Thermal management is a critical challenge for lithium-ion battery systems, especially in high-performance applications such as electric racing. In motorsports like the Formula Student Electric China (FSEC), the discharge conditions are extreme and variable, often leading to rapid heat accumulation within the battery pack. Ineffective heat dissipation can cause excessive temperature rise, severe temperature non-uniformity, accelerated degradation, and in severe cases, thermal runaway, resulting in a catastrophic loss of power during competition. Therefore, designing an efficient and compact thermal management system is paramount for ensuring the performance, safety, and longevity of the lithium-ion battery pack in racing environments.
Among various cooling methods, forced air cooling remains a popular choice for electric race cars due to its simplicity, reliability, and low cost. However, optimizing an air-cooling system for a densely packed lithium-ion battery pack within the strict spatial constraints of a race car chassis is non-trivial. This work presents a systematic study combining Computational Fluid Dynamics (CFD) simulation with the orthogonal experimental design method to analyze and optimize the air-cooling performance of a lithium-ion battery pack for an FSEC racing car. The primary objectives are to minimize the maximum temperature and the maximum temperature difference within the lithium-ion battery pack under simulated racing conditions.
Preliminary Design and Thermal Analysis of the Lithium-Ion Battery Pack
The lithium-ion battery pack under study is designed for an FSEC electric formula car. It consists of 35 prismatic lithium-ion cells (NCM chemistry) configured in a 35S1P arrangement, divided into five modules. The key specifications of a single lithium-ion battery cell are: length 148 mm, width 26.8 mm, height 98 mm, nominal capacity 50 Ah, and nominal voltage 3.65 V. The total pack has a nominal voltage of 127.75 V and a nominal energy of 6.39 kWh.
To simulate the demanding conditions of an FSEC event, four discharge scenarios were defined, encompassing both normal and extreme operational states for the lithium-ion battery pack.
| Operational State | High Current, Short Duration | Low Current, Long Duration |
|---|---|---|
| Normal Discharge | 2C for 30 seconds | 1C for 30 minutes |
| Extreme Discharge | 3C for 40 seconds | 2C for 30 minutes |
Based on FSEC rules and cell specifications, the thermal management targets were set as: Maximum Temperature ≤ 40°C and Maximum Temperature Difference ≤ 5°C.
The heat generation within the lithium-ion battery is a crucial input for simulation. The transient heat generation rate is calculated using a simplified Bernardi model, where the reversible heat is considered negligible compared to the irreversible Joule heating. The heat generation rate for a single lithium-ion battery cell is given by:
$$q = \frac{I^2 R}{V}$$
where \(q\) is the volumetric heat generation rate (W/m³), \(I\) is the discharge current (A), \(V\) is the cell volume (m³), and \(R\) is the equivalent internal resistance (Ω). The internal resistance \(R\) of the lithium-ion battery is a function of the State of Charge (SOC). An empirical relationship obtained from experiment at 25°C is:
$$R = 0.0225x^5 – 0.0519x^4 + 0.0326x^3 + 0.0029x^2 – 0.0071x + 0.0024$$
where \(x\) represents the SOC. The SOC as a function of time during constant current discharge is:
$$SOC = SOC_{initial} – \frac{I t}{3600 C_R}$$
Here, \(SOC_{initial}\) is the initial state of charge (taken as 1), \(t\) is time in seconds, and \(C_R\) is the rated capacity in Ah. The total heat dissipation requirement \(Q_{total}\) for the pack is the sum of the heat generated by all lithium-ion battery cells:
$$Q_{total} = q_{total} V_{total}$$
Based on these calculations, the required airflow for cooling was estimated. For instance, the airflow rate \(CFM\) needed can be estimated by:
$$CFM = \frac{Q_{total} \times 60}{\rho C_p \Delta T}$$
where \(\rho\) is air density (1.29 kg/m³), \(C_p\) is the specific heat of air (1005 J/(kg·K)), and \(\Delta T\) is the permissible temperature rise of the air (set to 20 K). Preliminary calculations suggested an inlet air velocity of approximately 3 m/s for a 50 mm diameter inlet.
The preliminary battery pack layout placed five modules (7 cells each) in a compact arrangement within a box of dimensions 544 mm × 419 mm × 164 mm. A single inlet and six outlet vents were designed on the battery box. Initial CFD simulations were conducted for all four discharge scenarios. The lithium-ion battery cell properties were set with anisotropic thermal conductivity: \(\lambda_x = 23.4, \lambda_y = 5.3, \lambda_z = 17.4 \text{ W/(m·K)}\). A User-Defined Function (UDF) was compiled to implement the time-dependent heat generation rate for each scenario.
The simulation results for the preliminary design revealed significant thermal issues, particularly under prolonged discharge, as summarized below:
| Discharge Scenario | Maximum Temp. (°C) | Minimum Temp. (°C) | Max. ΔT (°C) |
|---|---|---|---|
| 1C for 30 min | 31.36 | 28.38 | 2.98 |
| 2C for 30 s | 25.41 | 25.32 | 0.09 |
| 2C for 30 min | 49.55 | 38.70 | 11.10 |
| 3C for 40 s | 30.36 | 29.85 | 0.51 |
The results showed that while the short-duration scenarios were within limits, the prolonged 2C discharge caused a severe temperature rise to 49.55°C and a large temperature difference of 11.1°C, far exceeding the safety targets. The temperature contour and air streamlines indicated poor airflow distribution and noticeable heat accumulation in the rear corners of the battery box, highlighting the need for optimization of the lithium-ion battery cooling system.
Optimization Methodology: Orthogonal Experimental Design
To efficiently optimize the air-cooling system for the lithium-ion battery pack, an orthogonal experimental design was employed. This method allows for the investigation of multiple design factors and their levels with a significantly reduced number of experiments compared to a full factorial approach. Seven key factors influencing the cooling performance were identified, each with three levels.
| Factor | Description | Level 1 | Level 2 | Level 3 |
|---|---|---|---|---|
| A | Inlet Air Velocity (m/s) | 3 | 5 | 7 |
| B | Number of Inlets | 1 | 2 | 3 |
| C | Number of Outlet Grilles | 6 | 9 | 12 |
| D | Inlet Diameter (mm) | 50 | 60 | 70 |
| E | Outlet Grille Height (mm) | 10 | 15 | 20 |
| F | Inter-Cell Gap (mm) | 1.0 | 1.5 | 2.0 |
| G | Inter-Module Gap (mm) | 2.0 | 3.0 | 4.0 |
An \(L_{18}(3^7)\) orthogonal array was selected, which requires only 18 simulation runs. The 3C discharge for 40 seconds scenario was chosen as the baseline for this optimization study due to its representative high-load condition. The evaluation metrics were the maximum temperature (\(T_{max}\)), minimum temperature (\(T_{min}\)), and maximum temperature difference (\(\Delta T_{max}\)) of the lithium-ion battery pack at the end of the discharge cycle.
Analysis of Orthogonal Experiment Results and Optimal Solution Selection
The 18 simulations based on the orthogonal array were performed. Range analysis was conducted on the results for each of the three evaluation metrics to determine the influence order of the factors and the optimal level for each factor under that specific metric.
For Maximum Temperature (\(T_{max}\)): The primary goal is to minimize the peak temperature of the lithium-ion battery. The analysis revealed the following order of influence: B (Number of Inlets) > D (Inlet Diameter) > A (Inlet Velocity) > F (Inter-Cell Gap) > C (Outlet Number) > G (Inter-Module Gap) > E (Outlet Height). The optimal level combination for minimizing \(T_{max}\) was determined as \(B_3D_3A_3F_1C_1G_1E_2\).
For Minimum Temperature (\(T_{min}\)): While a lower minimum temperature is generally better, it must be considered in conjunction with uniformity. The influence order was: A > C > B > E > G > F > D. The optimal combination for this metric was \(A_3C_1B_3E_3G_2F_3D_3\).
For Maximum Temperature Difference (\(\Delta T_{max}\)): Minimizing the temperature spread is critical for the health and performance of the lithium-ion battery pack. The influence order was: E (Outlet Height) > C (Outlet Number) > G (Inter-Module Gap) > F (Inter-Cell Gap) > A (Inlet Velocity) > D (Inlet Diameter) > B (Number of Inlets). The optimal combination for the best uniformity was \(E_2C_3G_1F_2A_1D_2B_3\).
Three candidate optimal schemes were derived from the above analysis. To select the final optimal configuration for the lithium-ion battery cooling system, a comprehensive evaluation was necessary. The performance of the three candidate schemes was simulated and compared not only based on the three key metrics but also considering the visual temperature distribution uniformity and the degree of heat accumulation within the battery box, which are critical process-related factors.
| Candidate Scheme | \(T_{max}\) (°C) | \(T_{min}\) (°C) | \(\Delta T_{max}\) (°C) | Remarks on Uniformity & Heat Accumulation |
|---|---|---|---|---|
| 1: \(B_3D_3A_3F_1C_1G_1E_2\) | 29.80 | 28.88 | 0.89 | Good, but slightly inferior ΔT. |
| 2: \(A_3C_1B_3E_3G_2F_3D_3\) | 29.77 | 28.99 | 0.78 | Best overall uniformity, least heat accumulation. |
| 3: \(E_2C_3G_1F_2A_1D_2B_3\) | 29.88 | 29.09 | 0.79 | Good ΔT, but shows noticeable local heat spots. |
Based on this holistic comparison, Candidate Scheme 2 was selected as the final optimized configuration for the lithium-ion battery pack air-cooling system. It offered an excellent balance, achieving the lowest maximum temperature, a very competitive low temperature difference, and the most uniform temperature distribution with minimal localized heating.
Validation and Performance Evaluation of the Optimized Lithium-Ion Battery Cooling System
The optimized cooling system configuration was modeled and simulated across all four original FSEC discharge scenarios to validate its performance.
| Discharge Scenario | Maximum Temp. (°C) | Minimum Temp. (°C) | Max. ΔT (°C) | Status vs. Target |
|---|---|---|---|---|
| 1C for 30 min | 26.63 | 26.23 | 0.40 | Pass |
| 2C for 30 s | 25.06 | 25.03 | 0.03 | Pass |
| 2C for 30 min | 33.37 | 29.50 | 3.87 | Pass |
| 3C for 40 s | 29.77 | 28.99 | 0.78 | Pass |
The results demonstrate that the optimized lithium-ion battery cooling system successfully meets all thermal targets under the defined racing conditions. The most significant improvement is observed in the challenging 2C for 30 minutes scenario, where the maximum temperature was reduced from 49.55°C to 33.37°C, an improvement of 32.7%, and the maximum temperature difference was reduced from 11.1°C to 3.87°C, an improvement of 65.1%.
To further validate the simulation findings and the practical feasibility of the design, a physical prototype of the optimized lithium-ion battery pack was built and installed on an FSEC race car. Real-world driving tests were conducted, including a straight-line acceleration test (simulating 2C 30s) and an endurance driving test (simulating 1C 30min). Temperature sensors were placed at key locations corresponding to the simulated hot and cold spots. The test results showed close agreement with the simulation predictions. For the endurance test, the measured maximum pack temperature was 30.2°C with a maximum difference of 2.1°C, well within targets and with an error margin of less than 10% compared to simulation, confirming the reliability of the CFD model and the effectiveness of the optimized lithium-ion battery thermal management solution.
Comparative Analysis and Discussion of Optimization Effects
A direct comparison between the preliminary and optimized designs highlights the effectiveness of the systematic approach. For the 1C 30min discharge, the optimization reduced the maximum temperature from 31.36°C to 26.63°C (a 15.1% improvement) and slashed the maximum temperature difference from 2.98°C to 0.40°C (an 86.6% improvement).
The analysis of airflow streamlines provides clear insight into the reason for this improvement. In the initial design, airflow from the single inlet was primarily channeled through the central region of the pack, leaving the sides and rear corners with poor cooling and resulting in significant heat accumulation. The optimized design, featuring three inlets with a more distributed layout, wider air gaps between cells and modules, and an adjusted outlet configuration, promotes a much more uniform airflow distribution throughout the entire lithium-ion battery pack. This ensures that cool air effectively reaches all cells, minimizing hot spots and creating a more homogeneous thermal environment, which is crucial for the balanced aging and performance of the lithium-ion battery system.
Conclusion
This study successfully addressed the thermal management challenges of a lithium-ion battery pack for a high-performance electric race car by integrating CFD simulation with the orthogonal experimental design method. The process began with a preliminary design and identified its shortcomings under simulated FSEC racing cycles. A structured optimization was then conducted, investigating seven key design factors. The optimal solution was selected not only based on the primary metrics of maximum temperature and temperature difference but also by critically assessing the temperature distribution uniformity and heat accumulation patterns—process-related factors that are essential for a robust design.
The finalized air-cooling configuration for the lithium-ion battery pack demonstrated exceptional performance, meeting all thermal targets across normal and extreme discharge scenarios. The optimization yielded a maximum temperature reduction of up to 32.7% and a maximum temperature difference reduction of up to 86.6% in the most critical operating condition. Real-world vehicle testing validated the simulation results and the practical viability of the design.
The methodology presented, particularly the use of orthogonal experiments supplemented by visual analysis of flow and temperature fields, provides an efficient and effective framework for optimizing air-cooling systems. It significantly reduces the computational burden compared to exhaustive testing while leading to a high-performance outcome. This approach holds valuable reference significance for the design and optimization of thermal management systems not only for racing applications but also for other electric vehicles where efficient cooling of lithium-ion battery packs is paramount for safety, performance, and durability.