups to obtain

the optimum power and efficiency with minimal self-interference which will be discussed in

details after further verifications on the performance parameters involved.

4.7.2 Methodology

There are some conflicting factors that we have to trade off when choosing the most

appropriate phase arrangement for the generator to achieve desired performance. Before that,

we need to consider our design constraints and the ultimate goal of the overall design system,

such as the ways that the design constraints the performance’s parameters and followed by

optimization of the critical parameters and also investigation of the key risk variables when

the polyphase generator is work together with the gamma Stirling engine.

Polyphase generator is basically an AC generator, but most of the electrical devices

are powered by DC source. We will also look into the AC to DC conversion in order to

achieve 1kW effective power. Furthermore, we will try to map the design outcome with the

generators available in the market for comparison and as a reference for more reliable design

of the polyphase generator in order to complete the gamma Stirling engine system for more

practical applications.

4.8 Working Fluid

4.8.1 Introduction

Any working fluid with high specific heat capacity may be used for Stirling cycle

engine. With few exceptions the engines in 19th century used air as working fluid. Most of

them operated close to atmospheric temperature. The working fluid in a Stirling engine

should have flowing thermodynamic, heat transfer and gas dynamic properties:

1. High thermal conductivity

2. High specific heat capacity

3. Low viscosity

4. Low density

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However, for a better system performance in addition to above, ease of availability,

cost, safe operation, storage requirements are also important properties. The capability of

working fluid in terms of specific heat capacity, thermal conductivity and density is defined

by Martini [15] and Clarke [16] which is useful for preliminary selection of working fluid.

Capability factor= Thermal conductivitySpecific heat capacity × Density

4.8.2 Methodology

In Table 1 [7], various fluids are compared using capability factor as mentioned above.

Table 2 [7] shows the specific heat and specific heat ratios of various working fluid. From

both tables, it can be seen that Sodium-Potassium (NaK) eutectic has 32 times the heat

transfer capability than air, also with the highest capability factor. Therefore, NaK eutectic

will be chosen as the working fluid for the Stirling engine to be designed.

Table 1 Relative heat transfer characteristics for various gases

Table 2 Relative performance of selected working fluid

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5.0 Appendix

Calculation Model of a Gamma-type Stirling Engine

Expansion momental volume:

V E=V SE

2(1−cos x )+V DE

Compression momental volume:

V c=V SE

2(1+cos x )+

V SC

2{1−cos (x−dx )}+V DC

Total momental volume:

V=V E+V R+V C

Engine pressure:

P=Pmin √1−c2

1−c .cos( x−a)=

Pmin (1+c )1−c .cos (x−a )

=Pmin (1−c )

1−c . cos ( x−a )

Temperature ratio:

t=Tc

T E

Swept volume ratio:

v=V SC

V SE

Dead volume ratio (Expansion):

X DE=V DE

V SE

Dead volume ratio (Compression):

X DC=V DC

V SE

Volume ratio (Regeneration):

X R=V R

V SE

Coefficients:

a= tan−1 v sin dxt+cosdx−1

S= t+2 t X DE+4 t V R

1+ t+v+2 X DC+1

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B=√t 2+2 (t−1 ) v cosdx+v2−2 t+1

c= BS

Indicated Energy, Power and Efficiency

Indicated expansion energy:

W E=Pmax V SE πc . sin a

1+√1−c2. √1−c√1+c

Indicated compression energy:

W c=Pmax V SE πct . sin a

1+√1−c2. √1−c√1+c

Indicated energy per cycle of the engine:

W i=W e+W c=Pmax V SE πc (1−t)sin a

1+√1−c2. √1−c√1+c

Relations between Pmean, Pmin and Pmax:

Pmin

Pmean=√ 1−c

1+c

Pmax

Pmean=√ 1+c

1−c

Indicated expansion power:

LE=W E n

Indicated compression power:

LC=W C n

Indicated power of the engine:

Li=W i n

Efficiency of the engine:

e=W i

W E=1−t

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6.0 References

1. Kongtragool, B., Wongwises, S., 2007b. Performance of a twin power piston low

temperature differential Stirling engine powered by a solar simulator. Solar Energy

81, 884–895.

2. Robert Stirling, Patent no. 4081, Stirling air engine and the heat regenerator, 1816.

3. Pertescu S, Coastea M, Harman C, Florea T. Application of the direct method to

irreversible Stirling cycle with finite speed. Energy Convers Conserv Environ Impact

2002:589–609.

4. Mancini T, Heller P. Dish Stirling systems: an overview of development and status.

Trans ASME 2003;125:135–51.

5. Shoureshi R, Paynter HM. Low temperature Stirling engine for waste heat recovery.

Seventeenth intersociety energy conversion engineering conference, vol. 829284;

1982. p. 1716–20.

6. Normani, F., 2013. Stirling Engine Manual.

7. D.G. Thombarea, S.K. Vermab 2006, Technological development in the Stirling

cycle engines, Renewable & Sustainable Energy Reviews, Rajarambapu Institute of

Technology and Dr. Babasabeb Ambedkar Technological University.

8. Schmidt G. Classical analysis of operation of Stirling engine. A report published in

German Engineering Union (Original German), vol. XV; 1871. p. 1–12.

9. Beale WT, Wood JG, Chagnot BF. Stirling engine for developing countries.

American Institute of Aeronautics and Astronautics 1980;809399:1971–5.

10. Iwamoto S, Hirata K, Toda F. Performance of Stirling engines. JSME Int J

2001;44(1):140–7.

11. WORCESTER POLYTECHNIC INSTITUTE, Design of stirling engine for

electricity generation;

12. Main article: Radiator (cooler), Wikipedia.

13. Luca RAGGI, Masafumi KATSUTA, DESIGN OF A 1 KW CLASS GAMMA

TYPE STIRLING ENGINE.

14. Web link: https://web.stanford.edu/~hydrobay/lookat/pmg.html

15. Martini WR. Stirling engine design manual. Martini Engineering Publication.

16. Clarke MA, Reader GT, Taylor DR. Experiences in the commissioning of a prototype

20kW helium charged Stirling engine. Seventeenth intersociety energy conversion

engineering conference, vol. 829298; 1982. p. 1796–1800.

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