Energy storage technology serves as a core support for the development of new energy sources and is poised to drive revolutionary adjustments in the global energy landscape. Lithium batteries, with advantages such as high energy density and long cycle life, are widely used in electrochemical energy storage systems. The optimal operating temperature for lithium energy storage cells ranges between 25°C and 40°C. Temperatures that are too low or too high can lead to performance degradation and even trigger thermal runaway, making the design of a reliable and efficient thermal management system crucial. Current thermal management schemes for energy storage cells include air cooling, liquid cooling, phase change cooling, immersion cooling, heat pipe cooling, and coupled cooling. However, energy storage cells have large单体 capacity and high heat generation, and are limited by heat dissipation issues. Currently, the charge-discharge rates in practical applications are mostly 0.5C or 0.25C, with only a few scenarios like frequency regulation allowing short-term use of 1C rates. High rates are an inevitable direction for the development of electrochemical energy storage. This paper focuses on a prismatic lithium energy storage cell module, considers the heat generation of the cells and aluminum bars, and establishes an electric-thermal-fluid multi-physics coupled simulation model for the energy storage cell module. The temperature characteristics of the module under 1C conditions are analyzed through simulation for different liquid cooling schemes, and the effects of different schemes on the maximum temperature rise and temperature range of the module are compared. Finally, experiments verify the accuracy of the simulation analysis, ensuring the reliability of the conclusions.
The simulation geometric model includes energy storage cells, aluminum bars, liquid cold plates, and connecting tubes. The module consists of seven energy storage cells labeled C1 to C7. The energy storage cells are lithium iron phosphate type with a rated voltage of 3.2 V, rated capacity of 280 Ah, and dimensions of 174 mm × 204 mm × 71.6 mm. To explore liquid cooling schemes suitable for high-rate charge and discharge of large-capacity energy storage cells, cold plates are arranged on the bottom surface, large surfaces, and side surfaces, forming a total of nine arrangement schemes. For example, the double large surface + bottom surface scheme includes eight series-connected large surface cold plates and one bottom cold plate, while the side surface series + bottom surface scheme includes two series-connected side cold plates and one bottom cold plate. The gaps between the cold plates and energy storage cells are filled with thermal conductive material. The specific arrangements of other schemes are detailed in Table 1.
| Scheme Number | Configuration | Description |
|---|---|---|
| 1 | Bottom Surface | 1 bottom cold plate |
| 2 | Single Large Surface | 4 series-connected large surface cold plates arranged at intervals |
| 3 | Single Large Surface + Bottom | 4 series-connected large surface cold plates arranged at intervals + 1 bottom cold plate |
| 4 | Double Large Surface | 8 series-connected large surface cold plates |
| 5 | Double Large Surface + Bottom | 8 series-connected large surface cold plates + 1 bottom cold plate |
| 6 | Side Surface Series | 2 series-connected side cold plates |
| 7 | Side Surface Series + Bottom | 2 series-connected side cold plates + 1 bottom cold plate |
| 8 | Side Surface Parallel | 2 parallel-connected side cold plates |
| 9 | Side Surface Parallel + Bottom | 2 parallel-connected side cold plates + 1 bottom cold plate |
The electric-thermal-fluid coupled mathematical model is established as follows. For the aluminum bar heat generation analysis, during constant current charge and discharge of the module, the aluminum bars carry direct current, generating a steady electric field. The fundamental equations include the continuity equation for conduction current and the line integral equation for electric field strength:
$$ \nabla \cdot \mathbf{J} = 0 $$
$$ \nabla \times \mathbf{E} = 0 $$
where $\mathbf{J}$ is the current density and $\mathbf{E}$ is the electric field intensity. The heat generated by a metal conductor carrying a constant current can be calculated using Joule’s law in differential form:
$$ p = \mathbf{J} \cdot \mathbf{E} $$
where $p$ is the power density.
For heat transfer analysis, heat transfer occurs through conduction, convection, and radiation. In the module, heat sources include the energy storage cells and aluminum bars. The heat from the energy storage cells is primarily transferred to the cold plates via conduction, while the heat from the aluminum bars is mainly transferred to the cold plates through the energy storage cells via conduction. Subsequently, heat is carried away from the module through convection between the cold plates and the coolant. Additionally, heat can be dissipated through natural cooling and radiation, but their efficiency is relatively low under liquid cooling and can be neglected in the analysis. The heat conduction process is described by Fourier’s law:
$$ \mathbf{q} = -k \nabla T $$
where $\mathbf{q}$ is the heat flux vector, $k$ is the thermal conductivity, and $\nabla T$ is the temperature gradient. Heat convection is described by Newton’s law of cooling:
$$ q = h \Delta t $$
where $q$ is the convective heat flux, $h$ is the heat transfer coefficient, and $\Delta t$ is the temperature difference between the wall and the coolant.
For flow field analysis, the fundamental governing equations of computational fluid dynamics include the continuity equation, momentum equation, and energy equation. For incompressible fluid without considering gravity, the three equations are expressed as follows:
Continuity equation:
$$ \nabla \cdot \mathbf{v} = 0 $$
Momentum equation:
$$ \rho \left( \frac{\partial \mathbf{v}}{\partial t} + (\mathbf{v} \cdot \nabla) \mathbf{v} \right) = -\nabla P + \mu \nabla^2 \mathbf{v} $$
Energy equation:
$$ \rho C \left( \frac{\partial T}{\partial t} + \nabla \cdot (\mathbf{v} T) \right) = \nabla \cdot (k \nabla T) $$
where $\mathbf{v}$ is the fluid velocity vector, $P$ is the static pressure, $\rho$ is the density, $\mu$ is the dynamic viscosity, $C$ is the specific heat capacity, $T$ is the temperature, and $k$ is the thermal conductivity.
In summary, the heat generation power density distribution of the aluminum bars is first obtained through electric field simulation, and then the results are imported into fluid dynamics analysis software for simultaneous temperature and flow field solutions. The temperature characteristics of the energy storage cell module considering the heat generation of the cells and aluminum bars are obtained through electric-thermal-fluid multi-physics coupled simulation.
The simulation conditions are set as follows. The heat generation of the energy storage cells and aluminum bars is considered for steady-state simulation of the module under 1C conditions. It is assumed that the heat generation inside the energy storage cells is uniform, the coolant is a viscous incompressible fluid, the effects of natural cooling and radiation heat transfer are not considered, and the contact thermal resistance between the cell terminals and aluminum bars is neglected. The heat generation of each energy storage cell is 33 W. The heat generation of the aluminum bars is obtained through Maxwell electric field simulation. After obtaining the heat generation power, it is imported into Fluent for flow and temperature field simulation. The cold plates and aluminum bars are made of aluminum, and other physical parameters are shown in Table 2.
| Material | Density (kg/m³) | Specific Heat Capacity (J/(kg·K)) | Thermal Conductivity (W/(m·K)) |
|---|---|---|---|
| Energy Storage Cell | 2133 | 964 | 9.04 (x), 3.56 (y), 11.00 (z) |
| Coolant | 1071 | 3300 | 0.384 |
| Thermal Conductive Material | 3000 | 1150 | 2 |
The simulation results and analysis are as follows. For aluminum bar heat generation analysis, Maxwell calculations yield the current density and heat generation power density of the aluminum bars. The current is mainly distributed between the two terminals, with sparse distribution in the outer regions. The heat generation between the two terminals is relatively uniform, while the outer regions have lower heat generation power density, consistent with the current density distribution, indicating that areas outside the two terminals contribute little to the current-carrying capacity of the aluminum bars. The heat generation power of the aluminum bars is obtained by integrating equation (3):
$$ P = \int_V (\mathbf{J} \cdot \mathbf{E}) \, dV $$
where $P$ is the heat generation power of the aluminum bar and $V$ is the volume of the aluminum bar. The calculated heat generation power for a series aluminum bar is 1.63 W, for positive and negative aluminum bars is 1.14 W, and the total heat generation power for the module’s aluminum bars is 12.06 W.
For the analysis of the temperature distribution characteristics of the module, five schemes are selected: bottom cold plate, double large surface cold plates, double large surface + bottom cold plates, side surface series cold plates, and side surface series + bottom cold plates. The temperature nephograms of the module for these five schemes under a bottom cold plate flow rate of 1.7 L/min and large surface/side cold plate flow rate of 1 L/min are analyzed. In the bottom cold plate scheme, the temperature of the energy storage cells gradually increases from bottom to top, with the aluminum bars being the highest temperature components in the module, reaching a maximum temperature rise of 42 K. The highest temperature point is at the middle position of the aluminum bar connecting the two cell terminals. In the double large surface cold plate scheme, the coolant temperature gradually increases along the flow channel, causing the aluminum bar temperature to show the same trend, and the aluminum bar at the end of the flow channel reaches the maximum temperature rise of 14 K. Adding a bottom cold plate reduces the maximum temperature rise to 13 K. In the side surface series cold plate scheme, the temperature of the aluminum bars gradually increases along the flow channel, with the aluminum bar near the end of the flow channel reaching the maximum temperature rise of 14 K. Adding a bottom cold plate reduces the maximum temperature rise to 12 K.
The effect of flow rate on the temperature characteristics of the module is analyzed. The relationship between the maximum temperature rise $T$ of the positive aluminum bars of the energy storage cells and the coolant flow rate $Q$ for each scheme is obtained through simulation. In the bottom cold plate scheme, the maximum temperature rise of all aluminum bars decreases with increasing flow rate, but the rate of decrease gradually slows. Except for 0.5 L/min, the temperature rise of the C6 energy storage cell aluminum bar is the highest, while the differences between C2-C5 are small. This is because the C6 energy storage cell positive aluminum bar is near the outlet of the cold plate, where the coolant temperature is high, resulting in poor heat dissipation. At a flow rate of 8 L/min, the temperature rise of the C6 aluminum bar is 36.2 K, indicating that the bottom cold plate cannot control the energy storage cell temperature within 40°C under normal temperature conditions. After the flow rate reaches 1.5 L/min, increasing the flow rate has no significant effect on the maximum temperature rise, because the small contact area between the bottom cold plate and the energy storage cells limits the heat conduction efficiency.
In schemes with large surface or side cold plates, the maximum temperature rise of the aluminum bars increases from C6 to C2 due to the gradual increase in coolant temperature along the flow channel. Increasing the flow rate in each scheme can reduce the maximum temperature rise and temperature range, but the decrease becomes smaller. When the flow rate increases from 2 L/min to 3 L/min, the maximum temperature rise decrease for each scheme is within 0.6 K, and the temperature range decrease is within 0.4 K. Further increasing the flow rate cannot significantly improve the temperature rise and temperature uniformity of the module.
In schemes with side surface parallel cold plates, the temperature rise of the energy storage cell aluminum bars is highest for C2 and lower for C3 and C5 at all flow rates, because the positive aluminum bars of C3 and C5 are close to the first cold plate, while the positive aluminum bar of C2 is near the end of the second cold plate, and the coolant temperature increases along the flow channel, gradually reducing the heat dissipation capacity. In schemes with side surface parallel cold plates, the temperature rise of the C2 aluminum bar is the highest at all flow rates, because the coolant in both cold plates flows from the C6 energy storage cell side to the C2 energy storage cell side, and the coolant temperature gradually increases, reducing the heat dissipation effect. As the flow rate increases, the maximum temperature rise and temperature range in each scheme decrease, but the extent gradually diminishes. When the flow rate increases from 2 L/min to 3 L/min, the maximum temperature rise decrease for each scheme is within 0.5 K, and the temperature range decrease is within 0.3 K. Further increasing the flow rate cannot significantly improve the temperature rise and temperature uniformity of the module.
A comparative analysis of the liquid cooling effects of different schemes is conducted. Based on the previous analysis, the bottom cold plate scheme cannot meet the heat dissipation requirements under 1C conditions. The relationships between the maximum temperature rise $T_M$ and temperature range $R_T$ of the module and the flow rate $Q$ for the remaining eight schemes are shown in the analysis. The maximum temperature rise of all eight schemes decreases with increasing flow rate, and the rate of decrease gradually slows. Except for the scheme with single large surface cold plates, which always has a high maximum temperature rise, the other six schemes have differences in maximum temperature rise within 1 K at flow rates above 2 L/min, indicating similar effects in controlling the maximum temperature of the module. Adding a bottom cold plate in the single large surface cold plate scheme can reduce the maximum temperature rise of the module by more than 2 K within the analyzed flow rate range. Adding a bottom cold plate in the double large surface and side cold plate schemes can reduce the maximum temperature rise, but the reduction decreases with increasing flow rate. For the double large surface and side parallel schemes, the reduction is within 1 K at flow rates above 1 L/min, and for the side series scheme, the reduction is within 1 K at flow rates above 2 L/min.
The temperature range of all eight schemes decreases with increasing flow rate, and the rate of decrease gradually slows, with the differences between schemes gradually narrowing. The modules with side cold plates have better temperature uniformity, while the modules with large surface cold plates have relatively poor temperature uniformity, but the gap gradually narrows with increasing flow rate, and the difference is within 0.5 K at flow rates above 3 L/min. Adding a bottom cold plate in the side parallel cold plate scheme cannot reduce the temperature range of the module. Adding a bottom cold plate in the large surface or side series cold plate schemes can reduce the temperature range of the module, but the effect weakens with increasing flow rate. For the double large surface and side series schemes, the gain from adding a bottom cold plate is within 0.5 K after the flow rate reaches 1 L/min, and for the single large surface scheme, the gain is within 0.5 K after the flow rate reaches 2.5 L/min.
Experimental verification is conducted to validate the reliability of the simulation results. The temperature rise of the module under six schemes with double large surface cold plates, side surface series cold plates, and side surface parallel cold plates is tested at a total flow rate of 1 L/min for large surface/side cold plates. The experimental setup involves placing the energy storage cell module in an environmental test chamber, collecting voltage, current, temperature, and other information of the module through a battery management module, and uploading it to the control platform via charge-discharge equipment. The temperature changes of the aluminum bars and the test chamber environment are collected using thermocouples, with thermocouples placed in the central area of the aluminum bars for comparison with simulation results. The control platform sends charge-discharge commands to the charge-discharge equipment, which are then sent to the energy storage cell module through the battery management module to achieve precise control of the module’s charge-discharge process. The coolant temperature and flow rate are controlled by a liquid cooling unit. Other experimental conditions include a charge-discharge current of 280 A, operating program of charge for 1 hour, rest for 30 minutes, discharge for 1 hour, inlet temperature of 20°C, ambient temperature of 25°C, and coolant being 50% ethylene glycol aqueous solution.
The experimental results and analysis show that the maximum temperature rise errors of the positive aluminum bars of energy storage cells C2 to C6 between simulation and experiment are within 0.9 K for schemes with double large surface cold plates, within 0.8 K for schemes with side surface series cold plates, and within 0.6 K for schemes with side surface parallel cold plates. For the C2, C3, and C4 energy storage cells in the six schemes, the maximum temperature rise errors are within 0.8 K. The sources of error include simplifications in the simulation model, neglect of natural cooling and radiation heat transfer, and fluctuations in the actual environmental test chamber temperature and coolant supply temperature. The error differences for the six schemes are less than 0.9 K from both the scheme perspective and the energy storage cell perspective, indicating that the calculation results of the electric-thermal-fluid coupled simulation model established in this paper are credible.
In conclusion, an electric-thermal-fluid multi-physics coupled simulation model for high-rate energy storage cell modules is established, and the effects of cold plate arrangement schemes and coolant flow rate on the temperature characteristics of the module are studied. The main conclusions are as follows. The current density and heat generation power density distribution of the aluminum bars are consistent and mainly concentrated between the two terminals, indicating that areas outside the terminals contribute little to the current-carrying capacity of the aluminum bars, which can be used to optimize the design of the aluminum bar structure and improve the temperature characteristics of the module. Schemes with double large surface or side cold plates can control the maximum temperature rise of the module within 11 K, while schemes with single large surface cold plates can control it within 15 K. The bottom cold plate scheme cannot meet the heat dissipation requirements for high rates. Schemes with side cold plates are better at controlling the temperature range than those with large surface cold plates, but the difference narrows to within 0.5 K after the flow rate reaches 3 L/min. Increasing the coolant flow rate in each cold plate arrangement scheme can improve the cooling effect, reducing the maximum temperature rise and temperature range of the module, but the reduction gradually decreases, and the effect is not significant after the flow rate exceeds 3 L/min. Adding a bottom cold plate in large surface or side cold plate schemes can reduce the maximum temperature rise. The reduction is more than 2 K for the single large surface scheme, while for the double large surface and side schemes, the reduction decreases with increasing flow rate, falling to within 1 K after 2 L/min. When adding a bottom cold plate, the side parallel scheme cannot reduce the temperature range, while for the large surface or side series schemes, the reduction in temperature range decreases with increasing flow rate, falling to within 1 K after 1.5 L/min.
This paper conducts simulation and experimental research on liquid cooling schemes for high-rate energy storage cells, but does not explore liquid cooling schemes for higher charge-discharge rates or deeply analyze the impact of specific cold plate structures on cooling performance. Future work will build on this paper to conduct in-depth research on these aspects, improve the multi-physics coupled model by considering the non-uniform heat generation of energy storage cells and dynamic power changes, and provide more accurate guidance for the development of thermal management systems for high-rate energy storage cells.