







































H. Asemi et al. /Future Technology                                                                                                  May 2023| Volume 02 | Issue 02 | Pages 
01-10 

1 

 

 

 

Article 

Experimental investigation of gamma Stirling 

refrigerator to convert thermal to cooling 

energy utilizing different gases 
Hamidreza Asemi1, Sareh Daneshgar2, Rahim Zahedi3* 

1Faculty of Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran 
2Faculty of Electrical Engineering, Iran University of Science and Technology, Tehran, Iran 
3Department of Renewable energy and Environmental Engineering, University of Tehran, Tehran, Iran 

A R T I C L E   I N F O 
 

Article history: 
Received 08 September 2022  
Received in revised form 
16 October 2022 
Accepted 21 October 2022 
 
Keywords:  
Cooling, Air and Helium Gas,  
Gamma Stirling Refrigerators 
 
*Corresponding author 
Email address: rahimzahedi@ut.ac.ir 
 
 
DOI: 10.55670/fpll.futech.2.2.1 

A B S T R A C T 
 

In recent years, combined cooling, heat, and power (CCHP) systems have 
attracted increasing attention worldwide. Owing to their advantages of high 
overall thermal efficiency, fuel flexibility, low noise and vibration, and low 
emissions, Stirling engines are promising candidates for micro-CCHP systems. 
The Stirling Cycle is one of the thermodynamic cycles that is close to the Carnot 
cycle in terms of theory, and these advantages cause to use of Stirling engines 
in wide industries. The main objective of this research is an experimental 
investigation of the Stirling Gamma engine for refrigeration. In this 
investigation, the effect of working fluid air and Helium, the operating pressure 
of the working fluid, and dynamo power on refrigeration generation have been 
investigated. Results show that using air fluid with a power of 520.8 Watts and 
operating pressure of 3 bar in 10 minutes could reach to the temperature of -
23° Celsius and using Helium fluid with a power of 420 Watts and operating 
pressure of 6 bar and in 10 minutes could reach to temperature -21° Celsius. In 
the experimental implementation, it has been tried to reach lower than 10 % 
error results in various parts of the engine like insulation, leaking, belt lash, and 
measurement devices. Results show that increasing power supply, mean gas 
pressure, power supply turning on duration, and using fluids such as air and 
helium are effective in refrigeration. Also, by using helium instead of air, the 
amount of cooling output and engine output power decreases while engine 
efficiency increases. 
 

 

1. Introduction 

At Stirling motor is one of the types of heat air motors 
that, like other types of heat motors, can produce mechanical 
or electrical work by using heat exchange between heat and 
heat sinks [1]. Heat enters the engine at a warm temperature, 
part of it is converted to mechanical or electrical work, and 
the rest leaves the engine at a cooler temperature. The Stirling 
engine is simple in performance and has good torque, and if 
used in reverse can be a good alternative to refrigeration 
cycles [2]. Today, the introduction of new correlations and 
sealing materials, as well as the use of advanced software and 
computers that facilitate accurate and complex calculations, 
will accelerate the evolution of this engine. If it is not possible 
to optimize existing engines to reduce the amount of fuel and 
emissions, and noise to the international standards of 

environmental organizations, Stirling engines should 
definitely be considered [3]. 

1.1 Types of Stirling engines 
Stirling engines have been developed over the years, and 

various designs of this type of engine have been developed 
[4]. Different types of motor Stirling are known as alpha, beta, 
gamma, and free semolina. The principles of thermodynamics 
are the same for all of them, and their main difference is in the 
way the different components of the engine are placed next to 
each other. All Stirling engines have five inhibitory volumes, 
which are compression chamber, coolant, recovery, heating, 
and expansion chamber, respectively. 

1.1.1 Alpha type engine 
Alpha engines have two separate cylinders for 

compression and expansion spaces and one cylinder in each 

 

 

Future Technology 

Open Access Journal 

https://doi.org/10.55670/fpll.futech.2.2.1 

 

 

 

May 2023| Volume 02 | Issue 02 | Pages 01-10 

Journal homepage: https://fupubco.com/futech 

ISSN 2832-0379 

mailto:rahimzahedi@ut.ac.ir
https://fupubco.com/fuen
https://doi.org/10.55670/fpll.futech.2.2.1
https://fupubco.com/


H. Asemi et al. /Future Technology                                                                                                  May 2023| Volume 02 | Issue 02 | Pages 01-10 

2 

 

cylinder. The two separate cylinders are connected by a heat 
sink and a connecting pipe. The heating cylinder is placed next 
to the heat source, and the cooling cylinder is placed next to 
the heat sink. These types of engines, conceptually, have the 
simplest configuration among all types of Stirling engines. 
However, the need to seal both cylinders is one of its 
disadvantages, and the problem of heat cylinder sealing due 
to contact with the heat source is one of its technical problems 
[5]. Figure 1 shows the schematic of the alpha-type Stirling 
engine. 

 
Figure 1. Schema Alpha Type Stirling engine 

1.1.2 Beta type engine 
Figure 2 shows the beta type Stirling engine, the oldest 

building of Stirling engines. Robert Stirling's invention as the 
first Stirling engine had a beta structure. Beta engines use a 
configuration of power pump and displacement. The 
structure of the motor is such that both cylinders are placed 
in a cylinder linearly [6]. 

 
Figure 2. Schema Beta Type Stirling engine 

1.1.3 Gamma type engine 
The gamma-type Stirling engine, like the beta-type 

engine, has a moving pump configuration. In this type of 
motor, the pump and the displacement are in two separate 

cylinders. The Gamma Stirling Engine has a lower 
compression ratio than the Alpha and Beta models, but 
because only the power pump needs and it is sealed and the 
cylinders are separate [7]. It has the simplest mechanical 
arrangement among other types of Stirling engines [8]. Figure 
3 shows the scheme of the gamma-type Stirling engine. 

 

Figure 3. Schema Gamma Type Stirling engine 
 

1.2 Background 
Jahani Kaldehi et al. [9] designed a Stirling engine to 

generate electricity, heating, and cooling at the same time in a 
residential area with a different climate. The engine is alpha, 
and the system is simulated in GT Suite software. According 
to the results, the maximum efficiency is between 79 to 88% 
in different climatic conditions, and the designed system leads 
to a reduction of air pollution by reducing CO, CO2, and NOx, 
and the leakage of this system at low pressures showed a 
lower value. Prakash [10] investigated the effect of increasing 
efficiency due to the use of Stirling motor in the combined 
cycle of ironing and Stirling. The Stirling engine provides the 
required electrical load to the vehicle under test using a 
temperature difference of 75 ° C between heat and heat sinks. 
In this design, the Stirling engine rotates the car's power 
generator instead of the engine belt. In their research, 
Hushang et al. [11, 12] improved the gas transfer motors in 
the solar Stirling engine to increase efficiency and also 
improved the gas displacement variables, including the 
amplitude, state, and frequency of the Stirling motor so that 
the heat efficiency and production capacity The engine 
increases. In order to ensure the calculations of the 
mathematical model, an experiment was designed and 
performed on a gamma-type Stirling engine using a third-
order thermodynamic analysis program, during which the 
absolute fluid pressure, crankshaft angle, and velocity were 
read and recorded instantly [13]. Also, the generating power 
of the engine was measured using a generator, and the results 
of the mathematical model were compared with the 
measured values under the same test conditions and its 
performance was ensured, and the average error of the 
mathematical and experimental simulations was about 10%. 
Dai et al. [14] analyzed the Stirling engine process using 
limited-time thermodynamics and the hypothesis of uniform 
temperature distribution and investigated the effect of 
different variables and their limitations. Zia Bashar Hagh and 
Mahmoodi [15] conducted studies on beta-type Stirling 
engines and based on the obtained results, showed that by 
changing the operating gas and using Helium gas instead of 
air gas, the amount of heat output and engine output power 



H. Asemi et al. /Future Technology                                                                                                  May 2023| Volume 02 | Issue 02 | Pages 01-10 

3 

 

decreases while engine efficiency increases. Helium will be a 
good option if the heat input to the engine is high. Another 
result of this research is that the energy flow in the Stirling 
engine recovery is calculated to be approximately 5 times 
higher than that of the heater and 6 times higher than that of 
the coolant. Also, as the stroke diameter of the Stirling engine 
increases, the power decreases while the efficiency of the 
Stirling engine increases. L. Berrin et al. [16] examined the 
overall performance of the refrigerator for the Stirling pair 
heat engine and the amount of work related to the final 
cooling with respect to structural effects and variables such 
as the temperature ratio for the engine and its density. Ansari 
Nasab et al. [17] Studied the configuration of a Stirling engine 
with a molten carbonate fuel cell, a gas turbine to generate 
electricity, heating and cooling at the same time, and the 
fundamental and influential variables on the system's 
economically exergy as well as on system costs - through 
Sensitivity analysis has been reviewed, and finally, three 
strategies have been proposed to eliminate unnecessary costs 
that have improved the performance of the system. Damirchi 
et al. [18] used a gamma-type Stirling engine to generate heat 
and electricity simultaneously on a small scale, and at 
pressures of less than 1 MPa, the engine output power was 
compared experimentally by Schmidt analysis. 

Turkyilmazoglu et al. [19] presented a thermal response 
analysis of solid flammable targets at motion. In his research, 
the ignition time and heat flux are predicted regarding the 
given Peclet numbers. It was concluded that a solid flammable 
material at motion possesses less ignition time. In another 
study [20], the coupled energy equations governing the 
thermal phenomenon of particulate solids and cooling fluid 
present inside moving bed heat exchangers constructed via a 
parallel plate system is solved analytically. Results 
demonstrate how effective cooling can be achieved with a 
heat sink mounted on industrial moving bed heat exchangers. 
Katooli et al. [21] simulated and experimentally evaluated a 
Stirling refrigerator unit to convert mechanical, electrical 
energy into energy-cooling energy, and the effects of fluid 
pressure and generating power for cooling were investigated. 
Amarloo et al. [22] performed the thermodynamic analysis of 
the functional variables of the new three-cylinder structure of 
the Stirling engine and its simulation in GT Suite industrial 
analysis software. The results of the analysis showed that 
increasing the rotational speed is not suitable for increasing 
engine performance and has reduced engine efficiency. 

Modeling of gamma Stirling-based micro-CCHP systems 
using different gases as alternative fuels is required to study 
the influence of the cooling and heat temperatures on the 
system performance. Thus, an experimental analysis of 
Gamma Stirling engine that is in accordance with the intrinsic 
physical principles is essential. In this research, the 
conversion of electrical energy and mechanical energy for 
cooling has been done experimentally using a Gamma ST500-
type Stirling refrigerator and air and helium operating fluids 
at different powers and pressures. By increasing the input 
power of the motor, by changing the voltage, the current of 
the power supply, and the supply pressure of the operating 
fluid of the Stirling motor, a sub-zero degree of Celsius is 
achieved. According to the researchers, the above method is 
new and has not been done yet, and more accurate results 
have been obtained with less error and more accuracy.  

2. Methodology 

2.1 Accuracy, setup, and validation method 
The ST500 engine has been used by authors for 

validation. This program has been tested and validated in the 

past, and its results have been published in authoritative 
articles [10,11]. The Nlog program is written by MATLAB and 
is used for thermodynamic analysis of the Stirling engine. This 
program is a Stirling engine cycle analysis program that uses 
quadratic equations. This program calculates the heat output 
and output power of the Stirling engine. The number of errors 
in different parts of the engine, such as insulation, fluid 
leakage, belt looseness, and engine measuring devices, has 
reached about 10% so that the output results are as accurate 
as possible. 

2.1.1 Engine variables in the program – Nlog 
1. Geometric characteristics of all gas transmission 

channels, pipes, and expansion and compression 
chambers 

2. The geometry of connections between moving parts of 
the engine 

3. Initial engine pressure and initial temperatures 
anywhere 

4. Heat exchanger wall temperature (considered constant 
over time) 
The Nlog code divides all channels of gas transmission 

tubes in the engine into the volume of inhibitions and 
determines the dynamic and thermodynamic variables for 
each volume of inhibition by solving the equations of 
continuity, momentum, and energy. At the beginning and 
before performing various experiments, an attempt has been 
made to minimize the number of errors in different sections, 
and the output results have been studied as carefully as 
possible. 

2.1.2 Sources of error 
1. Insulation of the cooling motor 
2. The power transmission belt is not strong 
3. Heat dissipation from water transfer pipes and their 

insulation 
4. Leakage of operating fluid in the Stirling refrigerator 
5. Measuring devices errors 

Considering the power generation period and the Stirling 
engine flywheel and calculating the belt transmission ratio 
and the difference between periods, the belt error percentage 
is less than 10%, and therefore it can be said that the existing 
belt has good power transmission.  

2.2 Operating fluid 
In general, the best operating fluid is a fluid that, in 

addition to having physical transfer properties, has a strong 
heat transfer interval with a low drop due to aerodynamic 
traction. To achieve such a working fluid, the working fluid 
must have at least the following characteristics: 
1. Strong conductivity heat transfer coefficient 
2. Strong specific heat capacity 
3. Weak viscosity 
4. Weak density 
5. Strong heat transfer capability 

2.3 Mathematical Modeling 
In this paper, a dynamic, thermodynamic model that has 

been written and validated for the heating state of the Stirling 
engine in the past has been used [10]. One of the advantages 
of using a Stirling engine is the ability to reverse the work 
cycle. Therefore, it can be used to generate cooling by 
changing the program pattern.  

Also, for the validation of the cooling program, 
optimization, and production of cooling in the laboratory 
using the ST500 gamma type Stirling refrigerator, which was 
done for the first time in Iran Khodro Research and 



H. Asemi et al. /Future Technology                                                                                                  May 2023| Volume 02 | Issue 02 | Pages 01-10 

4 

 

Development Center (Ipco), the results have been analyzed 
and studied. The kinematic variables of the engine in question 
are shown in Figure 4.  

 
Figure 4. Kinematic variables ST500 

The Gamma type has been proposed for cooling 
applications in various industries, including automobile 
manufacturing. The variables φ, rc, l2, l1, d, c2, c1, and a1 to 
a3 are the structural variables of the engine and have a 
constant value. Equations (1) and (2) relate these variables to 
b1 and b2 (the vertical distance of the semicircle axis at any 
time up to the crankshaft direction) [23]. 

 l1
2 = rc

2 + b1
2 + 2rcb1 cos(θ)                                                          (1) 

 l2
2 = rc

2 + b2
2 + 2rcb1 cos(θ + φ)                                                 (2) 

By solving the previous equations for b1 and b2, they are 
expressed as functions of the crank angle shown in Equations 
(3) and (4). 

  𝑏1 = (𝑟𝑐
2 cos2 𝜃 + 𝑙1

2 − 𝑟𝑐
2)

1
2⁄ − 𝑟𝑐 cos 𝜃                                    (3) 

 𝑏2 = [
𝑟𝑐

2 cos(2𝜑+2𝜃)

2
+ 𝑙2

2 −
𝑟𝑐

2

2
]

1
2⁄

− 𝑟𝑐 cos(𝜑 + 𝜃)                     (4) 

Thus x1 (compression chamber length), x2 (heat 
chamber length), and x3 (cooling chamber length) are 
obtained in terms of the crankshaft angle shown in Equations 
(5) to (7). 

 𝑥1 = 𝑐1 − 𝑎1 − 𝑏1           (5) 
 𝑥2 = 𝑐2 − 𝑎2 −  𝑏2           (6) 
 𝑥3 = 𝑑 − 𝑎3 − 𝑥2           (7) 

Derivatives x1 and x2 with respect to the crankshaft 
angle are also shown in Equations (8) and (9). These 
equations will be used in the section on calculating dynamic 
equations. 

   
𝑑𝑥1

𝑑𝜃
=  

𝑟𝑐
2sin (2𝜃)

2(𝑙1
2−𝑟𝑐

2𝑠𝑖𝑛2𝜃)
1
2

=  𝑟𝑐sin (𝜃)                                                       (8)  

𝑑𝑥2

𝑑𝜃
=  

𝑟𝑐
2 sin(2𝜑+2𝜃)

2(
𝑟𝑐

2 cos(2𝜑+2𝜃)

2
+𝑙2

2−𝑟𝑐
2−

𝑟𝑐
2

2
)

1
2

− 𝑟𝑐 sin(𝜑 + 𝜃)                           (9) 

The first-time derivatives x1 and x2, which represent the 
velocity of the moving parts of the engine using equations 
(10) and (11), and their second derivatives, which represent 
their acceleration from equations (12) and (13) according to 
the rules of chain derivative Are calculated. 

�̇�1 =
𝑑𝑥1

𝑑𝑡
= �̇�

𝑑𝑥1

𝑑𝜃
                   (10)                 

 �̇�2 =
𝑑𝑥2

𝑑𝑡
= �̇�

𝑑𝑥2

𝑑𝜃
         (11) 

 �̈�1 =
𝑑2𝑥1

𝑑𝑡2
= �̇�

𝑑𝑥1̇

𝑑𝜃
         (12) 

 �̈�2 =
𝑑2𝑥2

𝑑𝑡2
= �̇�

𝑑𝑥2̇

𝑑𝜃
         (13) 

2.3.1 Kinetic equations of the model 
In this section, we seek to find a differential equation 

that solves the momentum and angular momentum of the 
crankshaft, and for this purpose, the Lagrange dynamic 
method is used. The general form of Lagrange equations is 
shown in Equations 14-17. The sum of the kinetic energies of 
all the moving parts of the engine will be in the variable Tθ, 
and the sum of the potential energies of the components will 
be in the variable Vθ. Lagrange is obtained by the difference of 
the total kinetic energy from the total potential energy, and 
finally, by placing Lagrange in in the principal Lagrange in 
equation (equation 17) and performing the necessary 
derivations, the dynamic differential equation of the Stirling 
engine is obtained. The torque is equivalent to the engine 
crankshaft while indicating the crankshaft angle [24]. 

 𝑇𝜃 = ∑
1

2
𝑚𝑖𝑥𝑖

2̇
𝑖=𝑛2

+ ∑
1

2
𝐽𝑖𝜃𝑖

2̇
𝑖=𝑛𝑟

                                                   (14) 

  𝑣𝜃 = ∑
1

2
𝑘𝑖𝑥𝑖

2
𝑖=𝑛𝑠

                                                                             (15) 

  𝑇𝜃 = 𝑇𝜃 − 𝑣𝜃 =
1

2
(∑ 𝑚𝑖𝑥𝑖

2̇
𝑖=𝑛1

+ ∑ 𝐽𝑖𝜃𝑖
2̇ −  ∑ 𝑘𝑖𝑥𝑖

2
𝑖=𝑛𝑠𝑖=𝑛𝑟

     

           (16) 

  
𝑑

𝑑𝑡
(

𝜕𝑙𝑒

𝜕�̇�
) − 

𝜕𝑙𝑒

𝜕𝜃
=  𝐼𝑐          (17) 

According to the number of variables considered, Lagrange in 
is obtained as an equation (18). 

 𝐿𝑒 =
1

2
𝑚1𝑥1

2̇ +
1

2
𝑚2𝑥2

2̇ +
1

2
𝐽𝑐𝜃2̇                (18) 

By substituting equations (10) and (11) in Equation (18), 
finally equation (19) is obtained. 

 𝐿𝜃 =
1

2
�̇� ⌊𝑚1 (

𝑑𝑥1

𝑑𝜃
)

2
+ 𝑚2 (

𝑑𝑥2

𝑑𝜃
)

2
+ 𝐽𝑐⌋                    (19)                      

The derivatives calculated in Equations (8) and (9) (in 
Equation 19) are placed, and Lagrange in is obtained in terms 
of crankshaft angle and crankshaft angle velocity according to 
Equation (20). 



H. Asemi et al. /Future Technology                                                                                                  May 2023| Volume 02 | Issue 02 | Pages 01-10 

5 

 

𝐿𝜃 =
1

2
�̇�{𝑚1 ⌊

𝑟𝑐
2𝑠𝑖𝑛2𝜃

√𝑙1
2−𝑟𝑐

2𝑠𝑖𝑛2𝜃
2 − 𝑟𝑐𝑠𝑖𝑛𝜃⌋

2

+

𝑚2 ⌊
𝑟𝑐

2sin (2𝜑+2𝜃)

√𝑟𝑐
2sin (2𝜑+2𝜃)

2
+𝑙2

2𝑟𝑐
2

2

2
− 𝑟𝑐sin (𝜑 + 𝜃⌋

2

+ 1}                              (20) 

Therefore, if the derivatives of the Lagrange equation are 

applied to the Lagrangin, one unit is added to the degree of the 

derivative in the equations, and the left part of the Lagrange 

equation becomes a function of the angle, velocity, and 

acceleration of the crankshaft to the form of equation (21) [25]. 

 
𝑑

𝑑𝑡
(

𝜕𝐿𝜃

𝜕�̇�
= 𝑓(�̈�, 𝜃, 𝜃)̇          (21) 

3. The Stirling engine used in this research 

In this research, the optimization process has been 

performed on the Stirling ST500 gamma-type engine 

manufactured by Ipco in Figure 5 to produce cooling. The 

technical specifications of this engine are also listed in Table 1 

[10]. 

Figure 5. Exterior view of Stirling engine 

Table 1. Stirling ST500 engine specifications 

 

 

 

 

 

 

 

 

 

 

 

 

4. Results and Discussion 

4.1 Test for Stirling refrigerator using air gas 
Figure 6 is a schematic of a Gamma Stirling engine for 

cooling production. Figure 7 shows the power generator 
connected to a power supply and used for the initial start of 
the motor. The power generator is also connected to the 
aircraft wheel using a belt. When the power supply is turned 
on, the power generator rotates. It rotates, and power is 
transmitted to the flywheel by the belt. In this case, according 
to the Stirling cycle, the heating part of the device cools down, 
and the temperature reaches below zero degrees after a few 
short minutes. Copper pipes have been used to measure the 
amount of heat transfer in the cooling section. To measure the 
amount of heat transfer, water is first pumped through a 
copper tube, and then the effluent is collected in an insulated 
chamber. By measuring the outlet water flow from the copper 
pipes as well as measuring the inlet and outlet water 
temperature of the copper pipes, the amount of heat transfer 
in the heating section of the device, according to Equation 
(22) has been obtained [26].          

 �̇� = �̇�𝑐𝑝∆𝑇          (22) 

 

Figure 6. Schematic diagram of Gamma type Stirling 

refrigerator 

 

 

Figure 7. Generator to produce power generators. 

Tables 2 and 3 show the initial conditions for the four 
different tests performed on the Stirling refrigerator to 
generate cooling using air gas. In these experiments, the air 
pressure of the operating fluid is 3 times, and the generating 
power is fixed at 200 and 430.8 watts. Experiments 1, 2, 3, and 
4 are performed for 2 to 10 minutes, and for all four tests, the 
discharge flux of the outlet water from the copper pipes is 

Technical characteristics Values (units) 

Output power 500 (watts) 

Heat efficiency 8.5% 

Standard charge pressure 8 (bar) 

Fluid factor Air, Helium 

Frequency of work 14 (Hertz) 

Coolant Water 

Movement range of the 
mandrel 

0.75 (Meter) 

Movement range of the gas 
displacer 

0.75 (Meter) 

Angle mode 90 (degrees) 

Type of heater Tube 20 (× 6 mm) 

Cooling type Tube 144 (× 13 mm square) 

Material retrieval Stainless steel 

Heat absorption 
temperature 

350 - 420 ° C 

Heat dissipation 
temperature 

30 - 50 ° C 

Maximum volume 3 - 10 × 1.79) cubic meters 

Minimum volume 1.37*10 

Compression ratio 1.3: 1 

 



H. Asemi et al. /Future Technology                                                                                                  May 2023| Volume 02 | Issue 02 | Pages 01-10 

6 

 

considered constant and equal. For a better comparison of the 
results, the input power is fixed by the power supply. 

Table 2. Different laboratory conditions for cooling 
production 

 
 

Table 3. Different laboratory conditions for cooling 
production 

 
Initially, the Stirling motor is started using a power 

supply in laboratory conditions at different power, pressure 
and temperatures. More detailed study and comparison, 
experiments have been performed for several times periods 
in different pressures, power and gases and at each stage, and 
the cooling temperature has been calculated. The voltage and 
current of the power supply were equal to 20 volts and 10 
amps, respectively, and the ambient temperature in all four 
experiments was constant and equal to 25 ° C. According to 
Figure 6, the temperature of the inlet and outlet parts of the 
copper pipes at the top and bottom (T4, T5) and the 
production cooling temperature (T1) have been measured by 
the temperature reader in Figure 8. 

The temperature sensor is connected to the temperature 
reader and using ADAM software (ADAM) has the ability to 
measure the temperatures of different parts of the test and 
finally gives us the temperatures at different times in the form 
of Excel output. The test is performed for several time 
intervals. At each stage, the internal pressure of the 
measuring device and the power and experimental efficiency 
have been calculated. Finally, with the increase of power 

generator power and fluid gas pressure, the production of the 
refrigerator and cooling work has been witnessed, and the 
temperature of T1 has reached about 7 ° C. Table 4 shows the 
initial conditions for the four different tests performed on the 
Stirling refrigerator to generate cooling using air gas. 

 
Figure 8. Temperature reader device output with Adam 
software 

Table 4. Different laboratory conditions for cooling 
production 

 

In these tests, the air pressure of the operating fluid is 3 
times, and the generating power is constantly considered to 
be 520.8 watts. Experiments 1, 2, 3, and 4 were performed for 
2 to 10 minutes. For all four tests, the discharge flux from the 
copper pipes is considered constant and equal. To better 
compare the results, the input power by the power supply 
was constant. The voltage and current of the power supply are 
equal to 31 volts, and 17 amps, respectively, and the ambient 
temperature in all four experiments is constant and equal to 
25 ° C. Heat transfer in the heating section of the Stirling 
engine, the temperature of the inlet and outlet parts of the 
copper pipes at the top and bottom (T4, T5), and the 
production cooling temperature (T1) have been measured by 
the temperature reader. The gas pressure, the temperature of 
T1 has reached about 23 ° C. In Figures 9 and 10, the cooling 
output is shown using the ST500 single gamma Stirling motor. 
Figure 10 shows the temperature-time diagram for the six 
experiments performed at pressures of 3 and 6 bar and 
different powers. As shown, when the power supply is turned 
on, the temperature of the heating part of the device 
decreases, and finally, after a certain period of time and 

Test 1              2                 3                4 

Period of source nutrition to 
be on (minutes) 

2              6                 8                10 

The medium gas pressure 3              3                3                  3 

Voltage consumption (volts) 20            20             20                20 

Electricity Consumption 
(amps) 

10             10             10               10 

Power consumption (watts) 200          200           200            200 

The initial temperature of 
cooling section (˚C) 

14              14             14              14 

The final temperature of 
cooling section (˚C) 

7,67           -2,52        -5,18        -7,11 

Fluid factor Air               Air             Air             Air 

Test 1              2                3                4 

Period of source nutrition 
to be on (minutes) 

2              6                8               10 

The medium of gas 
pressure (bar) 

3              3               3                 3 

Voltage consumption 
(volts) 

25,8      25,8          25,8           25,8 

Electricity consumption 
(amps) 

16,7       16,7         16,7            16,7 

Power consumption 
(watts) 

430,8    430,8      430,8          430,8  

The initial temperature of 
cooling section (˚C) 

17            17            17               17 

The final temperature of 
cooling section (˚C) 

6,7        -10,29      -15,85          -19 

Fluid factor Air           Air             Air              Air 

Test 1           2              3             4 
Period of source nutrition to be 
on (minutes) 

10         8              6             2 

The medium of gas pressure 
(bar) 

3           3              3              3 

Voltage consumption (volts) 31        31            31           31 
Electricity consumption (amps) 17        17            17           17 
Power consumption (watts) 520,8    520,8    520,8     520,8 
The initial temperature of 
cooling section (˚C) 

20         20           20           20 

The final temperature of cooling 
section (˚C) 

-23       -20         -13            5 

Fluid factor Air        Air           Air           Air  



H. Asemi et al. /Future Technology                                                                                                  May 2023| Volume 02 | Issue 02 | Pages 01-10 

7 

 

increasing the generating power and gas pressure, the 
temperature of the cooling part of the Stirling engine will be 
as shown in Figure 11. And the temperature of the cooling 
part of T1 has reached about -23 degrees Celsius. 

 
Figure 9. Cooling output by using Gamma Stirling 
refrigerator 

 
Figure 10. Display of the cooling output gamma Stirling 
refrigerator 

 
4.2 Test for Stirling refrigerator using helium gas 

Table 5 shows the initial conditions for four different 
experiments on the Stirling refrigerator to generate cooling 
using helium gas. In these experiments, the pressure of the 
operating fluid of the air is 3 times, and the generating power 
is constantly considered 240 watts. Experiments 1, 2, 3, and 4 
were performed over a period of 2 to 10 minutes. For all four 
tests, the discharge flux from the copper pipes is considered 
constant and equal. For a better comparison of the results, the 
input power is fixed by the power supply. The voltage and 
current of the power supply are equal to 20 volts and 12 amps, 
respectively, and the ambient temperature in all four 
experiments is constant and equal to 25 degrees Celsius. 
According to Figure 6, the temperature of the inlet and outlet 
parts of the copper pipes at the top and bottom) T4 and T5 
(and the production cooling temperature), T1 (measured by 
the temperature reader), and finally, the temperature of T1 
has reached about 10 ° C. Table 6 shows the initial conditions 
for the four different tests performed on the Stirling 

refrigerator to generate cooling using helium gas. In these 
tests, the air pressure of the operating fluid is 6 times, and the 
generating power is considered to be a constant 420 watts. 
Experiments 1, 2, 3, and 4 were performed over a period of 2 
to 10 minutes. For all four tests, the discharge flux of the outlet 
water from the copper pipes was considered constant and 
equal. In order to better compare the results, the input power 
The voltage and current of the power supply are equal to 20 
volts and 21 amps, respectively, and the ambient temperature 
in all four experiments is constant and equal to 25°C. 
According to Figure 6, the temperature of the inlet and outlet 
parts of the pipe. Copper at the top and bottom (T4 and T5) 
and the production cooling temperature (T1) are measured 
by the temperature reader, and finally, the temperature at T1 
has reached about -21 ° C. 

 
Figure 11. Temperature-time diagram for air gas tests at 
different pressures for the Stirling engine in cooling mode 

 
Table 5. Different laboratory conditions for cooling 
production 

 
 

Test 1                    2                     3                       4  

Period of source 
nutrition to be 
on (minutes) 

2                     6                     8                      10 

The medium of 
gas pressure 
(bar) 

3                    3                     3                         3 

Voltage 
consumption 
(volts) 

20                  20                  20                      20 

Electricity 
consumption 
(amps) 

12                  12                  12                       12 

Power 
consumption 
(watts) 

240                240               240                      240  

The initial 
temperature of 
cooling section 
(˚C) 

25                   25                  25                        25 

The final 
temperature of 
cooling section 
(˚C) 

10,12             -3,22            -7,77                   -9,78  

Working fluid  Helium         Helium           Helium          Helium   



H. Asemi et al. /Future Technology                                                                                                  May 2023| Volume 02 | Issue 02 | Pages 01-10 

8 

 

Also, Table 7 shows the comparison of the test results 
and numerical analysis for helium in the average 5 bar 
pressure with 300 W Stirling refrigerator power. Table 8 
shows the properties of the operating fluids used at zero 
Celsius degrees. Less viscous gases will have more output 
power under similar operating conditions.  

Table 6. Different laboratory conditions for cooling 
production 

 
 

Table 7. Comparison between the experiment and numerical 
simulations 

 
 
Table 8. Sutherland law viscosity variables for gases at 273°K 

 
Katooli et al. [21] experiment was obtained at 3 bar 

pressure and power of 441.14, 458.5 and 476 watts and was 
cooled using a gamma Stirling refrigerator and helium 
operating fluid as can be seen in Figure 12. Figure 13 shows 
the time-temperature diagram for the four performed 
experiments. As shown, when the power supply is turned on, 
the temperature of the heater section of the device decreases 
until the motor of the power supply is switched off. Finally, 
after a certain period of time, the generator power and gas 

pressure increase, the cooling temperature section of the 
Stirling refrigerator will be in the form of Figure 13, and the 
temperature of the cooling part (T1) will reach about -21 
Celsius degrees, which has been validated by the article [17], 
and with more experiments, more accurate results and 
graphs have been obtained.  

 

Figure 12. Temperature-time diagram for helium gas 
experiments [21] 

 
 

Figure 13. Temperature-time diagram for helium gas 
experiments at different pressures and Stirling refrigerator 
mode 

5. Conclusion 

In this research, a gamma Stirling motor has been set up 
to produce cooling using a power supply and using different 
gases at different powers and pressures. In order to increase 
the accuracy of ambient temperature and discharge flux, the 
output water from copper pipes is considered constant and 
equal, and to better compare the results with the research of 
others, the input power is also provided by the power supply. 
With a precise design, selecting and increasing the fluid 
pressure of the operating system of the Stirling engine and the 
power consumption of the generator will see a decrease in 
temperature on the cooling side of the Stirling engine, and it 
will become a refrigerator. Experiments have been performed 
for several time periods, and at each stage, the internal 
pressure of the measuring device and the power and 
experimental efficiency have been calculated. Finally, by 

Test 1                    2                        3                       4 

Period of source 
nutrition to be 
on (minutes) 

2                    6                        8                       10  

The medium of 
gas pressure 
(bar) 

6                    6                        6                         6 

Voltage 
consumption 
(volts) 

20                  20                     20                      20 

Electricity 
consumption 
(amps) 

21                  21                    21                      21 

Power 
consumption 
(watts) 

420                420                 420                    420
   

The initial 
temperature of 
cooling section 
(˚C) 

15                   15                    15                      15 

The final 
temperature of 
cooling section 
(˚C) 

6,23              -11,74           -17,33               -20,96 

Fluid factor Helium        Helium            Helium           Helium 

Time 
(min) 

Test temperature 
(C) 

Numerical 
temperature (C) 

Error 
(%) 

3 6.25 6.08 2.72 

6 -4.43 -4.59 3.61 

9 -10.12 -10.27 1.48 

Type of Gas Viscosity (N.s/m2) 

Air 1.716 e-5 

Argon 2.125 e-5 

Nitrogen 1.664 e-5 

Hydrogen 8.411 e-6 

Helium 1.864 e-4 



H. Asemi et al. /Future Technology                                                                                                  May 2023| Volume 02 | Issue 02 | Pages 01-10 

9 

 

using a new structure and connecting a gamma-type Stirling 
engine with a power supply and by increasing the engine 
speed and inlet power, the outlet temperature in the cooling 
part of the engine is reduced. The results of ST-500 Stirling 
refrigerator tests have been compared with the experimental 
results of other authorities, which have good compatibility, 
and more accurate results have been obtained. Heavier gases 
can also be used in Stirling refrigerators, but these gases are 
less efficient than lighter gases such as helium and hydrogen 
due to their properties. Hydrogen gas, due to its stronger heat 
capacity and less viscosity than helium gas, has higher output 
power, lower estimation error, and higher heat efficiency 
under similar operating conditions, and air can be used in 
smaller model engines. Theoretically, the use of a light gas 
such as hydrogen, air, or helium as the operating fluid is 
recommended due to its low viscosity, strong heat transfer 
coefficient, poor viscosity coefficient, low leakage potential, 
and lack of oxidizing properties. Although low molecular 
weight means an increase in the rate of fluid leakage from the 
engine, resulting in a drop in pressure, reduced efficiency, and 
increased costs (fluid refilling), the heat temperature of the 
heat exchanger can cause oxidation and corrosion of the 
components. It should be noted that one of the most effective 
factors in efficiency is the temperature of the heat source. In 
addition, increasing the input power of the power supply, 
increasing the initial supply pressure of the motor, and 
selecting the appropriate fluid will increase more cooling 
output in the heat sink of the Stirling refrigerator. In this 
research, the experiments with the Stirling Gamma engine for 
the generation refrigeration effect are performed. The result 
shows that air fluid with a power of 520.8 W at an operating 
pressure of 3 bar in 10 minutes could reach to temperature - 
23°C and Helium fluid using a power of 420 W at an operating 
pressure of 6 bar in 10 minutes could reach to temperature -
21°C. During experimental implementation, less than 10 
percent error is accomplished, resulting from various parts of 
the engine like insulation, leaking, belt lash and measurement 
devise. The results of this research can be used to produce 
cooling energy in various industries. 

Ethical issue 
The authors are aware of and comply with best practices 

in publication ethics, specifically with regard to authorship 
(avoidance of guest authorship), dual submission, 
manipulation of figures, competing interests, and compliance 
with policies on research ethics. The authors adhere to 
publication requirements that the submitted work is original 
and has not been published elsewhere. 

Data availability statement 
Datasets analyzed during the current study are available 

and can be given following a reasonable request from the 

corresponding author. 

Conflict of interest 

The authors declare no potential conflict of interest. 

List of Abbreviations and Symptoms Greek 

a1: Distance between the shaft axis and the surface of the 

shaft, m 

a2: Distance between the shaft axis and the displacement 

surface, m 

a3: Displacement height, m 

b1: Distance between the crankshaft and the crankshaft axis, 

m 

b2: The distance between the displacement shaft axis and the 

crankshaft axis is, m 

c1: Distance between the crankshaft and the crankshaft axis, 

m 

c2: The distance between the displacement bed and the 

crankshaft axis is, m 

l1: The length of the handle handle, m 

l2: Length of gas displacement pump handle, m 

L:  The length of the handle handle, m 

rc: Crankshaft radius, m 

Lθ: Lagrange in variable 

J: Number of network inputs 

Jc: Wheel rotational torque, m2kg 

X: Inhibition volume length, - m 

m: Mass of parts with reciprocating motion, kg 

θ: Angle of inclination, Radian 

θ: Crankshaft rotational speed, Radian /s 

θ-: Crankshaft rotational acceleration, Radian /s2 

Φ: Mode of movement of gas and displacement of gas, R 

References 

[1] Ghodrati, A., R. Zahedi, and A. Ahmadi, Analysis of cold 

thermal energy storage using phase change materials 

in freezers. Journal of Energy Storage, 2022. 51: p. 

104433. 

[2] Chen, W.-L., K.-L. Wong, and H.-E. Chen, An 

experimental study on the performance of the moving 

regenerator for a γ-type twin power piston Stirling 

engine. Energy conversion and management, 2014. 77: 

p. 118-128. 

[3] Zahedi, R., S. Daneshgar, and S. Golivari, Simulation and 

optimization of electricity generation by waste to 

energy unit in Tehran. Sustainable Energy 

Technologies and Assessments, 2022. 53: p. 102338. 

[4] Gheith, R., et al., Stirling engines. 2018, Elsevier. 

https://doi.org/10.1016/j.apenergy.2020.115123 

[5] Urieli, I. and D.M. Berchowitz, Stirling cycle engine 

analysis. 1984. 

https://www.osti.gov/etdeweb/biblio/6068495 

[6] Kongtragool, B. and S. Wongwises, A review of solar-

powered Stirling engines and low temperature 

differential Stirling engines. Renewable and 

Sustainable energy reviews, 2003. 7(2): p. 131-154. 

[7] Zahedi, R., et al., Development of a New Simulation 

Model for the Reservoir Hydropower Generation. 

Water Resources Management, 2022: p. 1-16. 

[8] Walker, G., Stirling-cycle machines. Oxford, Clarendon 

Press, 1973. 

[9] Kaldehi, B.J., et al., Designing a micro Stirling engine for 

cleaner production of combined cooling heating and 

power in residential sector of different climates. 

Journal of Cleaner Production, 2017. 154: p. 502-516. 

[10] Prakash, S. and A. Guruvayurappan. Using stirling 

engine to increase the efficiency of an IC engine. in The 

World Congress on Engineering 2011. 2011. London, 

UK. 

[11] Hooshang, M., R.A. Moghadam, and S. AlizadehNia, 

Dynamic response simulation and experiment for 

gamma-type Stirling engine. Renewable energy, 2016. 

86: p. 192-205. 



H. Asemi et al. /Future Technology                                                                                                  May 2023| Volume 02 | Issue 02 | Pages 01-10 

10 

 

[12] Hooshang, M., et al., Optimization of Stirling engine 

design parameters using neural networks. Renewable 

Energy, 2015. 74: p. 855-866. 

[13] Zahedi, R. and A.B. Rad, Numerical and experimental 

simulation of gas-liquid two-phase flow in 90-degree 

elbow. Alexandria Engineering Journal, 2021. 

[14] Dai, D., et al., Imperfect regeneration analysis of 

Stirling engine caused by temperature differences in 

regenerator. Energy Conversion and Management, 

2018. 158: p. 60-69. 

[15 Mahmoodi, M. and M. Ziabasharhagh, Numerical 

solution of beta-type Stirling engine by optimizing heat 

regenerator for increasing output power and 

efficiency. J Basic Appl Sci Res, 2012. 2: p. 1395-1406. 

[16] Erbay, L.B., M.M. Ozturk, and B. Doğan, Overall 

performance of the duplex Stirling refrigerator. Energy 

Conversion and Management, 2017. 133: p. 196-203. 

[17] Ansarinasab, H. and M. Mehrpooya, Investigation of a 

combined molten carbonate fuel cell, gas turbine and 

stirling engine combined cooling heating and power 

(CCHP) process by exergy cost sensitivity analysis. 

Energy conversion and management, 2018. 165: p. 

291-303. 

[18] Damirchi, H., et al., Micro combined heat and power to 

provide heat and electrical power using biomass and 

Gamma-type Stirling engine. Applied Thermal 

Engineering, 2016. 103: p. 1460-1469. 

[19] Turkyilmazoglu, M., Combustion of a solid fuel material 

at motion. Energy, 2020. 203: p. 117837. 

[20] Turkyilmazoglu, M., Cooling of particulate solids and 

fluid in a moving bed heat exchanger. Journal of Heat 

Transfer, 2019. 141(11). 

[21] Katooli, M.H., R.A. Moghadam, and A. Hajinezhad, 

Simulation and experimental evaluation of Stirling 

refrigerator for converting electrical/mechanical 

energy to cold energy. Energy conversion and 

management, 2019. 184: p. 83-90. 

[22] Amarloo, A., et al., Thermodynamic analysis of 

performance parameter of a novel 3 cylinder Stirling 

engine configuration. Modares Mechanical 

Engineering, 2017. 16(10): p. 448-458. 

[23] Daneshgar, S. and R. Zahedi, Optimization of power 

and heat dual generation cycle of gas microturbines 

through economic, exergy and environmental analysis 

by bee algorithm. Energy Reports, 2022. 8: p. 1388-

1396. 

[24] Beni, H.M. and H. Mortazavi, Mathematical modeling of 

the solar regenerative heat exchanger under turbulent 

oscillating flow: Applications of renewable and 

sustainable energy and artificial heart. Results in 

Engineering, 2021: p. 100321. 

[25] Lv, C., et al., Multivariable control of regeneratively-

cooled scramjet engine with two-stage kerosene 

injection based on H∞ method. Results in Engineering, 

2020. 7: p. 100161. 

[26] Zahedi, R. and S. Daneshgar, Exergy analysis and 

optimization of Rankine power and ejector 

refrigeration combined cycle. Energy, 2022. 240: p. 

122819. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 This article is an open-access article 

distributed under the terms and conditions of the Creative 

Commons Attribution (CC BY) license 

(https://creativecommons.org/licenses/by/4.0/). 


