Thermodynamic modeling and performance assessment of a domestic refrigeration system using selected hydrocarbon refrigerants with varying condenser lengths

1 Introduction

In recent years, increasing environmental and public health concerns have accelerated the adoption of hydrocarbons as viable refrigeration system alternatives. Reductions in energy consumption and greenhouse gas emissions have been major factors in refrigeration research (Kazmi et al., 2026). Therefore, different and new alternatives coupled with modifications in a refrigerator’s components to reduce energy use or achieve more efficient systems are important research areas in this field. Hence, numerous studies have focused on modeling and enhancing the performance of components, including compressors, evaporators, condensers, and capillary tube–suction line heat exchangers, to improve the energy efficiency of refrigeration systems. Notably, the variation in condenser and capillary tube lengths (Oyedepo et al., 2016; Babarinde et al., 2018) has drawn considerable attention. In addition, research on variations in refrigerant charges (Oyedepo et al., 2017) and alternatives to phased-out working fluids is being conducted.

Optimizing the safety, performance, and economy of existing and new refrigeration systems integrated with environmentally benign hydrocarbon refrigerants in accordance with EU517/2014 is an interesting and active research topic. Isobutane (R600a) and liquefied petroleum gas (LPG) refrigerants are popular retrofits for phased-out R12 and R134a working fluids within refrigeration systems. Similarities in thermophysical properties and improved latent heat transfer, energy and environmental conservation, compatibility with existing compressor lubricating oils, and availability of flammability control methods are among the reasons for their surging use (Senthilkumar et al., 2021). As highlighted by Mclinden et al. (2014), ideal specifications for using LPG and R600a as refrigerants in domestic refrigerators are needed. The cost, human errors, and time restrictions of practically adapting these refrigerants can be avoided by adopting numerical modeling examinations that eliminate the need for experimental analysis and provide similar accuracy and precision to practical tests (Elsheniti et al., 2024).

Many studies have focused on the optimal condenser length and refrigerant charge for enhancing the performance of refrigeration systems. Some of these studies only include experimental research; however, others also deal with the modeling of vapour compression liquid refrigeration systems to predict the system’s operating performance. Basha et al. (2015) performed an experimental analysis on a vapour compression refrigeration system to determine the optimum condenser length for optimal refrigeration system performance. In the study, four different condenser lengths of 9.14, 9.45, 9.75, and 10.1 m were used. The results of the study revealed that the performance indicators of the system increased with an increase in the condenser length. However, the condenser length of 9.75 m gave the highest net refrigeration effect, highest heat rejection, lowest power consumption, and highest coefficient of performance (COP). Hence, the study concluded that the condenser length of 9.75 m is the optimum length. Babu and Babu (2013) conducted an experimental analysis on a refrigerator fitted with various condenser lengths. Results of the study confirmed that an increase in the condenser length enhances the performance parameters of the refrigeration system. Borikar et al. (2023) investigated the effect of condenser geometry in a refrigerator system. The study aimed to establish the roles of the condenser and condenser geometry in the performance enhancement of the future generation of midsized refrigerators. The results of the study revealed that the combination of ambient temperature and condenser geometry produced an effect on COP and subcooling more experimentally and analytically than other combinations. Cho et al. (2020) conducted a numerical analysis on a domestic refrigeration system using R600a to reduce refrigerant charge by optimizing the geometry of a hot-wall condenser. In the study, a simulation model was developed to examine the transient state of the refrigeration system. The analysis showed that a reduction in the diameter and length of the hot-wall condenser resulted in a decrease in the electric power consumption. The optimum length was observed to be 70% less than the original length. As a result of these reductions, the mass flow rate was reduced by 14%. Mehta et al. (2014) conducted a thermal analysis on a domestic refrigerator’s hot-wall condenser. In the study, ANSYS 14 software was used to perform the simulation of the condenser configuration. The simulation results were experimentally validated using the actual refrigerating system.

A model is a simplified representation of an actual system at an instance in space or time that aids in the study and comprehension of its behavior. Models simplify real-world systems and have the capacity to examine complex concepts. Models are bounded by various rules described using equations (Wang et al., 2013). Different researchers have performed modeling and simulation of refrigeration systems to enhance the performance of the system. Reddy et al. (2020) conducted a comparative analysis on the use of artificial neural network (ANN) and multiple regression analysis (MRA) models for the simulation of a commercial domestic refrigeration system using mixtures of hydrocarbons as refrigerants. The results of the study showed that the ANN model has a better confidence coefficient than the MRA model. Cheng and Yuan (2013) developed a dynamic model of a domestic refrigerator with a heat storage condenser with a shape-stabilized phase change material. The model was validated using the experimental results. From the simulation results, it was concluded that the COP improved by 19% due to the use of a heat storage condenser with phase change material. Hermes et al. (2009) conducted a steady-state simulation to perform a numerical analysis on household freezers and refrigerators to determine energy consumption. The results of the study revealed that the prediction results of the energy consumption of the refrigeration system by the model had a band of deviation of ±5% when compared with the experimental results. Zsembinszki et al. (2017) presented a novel methodology for modeling a simple compression refrigeration system. In the study, three input parameters, such as ambient and cold room air temperatures and the degree of superheating, were considered. A calculation algorithm based on iterative loops was used in the model to determine the operating point of the system. The results of the study showed that the numerical results are in good agreement with the experiment; therefore, the model can be a reliable tool for detecting a system malfunction.

Numerous studies have been conducted on the simulation of vapour compression refrigeration systems using software. Many model-based evaluations of refrigerator performance exist in the literature. Prakash et al. (2015) adopted the Creo2.0 software for modeling and analyzing the heat transfer rate of various condenser geometries (circular and elliptical) for a domestic refrigeration system. The refrigeration system heat transfer rate was found to be higher for the elliptical condenser geometry because of the increased heat transfer surface area and slenderness ratio. The temperature distribution, thermal gradient, and heat flux of a condenser with various contact angles (90° and 180°) were modeled using ANSYS 14 software and compared with the experimental results of Mehta et al. (2014). Similar results from the authors’ models and experiments confirm the validity of the ANSYS model. The authors also established correlations between condenser geometries and heat transfer characteristics and concluded that increasing the condenser contact angle increases heat flux and temperature gradient. Elsheniti et al. (2024) developed a fully coupled transient model using COMSOL Multiphysics to simulate the integrated system, considering the practical limitations of the vapour compression system (VCS) and the dynamic nature of the adsorption system (ADS). The model combined a lumped model for the ADS with the manufacturer’s data for a VCS compressor at different condensing and evaporating temperatures. The results of the study revealed that the cascade system can enhance the cooling capacity of the VCS by 18.2%, lower the compressor power by 63.2%, and greatly enhance the COP by 221% compared with the conventional VCS. The study concluded that the application of the cascade VCS/ADS in such severe conditions is a more sustainable and energy-efficient solution to meet the growing need for refrigeration.

Because the overall performance of vapour compression refrigerators depends on their subcomponents (i.e., compressor, condenser, capillary tube, and evaporator), a model representation of these subcomponents is required. Brown et al. (2017) opined that CYCLE_D-HX is capable of accurately simulating all the subcomponents of vapour compression refrigerators. The software uses various equations to represent the behaviour of the refrigeration system and appropriate input parameters from user(s), and performance evaluations are accessible.

The aim of this study is to determine the thermodynamic performance of a modified test refrigeration system separately integrated with varying refrigerant types (R600a and LPG) and condenser lengths using the CYCLE_D-HX software. The primary justification for this research is the sparse investigation of the thermodynamic effects of these test conditions on the refrigerator system. This study helps in determining the combination of refrigerants and condenser length that produces the most efficient performance of a domestic refrigerator. This would lead to the development of an energy-efficient refrigeration system. Because of the use of refrigerants with low global warming potential, this study could lead to the development of more environmentally friendly refrigerators by replacing conventional refrigerants that are harmful to the environment with less harmful refrigerants. The importance of developing more efficient systems that consume less energy cannot be overstated as this would go a long way in preserving our planet.

2 Methodology

In this study, CYCLE_D-HX was used to model a test rig refrigerator and simulate its performance for different condenser lengths (2.5 and 5 m) using LPG and R600a hydrocarbon refrigerants. The model was built using the experimental data and specifications of the test rig domestic refrigerator (Table 1). During the experiment, the test refrigerator data were obtained from affixed pressure gauges, K-type thermocouples, a refrigerant flowmeter, and a wattmeter. The average experimental results from three experimental tests of the refrigerants and condenser lengths were separately inputted into the CYCLE_D-HX software to ensure the repeatability and accuracy of the experimental results. Because the thermodynamic performance of a refrigerator correlates to its cycle design and operational conditions, the CYCLE_D-HX software was employed to model the subcomponents of the refrigeration system and estimate its performance. Predefined settings within the software include the refrigerant type (LPG and R600a), cycle option (single stage with auxiliary liquid-suction heat exchanger), and cycle specifications for evaporator, condenser, compressor, and suction–discharge lines.

TABLE 1. Specifications of component parts of the refrigeration system.

2.1 System specification

The refrigerator under study is a domestic vapour compression refrigeration system. It has a compressor, a condenser, an evaporator, and a capillary tube. The configuration of the system is presented in Table 1.

2.2 Thermodynamic modeling of refrigeration components

In this study, the major components of the refrigerating system are modeled. Figure 1 is a schematic diagram of a refrigeration system showing its major components (compressor, condenser, capillary tube, and evaporator).

2.2.1 Thermodynamic modeling of a compressor

A compressor is used in a vapour compression refrigeration system to change the refrigerant from a low-pressure state to a high-pressure state, thereby also increasing the temperature of the refrigerant (Wang, 2001). For vapour compression refrigeration systems, a reciprocating compressor is mostly used. The compressor operation is summarized in the pressure–volume diagram in Figure 2.

Figure 2 shows the following processes: Process 4-1, suction; Process 1-2, compression; Process 2-3, discharge; and Process 3-4, expansion.

The following parameters are used in the thermodynamic modeling of the compressor.

Swept volume (V_p):

This is the volume of the refrigerant drawn into the cylinder (see Equation 1). It is given as the cylinder volume. This is mathematically expressed as follows (Miller and Miller, 2012):where D is the diameter of the compressor cylinder and L s t is the length of the compressor stroke.

V p = V 1 − V 3 = π D 2 4 L s t (1)

Suction volume (V_s):

This is the volume of the refrigerant drawn in during the suction process (see Equation 2). This is mathematically expressed as follows (Miller and Miller, 2012):

V s = V 1 − V 4 (2)

Clearance volume (Vc): This is the volume of space occupied by the compressed gas at the end of the compression stage (see Equation 3). This prevents the collision of the piston and the cylinder. This is mathematically expressed as follows (Arora, 2013):

Vc = C V p (3)

The clearance factor C is always 5% for all compressor sizes.

Suction pressure (P_s) and discharge pressure (P_d): Because of pressure losses along the flow line, the suction pressure P_s and discharge pressure P_d are lower than the pressures at the evaporator discharge and condenser input, respectively.

The suction pressure P_s is defined as the pressure of the refrigerant at the suction of the compressor (see Equations 4, 5). This is given as follows (Arora, 2013; Arora, 2011):

P s = P 1 f p s (4)

The discharge pressure P_d is defined as the pressure of the refrigerant at the discharge of the compressor. This is given as per the description in Equation 5:where the pressure fractions f p s andf p d at the suction and discharge valves are given as f p s = 0.95 and f p d = 0.95.

P d = P 2 f p d (5)

Compressor work:

This is the energy expended by the compressor in compressing the refrigerant from its state in the compressor suction to its state in the compressor discharge (Equations 6, 7) (Mohanraj et al., 2009; Raghunatha et al., 2020):

The compressor work (W) is also expressed as follows:where m r ˙ is the refrigerant’s mass flow rate.

W = m r ˙ h 1 − h 2 = m r ˙ C p T 1 − T 2 (6)

m r ˙ = 1 + C − C P d i s P S u c 1 γ . A . N V s u c (7)

Compressor efficiency:

As with all machines, compressors are not 100% efficient. The energy efficiency of a compressor can be modeled using the term isentropic efficiency.

Isentropic efficiency (ῃ_isent) is defined as the ratio of the work under isentropic conditions to the actual work of the compressor (see Equation 8). This is given as (Subbaiah and Nagamani, 2015)where W i s e n t is the isentropic work of the compressor and W a c t u a l is the actual work of the compressor.

ῃ isent = W i s e n t W a c t u a l (8)

2.2.2 Modeling heat transfer in a condenser

A condenser in a refrigerating system transfers heat from the working fluid to the low-temperature heatsink (Arora, 2011).

Thermodynamic modeling of heat transfer in an air-cooled condenser is as follows.

2.2.2.1 Theoretical analysis of heat transfer in an air-cooled condenser

A refrigerator with an air-cooled condenser is examined in this study. The natural convection method is used for cooling. Heat is transferred from the refrigerant to the tube’s inner wall, via the tube wall, to the fins, and finally to the surrounding air between the two fluids in a sequential manner. According to Patil and Sapali (2007), the overall heat transfer coefficient, U_o, is determined by the tube’s inner and outside film coefficients, the tube material’s thermal conductivity, k, and the tube’s interior and outside areas. In an air-cooled condenser, heat transfer is associated with the following: (i) external convective heat transfer coefficient h_e, which is the natural convection between the air and the external wall; (ii) thermal conductivity k, which is the conduction through the wall; and (iii) internal convective heat transfer coefficient h_o, which is the condensation of the refrigerant on the internal wall, the inside (A_i) and outside (A_o) sections of the tube (Amar et al., 2016).

The following assumptions are made for the analysis of the heat transfer rate in the air-cooled condenser:

• Steady operating conditions exist.
• Changes in the kinetic and potential energies of fluid streams are negligible.
• Fluid properties are constant.
• The tube is isothermal.
• The vapour velocity is low so that Re _vap < 35,000.

In this study, the log mean temperature difference (LMTD) method is used to assess the heat transfer performance of a domestic refrigerator with an air-cooled condenser. The simplified sequential steps of the LMTD method to analyse a finned-tube air-cooled condenser can be presented as follows:

2.2.2.1.1 Computation of heat transfer area in a fin air-cooled condenser

The condenser under investigation consists of tubes and fins. The air flows through the passages formed by the fins. Figure 3 shows a cross-sectional view of the plate fin-and-tube condenser and its side view. Heat transfer occurs from the fins and the exposed part of the tube.

Heat transfer occurs in the following areas of the air-cooled condenser:

The bare-tube area (A _*b*) is computed using Equations 9–11 (Nitsche and Gbadamosi, 2016b):

A b = D − t D B π d o (9)

The fin area (A _*f*) is calculated using the following equation:

A f = 2 D C − π d o 2 4 B (10)

The minimum flow area (A _*c*) is given by the following equation:

A c = D − t D 1 − d o B (11)

The total flow area (A_o) can be computed using Equation 12:

Ao = A b + A f (12)

The internal heat flow area (A _*i*) is determined using Equations 13:where B is the vertical spacing between the tubes in a row, C is the spacing between the tubes in different rows, D is the center-to-center spacing between the fins, T is the thickness of the fins, D_o is the outer diameter of the tube, and d _*i* is the inner diameter of the tube.

A i = π d i B (13)

2.2.2.1.2 Computation of the air-side convective heat transfer coefficient (h_e)

The air-side heat transfer coefficient (h _*e*) is calculated according to the geometry of the heat exchanger using Equations 14–20 (Maiorino et al., 2018):

h e = N u . k D h (14)

For the flow across tubes, the Nusselt number in free convection can be calculated from the Kays and London correlation (Equations 14–20) (Lin et al., 2020; Aprea et al., 2018):

N u = 0.117 R e 0.65 ⁡ Pr 1 3 (15)

R e = ρ V max D h μ (16)

D h = 4 A c P (17)

P = A o C 1000 (18)

V max = V f B B − d o (19)

V f = Q f A f (20)

where h_e is the air-side heat transfer coefficient, D_h is the hydraulic diameter, k is the thermal conductivity of air, and Q _*f* is the air volume flow rate.

2.2.2.1.3 Computation of the refrigerant convective heat transfer coefficient (h_o)

The internal convective heat transfer coefficient h _*o* during condensation of the refrigerant is determined by the following relation in Equations 21–25 (Khurmi et al., 2018):where Re _*m* is the Reynolds number of a mixture (liquid and gaseous refrigerants during condensation throughout the length of the condenser), and it is given as follows (Equations 22–25) (Mihailović et al., 2019; Cho et al., 2020):

N u = h o D i k f = 0.0265 R e m 0.8 . ⁡ Pr f 1 3 (21)

R e m = R e f 1 + ρ f ρ g 1 2 (22)

R e f = ρ f U . D i μ f = m ˙ r . D i A i μ f (23)

Pr f = C p f . μ f k f (24)

wherewhere k f, ρ f, C p f, and μ f are the thermal conductivity, density, specific heat, and viscosity of the refrigerant, respectively. Subscripts ‛f’ and ‛g’ denote the saturated liquid and dry saturated refrigerant, respectively.

m ˙ r = 210 N R E (25)

2.2.2.1.4 Computation of the mean temperature using the LMTD method

The rate of heat transfer varies along the heat exchanger’s length because the temperature differential between the two fluids is always changing, as shown in Figure 4. In this study, condensation is assumed to occur throughout the length of the condenser.

The LMTD method is used in this study to design condensers. This method is adopted because it helps to show how effectively the cool medium can extract heat from the hot medium by comparing their different temperatures at the hot and cold ends of the condenser. The LMTD method is important because a huge difference in temperature between the hot and cold fluids would promote better heat transfer in the condenser. Evidently, a greater LMTD would mean that the condenser requires a lesser heat transfer area, resulting in a simpler and cheaper condenser design (Nitsche and Gbadamosi, 2016a).

The mean temperature between the hot- and low-temperature mediums using the LMTD method (Equation 26) is expressed as follows (Nitsche and Gbadamosi, 2016a):where ΔT ₁ is the temperature difference between hot and cold fluids at one end of the heat exchanger and ΔT ₂ is the temperature differential between hot and cold fluids at the other end.

Δ T m = Δ T 1 − Δ T 2 ln Δ T 1 Δ T 2 (26)

2.2.2.1.5 Determination of the overall heat transfer coefficient (U_o)

The overall heat transfer coefficient is a complete measure of the effects of the heat transfer fluids and the heat exchanger on the heat transfer process. The overall heat transfer coefficient considers the individual heat transfer coefficients of each stream and the resistance of the pipe material. It can be calculated as the reciprocal of the sum of a series of thermal resistance values (see Equation 27). The overall heat transfer coefficient, U _*o*, based on the external transfer area of the condenser is given by the following equation (Lin et al., 2020):

U o = 1 A o A i . 1 h i + A o . ⁡ ln r o r i 2 π K L + 1 h o (27)

where

A_o is the outside tube area in m², A_i is the inside tube area in m², h_i is the convective heat transfer coefficient of the refrigerant in W/m² K, h_o is the convective heat transfer coefficient of air in W/m² K, K is the thermal conductivity of aluminum (237 W/m K), r _*o* is the outside radius of the pipe in m, and r_i is the inside radius of the pipe in m.

2.2.2.1.6 Determination of the heat transfer rate

The heat transfer rate in a condenser is a measure of the quantity of heat being transferred per second from the refrigerant at the condenser. This is computed as follows (Equation 28) (Arora, 2011):where U _*o* is the overall heat transfer coefficient, A_t is the heat transfer area of the condenser, and ΔT_m is the mean temperature difference between the refrigerant and the external fluid.

Q = U o A t Δ T m (28)

2.2.2.2 Modeling of the pressure drop in a condenser

As the refrigerant flows through the condenser, there is always a drop in the pressure of the refrigerant as it goes through the condensation process. This is due to variation in the fluid density as it changes phase. The frictional pressure drop model of a two-phase flow in the condenser (△ P c) is calculated using modified Chawala’s correlations (Equations 29–34) (Ali-Morad, 2018; Khatun and Chourasia, 2025): where f i is the interfacial friction factor, ⱷ is the surface tension parameter, j l is the liquid superficial velocity, f l is the liquid-phase Darcy friction factor, a v is the void fraction, and X is the Martinelli parameter.

△ P c = 1 2 f i G 2 x 2 p v * a v 2.5 L D h (29)

f i = A X a R e i b ⱷ c f l (30)

ⱷ = j l μ l σ (31)

j l = G 1 − x p l 1 − a v (32)

For R e l < 2100

A = 1.308 x 10 − 3 a = 0.427 b = 0.93

c = − 0.121 f l = 64 R e

For R e l < 3400

A = 25.64 a = 00.532 b = 0.327

c = 0.021 f l = 0.316 R e l − 0.25

a v = 1 + 1 − x x 0.74 p v p l 0.65 μ l μ v 0.13 − 1 (33)

X = 1 + 1 − x x 0.9 p v p l 0.5 μ l μ v 0.1 (34)

2.2.3 Thermodynamic modeling of a capillary tube

A capillary tube is a long, fixed-length tube with a very small diameter that is installed between the condenser and the evaporator. The capillary tube meters the refrigerant from the condenser to the evaporator. Because of its long length and small diameter, there is an associated fluid friction and pressure drop as the refrigerant flows through it. The frictional pressure drop is a key component of the pressure drop (see Equations 35–38). This is the reduction in pressure in the refrigerant due to the friction between the fluid and the walls of the capillary tube (Miller and Miller, 2012). The frictional pressure drop is computed as follows (Equations 35–38): where ρ is the density of the refrigerant . where D is the diameter of the capillary tube and v is the flow velocity.

Δ P f = ρ f Δ L D v 2 2 (35)

Friction factor , f = 64 R e (36)

The overall pressure drop of the refrigerant as it flows through the capillary tube is the total reduction in the refrigerant due to its flow through the capillary tube, and it is expressed as follows:where L is the length of the capillary tube.

Δ P = G Δ V + f v m e a n G Δ L 2 D (37)

Δ V = c h a n g e i n v o l u m e where m ˙ is the refrigerant’s mass flow rate and A is the cross-sectional area of the capillary tube.

G = m ˙ A (38)

2.2.4 Modeling of the heat transfer in an evaporator

As the refrigerant flows through the evaporator, heat is transferred from the refrigerated space to the refrigerant. This causes the refrigerant to change phase by boiling. This phase change is accompanied by heat absorption from the refrigerated space (Hundy et al., 2016).

The evaporative heat transfer coefficient (h i e is a measure of how much heat is transferred from the refrigerated space to the refrigerant as a result of phase change of the refrigerant from liquid to vapour in the refrigerant (see Equations 39–42). This coefficient is used to measure the performance of an evaporator (Kim and Cho, 2018). The evaporative heat transfer coefficient is computed as follows: where V r, ρ r, and µ r are the velocity, density, and average viscosity of the refrigerant, respectively. where C p r is the refrigerant’s specific heat capacity at constant pressure.

h i e = ḫ f N u d e (39)

Nu = 0.027 R e 0.8 ⁡ Pr 0.4 ⁡ μ m μ w 0.14 (40)

Reynolds number R e = V r d e ρ r µ r (41)

Pr = C p r µ r ḫ r (42)

2.3 Energy performance of a refrigeration system

The energy evaluation of the refrigeration system was performed as follows: initially, the amount of heat required to keep the refrigerated space cooled was calculated, the equivalent thermal energy of the energy supplied to the compressor was calculated, and the COP was determined. The COP of the refrigeration system is defined as the ratio of the useful energy, which is the rate of heat removal by the evaporator (also known as the refrigerating effect), to the required energy, which is the power required to operate the compressor (also known as the compressor work) (see Equation 43). The experimental data obtained were used to calculate the work performed (W) by the compressor, the refrigerating effect (RE), and COP of the refrigerator. The COP is given by Equation 43 (Çengel and Boles, 2015) as follows:

C O P = R e f r i g e r a t i n g E f f e c t C o m p r e s s o r w o r k = h 2 − h 1 h 1 − h 4 (43)

2.4 Modeling software

In this study, the CYCLE_D-HX software was used to model and simulate the performance of refrigeration systems using different refrigerants and condenser lengths. The model was built using experimental data from a domestic refrigerator. The CYCLE_D-HX software can model the components of a refrigeration system and simulate its performance based on the input parameters provided (Brignoli et al., 2017).

The CYCLE_D-HX software uses the temperature profiles of the heat source and heatsink and the temperature difference of the heat transfer fluids to model the refrigeration system’s condenser and evaporator operations. Therefore, it is possible for the software to compare the performance of a refrigeration system operated with different refrigerants based on their thermophysical properties (Brown et al., 2017).

Figures 5, 6 are screenshots of the CYCLE_D-HX software showing refrigeration cycle specifications and the summary output of the sample results using R600a as the refrigerant.

The CYCLE_D-HX software allows for refrigerant inputs of either a single component or a blend of components. The blend can be predefined or user combinations of refrigerants can be provided by the software. The software also allows the selection of refrigeration system components from a simple VCS to a more complex system involving intercoolers and economizers. In addition, there is an input option for different parameters that could help to determine the performance of the individual components of the refrigeration system (the input parameters of the heat exchangers from their geometry to the temperature profiles and the input parameters to compute the performance of the compressor and input parameters of the cooling capacity of the refrigeration system).

3 Results and discussion

In this section, the results of thermodynamic and heat transfer modeling and simulation of refrigeration systems are presented. The parameters that indicate refrigeration system performance are examined to determine the effect of variation in condenser lengths on the refrigeration system. The results of the following performance parameters are presented and discussed: the pull-down time, COP, power consumption, overall heat transfer coefficient (U), heat rejection rate (Q), and condenser pressure drop (ΔP) for various combinations of condenser lengths of 5 and 2.5 m and R600a and LPG refrigerants.

3.1 Effects of refrigerants and variation in condenser lengths on pull-down time

The pull-down time is a measure of how quickly the evaporator (cabinet) is cooled. According to the ISO-8187 standard for the considered refrigerator class, the pull-down time is defined as the time required for changing the evaporator chamber air temperature from ambient condition (32 °C) to the desired final temperature (−12 °C) (Bolaji, 2010; Oyedepo et al., 2016). An increase in the pull-down time implies inadequate capacity for the system. Figure 7 shows a comparison of the pull-down time for the refrigeration system operated with R600a and LPG, with the condenser length varying from 2.5 to 5 m. When the system was operated with R600a, operating temperatures of −5 °C and −11 °C were obtained at a pull-down time of 240 min with L = 2.5 and 5 m, respectively. For LPG, the operating temperatures obtained at a pull-down time of 240 min are −3 and −9 °C with L = 2.5 and 5 m, respectively. From this study, it can be deduced that the results obtained for R600a with L = 5 m comply with the ISO standards [the operating temperature is −11 °C, and the pull-down time is 240 min, as reported by Fatouh and El Kafafy (2006) and Oyedepo et al. (2017)]. Furthermore, the cabinet (evaporator) temperature decreased with time for both refrigerants. However, the system has a lower evaporator temperature when operated with R600a than when LPG was used as the working fluid. This may be due to R600a being a single component, refined, and easily compressed, allowing it to absorb more latent heat during expansion, but LPG being a mixture of gases may not be easily compressed, so it absorbs less latent heat during expansion.

3.2 Effects of refrigerants and variation in condenser lengths on COP

COP is the performance parameter of a refrigeration system. It is an expression of the efficiency of the refrigeration cycle and is defined as the ratio of heat absorbed in the refrigerated space to the equivalent thermal energy of the energy supplied to the compressor.

Figure 8 shows the effect of the condenser length (L) on the system’s COP using R600a and LPG. The COP decreases with time. At a condenser length of 2.5 m, the COP varied from 1.73 to 2.57 and 1.68 to 2.42 for LPG and R600a refrigerants, respectively. In contrast, at a condenser length of 5 m, the COP varied from 1.43 to 2.26 for LPG and from 1.34 to 2.20 for R600a.

The highest COP of 2.57 was obtained with LPG for the condenser length, L = 2.5 m, whereas the lowest COP of 1.34 was obtained with R600a at L = 5 m. On the basis of the results of this study, the average COP of the refrigerants is very close, but the average COP obtained using LPG is approximately 4.42% higher than that of R600a when a condenser length of 2.5 m was used. However, when a condenser length of 5 m was used, the average COP obtained using LPG is approximately 4.07% higher than that of R600a. This result agrees with that of Oyedepo et al. (2017).

3.3 Effects of refrigerants and variation in condenser lengths on electric power consumption

Figure 9 shows the variation of electric power consumption with time for R600a and LPG with condenser lengths of 2.5 and 5 m. The power consumption increases with time and with an increase in the condenser length. This is mainly due to an increase in mass flow rate of the refrigerant through the compressor. Figure 9 shows that the power consumption when operated with R600a and condenser lengths of 2.5 and 5 m varies from 1.65 to 2.37 kW and 1.82 to 2.98 kW, respectively. The power consumption when operated with LPG and condenser lengths of 2.5 and 5 m varies from 1.56 to 2.32 kW and 1.82 to 2.79 kW, respectively. The lowest power consumption of 1.56 kW is recorded at L = 2.5 m for LPG. The average power consumption for LPG is approximately 3.75% lower than that for R600a under a condenser length of 5 m, whereas it is approximately 16.02% lower than that for R600a when a condenser length of 2.5 m was used.

3.4 Effects of refrigerants and variation in condenser lengths on the heat rejection rate

The heat rejection rate in a refrigeration system is the total heat expelled to the environment. It indicates how much heat leaves the condenser compared with what is removed from the cool space. The heat rejection rate measures the heat removal efficiency from the system. It is the ratio of the heat rejected by the system to the heat absorbed by the system. A higher heat rejection ratio indicates better heat removal efficiency. Figure 10 presents the effect of variation in condenser length on the heat rejection rate of refrigeration systems operated with R600a and LPG. The heat rejection rate increases with an increase in condenser length. When the system is operated using R600a, the heat rejection rate varies from 5.65 to 6.37 kW and 5.82 to 6.98 kW for the condenser lengths of 2.5 and 5 m, respectively. However, when LPG was used as the working fluid, the heat rejection rate varied from 5.56 to 6.32 kW and 5.77 to 6.79 kW for the condenser lengths of 2.5 and 5 m, respectively. The average heat rejection rate of R600a is 1.23% higher than that of LPG when a condenser length of 2.5 m was used. In contrast, the average heat rejection rate of R600a is 1.85% higher than that of LPG when a condenser length of 5 m was used. Both hydrocarbons remarkably improve system efficiency by effectively transferring heat during condensation; however, R600a’s lower Global Warming Potential (GWP) makes it a preferred choice for modern systems. This result agrees with that of Agrawal et al. (2017).

3.5 Effects of refrigerants and variation in condenser lengths on the overall heat transfer coefficient

The overall heat transfer coefficient (U) in refrigeration systems quantifies how efficiently heat moves across heat exchanger surfaces (e.g., evaporators and condensers), combining convection on both sides and conduction through the wall, with typical values varying greatly by heat exchanger type and fluids. The larger the coefficient, the easier it is to transfer heat from its source to the heated medium.

Figure 11 presents the effects of variation in condenser lengths on the overall heat transfer coefficient of a refrigeration system using R600a and LPG as refrigerants. The overall heat transfer coefficient increases with an increase in the condenser length. When the system was operated with R600a, the overall heat transfer coefficient varied from 0.668 to 0.755 kW/m² °C and 0.687 to 0.822 kW/m² °C for the condenser lengths of 2.5 and 5 m, respectively. On the basis of the results of this study, the average overall heat transfer coefficients of the two refrigerants are very close. However, the average overall heat transfer coefficient of R600a is 0.98% greater than that of LPG when a condenser length of 2.5 m was used. Conversely, it is 1.39% greater than that of LPG when a condenser length of 5 m was used.

3.6 Effects of refrigerants and variation in condenser lengths on condenser pressure drop

Pressure drops in the condenser tubes of the refrigeration system are not only due to friction but also due to the change in phase from vapour to liquid. According to Ali-Morad (2018), a pressure drop occurred as the two-phase pressure dropped because of the condensation of the refrigerant inside the tube; thus, the pressure drop also increased when the vapour quality increased. The effect of pressure drop is detrimental to the performance of the refrigerating machine; hence, it is needed for modeling pressure drop in the condenser of the refrigeration system.

Figure 12 presents the effects of variation in condenser lengths on the pressure drop of a refrigeration system using R600a and LPG as refrigerants. The pressure drop increases with an increase in the condenser length. When the system was operated with R600a, the pressure drop varied from 21.0 to 39.3 kPa and 23.4 to 47.4 kPa for the condenser lengths of 2.5 and 5 m, respectively. However, when the system was operated with LPG, the pressure drop varied from 20.1 to 35,7 kPa and 22.8 to 43.4 kPa for condenser lengths of 2.5 and 5 m, respectively. On the basis of the results of this study, the average pressure drop of R600a is 7.46% greater than that of LPG when a condenser length of 2.5 m was used. In contrast, it is 6.50% greater than that of LPG when a condenser length of 5 m was used. Studies have shown that the pressure drop is strongly affected by the thermophysical properties of the refrigerants, such as density, latent heat, and kinematic viscosity (Fenouche and Ouadha, 2023). Hence, in the present work model comparison, LPG has the lowest pressure drop. A high-pressure drop will negatively affect the system’s performance and components’ reliability, whereas a low-pressure drop will prolong the equipment life and greatly improve its performance.

4 Conclusion

In this study, thermodynamic modeling and simulation of a refrigeration system using the CYCLE_D-HX software have been conducted. The system was modeled to run with hydrocarbon refrigerants (LPG and R600a) with varying condenser lengths (2.5 and 5 m). The performance indicators evaluated in this study were the pull-down time, COP, electric power consumption, heat rejection rate, overall heat transfer coefficient, and condenser pressure drop. Based on the results of this study, the following conclusions are drawn:

• When the system was operated with R600a, operating temperatures of −5 °C and −11 °C were obtained at a pull-down time of 240 min with L = 2.5 and 5 m, respectively. For LPG, the operating temperatures obtained at a pull-down time of 240 min are −3 °C and −9 °C with L = 2.5 and 5 m, respectively.
• The cabinet temperature for both LPG and R600a decreases with time and with an increase in the condenser length.
• The average COP obtained using LPG was approximately 4.42% higher than that using R600a when a condenser length of 2.5 m was used. Conversely, when a condenser length of 5 m was used, the average COP obtained using LPG was approximately 4.07% higher than that obtained using R600a.
• The average power consumption of the system with LPG was approximately 3.75% lower than that of R600a under a condenser length of 5 m, whereas it was approximately 16.02% lower than that with R600a when a condenser length of 2.5 m was used.
• The average heat rejection rate of the system with R600a was 1.23% higher than that with LPG when a condenser length of 2.5 m was used. Conversely, the average heat rejection rate with R600a was 1.85% higher than that with LPG when a condenser length of 5 m was used.
• The average overall heat transfer coefficient of the system with R600a was 0.98% greater than that with LPG when a condenser length of 2.5 m was used. Conversely, it was 1.39% greater than that with LPG when a condenser length of 5 m was used.
• The average pressure drop of the system with R600a was 7.46% greater than that with LPG when a condenser length of 2.5 m was used. Conversely, it was 6.50% greater than that with LPG when a condenser length of 5 m was used.

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Nomenclature

Abbreviations

ADS Adsorption System COP Coefficient of Performance D Diameter (m) GWP Global warming potential HRR LMTD Logarithmic Mean Temperature Difference (K) LPG Liquified Petroleum Gas VCS Vapor compression System

Symbols

A Area (m²) B Vertical Spacing between tube rows (m) C Clearance volume (m³) h enthalpy (kJ/kg) k Thermal conductivity (W/m²K) L length (m) ṁ Mass flow rate (kg/s) N Speed (m/s) P Pressure (kN/m²) Pr Prandtl number Q Heat transfer` (W) r radius (m) R600a Isobutane Re Reynold number T Temperature (K) U Overall heat transfer coefficient (W/m²C) v Velocity (m/s) V Volume (m³/kg) W Work input (kJ/kg)

Greek Letters

ρ Density (kg/m³) Δ T Mean temperature (K) △ P frictional Pressure Drop (N/m²) ⱷ Surface tension (N/m) f Darcy Friction Factor X Martinelli Parameter µ Viscosity (Kg/m.s) Γ Isentropic index ῃ Isentropic efficiency

Subscripts

f saturated liquid g saturated vapour o outside I inside 1 Suction 2 Discharge 3 Condensing r refrigerant isen isentropic

Footnotes

Edited by: Rahul R. Bhosale, University of Tennessee at Chattanooga, United States

Reviewed by: Younes Chiba, University of Medea, Algeria

Nalinikanta Panda, Gandhi Institute of Engineering and Technology University (GIET), India