With the growing global demand for green electricity, large-scale industrial and commercial energy storage systems have been widely deployed. However, energy storage cells face significant challenges, including poor thermal stability, increased side reactions under high-temperature conditions, and the risk of thermal runaway. To effectively maintain the operating temperature of battery packs within the optimal range of 20–35°C, this study employs an experimentally calibrated simulation model to numerically investigate three key factors influencing the thermal behavior of energy storage cells: channel aspect ratios, liquid cooling plate layouts, and inlet coolant flow rates. The results demonstrate that channel aspect ratios have a minor impact on cell temperature but significantly affect pressure drop and energy consumption. A bottom-and-side cooling layout reduces the maximum cell temperature by 21.8% and improves temperature uniformity by 68.1% compared to bottom-only cooling. Moderate flow rates of 10–12.5 L/min effectively constrain temperature rise and enhance uniformity while minimizing pressure drop and energy consumption. The combined optimal factors—channel aspect ratio W/H=3, bottom-and-side cooling, and 12.5 L/min flow rate—yield the best performance, with the bottom-and-side cooling playing a dominant role in the multi-factor cooling process.
The transition from fossil fuels to renewable energy sources is critical for mitigating climate change and ensuring sustainable development. Energy storage systems, which convert solar or wind energy into electrical energy stored in large battery packs, are pivotal in this shift. Lithium-ion batteries are widely adopted in these systems due to their high energy density, long cycle life, and lack of memory effect. However, as the demand for stored energy increases, energy storage cells generate substantial heat during charging and discharging, raising concerns about thermal stability and safety. Excessive temperatures accelerate aging and side reactions, while low temperatures increase internal resistance and reduce capacity. Moreover, temperature non-uniformity among energy storage cells can lead to capacity loss and reduced lifespan. Thus, effective thermal management is essential to maintain cells within 15–35°C and limit the maximum temperature difference to below 5°C.
Current cooling methods for energy storage cells include air cooling, liquid cooling, heat pipes, and phase change materials. Liquid cooling, particularly indirect liquid cooling using cold plates, is dominant in large-scale applications due to its efficiency and practicality. This study focuses on enhancing indirect liquid cooling by examining channel geometries, cooling plate arrangements, and flow rates. The numerical model is validated against experimental data, ensuring accuracy for subsequent analyses.
Numerical Model
Physical Model
The study examines a single battery pack from an energy storage system, configured as 1P52S. The energy storage cells are semi-solid type with a capacity of 280 Ah and dimensions of 173.8 mm × 71.6 mm × 207.2 mm. The pack includes cells, insulating plates, PC boards, thermal pads, and liquid cooling plates. The cooling plate features four parallel serpentine flow channels. Three channel aspect ratios (W/H = 7, 5, 3 with H = 6 mm) are analyzed to assess their impact on heat transfer and flow resistance. Two cooling layouts are considered: bottom-only cooling and bottom-and-side cooling. The material properties are summarized in Table 1.
| Component | Density (kg/m³) | Specific Heat (J/(kg·K)) | Thermal Conductivity (W/(m·K)) |
|---|---|---|---|
| Energy Storage Cell | 2152 | 1051.1 | λ_th = 1.04, λ_w, λ_h = 21.05 |
| Liquid Cooling Plate | 2680 | 880 | 237 |
| Thermal Silicone Gel | 2420 | 967 | 2.1 |
| Coolant | 1065 | 3394 | 0.419 |
| PC Board | 1200 | 1340 | 0.194 |
Governing Equations
The heat transfer in energy storage cells is governed by the energy conservation equation, Navier-Stokes equations, and continuity equation. The following assumptions are made: negligible contact resistances, constant material properties, and ignored radiation heat transfer.
The energy conservation equation for the battery is:
$$ \rho C_p \frac{\partial T}{\partial t} = \nabla \cdot (k \nabla T) + Q $$
where \( \rho \) is density, \( C_p \) is specific heat capacity, \( k \) is thermal conductivity, \( T \) is temperature, \( t \) is time, and \( Q \) is the heat generation rate.
The Navier-Stokes equations for the coolant flow are:
$$ \frac{\partial}{\partial t} (\rho \vec{v}) + \nabla \cdot (\rho \vec{v} \vec{v}) = -\nabla P + \mu \nabla^2 \vec{v} + \vec{F} $$
where \( \vec{v} \) is velocity vector, \( P \) is pressure, \( \mu \) is dynamic viscosity, and \( \vec{F} \) is body force.
The continuity equation is:
$$ \frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \vec{v}) = 0 $$
Heat Generation in Energy Storage Cells
The heat generation in energy storage cells during discharge includes irreversible and reversible components, modeled by the Bernardi equation:
$$ q_v = \frac{1}{V_b} \left( I^2 R + I T \frac{dE_{OC}}{dT} \right) $$
where \( I \) is current, \( R \) is internal resistance, \( V_b \) is cell volume, \( T \) is temperature, and \( \frac{dE_{OC}}{dT} = 0.00049 \, \text{V/K} \) is the temperature coefficient of the open-circuit voltage. The internal resistance varies with the state of charge (SOC), as shown in Table 2.
| SOC (%) | -20°C | -10°C | 0°C | 10°C | 25°C | 35°C | 45°C | 55°C |
|---|---|---|---|---|---|---|---|---|
| 5 | 5.34 | 3.66 | 1.73 | 1.24 | 0.57 | 0.46 | 0.34 | 0.23 |
| 10 | 5.05 | 3.47 | 1.63 | 1.18 | 0.53 | 0.43 | 0.33 | 0.22 |
| 15 | 4.75 | 3.29 | 1.56 | 1.13 | 0.51 | 0.42 | 0.32 | 0.23 |
| 20 | 4.46 | 3.11 | 1.50 | 1.09 | 0.49 | 0.40 | 0.32 | 0.23 |
| 25 | 4.17 | 2.93 | 1.45 | 1.06 | 0.47 | 0.39 | 0.31 | 0.23 |
| 30 | 3.88 | 2.76 | 1.41 | 1.03 | 0.46 | 0.39 | 0.31 | 0.23 |
| 35 | 3.64 | 2.59 | 1.38 | 1.00 | 0.45 | 0.38 | 0.30 | 0.23 |
| 40 | 3.43 | 2.46 | 1.34 | 0.98 | 0.44 | 0.37 | 0.30 | 0.23 |
| 45 | 3.24 | 2.33 | 1.32 | 0.96 | 0.43 | 0.37 | 0.30 | 0.23 |
| 50 | 3.14 | 2.24 | 1.29 | 0.94 | 0.43 | 0.36 | 0.29 | 0.23 |
| 55 | 3.12 | 2.20 | 1.27 | 0.93 | 0.42 | 0.36 | 0.29 | 0.23 |
| 60 | 3.09 | 2.18 | 1.25 | 0.92 | 0.42 | 0.36 | 0.29 | 0.23 |
| 65 | 3.05 | 2.15 | 1.24 | 0.91 | 0.43 | 0.37 | 0.30 | 0.24 |
| 70 | 3.01 | 2.13 | 1.23 | 0.91 | 0.42 | 0.36 | 0.30 | 0.23 |
| 75 | 2.97 | 2.10 | 1.22 | 0.90 | 0.41 | 0.35 | 0.29 | 0.23 |
| 80 | 2.93 | 2.07 | 1.21 | 0.89 | 0.41 | 0.35 | 0.29 | 0.23 |
| 85 | 2.88 | 2.04 | 1.19 | 0.87 | 0.40 | 0.34 | 0.29 | 0.23 |
| 90 | 2.83 | 2.00 | 1.17 | 0.86 | 0.39 | 0.34 | 0.28 | 0.23 |
| 95 | 2.79 | 1.97 | 1.16 | 0.85 | 0.39 | 0.33 | 0.28 | 0.23 |
| 100 | 2.77 | 1.97 | 1.17 | 0.86 | 0.39 | 0.34 | 0.29 | 0.23 |
The SOC is calculated as:
$$ \text{SOC}(t) = 1 – \frac{I t}{C_N} $$
where \( C_N \) is the nominal capacity.
Computational Domain and Boundary Conditions
The computational domain includes the physical model, air domain, and liquid domain. The initial temperature is 25°C, and the ambient temperature is 25°C. The battery pack walls undergo convective heat transfer with a coefficient of 5 W/(m²·K). The coolant inlet is a mass flow inlet at 0.1791 kg/s (equivalent to 10 L/min for water) and 22°C, while the outlet is a pressure outlet at atmospheric pressure. A 2 mm thermal silica gel layer reduces contact resistance between energy storage cells and the cooling plate. The discharge process is at 0.5C rate until 90% SOC is depleted (6480 s).
The energy consumption of the liquid cooling system is calculated as:
$$ Q_{ec} = \int_0^t \nabla P \cdot V_{in} \, dt $$
where \( \nabla P \) is the pressure drop and \( V_{in} \) is the inlet volumetric flow rate.
Model Validation
The numerical model is validated against experimental data for a single energy storage cell at 1C and 0.5C discharge rates. The temperature probe is placed at the center of the cell’s large surface. The maximum relative error is 2.9% at 0.5C, confirming the model’s accuracy. For the pack study, the temperature is monitored at the top cover surface, and the global maximum temperature difference is used to assess uniformity.
Results and Discussion
Effect of Channel Aspect Ratio on Cooling Performance
Under a constant inlet flow rate of 10 L/min, the channel aspect ratio (W/H) has a minor impact on the temperature of energy storage cells. The maximum temperature rise decreases slightly with smaller W/H ratios, but the reduction is less than 0.68% between W/H=7 and W/H=3. This is because smaller aspect ratios increase flow velocity and convective heat transfer coefficient, compensating for the reduced heat transfer area. However, the pressure drop and energy consumption are significantly affected. As shown in Table 3, reducing W/H from 5 to 3 decreases the pressure drop by 27.2% and energy consumption by 37.3%. Thus, smaller aspect ratios improve energy efficiency without compromising cooling performance.
| Aspect Ratio (W/H) | Maximum Temperature Rise (°C) | Pressure Drop (Pa) | Energy Consumption (J) |
|---|---|---|---|
| 7 | 7.70 | 1,200 | 850 |
| 5 | 7.62 | 950 | 600 |
| 3 | 7.58 | 690 | 430 |
Effect of Cooling Plate Layout on Thermal Management
The cooling plate layout profoundly influences the temperature distribution of energy storage cells. Compared to bottom-only cooling, the bottom-and-side cooling reduces the maximum temperature rise from 7.62°C to 0.51°C, a decrease of 21.8%. The global maximum temperature difference drops from 8.80°C to 3.00°C, improving uniformity by 68.1%. This is attributed to the enhanced heat transfer power, which increases by up to 333.85% in the initial phase and 107.52% at the end of discharge. The bottom-and-side cooling effectively mitigates vertical temperature gradients, prolonging the life of energy storage cells.
| Cooling Layout | Maximum Temperature Rise (°C) | Global Max Temperature Difference (°C) | Heat Transfer Power (W) |
|---|---|---|---|
| Bottom-only | 7.62 | 8.80 | 150 |
| Bottom-and-side | 0.51 | 3.00 | 450 |
Effect of Inlet Coolant Flow Rate on Cooling Performance
Varying the inlet flow rate from 5 to 15 L/min affects the temperature rise and uniformity of energy storage cells. As the flow rate increases, the maximum temperature rise decreases, but the rate of reduction diminishes. For instance, increasing the flow rate from 12.5 to 15 L/min only reduces the temperature by 0.20°C. Similarly, the global maximum temperature difference decreases from 2.8°C at 5 L/min to 1.3°C at 15 L/min, but the improvement becomes negligible beyond 12.5 L/min. However, higher flow rates escalate the pressure drop and energy consumption. Thus, moderate flow rates of 10–12.5 L/min are optimal, balancing cooling performance and energy efficiency.
| Flow Rate (L/min) | Max Temperature Rise (°C) | Global Max Temperature Difference (°C) | Pressure Drop (Pa) | Energy Consumption (J) |
|---|---|---|---|---|
| 5 | 8.50 | 2.80 | 300 | 200 |
| 7.5 | 8.00 | 2.10 | 500 | 350 |
| 10 | 7.62 | 1.80 | 750 | 520 |
| 12.5 | 7.50 | 1.50 | 1,000 | 700 |
| 15 | 7.48 | 1.30 | 1,300 | 900 |
Multi-Factor Comprehensive Cooling Analysis
The optimal factors—channel aspect ratio W/H=3, bottom-and-side cooling, and flow rate of 12.5 L/min—are combined to assess their synergistic effects. The multi-factor cooling achieves the lowest maximum temperature rise (0.4°C) and global maximum temperature difference (2.9°C). The bottom-and-side cooling alone yields similar results (0.5°C rise and 3.0°C difference), indicating its dominant role. In contrast, individual factors like W/H=3 or 12.5 L/min flow rate result in higher temperature rises (>7.3°C) and differences (>8.7°C). Thus, the bottom-and-side cooling is the primary driver in multi-factor cooling strategies for energy storage cells.
| Cooling Configuration | Max Temperature Rise (°C) | Global Max Temperature Difference (°C) |
|---|---|---|
| W/H=3 only | 7.58 | 8.70 |
| 12.5 L/min only | 7.50 | 8.80 |
| Bottom-and-side only | 0.51 | 3.00 |
| Multi-factor (W/H=3, bottom-and-side, 12.5 L/min) | 0.40 | 2.90 |
Conclusion
This numerical study investigates the thermal characteristics of energy storage cells under various cooling strategies. The channel aspect ratio has a minimal effect on cell temperature but significantly influences pressure drop and energy consumption, with W/H=3 offering the best trade-off. The bottom-and-side cooling layout drastically reduces the maximum temperature rise by 21.8% and improves temperature uniformity by 68.1% compared to bottom-only cooling. Moderate flow rates of 10–12.5 L/min optimize cooling performance and energy efficiency. The multi-factor approach combining W/H=3, bottom-and-side cooling, and 12.5 L/min flow rate achieves the best results, with the bottom-and-side cooling being the dominant factor. These findings provide valuable insights for designing efficient thermal management systems for energy storage cells, ensuring their safe and long-term operation in large-scale energy storage applications.