The rapid development and widespread adoption of electric vehicles (EVs) has placed unprecedented importance on the performance and safety of their energy storage systems. The EV battery pack, typically composed of numerous lithium-ion cells, is the heart of an electric vehicle. Its performance, lifespan, and, most critically, its safety are intrinsically linked to its operating temperature. During charging and discharging cycles, the movement of lithium ions within the cells generates significant heat due to internal resistance. If this heat is not efficiently dissipated, it can accumulate, leading to accelerated degradation, reduced capacity, and in extreme cases, thermal runaway—a serious safety hazard. Therefore, developing an effective and reliable thermal management system (TMS) is paramount for the success of any EV. This analysis delves into the critical factors influencing the cooling performance of an indirect refrigeration system for EV battery packs, providing insights for formulating optimal control strategies.
Various cooling methods have been explored for EV battery pack thermal management, including air cooling, liquid cooling, phase change material (PCM) cooling, heat pipe cooling, and composite methods. Air cooling, while simple, is highly susceptible to environmental conditions and often results in uneven temperature distribution across the battery pack. Liquid cooling, utilizing a coolant circuit, offers superior heat transfer coefficients and more uniform temperature control, making it the preferred choice for high-performance applications. Phase change materials absorb heat during melting, but challenges related to cost, stability under long-term cycling, and low thermal conductivity often limit their standalone application. Heat pipes are highly efficient but can be costly and complex to integrate. Consequently, indirect liquid cooling systems, where a refrigerant circuit cools a secondary coolant loop that interfaces with the battery, have gained significant traction due to their reliability, efficiency, and effectiveness in managing high thermal loads.
This study focuses on a specific indirect cooling architecture integrated with the vehicle’s air conditioning system. The core design involves adding a parallel battery cooling circuit to the existing HVAC refrigerant loop. Heat generated by the EV battery pack is transferred to a liquid coolant via cold plates attached to the battery modules. This warm coolant then flows through a plate heat exchanger (often called a chiller), where it is cooled by the refrigerant from the main air conditioning system. The refrigerant, undergoing a vapor-compression cycle (reverse Carnot cycle), ultimately rejects the absorbed heat to the ambient air through the condenser. In this scheme, the plate heat exchanger acts as the evaporator for the battery cooling loop. The mass flow rates of both the coolant and the refrigerant are controlled by an electric coolant pump and an electronic expansion valve (EXV), respectively. These two components are critical actuators whose operational settings—pump speed and EXV opening—directly determine the system’s cooling capacity, efficiency, and the temperature uniformity of the EV battery pack.
Theoretical Foundation and 1D Simulation Modeling
To systematically investigate the influence of the pump and expansion valve, a one-dimensional (1D) simulation model of the entire indirect refrigeration system for the EV battery pack was developed. This model integrates mathematical representations of each physical process and component.
Battery Heat Generation Model
The fundamental source of heat within the EV battery pack is electrochemical reactions and internal resistance. A widely accepted model for calculating the heat generation rate $ \dot{Q}_{gen} $ of a lithium-ion cell is the Bernardi model:
$$
\dot{Q}_{gen} = I \left[ (U_{ocv} – U_L) – T \frac{dU_{oc}}{dT} \right]
$$
where $ I $ is the current (A), $ U_{ocv} $ is the open-circuit voltage (V), $ U_L $ is the terminal voltage (V), $ T $ is the absolute temperature of the battery (K), and $ dU_{oc}/dT $ is the entropic coefficient (V/K). The total heat load from the EV battery pack is the sum of the heat generated by all individual cells.
Heat Transfer Fundamentals
Cooling the EV battery pack involves convective heat transfer from the battery cells to the cold plate and from the cold plate to the coolant. The general convective heat transfer equation is:
$$
Q = h A (T_{surface} – T_{fluid})
$$
where $ Q $ is the heat transfer rate (W), $ h $ is the convective heat transfer coefficient (W/m²·K), $ A $ is the effective heat transfer area (m²), $ T_{surface} is the temperature of the battery or cold plate surface (K), and $ T_{fluid} $ is the temperature of the coolant (K). The heat absorbed or released by the battery pack or coolant causing a temperature change is given by:
$$
Q = m c_p \Delta T
$$
where $ m $ is the mass (kg), $ c_p $ is the specific heat capacity (J/kg·K), and $ \Delta T $ is the temperature change (K).
Compressor Modeling
The compressor is the heart of the refrigerant cycle. Its model is based on performance maps correlating speed, pressure ratio, and efficiency. Key parameters include:
- Volumetric Efficiency ($ \eta_v $): Relates the actual mass flow rate to the theoretical displacement.
$$ \eta_v = \frac{\dot{m}_{actual}}{n \rho_{suct} V_{disp}} $$ - Isentropic Efficiency ($ \eta_{is} $): Compares the actual work to the ideal isentropic work.
$$ \eta_{is} = \frac{h_{dis, is} – h_{suct}}{h_{dis, actual} – h_{suct}} $$ - Mechanical Efficiency ($ \eta_{mec} $): Accounts for mechanical losses.
$$ \eta_{mec} = \frac{\dot{m}(h_{dis, actual} – h_{suct})}{\tau n} $$
Here, $ \dot{m} $ is mass flow rate (kg/s), $ n $ is rotational speed (rps), $ \rho_{suct} $ is suction density (kg/m³), $ V_{disp} $ is displacement volume (m³), $ h $ denotes specific enthalpy (J/kg), and $ \tau $ is torque (Nm).
Electronic Expansion Valve Modeling
The EXV is a critical control element that meters the flow of refrigerant into the evaporator/chiller. It causes a pressure drop, leading to an isenthalpic expansion of the refrigerant. The mass flow rate through the valve is modeled as an orifice flow:
$$
\dot{m}_{EXV} = C_d A \sqrt{2 \rho_{in} \Delta p}
$$
where $ C_d $ is the discharge coefficient, $ A $ is the effective flow area (m²) which is a function of the valve opening, $ \rho_{in} $ is the density of the refrigerant at the valve inlet (kg/m³), and $ \Delta p $ is the pressure drop across the valve (Pa). The opening of the EXV directly controls the flow area $ A $.
Component Parameters and Simulation Setup
The accuracy of the 1D system model depends on precise input parameters for each component, typically obtained from supplier data sheets. The key components for this EV battery pack cooling system are summarized below.
| Component | Key Parameters | Specification / Performance Data |
|---|---|---|
| Compressor | Type, Displacement, Refrigerant | Electric Scroll, 47 cc, R134a. Performance maps for cooling capacity, power, and COP vs. speed. |
| Coolant Pump | Max Power, Max Flow, Max Head | 135 W, 45 L/min, 13.6 m. Characteristic curves for head, efficiency, and power vs. flow rate. |
| Plate Heat Exchanger (Chiller) | Max Heat Transfer, Dimensions | 6 kW nominal capacity. Dimensions: 134 mm (L) x 64 mm (W) x 51 mm (H). |
| Condenser | Core Dimensions, Frontal Area | Core: 388.8 mm (W) x 466 mm (H) x 16 mm (D). Frontal area: ~0.181 m². |
| Battery Pack & Cold Plates | Heat Load, Target Temperature, Thermal Mass | Simulated based on Bernardi model. Target pack temperature: 25°C. Thermal properties defined for simulation. |
The simulation was conducted with a fixed compressor speed and a target EV battery pack temperature of 25°C. To isolate the effects of the actuators, single-variable studies were performed on the coolant pump speed and the EXV opening.
Analysis of Cooling Performance Influencing Factors
Impact of Coolant Pump Speed
The electric pump drives the coolant through the cold plates attached to the EV battery pack and the chiller. Its speed directly controls the coolant flow rate, which affects both the convective heat transfer coefficient at the cold plate and the temperature rise of the coolant across the battery pack. The simulation analyzed pump speeds from 1000 to 6000 rpm, with EXV opening fixed at 30% and compressor speed at 6500 rpm.
| Pump Speed (rpm) | Coolant Flow Rate (L/min) | Battery Inlet Temp. (°C) | Battery Outlet Temp. (°C) | Coolant ΔT (°C) | Chiller Cooling Power (W) |
|---|---|---|---|---|---|
| 1000 | 5.11 | 11.18 | 23.07 | 11.89 | 3635 |
| 2000 | 7.67 | 14.96 | 22.95 | 7.99 | 3664 |
| 3000 | 10.44 | 16.93 | 22.86 | 5.93 | 3701 |
| 4000 | 13.36 | 18.23 | 22.85 | 4.62 | 3719 |
| 5000 | 16.63 | 19.08 | 22.82 | 3.74 | 3781 |
| 6000 | 19.83 | 19.69 | 22.84 | 3.15 | 3825 |
The results reveal a non-linear relationship. As the pump speed increases from 1000 to 5000 rpm, the cooling power of the chiller (i.e., the heat removed from the coolant loop) steadily increases. This is because higher flow rates improve the heat transfer coefficient ($h$) at the cold plate, as indicated by correlations like the Dittus-Boelter equation for turbulent flow: $ Nu = 0.023 Re^{0.8} Pr^{0.4} $, where Nusselt number $Nu$ is proportional to $h$, and Reynolds number $Re$ is proportional to flow rate. Consequently, more heat is extracted from the EV battery pack. Furthermore, the temperature difference (ΔT) of the coolant across the battery pack decreases significantly, indicating better temperature uniformity within the EV battery pack, which is crucial for longevity.
However, the rate of improvement diminishes. The most significant jump in cooling performance occurs between 1000 and 2000 rpm. Beyond 5000 rpm, a counterintuitive effect is observed. At 6000 rpm, while the flow rate is highest and ΔT is lowest, the cooling power shows only a marginal increase from the 5000 rpm case, and the battery outlet temperature slightly increases. This suggests that excessive pump speed leads to diminished returns. The higher pump work adds parasitic load to the system, and the coolant may spend insufficient time in the chiller for optimal heat exchange with the refrigerant, reducing the overall system coefficient of performance (COP). Therefore, for this specific system, an optimal pump speed likely exists around 5000 rpm, balancing cooling performance against energy consumption.
Impact of Electronic Expansion Valve Opening
The EXV controls the refrigerant flow into the chiller, regulating its pressure and temperature. Its opening, often expressed as a percentage or duty cycle, is typically controlled to maintain a target superheat at the compressor inlet. The valve’s physical design, specifically its needle and seat diameter, determines the relationship between the commanded opening percentage and the actual flow area $A$ in Eq. (4). For a given target superheat (e.g., 7°C), different valve diameters require different optimal openings.
| Valve Needle Diameter (mm) | Corresponding Optimal EXV Opening (%) |
|---|---|
| 1.5 | 38.0 |
| 1.8 | 28.5 |
| 2.2 | 17.7 |
For a fixed valve diameter (1.5 mm in this study), the EXV opening was varied from 20% to 70% while keeping the pump and compressor speeds constant. The cooling performance was evaluated based on the battery pack’s cooldown rate and the steady-state chiller cooling power.
| EXV Opening (%) | Chiller Cooling Power (W) | Trend |
|---|---|---|
| 20 | 3026 | Increase → Peak → Decrease |
| 30 | 3263 | |
| 40 | 3311 | |
| 50 | 3290 | |
| 60 | 3242 | |
| 70 | 3182 |
The results demonstrate a clear optimal point. At a low opening (20%), the refrigerant mass flow rate is restricted. Although the pressure drop is high, leading to a low evaporation temperature and a potentially larger temperature difference with the coolant, the limited flow rate severely constrains the total heat absorption capacity of the refrigerant, resulting in low cooling power for the EV battery pack.
As the opening increases to 40%, the refrigerant flow reaches an optimal value. The evaporation pressure and temperature are balanced such that the refrigerant can absorb the maximum amount of heat from the coolant in the chiller. This corresponds to the peak chiller cooling power and the fastest cooldown rate for the EV battery pack.
Further increasing the EXV opening beyond 40% causes performance degradation. While the refrigerant flow rate increases, the reduction in pressure drop leads to a higher evaporation temperature. This reduces the log-mean temperature difference (LMTD) between the refrigerant and the coolant in the chiller, impairing heat transfer effectiveness. In extreme cases (e.g., 70% opening), excessive liquid refrigerant may flood the chiller and fail to evaporate completely, risking liquid slugging of the compressor. Thus, the cooling power declines. The relationship can be conceptually linked to the heat exchanger performance, where the heat transfer rate $Q$ is proportional to the overall heat transfer coefficient $U$, area $A$, and the LMTD: $ Q = U A \Delta T_{LMTD} $. An oversized EXV degrades $ \Delta T_{LMTD} $ faster than any gain from increased flow might improve $U$.
Conclusion and Implications for EV Battery Pack Thermal Management
This detailed investigation into an indirect refrigeration system for EV battery pack cooling highlights the critical and nuanced roles of the coolant pump and the electronic expansion valve. Through 1D system simulation and analysis, two key conclusions are drawn:
- Coolant Pump Speed: The cooling performance of the EV battery pack improves with increasing pump speed, but with progressively diminishing returns. An optimum speed exists, beyond which further increases yield minimal cooling benefit or even a slight degradation, while incurring higher parasitic energy consumption. For the studied system, this optimum was observed around 5000 rpm. Control strategies should avoid operating the pump at unnecessarily high speeds.
- Electronic Expansion Valve Opening: The EXV opening has a direct and pronounced effect on the refrigeration cycle’s ability to cool the EV battery pack. Performance exhibits a clear peak at a specific opening percentage. This optimal opening is influenced by the valve’s physical diameter. For a fixed system, operating the EXV at either too low or too high an opening significantly reduces the cooling capacity and efficiency. A superheat-based control strategy is essential to dynamically maintain the EXV near its optimal operating point under varying thermal loads on the EV battery pack.
These findings provide a fundamental basis for developing sophisticated control algorithms for EV battery pack thermal management systems. An optimal control strategy must coordinate the pump speed and EXV opening, along with compressor and fan speeds, to maintain the EV battery pack within its ideal temperature range with minimal temperature spread, while simultaneously minimizing the total energy consumption of the thermal management system itself. This holistic approach is vital for maximizing driving range, ensuring battery longevity, and guaranteeing the safety of electric vehicles.