Simulation and Experimental Study on the Oil Circulation Rate (OCR) of R290 Electrical Vehicle Compressors

Abstract

This paper establishes a simulation model for the performance of an R290 variable frequency compressor in automotive air conditioning and sets up a compressor performance testing system. It investigates the effects of different evaporation temperatures, condensation temperatures, compressor speeds, and pressure ratios on the oil circulation rate (OCR), as well as the impact of various oil circulation rates on the performance of the R290 compressor. As the comparison between simulation and experimental data shows, compressor performance predictions from the simulation model align with experimental results when the OCR is not taken into consideration. Experimental results indicate that the OCR increases with a rising evaporation temperature, decreases with a lowering condensation temperature, and increases with higher compressor speeds. The simulation model shows a minor deviation when predicting volumetric efficiency, while errors are larger when predicting isentropic efficiency and the discharge temperature. Isentropic efficiency and the discharge temperature show a notable impact from the OCR. Additionally, for system cooling capacity, power, and COP predictions, when the OCR is within the range of 2~10%, the accuracy of the simulation model proves satisfactory, with deviations within 5%.

1. Introduction

The variable frequency of electrical vehicle air conditioning compressors has been widely applied due to their precise temperature control, energy efficiency, comfort, and excellent noise and vibration characteristics. Lubricating oil in the compressor serves the purposes of cooling, lubrication, and sealing, which has a significant impact on the reliability of the compressor and the performance of the refrigeration system, particularly on the system’s pressure drop and heat exchange performance [1]. The lubricating oil content within automotive compressor systems can enhance the performance of compressors within a certain range. However, as compressor lubricating oil enters various components of the system through the discharge pipeline, its presence can lead to a reduction in the heat exchange capacity of the heat exchanger and also greatly affect the flow characteristics of the entire system, thereby impacting the operational stability of the air conditioning system [2]. Therefore, measuring the oil content and oil circulation rate (OCR) is of great importance for system performance and reliability [3]. Radulovic [4] looked into the potential of low-GWP refrigerant fluids (R152a, R1234yf, R1234ze(E), R290, R600a) and assessed their suitability to be utilized as replacements for the historically used R134a. Pressure ratios across the compressor stage were considered in the study. Compared to R134a, R290, R600a, and R152a had higher cooling capacities, although the compression work was notably higher as well. Overall, these refrigerant fluids could act as replacements for R134a. Chen [5] developed a simulation model for the detailed compression process of scroll compressors. A lumped parameter method was adopted to establish energy balance equations, and a recursive method was employed to solve these equations, obtaining parameters such as internal temperature and pressure and ultimately determining power and compressor efficiency. The results allow for the study of factors affecting compressor performance, including the impact of internal leakage and heat transfer losses, and thus provide a theoretical basis for the optimization of compressors. Zhong et al. [6] developed the validated zero-dimensional (0-D) and three-dimensional (3-D) simulation model, along with experiments, to investigate the distribution of performance loss and suction compression characteristics in high-speed R290 compressors. The results showed that the R290 compressor exhibits superior volumetric efficiency. However, the combination of increased over-compression loss and motor loss at high speeds resulted in an 11.7% rise in input power, leading to an 8.4% decline in thermodynamic performance for the R290 compressor under standard heating compared to the R32 compressor. Shao [7] developed a performance model for variable frequency compressors, which includes the refrigerant flow rate, power, and COP. With evaporation and condensation temperatures as variables, multi-coefficient models at different frequencies were established. The study also compared the model with test data provided by the compressor manufacturer, and the results showed small relative errors, making the model suitable for frequency conversion systems. Due to the use of a polynomial model, the study also explored issues related to power at 0 frequency and frequency at 0 flow, as well as the relationship between the COP and frequency. Yang [8] used a multilayer neural network to develop a fixed-speed model for scroll compressors with the R410a refrigerant. With evaporation temperatures ranging from −10 to 55 ℉ (−23.3 to 12.8 °C) and condensation temperatures from 80 to 150 ℉ (26.7 to 65.6 °C), they derived a ten-coefficient model for the compressor and simulated volumetric efficiency and isentropic efficiency. By adding coefficients, they applied the fixed-speed model to variable frequency compressors. Comparisons between simulation and experimental data showed a standard deviation of 0.4% and a maximum deviation of 1.3%. Cuevas [9] established a six-coefficient model and compared experimental and simulation data, which indicated that compressor performance is mainly influenced by the pressure ratio. Deviations at low speeds were mainly affected by internal leakage and a lack of lubrication. They also found that the efficiency of compressor inverters with power ranging from 1.5 to 6.5 kw is about 95% to 98%, indicating that the effect of the inverter-controlled compressor rotation speed on performance is relatively small. Eric Winandy [10] analyzed the flow, heat transfer, exhaust temperature, and shaft power of scroll compressors through experiments and simulations. Using an EES to simulate compression process losses, including heat transfer, volumetric ratio, power loss, and power coefficient, they found that about 5% to 13% of heat transfer losses (including leakage losses) affect the compressor’s flow.

Currently, the performance simulation models for compressors generally do not consider the impact of the oil circulation rate. During experimental processes, the OCR is either controlled within a very small range or its impact is ignored. Therefore, some scholars have analyzed the mechanism of oil circulation rates and their effects. Kim [11] studied the hysteresis situation of the refrigerant–oil mixture within the system, and the results showed that a lower mass flow rate or smaller OCR leads to less oil content, which causes hysteresis in the system. Navarro [12] tested the system and compressor performance when the R290 refrigerant replaced the R407C refrigerant. As the results indicated, the COP value of the R290 refrigerant is about 9% higher, and compressors perform better with R290 at medium- and low-pressure ratios than that with R407C, but the opposite is true with R290 at high pressure ratios. They also found that when the OCR value is between 0.35% and 1.4%, the performance of R290 and R407C is not significantly affected. Ossorio and others [13] studied the oil circulation rate of R290 variable frequency compressors at different compressor speeds, and the results showed that the oil circulation rate increases with compressor speed.

At present, the application of R290 in electrical vehicle air conditioning systems is still being studied. This paper establishes a performance simulation model for variable frequency compressors to analyze the thermodynamic properties of R290. An experimental system is set up to compare the effects of factors such as the compressor speed, operating condition, oil and refrigerant ratio, and OCR on compressor performance. A comparative analysis of the simulation and experimental results is also conducted.

2. Establishment of the Simulation Model

Compressor Simulation Model

The performance indicators of a compressor are mainly reflected by two parameters: the flow rate and power. The flow rate is determined by the suction volume and suction density of the compressor. Typically, the suction volume of a positive displacement compressor is not constant, which results in a deviation in the volumetric flow rate, represented by volumetric efficiency. Therefore, the actual mass flow rate is defined by the following formula:

(1)$m_r={\displaystyle \frac{{\eta }_v\times N\times V_d}{60\times v_{suc}}}$

where $m_r$ is the mass flow rate of the refrigerant, kg/s, $N$ is the compressor speed, rpm, ${\nu }_{suc}$ is the suction specific volume, m³/kg, $V_d$ is the theoretical swept volume, ml/rev, and ${\eta }_v$ is the volumetric efficiency.

The factors influencing volumetric efficiency include compression clearance and leakage due to the pressure ratio. Generally, the expression for volumetric efficiency can be defined as follows:

(2)${\eta }_v=1-C\times ({(\frac{P_{dis}}{P_{suc}})}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$n$}\right.}-1)$

where $C$ is the clearance volume ratio, $P_{dis}$ is discharge pressure, $P_{suc}$ is suction pressure, and $n$ is the polytropic index.

According to the above formula, Negrão and others [14] expressed the compressor’s volumetric efficiency as follows:

(3)${\eta }_v=b_1+b_2\times ({(\frac{P_{dis}}{P_{suc}})}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$k$}\right.})$

where $b_1$ and $b_2$ are the volumetric efficiency coefficients, and $k$ is the adiabatic index of the refrigerant.

According to the ASHRAE Toolkit, the shaft power of the compressor can be expressed as

(4)$W=(1+\alpha )W_t+W_{loss}$

where $W_{loss}$ is the loss constant due to mechanical efficiency, and $\alpha$ is the ratio of mechanical loss to power consumption $W_t$.

Assuming the compression process is considered an ideal isentropic process ($p{v}^k=Const$), the theoretical power per unit mass flow rate of the compressor can be expressed as follows:

(5)$W_i={\displaystyle {\int }_{suc}^{dis}vdp=}{P}_{suc}\times V_{suc}\times {\displaystyle \frac{k}{k-1}}\times \left[{(\frac{P_{dis}}{P_{suc}})}^{\frac{k-1}{k}}-1\right]$

where $W_i$ is the ideal power consumption, W.

In the above formula, k cannot represent the actual polytropic compression process. Therefore, building on Negrão [14], Li [15] calculates the actual power of the compressor using the following equation:

(6)$W=P_{suc}\times V_{suc}\times a_1\times \left[{(\frac{P_{dis}}{P_{suc}})}^{a_2+\frac{k-1}{k}}+\raisebox{1ex}{$a_3$}\!\left/ \!\raisebox{-1ex}{$P_{dis}$}\right.\right]+W_{loss}$

Thus, the isentropic efficiency of the compressor can be calculated using the following equation:

(7)${\eta }_{is}={\displaystyle \frac{V_{suc}\times (h_{is}-h_{suc})}{v_{suc}\times W}}$

where $a_1$, $a_2$, $a_3$ are the shaft power coefficients, ${\eta }_{is}$ is the isentropic efficiency, $V_{suc}$ is the actual suction volume, m³/s, and $W$ is the actual power consumption, W.

The above formulas apply to a compressor at a fixed frequency or a variable frequency compressor operating at its rated frequency. For variable frequency compressors operating at non-rated frequencies, the volumetric efficiency and isentropic efficiency need to be adjusted through speed or frequency. This can be calculated using Equations (8) and (9) [15]:

(8)${\displaystyle \raisebox{1ex}{${\eta }_v$}\!\left/ \!\raisebox{-1ex}{${\eta }_{v,ref}$}\right.}=d_1+d_2\times {\displaystyle \raisebox{1ex}{$N$}\!\left/ \!\raisebox{-1ex}{$N_{ref}$}\right.}+d_3\times {({\displaystyle \raisebox{1ex}{$N$}\!\left/ \!\raisebox{-1ex}{$N_{ref}$}\right.})}^2$

(9)${\displaystyle \raisebox{1ex}{${\eta }_{is,ref}$}\!\left/ \!\raisebox{-1ex}{${\eta }_{is}$}\right.}=e_1+e_2\times {\displaystyle \raisebox{1ex}{$N$}\!\left/ \!\raisebox{-1ex}{$N_{ref}$}\right.}+e_3\times {({\displaystyle \raisebox{1ex}{$N$}\!\left/ \!\raisebox{-1ex}{$N_{ref}$}\right.})}^2$

where $d_1$, $d_2$, $d_3$ are the volumetric efficiency coefficients for the variable frequency compressor, where $d_1$ + $d_2$ + $d_3$ = 1, $e_1$, $e_2$, $e_3$ are the isentropic efficiency coefficients, where $e_1$ + $e_2$ + $e_3$ = 1, ${\eta }_{v,ref}$ is the volumetric efficiency at variable frequency speed, ${\eta }_{is,ref}$ is the isentropic efficiency at variable frequency speed, $N_{ref}$ is the speed of the variable frequency compressor, rpm, and $N$ is the rated speed of the variable frequency compressor, rpm.

As the above model shows, the volumetric efficiency is proportional to the pressure ratio of the compressor’s suction and discharge, and it is related to the type of refrigerant. The isentropic efficiency of the compressor is inversely related to the suction-specific volume of the refrigerant, and it is dependent on suction and discharge parameters.

Through the establishment of an experimental setup for electrical vehicle compressors, experimental conditions are created, along with simulation results and experimental data, to compare the impact of lubricating oil on compressor performance and assess the applicability of the simulation model.

3. Experimental Setup and Data Processing

3.1. Experimental Setup

Figure 1 shows the testing setup of the refrigeration system performance for electrical vehicle compressors. The testing setup consists of a refrigerant cycle, a secondary refrigerant (R245fa) cycle, and a constant-temperature water cycle. Low-temperature, low-pressure refrigerant vapor leaves the evaporator and enters the compressor, becoming high-temperature, high-pressure vapor, which then enters the condenser. The condensed liquid refrigerant passes through the liquid receiver and enters the subcooler. The subcooled refrigerant then passes through the pneumatic control valve for throttling, forming low-temperature, low-pressure wet vapor. This vapor enters the evaporator for heating and evaporation, thus completing the cycle. The secondary refrigerant in the calorimeter controls the refrigeration capacity and evaporation pressure, while the constant-temperature water tank controls the condensation pressure and subcooling degree. Table 1 shows the testing conditions, where the variation patterns of system refrigeration capacity, power, COP, compressor isentropic efficiency, volumetric efficiency, and discharge temperature are obtained by changing testing parameters, such as compressor speed, evaporation temperature, and condensation temperature.

Figure 1

Experimental system: (a) Schematic drawing of experimental setup; (b) Photos of experimental system. 1. Electric Vehicle Compressor (EVS36 Series, scroll compressor, the detail parameters are shown in Table 2); 2. Oil Separator; 3. Condenser; 4. High-Pressure Liquid Receiver; 5. Subcooler; 6. Pneumatic Control Valve; 7. Calorimeter; 8. Evaporator; 9. Secondary Refrigerant; 10. Electric Heater; 11. Safety Valve; 12. Constant-Temperature Water Tank; 13. Refrigerant Mass Flow Meter; 14. Filter; 15. Sight Glass; 16. Tempered Glass Tube; 17. Float Flow Meter 1; 18. Float Flow Meter 2; 19. Power Meter 1; 20. Power Meter 2; T and P are Temperature and Pressure, respectively.

[Figure omitted. See PDF]

3.2. Data Processing

The compressor was tested using an R290 refrigerant according to the conditions listed in Table 1. The compressor’s suction and discharge temperature, pressure, and mass flow rate were tested by adjusting the compressor speed. During the experiment, the calorimeter maintained a dual-sided thermal balance, meaning the error of the cooling capacity on the refrigerant side and the electric heating power on the secondary refrigerant side was kept within 5%, indicating that the test setup met the requirements for thermal loss.

Figure 2 is the pressure–enthalpy diagram of the test system. Points 1 to 2 represent the actual compression process, point 2s represents the ideal isentropic compression process, point 3 is the state at the outlet of the condenser, and point 3s is the state at the outlet of the subcooler. As shown in the figure, the enthalpy value remains constant from point 3s to point 4, so the process from point 3s to point 1 is considered as a whole. The evaporator outlet state at point 1 consists of the evaporated gaseous refrigerant, lubricating oil, and liquid refrigerant dissolved in the lubricating oil. The amount of liquid refrigerant dissolved in the lubricating oil can be determined by consulting the solubility characteristic curve:

Therefore, the flow expression at the evaporator outlet state at point 1 is as follows:

(10)$m_{mix}=m_{1,rG}+m_o+m_{1,rL}$

where $m_{1,rG}$ is the mass flow rate of vapor refrigerant at the outlet of the evaporator (compressor suction), kg/s; $m_{1,rL}$ is the mass flow rate of liquid refrigerant dissolved in the oil at the outlet of the evaporator (compressor suction), kg/s.

The formula for calculating the nominal cooling capacity of the system is as follows:

(11)$Q=m_{1,rG}\times (h_1-h_{3,sub})$

where $Q$ is the nominal cooling capacity, kw; $h_{3,sub}$ is the enthalpy at the outlet of the subcooler, kJ/kg.

Due to the superheat at the outlet of the evaporator, the temperature and enthalpy of the lubricating oil at the inlet of the evaporator and inlet of the expansion valve differ, and the enthalpy of the liquid refrigerant dissolved in the lubricating oil also changes. Therefore, the heat exchange in the evaporator includes the heat released by the lubricating oil and the liquid refrigerant. The heat balance is achieved using electric heating in the calorimeter; thus, the heat balance equation is as follows:

(12)$Q_e=W_e+m_o\times (h_{in,oil}-h_{out,oil})+m_{1,rL}\times (h_{in,rL}-h_{out,rL})$

where $h_{out,oil}$, $h_{in,oil}$ are the enthalpies of the lubricating oil at the outlet of the evaporator and before the expansion valve, respectively, kJ/kg; $h_{out,rL}$, $h_{in,rL}$ are the enthalpies of the liquid refrigerant dissolved in the lubricating oil at the outlet of the evaporator and before the expansion valve, respectively, kJ/kg; $W_e$ is the electric power measured by the calorimeter, representing the actual cooling capacity of the system, kW.

The power W of the compressor is measured using a power meter, so the enthalpy at point 2 can be calculated using the following heat balance equation:

(13)$W=(h_2-h_1)\times m_{1,rG}$

where h₁ is the enthalpy at the inlet of the compressor, kJ/kg; h₂ is the enthalpy at the outlet of the compressor, kJ/kg; W is the compressor power, kW;

The volumetric efficiency η_v of the compressor can be obtained from Equation (1):

(14)${\eta }_v={\displaystyle \frac{60\times v_1\times m_{1,rG}}{N\times V_d}}$

where ${\nu }_1$ is the specific volume at point 1 (compressor suction), m³/kg.

The isentropic efficiency η_is of the compressor is

(15)${\eta }_{is}={\displaystyle \frac{h_{2,is}-h_1}{h_2-h_1}}$

where $h_{2,is}$ is the theoretical enthalpy at the outlet of the compressor, kJ/kg; h₂ is the actual enthalpy at the outlet of the compressor, kJ/kg.

The mass flow rate and mixture density at point 3s (at the outlet of subcooler) are obtained through a mass flow meter. The mass flow rate of the mixture is the sum of the mass flows of the lubricating oil and the refrigerant liquid, as shown in the following equation:

(16)$m_{mix}=m_o+m_{rL}$

where $m_o$ is the mass flow rate of the lubricating oil, kg/s; $m_{rL}$ is the mass flow rate of the refrigerant liquid, kg/s; $m_{mix}$ is the total mass flow rate of the mixture, kg/s.

The density of the mixture is obtained by mixing the liquid phase refrigerant and the compressor oil and is calculated as follows:

(17)${\rho }_{mix}\left(T,P\right)={\displaystyle \frac{m_o+m_{rL}}{V}}$

where ${\rho }_{mix}\left(T,P\right)$ is the density of the mixture, kg/m³; $V$ is the volumetric flow rate of the mixture, m³/s.

Assuming that the volume of the mixture after combining the compressor oil and refrigerant is the sum of the volumes before mixing (with theoretical errors), Formula (18) is calculated as follows:

(18)${\rho }_{mix}={\displaystyle \frac{m_o+m_{rL}}{V_o+V_{rL}}}={\displaystyle \frac{m_o+m_{rL}}{\raisebox{1ex}{$m_o$}\!\left/ \!\raisebox{-1ex}{${\rho }_o$}\right.+\raisebox{1ex}{$m_{rL}$}\!\left/ \!\raisebox{-1ex}{${\rho }_{rL}$}\right.}}$

where ${\rho }_{mix}$ is the density of the mixture, kg/m³; $m_o$ is the mass flow rate of the lubricating oil, kg/s; $m_{rL}$ is the mass flow rate of the refrigerant liquid, kg/s; ${\rho }_o$ is the density of the lubricating oil, kg/m³; ${\rho }_{rL}$ is the density of the refrigerant liquid, kg/m³.

From Formula (19):

(19)$\omega ={\displaystyle \frac{m_o}{m_o+m_{rL}}}$

Formula (20) is calculated as follows:

(20)${\displaystyle \frac{1}{{\rho }_{mix}\left(T,P\right)}}={\displaystyle \frac{\omega }{{\rho }_o\left(T\right)}}+{\displaystyle \frac{1-\omega }{{\rho }_{rL}\left(T,P\right)}}$

where $\omega$ is the oil circulation rate.

Thus, the refrigerant flow rate $m_{rL}$, oil flow rate $m_o$, and oil circulation rate $\omega$ under state 3s can be determined.

The properties of the R290 refrigerant used in the equations above, such as enthalpy, can be obtained using REFPROP 9.0 [16].

4. Thermal Balance Verification and Uncertainty Analysis of the Test Setup

4.1. Thermal Balance Verification

The thermal balance of the experimental system is verified to ensure the reliability of the experimental data. The verification experiment is conducted under conditions of an evaporation temperature of 0 °C, a condensation temperature of 60 °C, and at variable compressor speeds. The refrigerant’s superheat is set to 10 °C, and the subcooling is set to 5 °C. The cooling capacity on the measured refrigerant side is calculated using the enthalpy difference and flow rate, and the electric heating power on the secondary refrigerant side is obtained through power meter one. The verification results, as shown in Figure 3, indicate that the deviation in cooling capacity on both sides is within the ±5% error range, demonstrating that the experimental system has a very low heat leakage rate. Therefore, the experimental data measured by this test setup are reliable.

4.2. Uncertainty Analysis

When measuring parameters such as the temperature, pressure, and flow rate, the measuring instruments themselves have a certain degree of precision, which results in deviation in the measured results, known as uncertainty. When these basic quantities are used to obtain properties such as enthalpy and physical quantities like cooling capacity and COP, there will inevitably be a transmission of errors. The following represents the basic formula for error transmission, and uncertainty is calculated using the differential method [17].

(21)$\begin{array}{l}z=f\left(x,y\right)=xy\\ \Rightarrow \left({\displaystyle \frac{\partial f}{\partial x}}\right)=y={\displaystyle \frac{z}{x}},\left({\displaystyle \frac{\partial f}{\partial y}}\right)=x={\displaystyle \frac{z}{y}}\\ {\left({\alpha }_z\right)}^2={\left({\displaystyle \frac{z}{x}}\right)}^2{\left({\alpha }_x\right)}^2+{\left({\displaystyle \frac{z}{y}}\right)}^2{\left({\alpha }_y\right)}^2\\ \Rightarrow {\displaystyle \frac{{\alpha }_z}{z}}=\sqrt{{\left({\displaystyle \frac{{\alpha }_x}{x}}\right)}^2+{\left({\displaystyle \frac{{\alpha }_y}{y}}\right)}^2}\end{array}$

The basic parameters and uncertainties of the test setup are shown in Table 3.

5. Analysis of Simulation Model and Experimental Results

5.1. Validation of Compressor Performance Simulation Model

Using the experimental setup and oil separation system, the OCR within the system was kept below 1%. The testing conditions included an evaporation temperature of 0 °C, a condensation temperature of 60 °C, and a speed range of 2400 to 4800 rpm. As shown in Figure 4 and Figure 5, the OCR is less than 0.5%. Comparing the experimental OCR with the simulation model results indicates that the compressor speed has a minor impact on compressor efficiency. Therefore, from both the experimental and simulation results, when the OCR is minimal, it can be approximated to the volumetric efficiency and isentropic efficiency when the OCR is 0, which is consistent with the simulation model results without the influence of lubricating oil, which are derived from Li’s [13] study.

5.2. Simulation Analysis of the Impact of OCR on Compressor Performance

5.2.1. Experimental Results of OCR with Changing Conditions

In refrigeration systems, the OCR needs to consider the heat transfer performance of the heat exchangers and the lubrication of the compressor. An excessively low oil circulation rate can lead to inadequate lubrication for the compressor, while too high an oil circulation rate can significantly reduce the heat transfer coefficient of the system’s heat exchangers. Typically, the system oil circulation rate is maintained between 2% and 10%. By adjusting the charge amount, the oil content for most operation conditions is maintained between 2% and 10% to test the system and compressor performance.

Figure 6 shows how the OCR varies with speed under different conditions. The figure indicates that a lower evaporation temperature results in a lower OCR. For instance, when changing from 10/50 °C to 0/50 °C and from 5/55 °C to 0/55 °C, each 10 °C decrease in evaporation temperature leads to about a 1% reduction in the OCR. As the evaporation temperature is lower, the viscosity of lubricating oil decreases. Under the same compressor speed, the oil mass flow rate becomes smaller, so the OCR also decreases. This trend is more notable at 3000 rpm. Changes from 10/45 °C to 0/45 °C show minimal shifts in an OCR below 3000 rpm, possibly influenced by testing deviations. The figure also reveals that a lower condensation temperature leads to a higher OCR. For example, changing from 0/50 °C to 0/45 °C and from 10/50 °C to 10/45 °C results in approximately a 2% increase in the OCR for every 5 °C drop in the condensation temperature. This is because when the condensation temperature decreases, the pressure ratio also decreases. Therefore, the mass flow rate increases under the same compressor speed. Then, the OCR rises rapidly. And, changes in the condensation temperature have a more pronounced effect on the OCR. This conclusion suggests that when the compressor operates under low evaporation and high condensation conditions, such as during winter heating, the system’s OCR is at its minimum, where it is necessary to note the compressor’s oil return in order to avoid insufficient lubricating oil due to a low OCR. Conversely, in high evaporation and low condensation conditions, such as in spring and autumn, the system’s OCR is at its maximum, requiring attention to the heat transfer impact of the heat exchangers.

5.2.2. Experimental Results on the Impact of OCR on Compressor Performance

Figure 7, Figure 8 and Figure 9 present the experimental results of the compressor performance, specifically illustrating the changes in isentropic efficiency, volumetric efficiency, and the discharge temperature with variable compressor speeds under different conditions.

Figure 7 shows that isentropic efficiency peaks at an optimal value as compressor speed increases, and this peak occurs sooner as the evaporation temperature rises. The curve for isentropic efficiency has a marked inflection point: when the pressure ratio is 2.41, the inflection point occurs at a speed of 2400 rpm, whereas at a pressure ratio of 4.02, it occurs at 5400 rpm. After these points, the curve flattens with minor changes. According to Li [13], isentropic efficiency decreases with an increasing pressure ratio. At low speeds, the low flow rate means less oil can be carried out from the compressor oil sump, leading to poor cooling and lubrication, hence a rapid decrease in isentropic efficiency. At high speeds, as the oil content is higher and lubrication is sufficient, friction losses in the compressor remain relatively constant, leading to consistent isentropic efficiency with minor influence from the pressure ratio.

Figure 8 indicates that volumetric efficiency increases rapidly with the compressor speed before reaching the rated compressor speed and then levels off after surpassing it. As the compressor speed increases, the effect of the pressure ratio on volumetric efficiency diminishes. At a low pressure ratio of 2.41, volumetric efficiency reaches a maximum of up to 90% at a speed of 3600 rpm. As the pressure ratio increases, internal leakage also increases, resulting in lower volumetric efficiency, as described by Equation (3). At low compressor speeds, less oil is drawn from the compressor oil sump, leading to poor sealing and a rapid decline in volumetric efficiency. As the compressor speed increases, sealing improves and eventually reaches an optimal level, causing volumetric efficiency to stabilize.

Figure 9 demonstrates that the discharge temperature is related to evaporation and condensation temperatures. According to Shaik [18], a lower evaporation temperature leads to a higher discharge temperature under the same condensation temperature. For example, in transitions from 10/50 °C to 0/50 °C and 5/55 °C to 0/55 °C, a 10 °C drop in the evaporation temperature results in approximately a 10 °C increase in the discharge temperature. As the evaporation temperature decreases, the pressure ratio increases. Therefore, the refrigerant mass flow rate decreases under the same condensation temperature. Since there is an irreversible loss in the compression process, the refrigerant steam absorbs this part of the heat, resulting in an increase in the discharge temperature. Additionally, a higher condensation temperature leads to a higher discharge temperature. This is shown by transitions from 0/50 °C to 0/45 °C and 10/50 °C to 10/45 °C, where a 5 °C drop in the condensation temperature results in approximately a 15 °C decrease in the discharge temperature. Because the condensation temperature decreases, the pressure ratio decreases. Therefore, the refrigerant mass flow rate increases under the same evaporation temperature. Then, the discharge temperature decreases. The figure also shows that with increasing speed, the discharge temperature decreases, primarily because as the compressor speed increases, the oil content in the refrigerant increases, and more liquid refrigerant is dissolved within the oil, thereby lowering the discharge temperature. However, at significantly high compressor speeds, growing mechanical losses reduce the cooling effect of increased oil content, causing the discharge temperature to stabilize or rise slightly.

5.2.3. Simulation Results on the Impact of OCR on Compressor Performance

Using the theoretical model from the previous section, simulations were conducted, and the experimental and simulated data of the compressor performance were compared. Figure 10, Figure 11 and Figure 12 present the comparison of simulated and experimental data for isentropic efficiency, volumetric efficiency, and the discharge temperature, respectively.

Figure 10 indicates that the simulation error for isentropic efficiency is within 10%, and the average error is 1.3%. At high compressor speeds and a low pressure ratio of 2.41, the experimental values are lower than the simulated ones, where the oil content is the highest. Conversely, at low compressor speeds and a high pressure ratio of 4.02, the experimental values are higher than the simulated ones, where the oil content is the lowest. These two cases have relatively large errors.

Figure 11 shows that the simulation error for volumetric efficiency is within 5%, with an average error of 0.5%. Therefore, the influence of oil content on the model is not significant when compared to the experimental data. The simulation model shows good applicability with a maximum 10% OCR from the experimental data.

Figure 12 indicates that the simulation error for the discharge temperature is within 5 °C, with an average error of 0.68 °C. The largest deviations occur at low or high compressor speeds. As can be seen from Figure 9, discharge temperatures at low and high compressor speeds are higher than those at rated compressor speeds. By comparing simulation model data with experimental data, it is shown that the discharge temperature is significantly affected by the oil content, suggesting that further optimization regarding the impact of the OCR is needed.

In addition to the simulation and experimental comparison for compressor performance, simulations for compressor power, cooling capacity, and the COP were also conducted. Figure 13, Figure 14 and Figure 15 compare the deviations between simulated and experimental values for compressor power, cooling capacity, and COP, respectively. In Figure 13, the minimum error for power between simulated and experimental values is 0.12%, with a maximum error of 9.8% and an RMS deviation of 2.6%. In Figure 14, the minimum error for cooling capacity is 0.06%, with a maximum error of 9.4% and an RMS deviation of 2.8%. In Figure 15, the minimum error for the COP is 0.47%, with a maximum error of 10.3% and an RMS deviation of 2.9%. However, when the OCR is within the range of 2–10%, the simulation model matches well with deviations under 5%, with RMS errors of 3.0%, 2.8%, and 2.1%, respectively. The figures indicate that when the oil content under working conditions exceeds 10%, the deviation in simulated values is relatively large. Since the relationship between isentropic efficiency and the compressor speed in Figure 7 is more akin to a fourth-degree polynomial, using a second-degree polynomial for the simulation model results in larger deviations. Particularly, with the inflection point at low compressor speeds, in Figure 13, the power deviation is larger at low compressor speeds and smaller at high compressor speeds. From the previous discussion on the solubility characteristics of refrigerant and oil, more refrigerant is dissolved in the oil at the inlet of the evaporator, and a significant amount of liquid refrigerant dissolved in the oil volatilizes at the outlet of the evaporator. While the simulation retains calculations on solubility, the actual process may be more unstable, with greater deviations in cooling capacity as the oil content increases, as shown in Figure 14. Consequently, the added deviations in power and cooling capacity result in even larger deviations in COP, as seen in Figure 15.

6. Conclusions

This study used a semi-empirical compressor simulation model and established a compressor experimental setup to investigate the impact of oil charge on the OCR and the effect of the OCR on compressor performance, considering factors such as evaporation temperature, condensation temperature, and compressor speed variations. Based on the experimental results, a comparison between experimental and simulated data was conducted, leading to the following conclusions:

• (1). Oil charge has a significant impact on the system’s OCR, and a greater oil charge leads to a higher OCR. A fitting relationship between the oil charge and OCR was obtained. When the OCR is approximately zero, the simulation model aligns well with the experimental values.

• (2). The OCR increases with increasing compressor speed, decreases with lower evaporation temperatures, and increases with higher condensation temperatures. And the condensation temperature has a greater impact on the OCR than the evaporation temperature.

• (3). The OCR significantly affects the isentropic efficiency and discharge temperature of the compressor but has a smaller impact on volumetric efficiency. At low compressor speeds, a low OCR leads to a rapid decline in isentropic efficiency. At high compressor speeds, isentropic efficiency tends to be consistent. As compressor speed increases, the discharge temperature first decreases and then gradually levels off. Volumetric efficiency increases with the compressor speed and levels off after surpassing the rated compressor speed. And the OCR shows little impact on volumetric efficiency.

• (4). The simulation model for volumetric efficiency has the highest accuracy, while isentropic efficiency and the discharge temperature show a notable impact from the OCR. At certain low and high compressor speeds, the impact of the OCR needs to be considered for adjusting the simulation model.

The variable frequency of electrical vehicle air conditioning compressors has been widely applied due to their precise temperature control, energy efficiency, comfort, and excellent noise and vibration characteristics. However, lubricating oil in the compressor has a significant impact on the reliability of the compressor and the performance of the refrigeration system. Therefore, it is necessary to analyze the mechanism of the oil circulation rate and its effects. From the above analysis, it can be seen that there are three main factors that ensure the best performance of the compressor, such as the oil charge, compressor speed, and appropriate operating conditions (e.g., condensation temperature and evaporation temperature).

Author Contributions

Software, H.C.; data curation, X.L.; Writing—original draft, J.C.; Writing—review & editing, L.H.; Supervision, L.T.; Project administration, X.W. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Data is contained within the article.

Conflicts of Interest

Author Jianhong Chen was employed by the company Zhejiang Zhongguang Electrical Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Nomenclature

a1, a2, a3	fitting parameters for shaft power model(they are 0.333, 1.197 and 440.393, respectively) [13]
b1, b2	fitting parameters for mass flow rate model(they are 1.047 and −0.051, respectively) [13]
d1, d2, d3	fitting parameters for volumetric efficiency model(they are 0.693, 0.543 and −0.236,respectively) [13]
e1, e2, e3	fitting parameters for isentropic efficiency model(they are 1.599, −1.060 and 0.461, respectively) [13]
h 1	the enthalpy at the inlet of the compressor [kJ/kg]
h 2	the actual enthalpy at the outlet of compressor [kJ/kg]
h 3,sub	the enthalpy at the outlet of subcooler [kJ/kg]
h 2,is	the theoretical enthalpy at the outlet of compressor [kJ/kg]
hin,oil	the enthalpy of the lubricating oil before the expansion valve [kJ/kg]
hout,oil	the enthalpy of the lubricating oil at the outlet of evaporator [kJ/kg]
hin,rL	the enthalpy of the liquid refrigerant dissolved in the lubricating oil before the expansion valve [kJ/kg]
hout,rL	the enthalpy of the liquid refrigerant dissolved in the lubricating oil at the outlet of evaporator [kJ/kg]
m 1,rG	mass flow rate of vapor refrigerant at the outlet of evaporator [kg/s]
m 1,rL	mass flow rate of liquid refrigerant dissolved in the oil at the outlet of evaporator [kg/s]
m	mass flow rate [kg/s]
η	efficiency
N	compressor speed [rpm(r/min)]
V	compressor displacement [ml/rev]
v	specific volume [m3/kg]
C	clearance fraction
P	pressure [kPa]
n	polytropic index
k	refrigerant isentropic coefficient
$\alpha$	ratio of electromechanical losses to Wt
Wloss	constant part of power loss [W]
Wt	polytropic compression power [W]
W	compressor power [W]
Q	cooling capacity [kW]
ρ	density [kg/m3]
ε	pressure ratio (condensation temperature/evaporation temperature)
$\omega$	oil circulation rate
WT	oil/refrigerant proportion weight charge
Subscripts
v	volumetric efficiency
dis	discharge
suc	suction
d	displacement
is	isentropic
ref	reference
rG	gas refrigerant
rL	liquid refrigerant
o	oil
mix	mixture
e	electric power
r	refrigerant
i	idea
sub	subcooler
Abbreviations
OCR	oil circulation rate
RMS	root mean square
COP	coefficient of performance
EES	engineering equation solver

Footnotes

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Figures and Tables

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Figure 2. Thermodynamic cycle.

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Figure 3. Comparison of cooling capacity on measured refrigerant side and electric heating power on secondary refrigerant side.

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Figure 4. Calculated data vs. test data for volumetric efficiency based on OCR ≈ 0.

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Figure 5. Calculated data vs. test data for isentropic efficiency based on OCR ≈ 0.

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Figure 6. OCR vs. compressor speed with different temperature conditions based on specific oil/refrigerant proportion weight charge (15.4%).

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Figure 7. Isentropic efficiency vs. compressor speed with different temperature conditions.

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Figure 8. Volumetric efficiency vs. compressor speed with different temperature conditions.

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Figure 9. Discharge temperature vs. compressor speed with different temperature conditions.

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Figure 10. Calculated data vs. test data for isentropic efficiency.

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Figure 11. Calculated data vs. test data for volumetric efficiency.

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Figure 12. Calculated data vs. test data for discharge temperature.

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Figure 13. Calculated data vs. test data for power.

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Figure 14. Calculated data vs. test data for cooling capacity.

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Figure 15. Calculated data vs. test data for COP.

Table 1

Experimental conditions.

Parameters	Evaporation Temperature/°C	Condensation Temperature/°C	Compressor Speed /rpm
Operation conditions range	0 °C, 5 °C, 10 °C	45 °C, 50 °C, 55 °C, 60 °C	1000~6000

Table 2

Parameters of EVS36 scroll compressor.

Parameters	Base Circle Radius/mm	Involute Starting Angle/(°)	Maximum Angle of Intermediate Scroll Profile/(°)	Suction Volume/cm3	Scroll Wrap Height/mm
Values	2.8	40.5	810	35	22.3

Table 3

Uncertainty analysis.

	Parameter	Uncertainty
Primary measurements	Temperature/°C	±0.1 °C
	Pressure/MPa	±0.2%
	Refrigerant Mass Flow Rate/(kg/h)	±0.1%
	Electric Heating Power/kW	±0.15%
Dependent quantities	Enthalpy Difference on Refrigerant Side /(kJ/kg)	±0.218
	Electric Heating Power (Q1) /kW	±3.75%
	Cooling Capacity (Q0) /kW	±2.01%
	Oil Circulation Rate (OCR)	±0.883%

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