In recent years, global environmental pollution, energy crises, and climate change have intensified, drawing increasing attention to new energy technologies worldwide. With the proposal of carbon peak and carbon neutrality goals, there has been a significant push to adjust energy structures and promote technological innovations, aiming to reduce reliance on traditional fossil fuels and accelerate the adoption of renewable energy sources. Among these, energy storage technology has emerged as a critical component, with lithium-ion batteries being widely utilized in commercial and residential cell energy storage systems due to their advantages in power, capacity, and durability. However, lithium-ion battery cells generate substantial heat during charging and discharging processes, originating from reaction heat, side reaction heat, Joule heat, and polarization heat. This heat accumulation can severely impact battery lifespan and safety, especially in large-scale containerized cell energy storage systems where multiple battery cells are connected in series and parallel within each battery pack. If not dissipated promptly, it can lead to reduced efficiency, thermal runaway, or even fire and explosion hazards. Therefore, designing an effective thermal management system for cell energy storage systems is paramount to mitigate these risks.
Current cooling methods for cell energy storage systems primarily include air cooling, liquid cooling, and phase change material cooling. Liquid cooling, which uses a liquid coolant as a heat exchange medium, circulates the coolant through channels within cold plates, where convective heat transfer removes the heat generated during battery operation. This method is favored for its high cooling efficiency and relatively low cost, prompting extensive research into enhancing its performance. Studies have shown that optimizing the flow channel structure of liquid cooling systems is key to improving heat dissipation, with focuses on enhancing flow distribution uniformity and reducing flow resistance. For instance, biomimetic channel designs inspired by insect wing veins have demonstrated superior temperature uniformity and lower flow resistance compared to traditional parallel channels. Similarly, bidirectional parallel flow channels with optimized baffle lengths can improve flow distribution and cooling effectiveness. Moreover, in large cell energy storage systems comprising multiple battery packs, optimizing the overall layout, such as outlet positions and cold plate arrangements, can reduce temperature differences across the entire system. This paper proposes a novel stamped flow channel structure for liquid cooling in cell energy storage systems and employs computational fluid dynamics (CFD) simulations to analyze its thermal and flow characteristics, with the goal of optimizing design parameters for better performance.
The physical model of the cell energy storage system under investigation consists of a liquid cold plate assembly and a battery pack. The cold plate assembly includes a base plate, a flow channel plate, and inlet/outlet nozzles, while the battery pack comprises 52 lithium-ion phosphate (LFP) battery cells arranged in a specific configuration. The dimensions of the components are summarized in the table below, which provides a detailed overview of the system’s geometry. The battery cells are placed on top of the base plate, with a thermal interface material (thermal grease) having a thermal conductivity of 0.8 W/(m·K) applied to reduce thermal resistance. Between the battery cells, foam padding with a thermal conductivity of 0.022 W/(m·K) is inserted to minimize heat transfer and prevent local hot spots. The flow channel plate is manufactured using a stamping process to create recessed channels, and it is welded to the base plate via brazing to form the complete cold plate. The flow channel structure features a depth of 4.5 mm, with an inlet that splits into three parallel branches, two of which further subdivide, and an outlet that merges two main branches into a single exit. All branches follow a serpentine path to maximize surface area for heat exchange.
| Component | Dimensions (mm) |
|---|---|
| Base Plate | Length 1145 × Width 800 × Thickness 1.2 |
| Flow Channel Plate | Length 1145 × Width 800 × Thickness 1.0 |
| Battery Cell | Width 173.8 ± 0.8, Thickness 71.7 ± 0.8, Height 207.2 ± 0.8 |
| Nozzle Inner Diameter | 10 |
For the CFD simulations, the three-dimensional model is discretized using unstructured polyhedral grids to balance computational accuracy and cost. Local mesh refinement is applied in critical regions, such as near the flow channel walls, to capture detailed flow and heat transfer phenomena. Boundary layer grids are implemented at the channel walls to resolve near-wall flows, with the first layer thickness set to 0.2 mm to ensure a y+ value below 5, using 3 layers and a growth rate of 1.1. A mesh independence study is conducted to validate the grid resolution, comparing three different mesh sizes as shown in the table below. The results indicate that the differences in key parameters, such as outlet total pressure and average battery pack temperature, are less than 1% between the finest meshes, confirming that the selected mesh is adequate for reliable simulations.
| Mesh ID | Maximum Grid Size (mm) | Minimum Grid Size (mm) | Number of Elements | Outlet Total Pressure (Pa) | Average Battery Top Temperature (°C) |
|---|---|---|---|---|---|
| #1 | 17 | 1.5 | 2,817,518 | 705.07 | 34.17 |
| #2 | 16 | 1.2 | 4,055,112 | 701.46 | 34.51 |
| #3 | 15 | 1.0 | 5,547,631 | 700.81 | 34.77 |
The governing equations for the fluid flow and heat transfer are based on the Reynolds-averaged Navier-Stokes (RANS) equations, which include conservation of mass, momentum, and energy. These equations are solved using the finite volume method in the ANSYS Fluent solver. The mass conservation equation is given by:
$$\frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \mathbf{v}) = 0$$
The momentum conservation equation is expressed as:
$$\frac{\partial (\rho \mathbf{v})}{\partial t} + \nabla \cdot (\rho \mathbf{v} \mathbf{v}) = -\nabla p + \nabla \cdot \mathbf{\tau} + \rho \mathbf{g}$$
where $\rho$ is the fluid density, $\mathbf{v}$ is the velocity vector, $p$ is the pressure, $\mathbf{\tau}$ is the stress tensor, and $\mathbf{g}$ is the gravitational acceleration. The energy conservation equation is:
$$\frac{\partial (\rho e)}{\partial t} + \nabla \cdot (\rho e \mathbf{v}) = -\nabla \cdot \mathbf{q} + \nabla \cdot (\mathbf{\tau} \cdot \mathbf{v}) + \rho \mathbf{g} \cdot \mathbf{v}$$
Here, $e$ represents the total energy per unit mass, and $\mathbf{q}$ is the heat flux vector. To close the RANS equations, the SST k-ω turbulence model is employed, which combines the advantages of k-ε and k-ω models for accurate boundary layer predictions. The transport equations for turbulent kinetic energy $k$ and specific dissipation rate $\omega$ are:
$$\frac{\partial (\rho k)}{\partial t} + \nabla \cdot (\rho k \mathbf{v}) = \nabla \cdot [(\mu + \sigma_k \mu_t) \nabla k] + P_k – \beta^* \rho k \omega$$
$$\frac{\partial (\rho \omega)}{\partial t} + \nabla \cdot (\rho \omega \mathbf{v}) = \nabla \cdot [(\mu + \sigma_\omega \mu_t) \nabla \omega] + \alpha \frac{\omega}{k} P_k – \beta \rho \omega^2$$
where $\mu$ is the dynamic viscosity, $\mu_t$ is the turbulent viscosity, and $P_k$ is the production term for turbulent kinetic energy. The constants $\sigma_k$, $\sigma_\omega$, $\beta^*$, $\alpha$, and $\beta$ are model coefficients. The material properties used in the simulations are listed in the table below, which includes the coolant (a 50% ethylene glycol solution), aluminum for the plates, and LFP for the battery cells. These properties are critical for accurately modeling the thermal behavior of the cell energy storage system.
| Material | Density (kg/m³) | Specific Heat (J/(kg·K)) | Thermal Conductivity (W/(m·K)) | Viscosity (kg/(m·s)) |
|---|---|---|---|---|
| 50% Ethylene Glycol | 1074.194 | 3273 | 0.382 | 4.216e-03 |
| Aluminum (Base/Channel Plate) | 2719 | 871 | 202.4 | – |
| LFP Battery Cell | 2284 | 1060 | kx=9.04, ky=11, kz=3.56 | – |
Boundary conditions are set to simulate realistic operating scenarios. The coolant inlet is defined as a mass flow inlet with a flow rate of 5 L/min (varied in subsequent analyses) and an initial temperature of 18°C. The outlet is set as a pressure outlet with gauge pressure of 0 Pa. The battery cells are assigned a heat generation rate of 14 W per cell, corresponding to a 0.5 C discharge rate, with an initial temperature of 35°C. All external surfaces of the battery pack and cold plate assembly are considered adiabatic, neglecting natural convection and radiation with the environment for simplification. The pressure-velocity coupling is handled using the SIMPLEC algorithm, and second-order discretization schemes are applied for pressure, momentum, and energy equations to ensure accuracy. The Reynolds number for the flow is calculated as Re = 2703.4, indicating a transitional flow regime between laminar and turbulent, which justifies the use of the SST k-ω model.
To validate the CFD model, simulations are compared with experimental data from literature for battery cells at different discharge rates (1 C, 2 C, 3 C). The results show excellent agreement, with temperature trends matching closely and errors within acceptable limits, confirming the model’s reliability for thermal analysis of cell energy storage systems. This validation step is crucial for ensuring that the simulations accurately represent real-world behavior, particularly for optimizing thermal management in such systems.
The analysis begins with the baseline case at an inlet flow rate of 5 L/min. The pressure distribution within the flow channels reveals a total pressure drop of 9.828 kPa from inlet to outlet, indicating moderate flow resistance. The velocity streamlines show that the flow is evenly distributed across the branches without significant recirculation or vortices, suggesting efficient channel utilization. The temperature field of the coolant indicates a rise from 18°C at the inlet to 20.49°C at the outlet, with a temperature increase of 2.49°C due to heat absorption from the battery pack. The battery pack’s top surface temperature distribution is visualized, showing a maximum temperature of 35.17°C and a minimum of 33.77°C, resulting in a maximum temperature difference of 1.40°C. This uniformity is relatively good, but the higher temperatures are observed in the fourth row of batteries, which are located above the outlet branches where the coolant is warmest. In contrast, the first and third rows, positioned above inlet branches with cooler coolant, exhibit lower temperatures. This pattern highlights the impact of flow path on thermal performance in cell energy storage systems.
To investigate the influence of inlet flow rate on cooling performance, simulations are conducted at varying flow rates: 5, 8, 10, 12, and 15 L/min. The results are summarized in the table below, which presents key metrics such as average battery temperature, maximum temperature difference, flow resistance, and system thermal resistance. As the flow rate increases, the average battery temperature decreases, but the rate of improvement diminishes. For instance, when the flow rate rises from 5 to 8 L/min, the average temperature drops by 0.30°C per L/min, but from 12 to 15 L/min, the drop is only 0.08°C per L/min. Concurrently, the flow resistance increases significantly, from 9.828 kPa at 5 L/min to 59.441 kPa at 15 L/min, indicating a quadratic relationship with flow rate. The maximum temperature difference initially decreases from 1.40°C to 1.22°C at 8 L/min but then gradually increases to 1.39°C at 15 L/min, suggesting an optimal flow rate for temperature uniformity. The system thermal resistance, defined as the temperature rise per unit heat load, decreases slightly from 23.58°C/kW to 21.79°C/kW, but the gains are marginal compared to the substantial increase in pumping power required due to higher flow resistance. This underscores the need to balance cooling performance and energy consumption in cell energy storage systems.
| Inlet Flow Rate (L/min) | Average Battery Temperature (°C) | Maximum Temperature Difference (°C) | Flow Resistance (kPa) | System Thermal Resistance (°C/kW) |
|---|---|---|---|---|
| 5 | 34.17 | 1.40 | 9.828 | 23.58 |
| 8 | 33.21 | 1.22 | 21.456 | 22.94 |
| 10 | 32.85 | 1.25 | 31.789 | 22.63 |
| 12 | 32.61 | 1.32 | 44.112 | 22.37 |
| 15 | 32.37 | 1.39 | 59.441 | 21.79 |
The relationship between flow rate and performance can be further analyzed using dimensionless numbers. The Nusselt number (Nu), which characterizes convective heat transfer, is related to the Reynolds number (Re) and Prandtl number (Pr) by correlations such as $$Nu = C Re^m Pr^n$$, where C, m, and n are constants. For internal flows, increasing Re enhances Nu, but the effect saturates at higher flow rates due to boundary layer development. Similarly, the pressure drop Δp can be estimated using the Darcy-Weisbach equation: $$\Delta p = f \frac{L}{D_h} \frac{\rho v^2}{2}$$, where f is the friction factor, L is the channel length, D_h is the hydraulic diameter, and v is the flow velocity. As flow rate increases, v rises, leading to a quadratic increase in Δp, which aligns with the simulation results. This analysis emphasizes that simply increasing flow rate is not efficient for cell energy storage systems; instead, structural optimizations are needed.
To improve temperature uniformity, the flow channel structure is optimized by introducing convex hulls (bumps) in the outlet branches. These convex hulls act as turbulators, enhancing fluid disturbance and disrupting the thermal boundary layer, thereby intensifying convective heat transfer. The optimization involves merging the four outlet branches into two and adding varying numbers of equally spaced convex hulls, as shown in schematics. The impact is evaluated by analyzing the vortex structures using the swirling strength method, which quantifies rotational flow intensity. The swirling strength λ_ci is derived from the velocity gradient tensor ∇v, where the imaginary part of its eigenvalues indicates vortex core regions. The equation is: $$\nabla \mathbf{v} = \mathbf{S} + \mathbf{\Omega}$$, with $\mathbf{S}$ as the strain rate tensor and $\mathbf{\Omega}$ as the rotation rate tensor. Higher λ_ci values signify stronger vortices, which promote mixing and heat transfer.
Simulations are performed for the original channel and optimized versions with 3, 4, and 10 pairs of convex hulls, all at an inlet flow rate of 5 L/min. The results, summarized in the table below, show that as the number of convex hulls increases, the average swirling strength in the outlet branches rises, indicating enhanced flow disturbance. Concurrently, the maximum temperature difference of the battery pack decreases, improving temperature uniformity. For example, with 10 pairs of convex hulls, the maximum temperature difference drops to 1.15°C compared to 1.40°C for the original design. However, the improvement rate diminishes with more convex hulls, suggesting a point of diminishing returns. Additionally, the flow resistance increases slightly due to the added obstructions, but this is offset by the better thermal performance. The table also includes the average battery temperature and flow resistance for each configuration, highlighting the trade-offs in optimizing cell energy storage systems.
| Channel Design | Number of Convex Hull Pairs | Average Swirling Strength (λ_ci) in Outlet Branches | Maximum Temperature Difference (°C) | Average Battery Temperature (°C) | Flow Resistance (kPa) |
|---|---|---|---|---|---|
| Original | 0 | 0.005 | 1.40 | 34.17 | 9.828 |
| Optimized | 3 | 0.012 | 1.28 | 34.05 | 10.124 |
| Optimized | 4 | 0.015 | 1.22 | 33.98 | 10.356 |
| Optimized | 10 | 0.021 | 1.15 | 33.91 | 11.023 |
The enhancement in heat transfer due to convex hulls can be explained by the field synergy principle, which states that better alignment between velocity and temperature gradient vectors improves convective heat transfer. The field synergy number Fc is defined as: $$Fc = \int \mathbf{v} \cdot \nabla T \, dV$$, where $\mathbf{v}$ is the velocity vector and $\nabla T$ is the temperature gradient. By introducing convex hulls, the flow direction is altered, increasing the dot product $\mathbf{v} \cdot \nabla T$ and thus enhancing Fc. This principle is particularly relevant for cell energy storage systems, where efficient heat removal is critical. Additionally, the boundary layer theory indicates that turbulators reduce the thermal boundary layer thickness δ_t, given by $$\delta_t \sim \frac{x}{Re_x^{1/2} Pr^{1/3}}$$ for laminar flows, where x is the distance along the surface. In turbulent flows, the effect is more pronounced, leading to higher heat transfer coefficients. The use of convex hulls effectively transitions the flow to a more turbulent state, boosting performance.
Further analysis considers the overall energy efficiency of the cell energy storage system. The pumping power P_pump required to overcome flow resistance is calculated as: $$P_{pump} = \dot{m} \frac{\Delta p}{\rho}$$, where $\dot{m}$ is the mass flow rate. For the optimized design with 10 convex hulls at 5 L/min, P_pump increases slightly compared to the original, but the reduction in maximum temperature difference improves battery longevity and safety. In practical applications, a holistic approach is needed, considering manufacturing constraints—such as the stamping process for convex hulls—and system-level integration. For instance, in large-scale cell energy storage systems comprising multiple packs, optimizing the coolant distribution network can further reduce temperature variations. Parameters like channel width, branching angles, and manifold designs can be tuned using DOE methods or machine learning algorithms to achieve optimal performance.
In conclusion, this study demonstrates the effectiveness of CFD simulations in analyzing and optimizing liquid cooling for cell energy storage systems. The proposed stamped flow channel structure shows good temperature uniformity with a maximum difference of 1.40°C at 5 L/min, but increasing flow rate leads to diminishing cooling improvements and significantly higher flow resistance. Optimization via convex hulls enhances flow disturbance and heat transfer, reducing the maximum temperature difference to 1.15°C with 10 pairs of hulls. However, the benefits plateau with more hulls, indicating a need for balanced design. Future work could explore advanced materials, hybrid cooling methods, or dynamic control strategies to further enhance thermal management. By integrating these insights, designers can develop more efficient and reliable cell energy storage systems, contributing to the advancement of renewable energy technologies and global sustainability goals.