The thermal management of the power source is a paramount challenge in the design and operation of electric vehicles (EVs). For electric buses, which demand high energy and power outputs over extended duty cycles, this challenge is particularly acute. The core of this issue lies with the EV battery pack. During operation, especially under high-load conditions such as acceleration or climbing, the electrochemical cells within the pack generate significant heat. If this heat is not efficiently dissipated, it accumulates, leading to elevated operating temperatures. Consequences range from accelerated degradation and reduced capacity to, in extreme cases, thermal runaway—a severe safety hazard. Therefore, a meticulous analysis of the thermal behavior of the EV battery pack is not merely an exercise in performance optimization but a critical safety imperative. This study focuses on the thermal management system of a specific pure electric bus EV battery pack, employing computational fluid dynamics (CFD) simulation to evaluate its heat dissipation performance under various operational and environmental conditions.
The primary heat generation originates from the individual battery cells. To accurately model this in a simulation, the heat generation rate of a single cell must be quantified. This analysis employs the widely recognized Bernardi heat generation model, which is based on the principle of energy conservation. The model primarily accounts for irreversible Joule heating due to internal resistance and reversible entropic heat. The general form of the Bernardi equation is:
$$ q = \frac{I}{V} \left[ (E_0 – E) + T \frac{dE_0}{dT} \right] $$
Where \( q \) is the volumetric heat generation rate (W/m³), \( I \) is the operational current (A), \( V \) is the volume of the cell (m³), \( E_0 \) is the open-circuit voltage (V), \( E \) is the operating terminal voltage (V), \( T \) is the absolute temperature (K), and \( \frac{dE0}{dT} \) is the entropy coefficient (V/K).
For simplification and based on available cell data, the voltage difference \( (E_0 – E) \) is often dominated by the internal resistance. However, using parameters from the cell manufacturer for this specific EV battery pack, the calculation can be streamlined. The key parameters for a single cell are: Volume \( V = 0.001916784 \, \text{m}^3 \), Nominal Current \( I_{\text{nom}} = 228 \, \text{A} \), and Entropy Coefficient \( \frac{dE_0}{dT} = 0.000469 \, \text{V/K} \). At a reference ambient temperature of 300 K (26.85°C), and assuming the terminal voltage is close to the open-circuit voltage under nominal conditions, the entropic term becomes the primary contributor. Thus, the base heat generation rate at 1C discharge (where \( I = I_{\text{nom}} \)) is calculated as:
$$ q_{1C} = \frac{I_{\text{nom}}}{V} \cdot T \cdot \frac{dE_0}{dT} = \frac{228}{0.001916784} \times 300 \times 0.000469 \approx 1498 \, \text{W/m}^3 $$
This value serves as the foundational heat source input for the cell domains in the CFD model. The heat generation rate scales linearly with the discharge current, allowing us to model different discharge rates (C-rates) by proportionally scaling \( q \).
Establishing the Finite Element Simulation Model
The first step in the simulation workflow is to create an accurate digital representation of the physical EV battery pack. The pack in question consists of 48 prismatic lithium-ion cells, arranged in a 3-by-16 configuration (3 modules in parallel, each with 16 cells in series). To ensure mechanical stability and promote thermal conduction between cells, silicone gap pads are placed between adjacent cells. The most critical component for active thermal management is the liquid-cooling plate located at the bottom of the pack. This plate features a serpentine channel design, maximizing the contact surface area with the cell bottoms to enhance heat extraction efficiency. A 50% by weight ethylene glycol-water solution serves as the coolant. The outer casing of the pack, which has minimal direct impact on the internal cell temperature distribution in this sealed, actively cooled system, is omitted from the model to reduce computational complexity.
The 3D geometry is imported into ANSYS Workbench. The fluid domain (coolant channels) and solid domains (cells, cooling plate, gap pads) are properly defined within the Design Modeler module. Inlet and outlet boundaries for the coolant flow are explicitly set. Subsequently, a high-quality volumetric mesh is generated using the Fluent meshing tools, resulting in a model with approximately 940,000 elements and 3.54 million nodes, ensuring sufficient resolution for accurate thermal and flow field predictions.
The material properties assigned to each component are crucial for the fidelity of the thermal simulation. These properties are summarized in the table below.
| Material | Density (kg/m³) | Specific Heat (J/(kg·K)) | Thermal Conductivity (W/(m·K)) | ||
|---|---|---|---|---|---|
| X | Y | Z | |||
| Silicone Gap Pad | 2750 | 1500 | 2 | 2 | 2 |
| Aluminum Cooling Plate | 2719 | 871 | 202.4 | 202.4 | 202.4 |
| Battery Cell | 2525 | 961 | 3 | 9 | 11 |
| Coolant (50% EG) | 1073 | 3300 | 0.38 | 0.38 | 0.38 |
The boundary conditions complete the setup of the numerical model. The realizable k-epsilon turbulence model with standard wall functions is selected to resolve the coolant flow, which is expected to be turbulent at the given flow rates. Each cell is assigned a volumetric heat source based on the calculated \( q \) value. The external surfaces of the EV battery pack assembly are subjected to a natural convection boundary condition with the ambient air, with a heat transfer coefficient of 5 W/(m²·K). The coolant inlet is defined as a velocity inlet, with an initial baseline velocity of 0.1 m/s, and the temperature is set equal to the ambient temperature. The outlet is defined as a pressure outlet at 0 Pa gauge pressure.
Impact of Discharge Rate on Pack Thermal Performance
The discharge rate, or C-rate, directly correlates to the operating current and thus the heat generation rate within each cell of the EV battery pack. To analyze this effect, simulations were conducted with ambient temperature fixed at 300 K and coolant inlet velocity fixed at 0.1 m/s. The discharge rate was varied from 0.25C to 2.0C. The corresponding volumetric heat generation rates were calculated proportionally from the base \( q_{1C} \) value:
$$ q_{nC} = n \times q_{1C} $$
where \( n \) is the C-rate (0.25, 0.5, 0.75, 1.0, 1.25, 1.5, 1.75, 2.0). The simulation results clearly show a strong linear correlation between the discharge rate and the maximum temperature \( T_{max} \) within the EV battery pack. The minimum temperature \( T_{min} \) remains constant at the coolant inlet temperature of 300 K. The temperature distribution shows a gradient from the bottom (cooled by the cold plate) to the top, and from the coolant inlet to the outlet. The hottest spot consistently appears at the top of the pack near the coolant outlet.
| Discharge Rate (C) | Heat Gen. Rate, q (W/m³) | Pack T_min (K / °C) | Pack T_max (K / °C) | Maximum Temperature Rise ΔT_max (°C) |
|---|---|---|---|---|
| 0.25 | 374.5 | 300.0 / 26.85 | 300.8 / 27.65 | 0.80 |
| 0.50 | 749.0 | 300.0 / 26.85 | 301.6 / 28.45 | 1.60 |
| 0.75 | 1123.5 | 300.0 / 26.85 | 302.4 / 29.25 | 2.40 |
| 1.00 | 1498.0 | 300.0 / 26.85 | 303.2 / 30.05 | 3.20 |
| 1.25 | 1872.5 | 300.0 / 26.85 | 304.0 / 30.85 | 4.00 |
| 1.50 | 2247.0 | 300.0 / 26.85 | 304.8 / 31.65 | 4.80 |
| 1.75 | 2621.5 | 300.0 / 26.85 | 305.6 / 32.45 | 5.60 |
| 2.00 | 2996.0 | 300.0 / 26.85 | 306.4 / 33.25 | 6.40 |
The data reveals a perfectly linear relationship: \( \Delta T_{max} = 3.2 \times n \). Even at the maximum simulated discharge rate of 2C, the peak temperature of the EV battery pack is only 33.25°C, which is a modest 6.4°C above ambient. This indicates that the liquid cooling system is highly effective at managing heat, even under high-power demands, allowing the electric bus to utilize the full 2C capability for peak power requirements like acceleration without risking excessive cell temperatures.
Effect of Coolant Flow Rate on Thermal Management
The velocity of the coolant directly influences the convective heat transfer coefficient at the interface between the cold plate and the liquid. Higher flow rates typically enhance heat removal but also increase the pumping power required. To study this trade-off, simulations were run with a fixed discharge rate of 1C (q = 1498 W/m³) and ambient temperature of 300 K, while varying the coolant inlet velocity from 0.1 m/s to 0.6 m/s.
The results demonstrate a non-linear, diminishing-returns relationship between flow rate and the maximum temperature of the EV battery pack. Increasing the flow rate initially causes a significant drop in \( T_{max} \), but the benefit gradually tapers off. The minimum temperature remains anchored at the inlet temperature.
| Coolant Velocity (m/s) | Pack T_min (K / °C) | Pack T_max (K / °C) | Maximum Temperature Rise ΔT_max (°C) | Relative Reduction in ΔT_max (%) |
|---|---|---|---|---|
| 0.10 | 300.0 / 26.85 | 303.2 / 30.05 | 3.20 | 0.0 (Baseline) |
| 0.20 | 300.0 / 26.85 | 302.2 / 29.35 | 2.50 | 21.9 |
| 0.30 | 300.0 / 26.85 | 301.5 / 28.65 | 1.80 | 43.8 |
| 0.40 | 300.0 / 26.85 | 301.1 / 28.25 | 1.40 | 56.3 |
| 0.50 | 300.0 / 26.85 | 300.9 / 28.05 | 1.20 | 62.5 |
| 0.60 | 300.0 / 26.85 | 300.8 / 27.95 | 1.10 | 65.6 |
The data suggests that for this specific EV battery pack and cooling system design, increasing the flow rate beyond approximately 0.3 m/s yields progressively smaller thermal benefits. At 0.3 m/s, the maximum temperature rise is already reduced to 1.8°C, representing an excellent balance between cooling performance and the parasitic energy required to run the coolant pump. This non-linear trend is characteristic of convective cooling systems, where the heat transfer coefficient \( h \) scales with flow velocity \( v \) raised to a power less than 1 (e.g., \( h \propto v^{0.8} \) in turbulent pipe flow), leading to diminishing returns.
Influence of Ambient Air Temperature
The operating environment of an electric bus can vary drastically. The ambient air temperature affects both the starting temperature of the coolant and the heat rejection capability to the environment. To evaluate this, simulations were conducted with a fixed 1C discharge and a coolant velocity of 0.1 m/s, while the ambient temperature \( T_{amb} \) was varied from 280 K (6.85°C) to 320 K (46.85°C). Importantly, the cell heat generation rate \( q \) is also a function of temperature, as per the Bernardi model \( q \propto T \). Therefore, \( q \) was recalculated for each ambient temperature case.
$$ q(T) = \frac{I_{\text{nom}}}{V} \cdot T \cdot \frac{dE_0}{dT} $$
The results show a clear linear relationship between ambient temperature and both the minimum and maximum temperatures of the EV battery pack. However, the temperature span \( (T_{max} – T_{min}) \) within the pack also increases with ambient temperature, indicating a greater thermal gradient under hotter conditions.
| Ambient Temp, T_amb (K / °C) | Adjusted Heat Gen. Rate, q (W/m³) | Pack T_min (K / °C) | Pack T_max (K / °C) | Pack Temperature Span (K / °C) |
|---|---|---|---|---|
| 280 / 6.85 | 1397.2 | 280.0 / 6.85 | 280.74 / 7.59 | 0.74 / 0.74 |
| 290 / 16.85 | 1447.6 | 290.0 / 16.85 | 291.04 / 17.89 | 1.04 / 1.04 |
| 300 / 26.85 | 1498.0 | 300.0 / 26.85 | 303.20 / 30.05 | 3.20 / 3.20 |
| 310 / 36.85 | 1548.4 | 310.0 / 36.85 | 314.00 / 40.85 | 4.00 / 4.00 |
| 320 / 46.85 | 1598.8 | 320.0 / 46.85 | 325.20 / 52.05 | 5.20 / 5.20 |
The linear increase in \( T_{max} \) with \( T_{amb} \) is evident. At an extreme ambient of 46.85°C, the EV battery pack reaches a maximum temperature of 52.05°C. While this may still be below immediate critical limits, sustained operation at such elevated temperatures would accelerate aging. Furthermore, the internal temperature gradient increases from 0.74°C to 5.2°C, which can lead to cell-to-cell imbalances over time. This analysis underscores the importance of effective thermal management, particularly for electric buses operating in hot climates, and may necessitate control strategies that derate power or increase coolant flow when ambient temperatures are very high.
Conclusion and Engineering Implications
This comprehensive CFD-based simulation study provides valuable insights into the thermal behavior of a liquid-cooled electric bus EV battery pack. The analysis of three critical parameters—discharge rate, coolant flow velocity, and ambient temperature—reveals distinct trends that inform design and control strategies.
The maximum temperature within the EV battery pack exhibits a linear increase with discharge rate. The cooling system demonstrated robust performance, maintaining cell temperatures within a safe and moderate range even at the maximum 2C discharge, enabling the full use of the battery’s power capability. The relationship between coolant flow rate and cooling performance is non-linear, characterized by diminishing returns. For the studied system, a flow rate around 0.3 m/s appears to be a sweet spot, offering substantial cooling (ΔT_max = 1.8°C at 1C) without the excessive pumping penalty of higher flows. This finding is crucial for optimizing the energy efficiency of the thermal management system itself. Ambient temperature has a direct and linearly amplifying effect on pack temperature. In hot environments, the pack not only operates at a higher absolute temperature but also experiences greater internal temperature gradients, potentially impacting longevity and uniformity.
In summary, the simulation methodology employed here serves as a powerful and cost-effective tool for analyzing and optimizing the thermal management system of an EV battery pack. The results validate the effectiveness of the serpentine-channel liquid cooling design for the demanding duty cycle of an electric bus. Furthermore, the quantified relationships between operational parameters and thermal response provide a solid foundation for developing advanced battery thermal management system (BTMS) control algorithms, ensuring both the performance and safety of the vehicle’s most critical and expensive component.