The thermal management system in an electric vehicle car is a critical component that directly impacts passenger comfort and, more importantly, the vehicle’s driving range. Among all ancillary systems, the air conditioning (A/C) unit is one of the most significant energy consumers. Therefore, optimizing its efficiency is paramount for extending the mileage of an electric vehicle car. In the pursuit of environmentally friendly and efficient refrigerants, carbon dioxide (CO₂) has emerged as a promising alternative to traditional hydrofluorocarbon (HFC) refrigerants. Its negligible global warming potential (GWP), non-toxicity, and excellent thermophysical properties make it particularly attractive for automotive applications. However, due to its relatively low critical temperature (approximately 31.1°C), a CO₂-based A/C system in an electric vehicle car predominantly operates in a transcritical cycle under most ambient conditions.
In a transcritical CO₂ cycle, the high-side heat exchanger, known as the gas cooler, operates above the critical pressure. The thermophysical properties of supercritical CO₂, such as specific heat, density, and thermal conductivity, exhibit dramatic and non-linear variations with small changes in temperature and pressure, especially near the pseudo-critical region. This characteristic makes the heat transfer efficiency of the gas cooler highly sensitive to operating conditions, including pressure, refrigerant inlet temperature, and, crucially, the air-side heat transfer conditions.
The compact packaging typical of an electric vehicle car front compartment introduces a unique engineering challenge. The gas cooler is often installed in a tightly packed front-end module alongside other heat exchangers like the radiator and the power electronics cooler. This layout inevitably leads to a “partial thermal shading” effect, where an upstream heat exchanger blocks a portion of the gas cooler. This shading effect degrades the local air-side conditions for the gas cooler in the blocked area, typically resulting in increased air inlet temperature and reduced air velocity. For an electric vehicle car A/C system, this translates to a compromised cooling capacity of the gas cooler, forcing the system to operate at a higher discharge pressure to reject the necessary heat, which in turn increases compressor power consumption and reduces the overall Coefficient of Performance (COP). This performance penalty directly and negatively affects the driving range of the electric vehicle car.
Simultaneously, the refrigerant charge amount is another pivotal parameter determining the performance of any refrigeration system, and this is especially true for transcritical CO₂ systems due to the refrigerant’s high sensitivity to operating states. An optimal charge amount yields the best compromise between cooling capacity and system efficiency (COP). An undercharged system suffers from high superheat at the evaporator outlet, reduced cooling capacity, and potentially excessive compressor discharge temperature. Conversely, an overcharged system leads to a sharp increase in compressor power, reduced COP, and risks such as high-pressure safety valve actuation or even compressor liquid slugging. For an electric vehicle car application, where energy efficiency is directly linked to range, identifying and maintaining the optimal charge is crucial.
While the phenomenon of thermal shading is recognized and the importance of charge optimization is well-established, existing research often treats these factors in isolation. There is a significant gap in understanding the quantitative coupling between them: specifically, how does partial thermal shading on the gas cooler affect the optimal refrigerant charge amount required for a transcritical CO₂ A/C system in an electric vehicle car? This knowledge gap can lead to suboptimal system performance and energy waste in real-world, complex thermal environments. This article aims to address this by developing a simulation model of a transcritical CO₂ cycle that integrates the effects of localized thermal shading on the gas cooler. Through numerical analysis, we will elucidate the mechanism and establish quantitative relationships between shading characteristics, shading location, system performance, and the resulting shift in the optimal refrigerant charge amount. The findings are intended to provide theoretical guidance and engineering insights for the design and calibration of high-performance, natural-refrigerant-based A/C systems for the modern electric vehicle car.
Theoretical Foundation and System Modeling
The core thermodynamic cycle for an electric vehicle car air conditioner using CO₂ is the transcritical cycle. Its basic schematic and corresponding pressure-enthalpy (p-h) diagram are presented below. The main components include a compressor, a gas cooler, an expansion device (such as an internal heat exchanger or an ejector in advanced systems, but a simple expansion valve is considered here for fundamental analysis), and an evaporator.
The cycle process can be described as follows:
1. Compression (1-2): Low-pressure, superheated vapor from the evaporator is compressed to a supercritical pressure (above ~73 bar) in the compressor. The process is polytropic and results in a significant temperature rise.
2. Gas Cooling (2-3): The high-pressure, high-temperature supercritical fluid rejects heat to the ambient air in the gas cooler. This is not a condensation process but a continuous cooling of the supercritical fluid. The refrigerant remains in a single supercritical phase throughout this component.
3. Expansion (3-4): The high-pressure fluid is expanded to a low pressure, causing a substantial temperature drop. A two-phase mixture of liquid and vapor is typically formed at the evaporator inlet.
4. Evaporation (4-1): The low-pressure mixture absorbs heat from the cabin air in the evaporator, completely evaporating and becoming superheated vapor at the compressor inlet.
The performance of this cycle for an electric vehicle car is evaluated using two primary metrics: Cooling Capacity ($Q_{eva}$) and Coefficient of Performance ($COP$).
The cooling capacity, representing the useful thermal energy removed from the cabin, is calculated from the refrigerant side as:
$$Q_{eva} = \dot{m}_{ref} \cdot (h_1 – h_4)$$
where $\dot{m}_{ref}$ is the refrigerant mass flow rate, and $h_1$ and $h_4$ are the specific enthalpies at the evaporator outlet and inlet, respectively.
The COP, indicating the system’s energy efficiency, is the ratio of cooling capacity to the total compressor power input:
$$COP = \frac{Q_{eva}}{W_{comp}}$$
A higher COP means less battery energy is consumed per unit of cooling provided, which is a direct benefit for the driving range of the electric vehicle car.
To analyze the impact of charge amount, we define a Comprehensive Performance Index ($CPI$) that balances both cooling capacity and efficiency, as both are critical for an electric vehicle car application.
$$CPI = \omega \cdot \frac{Q_{eva}}{Q_{eva,max}} + (1-\omega) \cdot \frac{COP}{COP_{max}}$$
Here, $Q_{eva,max}$ and $COP_{max}$ are the maximum achievable values for a given set of operating conditions across all charge amounts, used for normalization. $\omega$ is a weighting factor between 0 and 1. Given the paramount importance of energy efficiency for electric vehicle car range, a weighting favoring COP (e.g., $\omega=0.3$) is often appropriate. The charge amount corresponding to the peak $CPI$ is defined as the optimal charge amount for that specific operating condition.
To simulate the system, a steady-state model was developed based on core conservation equations. The gas cooler and evaporator are modeled using a finite-volume approach, dividing them into small control volumes. For each control volume, the governing equations for the refrigerant side are:
Mass conservation:
$$\frac{d\dot{m}_{ref}}{dx} = 0$$
Energy conservation:
$$\dot{m}_{ref} \frac{dh}{dx} = \frac{U \cdot A_{surf} \cdot (T_{air} – T_{ref})}{L}$$
where $U$ is the overall heat transfer coefficient, $A_{surf}$ is the heat transfer surface area in the control volume, $T_{air}$ and $T_{ref}$ are the local air and refrigerant temperatures, and $L$ is the length of the heat exchanger.
The air-side flow is treated as one-dimensional. The heat transfer and pressure drop correlations for both refrigerant and air sides are implemented based on established literature for microchannel heat exchangers, which are common in electric vehicle car applications. The compressor model maps the mass flow rate and power consumption as functions of suction pressure, discharge pressure, and rotational speed. The expansion valve is modeled as a simple isenthalpic process.
The key innovation in this model is the ability to impose non-uniform boundary conditions on the gas cooler’s air side to simulate partial thermal shading. The gas cooler face is divided into shaded and unshaded zones. In the unshaded zone, the air inlet conditions (velocity $v_{unshaded}$, temperature $T_{unshaded}$) are set to the nominal ambient or vehicle forward speed conditions. In the shaded zone, the conditions are degraded to represent the wake from an upstream heat exchanger: reduced velocity and increased temperature. The shading intensity can be characterized by two parameters:
Velocity reduction ratio:
$$\beta_v = \frac{v_{unshaded} – v_{shaded}}{v_{unshaded}} \times 100\%$$
Temperature increase ratio:
$$\beta_T = \frac{T_{shaded} – T_{unshaded}}{T_{unshaded}} \times 100\%$$
where the subscript $shaded$ denotes the conditions in the blocked region.
The model was validated against experimental data from a transcritical CO₂ system test bench. Under a range of operating conditions typical for an electric vehicle car (evaporator air inlet from 15°C to 40°C, gas cooler air inlet from 15°C to 45°C, compressor speed from 800 to 8000 rpm), the simulated cooling capacity and COP showed good agreement with measurements, with relative errors generally within ±10%. This validated model serves as the tool for the subsequent investigation.
Determining the Optimal Charge under Uniform Conditions (No Shading)
Before investigating the shading effect, it is essential to establish a baseline: the optimal refrigerant charge amount for the system under ideal, uniform air flow conditions. This serves as the reference point against which all shading scenarios will be compared. The baseline operating conditions for this electric vehicle car analysis are set as follows: evaporator inlet air at 27°C, 40% relative humidity with a face velocity of 1.5 m/s; gas cooler inlet air at 35°C with a uniform face velocity; compressor speed fixed at 5000 rpm; and a fixed evaporator outlet superheat of 5 K. The refrigerant charge amount is varied from 0.35 kg to 0.70 kg.
The system performance under these uniform conditions reveals fundamental trends. Figure 4(a) in the reference material shows the variation of cooling capacity with charge amount. At very low charge levels, the system is severely undercharged. The refrigerant mass flow rate is low, leading to poor utilization of the evaporator’s heat transfer area and consequently low cooling capacity. As the charge amount increases, the mass flow rate rises, more effectively utilizing the evaporator and increasing the cooling capacity. However, this increase is not linear. Beyond a certain point, further increasing the charge leads to a diminishing return in cooling capacity because the system becomes limited by other factors, such as the gas cooler’s ability to reject heat.
More critically, the COP shows a distinct peak, as illustrated in Figure 4(b). Initially, with increasing charge, COP rises as the system moves towards its design point, where the compressor operates more efficiently and the heat exchangers are properly utilized. After reaching a maximum, COP begins to decline. This decline in an overcharged state is primarily due to the rapid increase in compressor power. The additional refrigerant increases the system’s high-side pressure, which significantly raises the compression work required. For an electric vehicle car, this translates directly to higher battery drain per unit of cooling.
By applying the Comprehensive Performance Index ($CPI$) with a weight $\omega=0.3$, we obtain a single curve, Figure 4(c), that balances the need for cooling ($Q_{eva}$) and efficiency ($COP$). The $CPI$ curve exhibits a clear maximum. The refrigerant charge amount corresponding to this maximum $CPI$ is defined as the optimal charge for the given operating condition. For the baseline case with a gas cooler air velocity of 2 m/s, this optimal charge is determined to be 0.50 kg.
This analysis was repeated for different gas cooler face velocities (2, 4, 6, 8 m/s) and different compressor speeds (3000, 4000, 5000, 6000 rpm). A summary of the findings is presented in the table below.
| Parameter Variation | Effect on Cooling Capacity ($Q_{eva}$) | Effect on COP | Effect on Optimal Charge |
|---|---|---|---|
| Increased Gas Cooler Velocity (at fixed charge & comp. speed) | Moderate increase. Enhances heat rejection. | Moderate increase. Reduces compressor pressure ratio. | Negligible change. Optimal charge remains ~0.50 kg. |
| Increased Compressor Speed (at fixed charge & gas cooler velocity) | Significant increase. Raises refrigerant mass flow. | Significant decrease. Power consumption rises sharply. | Shift towards higher charge. System requires more refrigerant to utilize higher flow at higher speeds effectively. |
| Increased Refrigerant Charge (at fixed comp. speed & gas cooler velocity) | Increases to a plateau. Follows trend in Fig. 4(a). | Exhibits a distinct maximum. Follows trend in Fig. 4(b). | Defines the $CPI$ peak. The central variable of this study. |
The key conclusion from this baseline study is that while operating parameters like fan speed and compressor RPM influence performance, the refrigerant charge amount has a profound and non-linear effect on the overall system efficiency and cooling output. For the standard operating condition chosen for this electric vehicle car study, 0.50 kg is established as the reference optimal charge under ideal, unshaded conditions.
Influence of Thermal Shading Characteristics on Optimal Charge
We now introduce the primary disturbance: partial thermal shading on the gas cooler. As explained, this is a common scenario in the crowded front end of an electric vehicle car. The shading effect has two main components: a reduction in local air velocity ($\beta_v > 0$) and an increase in local air temperature ($\beta_T > 0$). It is important to decouple these effects to understand their individual and combined impacts.
First, consider a case where the upstream heat exchanger (e.g., a radiator with no active heat load) causes only airflow blockage but no temperature rise. This is a pure velocity reduction scenario ($\beta_v > 0, \beta_T = 0$). The simulation shows that a reduction in local air velocity alone does degrade gas cooler performance, as it lowers the convective heat transfer coefficient. However, the impact on the overall system performance of the electric vehicle car A/C is relatively moderate. The reduction in gas cooler efficiency can be partially compensated by a slight increase in the refrigerant side log-mean temperature difference. Consequently, while both $Q_{eva}$ and $COP$ decrease compared to the unshaded case, the shape of the $CPI$ vs. charge curve remains largely unchanged, and the charge amount corresponding to the $CPI$ peak does not shift significantly. The optimal charge remains at approximately 0.50 kg even with up to 50% local velocity reduction. This indicates that airflow obstruction alone, while undesirable, does not fundamentally alter the system’s charge requirement.
The situation changes dramatically when the shading includes a temperature increase, which is the realistic case when the upstream heat exchanger is rejecting waste heat (e.g., from the powertrain or battery). We analyze a coupled scenario where the shaded region experiences both a 50% reduction in velocity and a 50% increase in inlet air temperature relative to the ambient ($\beta_v = 50\%, \beta_T = 50\%$). For this analysis, the shading is applied to the bottom one-third of the gas cooler face, a typical location for a radiator in an electric vehicle car layout.
The impact is severe. The local temperature rise in the shaded zone drastically reduces the temperature difference between the hot supercritical CO₂ and the cooling air. This significantly impairs the heat rejection capability of that portion of the gas cooler. The system responds by raising the discharge pressure to try to maintain the heat rejection rate, which in turn increases compressor power disproportionately. The thermodynamic cycle on a p-h diagram shifts upwards and to the right, indicating higher pressures and temperatures throughout.
The performance curves under this strong shading tell a different story. Both $Q_{eva}$ and $COP$ are substantially lower across all charge amounts compared to the unshaded baseline. More importantly, the $CPI$ curve is not only depressed but its peak is shifted to the right. This is a critical finding. It means that to achieve the best possible performance (the highest $CPI$) under these degraded thermal conditions, the system requires more refrigerant than it does under ideal conditions.
The mechanism behind this shift is related to refrigerant mass flow and heat exchanger utilization. Under severe shading, the gas cooler’s effectiveness drops. To compensate and achieve a usable cooling capacity, the system needs a higher refrigerant mass flow rate to transport the required heat load. Increasing the total charge amount in the system is one way to increase this mass flow rate for a given compressor speed. Essentially, the system is trading off the inefficiency caused by higher pressure (from overcharge) against the inefficiency caused by poor heat rejection (from shading), seeking a new, shifted optimum.
The degree of optimal charge shift depends on the shading intensity. The table below summarizes the results for different levels of coupled ($\beta_v = \beta_T$) shading at the gas cooler bottom.
| Shading Intensity ($\beta_v = \beta_T$) | Optimal Charge Amount | Charge Increase vs. Baseline | Performance at Optimal Charge (vs. Unshaded Baseline at its Optimum) |
|---|---|---|---|
| 0% (Baseline) | 0.50 kg | 0% | $Q_{eva,base}$, $COP_{base}$ |
| 30% | 0.55 kg | +10% | $Q_{eva}$ ~ -15%, $COP$ ~ -25% |
| 50% | 0.60 kg | +20% | $Q_{eva}$ ~ -40%, $COP$ ~ -50% |
This quantitative relationship highlights a key design insight for electric vehicle car thermal management: if a gas cooler is subjected to significant thermal shading (characterized primarily by air pre-heating), the system’s refrigerant charge should be increased above the ideal-condition value to recover a portion of the lost performance. Failing to do so will result in operation at a charge level that is effectively “undercharged” relative to the new, shaded optimum, leading to even greater performance penalties.
The Critical Role of Shading Location
The location of the thermal shade on the gas cooler face is not a trivial detail; it is a critical factor that dramatically influences how the system’s optimal charge amount shifts. This is because the internal refrigerant flow path and temperature distribution within the gas cooler are highly organized. A shade affecting a high-temperature region at the refrigerant inlet has different consequences than one affecting a low-temperature region near the outlet.
To investigate this, six distinct shading locations were simulated, each covering one-third of the gas cooler’s frontal area, all with a strong shading intensity of $\beta_v = \beta_T = 50\%$. The locations are: Top, Bottom, Left side, Right side, Center-Vertical (a vertical strip), and Center-Horizontal (a horizontal strip). The results reveal striking differences.
1. Top Shading: When the shade covers the top section of the gas cooler, which often corresponds to the refrigerant inlet header area, the impact on system performance is surprisingly the smallest among all parallel-flow shading scenarios. The refrigerant enters this region at its highest temperature. Even though the cooling air is pre-heated by 50%, the temperature difference ($\Delta T$) between the refrigerant and air remains relatively large, allowing for decent heat transfer. Therefore, the performance degradation is moderate. Crucially, the $CPI$ peak for this case occurs at the same charge amount as the unshaded baseline: 0.50 kg. No charge increase is needed because the high-grade thermal energy at the inlet can still be effectively rejected despite the shading.
2. Bottom Shading: This is the worst-case scenario and mirrors the analysis in the previous section. The bottom section of the gas cooler is where the refrigerant temperature is lowest, approaching the gas cooler exit. Here, the temperature difference available for heat transfer is already small. A 50% pre-heating of the cooling air severely erodes this small $\Delta T$, drastically reducing the heat transfer rate in this zone. This creates a major bottleneck. To compensate, the system requires a significant increase in refrigerant charge to boost mass flow and pressure. The $CPI$ peak shifts markedly to 0.60 kg, a 20% increase from baseline. Even at this new optimum, the system’s $Q_{eva}$ and $COP$ are far below the unshaded performance.
3. Side Shading (Left & Right) and Center-Vertical Shading: These shading patterns block vertical sections of the gas cooler. In a typical multi-pass microchannel gas cooler, this means the shading affects several tube passes along their entire length. The impact is significant and fairly consistent across these locations. They degrade performance more than top shading but less than bottom shading. The optimal charge amount for all these cases increases to 0.55 kg, a 10% increase from the baseline. The uniform degradation along the flow path necessitates a moderate charge increase to recover performance.
4. Center-Horizontal Shading: This is similar to a combination of partial top and bottom shading effects. It blocks the central section of all tube passes. Its impact is severe, close to that of bottom shading, because it affects the crucial mid-to-lower temperature regions of the refrigerant flow. The optimal charge also increases to 0.55 kg.
The following table consolidates the effect of shading location on the optimal charge and the resulting performance of the electric vehicle car A/C system.
| Shading Location (1/3 area, $\beta=50\%$) | Optimal Charge (M_opt) | Charge Increase vs. Baseline | Performance at M_opt (vs. Unshaded Baseline at M=0.50kg) | Mechanism |
|---|---|---|---|---|
| None (Baseline) | 0.50 kg | 0% | Reference $Q_{eva}$, $COP$ | Ideal heat rejection. |
| Top | 0.50 kg | 0% | Minor reduction in $COP$, negligible change in $Q_{eva}$. | Large initial $\Delta T$ mitigates pre-heating effect. |
| Left, Right, Center-Vertical | 0.55 kg | +10% | Significant reduction in both $Q_{eva}$ (~12%) and $COP$ (~22%). | Uniform degradation across multiple flow passes. |
| Center-Horizontal | 0.55 kg | +10% | Significant reduction, similar to side shading. | Affects mid-section of all passes, harming mid-range heat transfer. |
| Bottom | 0.60 kg | +20% | Severe reduction in $Q_{eva}$ (~40%) and $COP$ (~52%). | Pre-heating catastrophically reduces the already-small $\Delta T$ at the low-temperature end. |
The performance gain achieved by shifting to the new, location-dependent optimal charge is substantial. For example, for the severe bottom shading case, increasing the charge from the baseline 0.50 kg to the shaded optimum of 0.60 kg results in a performance recovery of approximately 17% in cooling capacity and 14% in COP. While still far from unshaded performance, this optimization is crucial for making the system operational and minimizing the range penalty for the electric vehicle car.
Conclusion and Implications for Electric Vehicle Car Design
This investigation into the impacts of partial thermal shading on the optimal refrigerant charge amount for a transcritical CO₂ air conditioning system yields several critical conclusions with direct implications for the design and engineering of electric vehicle car thermal management systems.
Firstly, it is unequivocally demonstrated that thermal shading, particularly when it involves pre-heating of the cooling air, causes significant performance degradation in transcritical CO₂ A/C systems. This degradation manifests as reduced cooling capacity and, more detrimentally for an electric vehicle car, a sharply lower Coefficient of Performance (COP), which directly translates to increased energy consumption and reduced driving range.
Secondly, and most importantly, this degradation alters the fundamental system characteristic by shifting the optimal refrigerant charge amount. The system’s best-compromise performance (balancing capacity and efficiency) under shaded conditions is achieved at a higher total charge than under ideal, unshaded conditions. The required charge increment is quantitatively linked to both the intensity and the location of the shade.
- Shading Intensity: Stronger shading (higher $\beta_T$) necessitates a larger increase in optimal charge. For the studied case, a 50% coupled shading required a 20% charge increase.
- Shading Location: This is the paramount factor. Shading that affects the low-temperature exit region of the gas cooler (e.g., bottom) has the most severe impact, demanding the largest charge increase (+20%). Shading that affects the high-temperature inlet region (top) has minimal impact and requires no charge adjustment. Shading affecting vertical sections (sides) requires a moderate charge increase (+10%).
The underlying mechanism is rooted in heat exchanger theory. Shading reduces the local log-mean temperature difference ($\Delta T_{LM}$) in the affected region. To compensate for the reduced heat transfer driving force and maintain system capacity, the refrigerant mass flow rate must be increased. Raising the total system charge is one effective way to achieve this higher mass flow at a given compressor speed, albeit at the cost of operating at higher pressures. The new optimal charge represents the balance point where the penalty of higher pressure is outweighed by the benefit of recovered heat transfer.
For engineers designing the front-end module of an electric vehicle car, these findings offer clear guidance:
- Avoid Shading Where Possible: The primary design goal should be to minimize or eliminate thermal shading on the CO₂ gas cooler. This could involve careful component layout, ducting, or even separate cooling air pathways.
- Strategic Placement if Shading is Unavoidable: If shading is inevitable due to packaging constraints, the upstream heat exchanger should be positioned to shade a less critical area of the gas cooler. Specifically, for a gas cooler with a horizontal refrigerant flow path, it is preferable for the shade to fall on the top (refrigerant inlet) section rather than the bottom (outlet) section. Vertical shading (sides) is preferable to horizontal bottom shading.
- Calibrate Charge for Real Conditions: The system’s refrigerant charge should not be calibrated solely on a test bench with ideal, uniform airflow. The final charge amount must be determined considering the actual installed configuration and the associated thermal shading effects. A one-size-fits-all charge specification may lead to severely suboptimal performance in the real electric vehicle car.
- Consider Adaptive Strategies: For advanced thermal management systems, there is potential for adaptive control strategies that modulate charge (in systems with an accumulator or receiver) or adjust compressor and fan operation based on inferred or measured shading conditions (e.g., from temperature sensors on the gas cooler face).
In conclusion, the integration of a transcritical CO₂ A/C system into the compact architecture of an electric vehicle car requires a holistic approach that accounts for coupled thermal interactions. Recognizing that partial thermal shading not only reduces performance but also changes the system’s fundamental requirement for refrigerant charge is a vital step towards optimizing these systems. By implementing the insights from this analysis—particularly regarding the critical importance of shading location—designers can better mitigate performance losses, enhance energy efficiency, and ultimately contribute to extending the driving range of electric vehicle cars equipped with this promising, environmentally benign technology.