In my research, I focused on a 50 Ah energy storage battery module comprising 26 cells arranged in two columns. The objective was to quantitatively compare the heat transfer characteristics of parallel-flow air cooling and liquid cooling systems. Using numerical simulations, I evaluated performance metrics including maximum temperature, temperature uniformity, flow resistance, and overall thermo-hydraulic efficiency under varying operating conditions. The study also examined the influence of ambient temperature on system behavior. My findings provide a systematic reference for selecting appropriate cooling strategies in energy storage battery applications.
1. Model Configuration and Numerical Setup
I designed two separate thermal management configurations: an air-cooled module with a parallel channel structure and a liquid-cooled module using an indirect cold plate with parallel direct-current channels. For the air-cooled version, air entered from a lower plenum, flowed through gaps between cells, and exited through an upper plenum. The liquid-cooled design incorporated a cold plate with 3.5 mm thick channels and coolant composed of a 50% ethylene glycol–water solution. The battery cells were modeled as homogeneous heat sources with a total heat generation of 822.12 W during constant-current charging.
I employed the finite volume method with the SIMPLE algorithm and the standard k-ε turbulence model. The governing equations included continuity, momentum, energy, and turbulence transport equations:
$$ \frac{\partial \rho_f}{\partial t} + \nabla \cdot (\rho_f \mathbf{u}) = 0 $$
$$ \frac{\partial (\rho_f \mathbf{u})}{\partial t} + \nabla P = \mu \nabla^2 \mathbf{u} $$
$$ \rho_f c_f \frac{\partial T_f}{\partial t} + \nabla (\rho_f c_f \mathbf{u} T_f) = \nabla (\lambda_f \nabla T_f) $$
$$ \rho_b c_b \frac{\partial T_b}{\partial t} = \lambda_x \frac{\partial^2 T_b}{\partial x^2} + \lambda_y \frac{\partial^2 T_b}{\partial y^2} + \lambda_z \frac{\partial^2 T_b}{\partial z^2} + q_b $$
$$ \frac{\partial (\rho_f k)}{\partial t} + \frac{\partial (\rho_f k u_i)}{\partial x_i} = \frac{\partial}{\partial x_j} \left[ \left( \mu + \frac{\mu_t}{\sigma_k} \right) \frac{\partial k}{\partial x_j} \right] + G_k + G_b – \rho_f \varepsilon – Y_M + S_k $$
$$ \frac{\partial (\rho_f \varepsilon)}{\partial t} + \frac{\partial (\rho_f \varepsilon u_i)}{\partial x_i} = \frac{\partial}{\partial x_j} \left[ \left( \mu + \frac{\mu_t}{\sigma_\varepsilon} \right) \frac{\partial \varepsilon}{\partial x_j} \right] + \frac{\varepsilon}{k} (C_{1\varepsilon} G_k – C_{2\varepsilon} \rho_f \varepsilon + C_{3\varepsilon} G_b) + S_\varepsilon $$
Material properties were set as follows:
| Material | Density (kg/m³) | Dynamic viscosity (mPa·s) | Specific heat (J/(kg·K)) | Thermal conductivity (W/(m·K)) |
|---|---|---|---|---|
| Air | 1.205 | 0.0183 | 1013 | 0.0267 |
| Coolant (50% EG) | 1071.1 | 3.94 | 3300 | 0.384 |
| Battery cell | 2230 | — | 982 | λx=λz=23.88, λy=0.65 |
| Aluminum alloy | 2680 | — | 947 | 156 |
I performed grid independence tests using a Poly-Hexcore mesh with approximately 5.64 million cells. The maximum temperature \(T_{\text{max}}\) and pressure drop \(\Delta P\) changed by less than 0.5% when further refining the mesh, confirming grid independence.
2. Comparison of Flow Rates and Temperature Differences
Based on the energy balance \(q_b = Q \rho_f c_f \Delta T_f\) and a fixed heat generation of 822.12 W, I calculated the required volumetric flow rates for both cooling media at various prescribed temperature rises \(\Delta T_f\) (1–10 °C). The results are summarized in the table below:
| \(\Delta T_f\) (°C) | Air flow rate \(Q_{\text{air}}\) (m³/h) | Coolant flow rate \(Q_{\text{liquid}}\) (×10⁻³ m³/h) |
|---|---|---|
| 1 | 39.873 | 13.770 |
| 2 | 19.937 | 6.885 |
| 4 | 9.968 | 3.443 |
| 6 | 6.646 | 2.295 |
| 8 | 4.984 | 1.721 |
| 10 | 3.987 | 1.377 |
Due to the much lower density and specific heat of air, the required volumetric flow rate for air was approximately 2896 times that of the coolant. My simulation results matched the prescribed \(\Delta T_f\) values within ±5%, validating the computational approach.
3. Heat Transfer Performance
I evaluated the thermal performance of both cooling systems by monitoring the maximum, minimum, and average cell temperatures, as well as the maximum temperature difference across the module. The results for different \(\Delta T_f\) values are shown below:
| \(\Delta T_f\) (°C) | Air \(T_{\text{max}}\) (°C) | Air \(T_{\text{min}}\) (°C) | Air \(T_{\text{ave}}\) (°C) | Air \(\Delta T_c\) (°C) | Liquid \(T_{\text{max}}\) (°C) | Liquid \(T_{\text{min}}\) (°C) | Liquid \(T_{\text{ave}}\) (°C) | Liquid \(\Delta T_c\) (°C) |
|---|---|---|---|---|---|---|---|---|
| 1 | 25.2 | 23.8 | 24.5 | 1.4 | 27.7 | 24.0 | 26.0 | 3.7 |
| 2 | 26.8 | 23.9 | 25.3 | 2.9 | 27.9 | 23.9 | 26.1 | 4.0 |
| 4 | 30.2 | 24.2 | 27.0 | 6.0 | 28.5 | 23.8 | 26.3 | 4.7 |
| 6 | 34.0 | 24.6 | 28.9 | 9.4 | 29.2 | 23.7 | 26.4 | 5.5 |
| 8 | 37.9 | 25.0 | 30.8 | 12.9 | 29.9 | 23.7 | 26.6 | 6.2 |
| 10 | 42.1 | 25.5 | 32.9 | 16.6 | 30.6 | 23.7 | 26.8 | 6.9 |
I observed that as \(\Delta T_f\) increased, the temperatures of the air-cooled module increased more rapidly than those of the liquid-cooled module. For \(\Delta T_f \ge 2\) °C, the liquid-cooled system yielded lower \(T_{\text{max}}\) values, indicating superior cooling. However, at \(\Delta T_f = 1\) °C, the air-cooled approach achieved a lower maximum temperature by about 2.5 °C. This suggests a crossover point exists—around \(\Delta T_f = 1.76\) °C for maximum temperature and around \(\Delta T_f = 3.15\) °C for maximum temperature difference—where the preferred cooling method changes.
I further quantified the heat transfer performance using the Colburn factor \(J\):
$$ J = \frac{Nu}{Re \, Pr^{1/3}} $$
Since the total heat transfer was fixed, \(J\) was independent of \(\Delta T_f\). For my simulations, the liquid-cooled module achieved \(J = 9.67 \times 10^{-3}\), while the air-cooled module gave \(J = 2.91 \times 10^{-3}\). Therefore, the liquid cooling heat transfer performance was about 3.32 times that of air cooling.
To understand spatial temperature uniformity, I examined the distribution across the 13 cells in column A at \(\Delta T_f = 6\) °C. The results showed that liquid cooling maintained a nearly constant cell-to-cell temperature difference of only 0.5 °C, whereas air cooling exhibited a variation of 6.1 °C. This indicates that liquid cooling provides far better temperature uniformity within the energy storage battery module.
4. Flow Resistance Characteristics
Flow resistance is a crucial factor in pump or fan power consumption. I recorded the pressure drop \(\Delta P\) across each cooling system for different \(\Delta T_f\) values:
| \(\Delta T_f\) (°C) | \(\Delta P_{\text{air}}\) (Pa) | \(\Delta P_{\text{liquid}}\) (Pa) |
|---|---|---|
| 1 | 260 | 7600 |
| 2 | 130 | 3500 |
| 4 | 65 | 1700 |
| 6 | 40 | 1050 |
| 8 | 28 | 720 |
| 10 | 20 | 520 |
Both systems exhibited a nonlinear decrease in \(\Delta P\) as \(\Delta T_f\) increased (i.e., as flow rate decreased). The liquid-cooled module consistently showed higher pressure drops, though the difference narrowed at larger \(\Delta T_f\). I attributed the primary hydraulic losses in both designs to the dividing and combining manifolds.
To compare flow resistance on a normalized basis, I used the friction factor \(F\):
$$ F = \frac{2 \Delta P}{\rho_f u^2} $$
At \(\Delta T_f = 1\) °C, \(F\) for liquid cooling was about 17.6 times that for air cooling; at \(\Delta T_f = 10\) °C, the ratio dropped to about 5.2. This indicates that the liquid-cooled system inherently generates higher resistance, especially at high flow rates.
5. Overall Thermo-Hydraulic Performance
To balance heat transfer enhancement against pumping penalty, I introduced the overall performance factor \(\theta = J / F\). A higher \(\theta\) indicates better efficiency (more heat transfer per unit pressure loss). The computed values are:
| \(\Delta T_f\) (°C) | \(\theta_{\text{air}}\) (×10⁻³) | \(\theta_{\text{liquid}}\) (×10⁻³) |
|---|---|---|
| 1 | 2.30 | 4.40 |
| 2 | 2.28 | 3.80 |
| 4 | 2.25 | 3.10 |
| 6 | 2.22 | 2.85 |
| 8 | 2.21 | 2.70 |
| 10 | 2.20 | 2.80 |
Across the entire range of \(\Delta T_f\), the liquid-cooled system exhibited a \(\theta\) factor that was 1.27 to 1.71 times higher than that of the air-cooled system. This confirms that liquid cooling offers superior overall thermo-hydraulic performance, despite its higher flow resistance, because the improvement in heat transfer more than compensates for the increased pumping demand.
6. Influence of Ambient Temperature
I also examined the impact of ambient temperature \(T_e\) on module performance at a fixed \(\Delta T_f = 6\) °C. Five ambient temperatures were tested: 0, 5, 10, 20, and 30 °C. The results are summarized in the table below:
| \(T_e\) (°C) | Air \(T_{\text{max}}\) (°C) | Air \(T_{\text{min}}\) (°C) | Air \(T_{\text{ave}}\) (°C) | Air \(\Delta T_c\) (°C) | Liquid \(T_{\text{max}}\) (°C) | Liquid \(T_{\text{min}}\) (°C) | Liquid \(T_{\text{ave}}\) (°C) | Liquid \(\Delta T_c\) (°C) |
|---|---|---|---|---|---|---|---|---|
| 0 | 32.5 | 20.9 | 26.7 | 11.6 | 28.7 | 23.6 | 26.1 | 5.1 |
| 5 | 33.0 | 22.4 | 27.5 | 10.6 | 28.8 | 23.6 | 26.2 | 5.2 |
| 10 | 33.5 | 24.0 | 28.3 | 9.5 | 28.9 | 23.6 | 26.2 | 5.3 |
| 20 | 34.0 | 24.6 | 28.9 | 9.4 | 29.2 | 23.7 | 26.4 | 5.5 |
| 30 | 36.8 | 29.2 | 31.9 | 7.5 | 29.8 | 23.6 | 26.7 | 6.2 |
When the ambient temperature rose from 0 °C to 30 °C, the air-cooled \(T_{\text{max}}\) increased by 4.3 °C, while the liquid-cooled \(T_{\text{max}}\) increased by only 1.1 °C. The maximum temperature difference \(\Delta T_c\) in the air-cooled module actually decreased by 4.1 °C because the minimum temperature rose faster than the maximum. Nevertheless, the overall temperature uniformity of liquid cooling remained far superior. The liquid-cooled system’s \(T_{\text{ave}}\) and \(\Delta T_c\) changed by only 0.67 °C and 1.0 °C, respectively, over the entire ambient range. Hence, liquid cooling demonstrates much stronger robustness to ambient temperature variations, making it more suitable for environments with large seasonal or diurnal temperature swings for energy storage battery applications.
7. Conclusions
Through my comprehensive numerical study on the energy storage battery module, I have drawn the following key conclusions:
- Regarding heat transfer performance, there exists a critical cooling medium temperature rise (about 1.76 °C for maximum temperature and about 3.15 °C for maximum temperature difference) that determines whether air cooling or liquid cooling is superior. Overall, the liquid cooling heat transfer factor \(J\) is 3.32 times that of air cooling.
- Liquid cooling provides much better cell-to-cell temperature uniformity; the maximum temperature difference across cells is only 0.5 °C for liquid cooling versus 6.1 °C for air cooling at \(\Delta T_f = 6\) °C.
- Liquid cooling exhibits significantly higher flow resistance, with a friction factor \(F\) 5.2 to 17.6 times that of air cooling. The manifolds are the main contributors to pressure loss in both systems.
- When evaluating overall thermo-hydraulic performance via \(\theta = J/F\), liquid cooling outperforms air cooling by a factor of 1.27 to 1.71, and this advantage becomes more pronounced at lower flow rates (higher \(\Delta T_f\)).
- Liquid cooling is far less sensitive to changes in ambient temperature. Over a 0–30 °C range, its maximum temperature rises only 1.1 °C, whereas air cooling rises 4.3 °C. This makes liquid cooling the preferred choice for energy storage battery systems deployed in variable climates.
My findings provide a quantitative foundation for selecting and optimizing cooling strategies in energy storage battery modules, emphasizing the trade-offs between thermal performance, flow resistance, and environmental adaptability.