Thermodynamic analysis of a linear compressor vapour compression system

Linear compressors are advantageous in terms of miniaturization, high efficiency, and continuous operation without a crank mechanism. The drop-in replacement for R134a in domestic refrigerators is R1234yf. This study aims to investigate the linear compressor thermodynamic performance in vapour compression system with R1234yf by modelling and measuring key parameters such as pressure-volume (P-V) diagram, refrigerant distribution, mass flow rate, volumetric efficiency, cooling capacity, and coefficient of performance (COP). Results show that at 40 °C condenser temperature and 2 pressure ratio, the linear compressor vapour compression system achieved a maximum 299.1 W cooling capacity, which gives 4.12 COP. The thermodynamic analysis calculations are in good agreement to the results of experimental measurements, verifying the accuracy of the model.


Introduction
As science and technology advance and living standards improve, people have raised their expectations for storage and transportation of various products.This demand has spurred the development of refrigeration technology and provided favorable conditions for the growth of refrigerators.Vapour compression technology is commonly utilized in household refrigerators and accounts for 17% of the global energy demand [1].This level of consumption directly influences both energy production capacity and environmental impact, ultimately impacting the global economy.Enhancing the vapour compression refrigeration systems efficiency has a potential to generate substantial energy savings for the vast number of refrigerators sold globally.As a key component of vapour compression refrigeration systems, compressors play a crucial role in this effort.Conventional reciprocating compressors rely on a crank linkage mechanism which causes rubbing, wear and power loss as it converts rotary movement into linear ones.This reduces the conventional compressor's efficiency and stability.By eliminating the need for a cross-rod mechanism, linear Compressor is able to improve its efficiency by having the motor directly drive the piston in the cylinder in a linear reciprocating motion.Liang et al [2] experimentally compared the linear and crank-driven compressors and showed that linear compressors have an adiabatic efficiency over 20% higher than crank-driven compressors.Ku et al. conducted experiments on domestic refrigerators to assess the linear and crank-driven compressors energy efficiency [3].Their study revealed that the novel linear compressor was 20% more efficient with an additional 8% cooling capacity compared to a brushless direct current (DC) reciprocating compressor.Bansal et al. conducted a comprehensive analysis of advancements in domestic appliances and emphasized that linear compressors exhibit higher efficiency, making them a more favorable choice for regulating refrigeration capacity [4].
R134a is a widely used commercial refrigerant that has a 1430 global warming potential (GWP) which will require replacement by a refrigerant with lower GWP values beginning in 2022 [5].R1234yf, a synthetic refrigerant, possesses GWP values of 4 and displays diminished flammability while exhibiting thermodynamic properties akin to R134a [6].Navarro-Esbri et al. explored the energy efficiency of vapor compression systems utilizing R1234yf and R134a and showed that R1234yf has a COP approximately 19% smaller than that of R134a, and the findings also showed a significant improvement in energy efficiency using R1234yf by integrating an internal heat exchanger [7].Cho et al. compared R134a and R1234yf in vehicle air-conditioning systems and demonstrated lower compressor power consumption and cooling capacity of R1234yf compared to R134a, by 4% and 7%, respectively [8].Sánchez's assessment of the energy impact of different low-GWP alternatives to R134a in beverage coolers showed that R1234yf imposes a penalty on energy consumption of up to 4.1% [9].Yataganbaba et al. analyzed the energy efficiency of R1234yf as a potential replacement for R134a in a two-evaporator vapour compression refrigeration system.The results indicate that although certain performance parameters of R1234yf are lower than 134a, the differences are minimal.Considering its environmentally friendly properties, R1234yf presents itself as a viable alternative to R134a [10].
All of the above performance evaluations for R1234yf were performed in a vapour compression system using a reciprocating linear compressor.Lubricants are usually required.However, there is concern that oil-based lubricants may leak through gaps in the compressor components and mix with the refrigerant.The presence of a lubricant in a system can negatively affect the operation fluid's thermodynamic properties and lead to performance degradation [11].Oil lubrication can significantly impact on heat transfer and pressure drop, and in order on account of more accurate performance evaluation of R1234yf, it would be beneficial to conduct the study without oil lubrication.
In this study, the vapour compression system using oil-free linear compressor is capable of using R1234yf without modification [12].This study aims to evaluate the thermodynamic performance of a vapour compression system with a linear compressor that uses R1234yf via experimental and modeling work.

Experimental equipment
This paper utilizes experimental equipment to assess the linear compressor vapour compression system, as shown in Figure 1.The system operates by compressing high-temperature, high-pressure gas which is then discharged into condenser.Refrigerant is condensed through a reduction in pressure by the expansion valve and flows to the evaporator before returning to the compressor's main body.As the new oil-free linear compressor eliminates the need for a lubrication system, any refrigerant leakage from the piston and cylinder clearance seal can cause an ongoing increase in pressure inside the compressor body.To address this, the leaking refrigerant is returned to the compressor working circuit via the return pipe.Additionally, the pulse width modulator is utilized to adjust the leakage flow of the needle valve, enabling control over the linear compressor body pressure, ensuring that the piston remains in its balanced position and preventing piston offset.In this study, a vapor compression system equipped with a linear compressor used four pressure sensors in order to determine the pressure at the compressor discharge port, the evaporator inlet, the compressor suction port, and the main body of the compressor.Each pressure sensor is equipped with a DC power supply ranging from 9-30V and outputs a DC voltage ranging from 0-5V.Additionally, eight thermocouples measure temperatures at various locations within the system, including the compressor main body, compressor discharge, condenser outlet, evaporator inlet, evaporator wall, evaporator outlet, compressor suction port, and motor coil.In order to determine mass flow rate of main and leakage circuits, two mass flow meters are employed.Furthermore, two displacement sensors are employed to monitor the piston's position inside compressor.Low-frequency and high-frequency data collectors are utilized for experimental data collection.
This paper aimed to evaluate the performance of R1234yf refrigerant under varying piston stroke, pressure ratio, and condenser temperature conditions while verifying the accuracy of thermodynamic analysis.The experimental bench contained 250g of refrigerant, with the piston stroke and compression ratio adjusted using a proportional-integral-derivative (PID) controller and expansion valve.Electric heater for evaporator was adjusted to ensure complete evaporation of the refrigerant into gaseous form, while the cooling water flow rate was manually changed to maintain the desired operating temperature (40°C, 50°C) at the condenser outlet.To maintain a constant average piston position, the needle valve was manually adjusted [13].The specific experimental working parameters are summarized in Table 1.Suction temperature (°C) 20-30

Thermodynamic analysis
In this study, the thermodynamic analysis of a vapour compression system equipped with a linear compressor was carried out.P-V model, mass flow rate, volumetric efficiency, cooling capacity, and COP of this system were analyzed.In addition, it was studied the distribution of R1234yf in each component for different pressure ratios.

P-V diagram
Figure 2 illustrates a linear compressor schematic.From Figure 2, it is clear that the initial distance from the piston face to the front of the cylinder is 7.57 mm.Cylinder volume is represented by minimum cylinder volume ( ), maximum cylinder volume ( ), and cylinder volume (V) using the following equation: .
where, S represents compressor stroke, x denotes piston offset, D signifies piston diameter, f denotes operating frequency and t denotes time.
As compressor utilize piston and cylinder clearance seal, gas leakage occurs during compression process, and heat transfer through the cylinder wall is inevitable, leading to non-adiabatic or nonisentropic processes during compression and expansion.
The cylinder pressure of compression and expansion are expressed by Equation ( 4): (5) where, is suction pressure, is discharge pressure, n is polytropic index.

Mass flow rate and volumetric efficiency
Linear compressor piston and cylinder have radial clearance which can result in gas leakage during compressor operation.Leakage mass flow rate through clearance is obtained using Equation ( 6) as pointed out by Liang et al [14].Hence, mass flow rate for condenser is obtained from Equation ( 7): The calculation involves determining the cylinder volumes ( and ) at the beginning and end of the discharge process, as well as the cylinder pressure ( ), the cylinder temperature ( ), the compressor body pressure ( ), the discharge pressure ( ), the discharge temperature ( ), the operating frequency (f), and the specific gas constant ( ).
Volumetric efficiency, , is represented using Equation ( 8): where, A denotes piston area, S refers to compressor stroke, and represents suction pressure.) is determined by measuring the voltage and current as follow: (10) where, , , represent voltage, current and the period.
Finally, to obtain the COP, it is necessary to divide cooling capacity ( ) by compressor power input ( ) according to Equation ( 11), defined as: (11)

Refrigerant distribution
The refrigerant circuit of a linear compressor vapour compression system comprises evaporator, condenser, vapour line, liquid line, and filter.Specifically, the vapour line is composed of the condenser inlet line and the evaporator outlet line, while liquid line is comprised of the condenser outlet line.
Evaporator inlet line is operated to act the two-phase line and maintains constant void ratio.Detailed specifications of the parameters and phase length of the linear compressor vapour compression system are available in Chen's comprehensive analysis [15].The mass of two-phase and single-phase refrigerant in the heat exchanger is given by: 1 (13) where, denotes two-phase cross-sectional area, denotes heat exchangers cross-sectional area, denotes two-phase length, is the single-phase length, is the void fraction, denotes vapour refrigerant density and denotes liquid refrigerant density.
Refrigerant mass in single-phase form in filters and pipes is given by Equation ( 14): ( 14) where, denotes single-phase line cross-sectional area.Before refrigerant enters evaporator, it accumulates in the pipes in the form of a two-phase flow.Therefore, the mass of refrigerant in the pipes in calculated by Equation ( 15): (15)

Results and discussions
Figure 3 displays relationships between in-cylinder pressure and volume of R1234yf.It shows that when the compressor piston stroke, compression ratio and condenser temperature are fixed at 11mm, 2.0, and 50°C respectively, the P-V diagrams from modeled and experiment data are in good agreement as far as the trend of each cycle is concerned, with an average pressure in the cylinder of 7 bar.However, the model doesn't consider valve effects and there's a certain error between the suction and exhaust pressure, with the maximum error being 13.1% between model results and experimental data.Figure 4 illustrates the R1234yf thermodynamic evaluation and measured mass flow rate as the pressure ratio is varied while the condenser temperature is maintained at 50°C and the piston stroke values are maintained at 11 mm and 12 mm.With a constant piston stroke, R1234yf's mass flow rate decreases with an increase in the pressure ratio.Conversely, as the pressure ratio is stable, R1234yf's mass flow rate tends to have an increasing effect as the piston stroke rises.Although model and experimental trends exhibit general consistency, subpar thermal conductivity and high viscosity of liquid R1234yf lead to inadequate heat transfer coefficients within the condenser, causing analysis results to be roughly 20% higher than actual measurements.Additionally, refrigerant leakage resulting from piston-cylinder clearance during operation causes measured values to be lower compared to calculated ones.
Figure 5 exhibits the relationship between volumetric efficiency and pressure ratio for 50°C condenser temperature and 11, 12 mm compressor piston strokes.The model aligns closely to experimental data, having 7.1% mean error.As the compressor stroke remains stable, the volumetric efficiency decreases as the pressure ratio increases.Conversely, when pressure ratio is fixed, an augmentation in piston stroke results in increased volumetric efficiency.Measured volumetric efficiency is highest for piston stroke equal to 12 mm and pressure ratio equal to 2, attaining a value of 0.55.Conversely, with a constant pressure ratio, cooling capacity and COP decrease as the condition of the condenser temperature rises.At 40°C condenser temperature and 2.0 pressure ratio, the maximum cooling capacity achieved by the linear compressor vapour compression system is 299.1 W with a COP of 4.12.Figure 7 illustrates the varying refrigerant distribution for different pressure ratios under fixed compressor stroke and refrigerant charge values (11 mm and 250 g).With increasing pressure ratio, there's a significant rise in refrigerant mass ratio found in the condenser.Although refrigerant accumulation in vapour lines and filters reduces slightly due to decreases in refrigerant vapour density, the refrigerant is still mostly stored in condenser under all operating conditions.The results of the findings confirm that condensers consistently show the highest refrigerant distribution in vapor compression systems.The condenser holds the highest percentage of refrigerant at 3.0 pressure ratio, where it can reach 73.2%.

Conclusions
The present work has carried out an analysis of thermodynamics of a linear compressor vapor compression system using R1234yf, utilizing both models and measurements to investigate its performance.The results exhibit that there is a well-matched relationship among model and experimental data.The main findings resulting in the analysis are listed below:  P-V diagram for the model and experiment aligns with the trend of each cycle, with the maximized error measuring 13.1% from the model to the experimental data. With the constant piston stroke, R1234yf's mass flow rate and volumetric efficiency decrease by increasing the pressure ratio.Because of R1234yf's inadequate heat transfer coefficient in condenser, analytical mass flow rate outcomes were approximately 20% higher than measured values. When the pressure ratio remains steady, cooling capacity and COP reduce as condenser temperature increases.Experiential maximum cooling capacity of the linear compressor vapour compression system utilizing R1234yf is 299.1 W, with a COP of 4.12. A substantial increase in the refrigerant mass fraction in condenser is observed as pressure ratio rises.Up to 70% of the refrigerant stores in the condenser.

Figure 1 .
Figure 1.The comprehensive experimental setup of a linear compressor vapour compression system.

Figure 2 .
Figure 2. The schematic diagram of the linear compressor.

Figure 3 .
Figure 3. P-V diagram.Figure4illustrates the R1234yf thermodynamic evaluation and measured mass flow rate as the pressure ratio is varied while the condenser temperature is maintained at 50°C and the piston stroke values are maintained at 11 mm and 12 mm.With a constant piston stroke, R1234yf's mass flow rate decreases with an increase in the pressure ratio.Conversely, as the pressure ratio is stable, R1234yf's mass flow rate tends to have an increasing effect as the piston stroke rises.Although model and experimental trends exhibit general consistency, subpar thermal conductivity and high viscosity of liquid R1234yf lead to inadequate heat transfer coefficients within the condenser, causing analysis results to be roughly 20% higher than actual measurements.Additionally, refrigerant leakage resulting from piston-cylinder clearance during operation causes measured values to be lower compared to calculated ones.Figure5exhibits the relationship between volumetric efficiency and pressure ratio for 50°C condenser temperature and 11, 12 mm compressor piston strokes.The model aligns closely to experimental data, having 7.1% mean error.As the compressor stroke remains stable, the volumetric efficiency decreases as the pressure ratio increases.Conversely, when pressure ratio is fixed, an augmentation in piston stroke results in increased volumetric efficiency.Measured volumetric efficiency is highest for piston stroke equal to 12 mm and pressure ratio equal to 2, attaining a value of 0.55.

Figure 4 .
Figure 4. Relationship between mass flow and pressure ratio.

Figure 5 .
Figure 5. Relationship between volumetric efficiency and pressure ratio.

Figure 6 demonstrates
Figure 6 demonstrates R1234yf's cooling capacity versus COP for a constant 11 mm compressor piston stroke and two different sets of condenser temperatures, 40°C and 50°C.When the condenser temperature is constant, cooling capacity and COP are all increasing as the pressure ratio decreases.Conversely, with a constant pressure ratio, cooling capacity and COP decrease as the condition of the condenser temperature rises.At 40°C condenser temperature and 2.0 pressure ratio, the maximum cooling capacity achieved by the linear compressor vapour compression system is 299.1 W with a COP of 4.12.

Figure 6 .
Figure 6.Relationship between compressor cooling capacity and pressure ratio.

Figure 7 .
Figure 7. Refrigerant distribution for different pressure ratios.