Effective thermal management is a critical pillar for the safety, longevity, and reliable performance of lithium ion batteries, especially in demanding applications like electric vehicles. Among various cooling strategies, liquid cooling stands out due to its superior heat transfer capacity and compactness. The design of the cooling plate’s internal flow channel is a primary lever for optimizing this system’s performance. While channel geometry, coolant parameters, and operating conditions have been extensively studied, the strategic management of fluid flow direction within these channels presents a significant yet less explored opportunity for enhancing thermal uniformity and peak temperature control. This study investigates the influence of alternating fluid flow directions in a novel sinusoidal-channel cold plate on the thermal behavior of a lithium ion battery module. We employ a coupled numerical model to analyze the effects under varying discharge rates, inlet temperatures, and inlet velocities, providing insights into a nuanced approach for advancing lithium ion battery thermal management systems.
The core of our analysis is a lithium ion battery module paired with a bespoke liquid-cooling plate. The module consists of prismatic lithium ion battery cells, each with dimensions of 180 mm × 100 mm × 14 mm. A cooling plate of matching footprint (180 mm × 100 mm) and a thickness of 6 mm is placed between cells. To enhance convective heat transfer area compared to a traditional straight channel, we designed a flow path based on a sine function. The geometry of the central channel is defined by the function \(y = A \sin(\omega x)\), where \(A\) is the amplitude and \(\omega\) is the frequency. After parametric investigation, a configuration with seven parallel channels, an amplitude \(A = 6\) mm, a frequency \(\omega = 4/26\), a channel width of 6 mm, and a depth of 3 mm was selected for its favorable balance between cooling performance and pressure drop. The thermophysical properties of the lithium ion battery, the aluminum cooling plate, and the water coolant are summarized in Table 1.
| Material | Density, \(\rho\) (kg/m³) | Specific Heat, \(C_p\) (J/(kg·K)) | Thermal Conductivity, \(k\) (W/(m·K)) | Dynamic Viscosity, \(\mu\) (Pa·s) |
|---|---|---|---|---|
| Lithium Ion Battery | 3000 | 1005.91 | \(k_x=k_y=0.302\), \(k_z=22.48\) | — |
| Cooling Plate (Aluminum) | 2719 | 871 | 202.4 | — |
| Coolant (Water) | 997.5 | 4179 | 0.613 | 0.0007 |
The mathematical model governing the system’s behavior integrates fluid dynamics and heat transfer. For the incompressible coolant flow (assumed laminar), the continuity and momentum (Navier-Stokes) equations are solved:
$$
\nabla \cdot \vec{v} = 0
$$
$$
\rho_w \left( \frac{\partial \vec{v}}{\partial t} + (\vec{v} \cdot \nabla) \vec{v} \right) = -\nabla P + \mu \nabla^2 \vec{v}
$$
where \(\vec{v}\) is the velocity vector, \(P\) is pressure, and \(\rho_w\) and \(\mu\) are the density and dynamic viscosity of water, respectively. The energy conservation equations for the coolant, the solid cooling plate, and the lithium ion battery are given by:
$$
\rho_w C_{p,w} \frac{\partial T_w}{\partial t} + \rho_w C_{p,w} \vec{v} \cdot \nabla T_w = \nabla \cdot (k_w \nabla T_w)
$$
$$
\rho_c C_{p,c} \frac{\partial T_c}{\partial t} = \nabla \cdot (k_c \nabla T_c)
$$
$$
\rho_b C_{p,b} \frac{\partial T_b}{\partial t} = \nabla \cdot (k_b \nabla T_b) + \dot{Q}_{gen}
$$
The subscript \(b\) denotes the lithium ion battery, and \(\dot{Q}_{gen}\) is the volumetric heat generation rate during discharge. This heat generation is a critical source term and is modeled as a 6th-order polynomial function of time, with coefficients that depend on the discharge rate (\(C\)-rate):
$$
\dot{Q}_{gen} = A_1 t^6 + A_2 t^5 + A_3 t^4 + A_4 t^3 + A_5 t^2 + A_6 t + A_7
$$
The coefficients \(A_1\) through \(A_7\) for different discharge rates are provided in Table 2.
| C-rate | \(A_1\) | \(A_2\) | \(A_3\) | \(A_4\) | \(A_5\) | \(A_6\) | \(A_7\) |
|---|---|---|---|---|---|---|---|
| 1C | 4.9132×10⁻¹⁶ | -3.7742×10⁻¹² | 1.0679×10⁻⁸ | -1.3417×10⁻⁵ | 7.6000×10⁻³ | -2.2208 | 1.7152×10⁴ |
| 2C | 1.2578×10⁻¹³ | -4.8310×10⁻¹⁰ | 6.8347×10⁻⁷ | -4.2934×10⁻⁴ | 1.2160×10⁻¹ | -17.763 | 6.6623×10⁴ |
| 3C | 3.2235×10⁻¹² | -8.2542×10⁻⁹ | 7.7851×10⁻⁶ | -3.2303×10⁻³ | 6.1570×10⁻³ | -59.961 | 1.4841×10⁵ |
The system’s performance is evaluated using four key metrics focusing on the most thermally stressed cell (B1):
- Maximum Temperature (\(T_{max}\)): The peak temperature within the lithium ion battery cell.
- Temperature Difference (\(\Delta T\)): The difference between the maximum and minimum temperature within a single lithium ion battery cell, indicating internal thermal uniformity: \(\Delta T = T_{max} – T_{min}\).
- Temperature Standard Deviation (\(S\)): A measure of temperature consistency across multiple lithium ion battery cells in the module. A lower \(S\) signifies better thermal uniformity across the pack. It is calculated from the \(\Delta T\) of each cell: \(S = \sqrt{ \frac{\sum_{i=1}^{n} (\Delta T_i – \overline{\Delta T})^2}{n} }\).
- Pressure Drop (\(\Delta P\)): The pumping power penalty across the cooling plate.
The central investigation revolves around manipulating the flow direction in the seven parallel sinusoidal channels. We define the “staggered flow count” as the number of adjacent channel pairs where the fluid flows in opposite directions. Four distinct flow schemes, alongside a baseline uniform flow direction case, are analyzed (see conceptual diagram below). Scheme 1 has alternating flow in every adjacent channel (staggered count = 6), representing the most aggressive mixing strategy. Scheme 4 has the least alternation (staggered count = 2). The core question is how this strategic staggering influences the thermal metrics of the lithium ion battery under different operational stresses.
Before examining flow direction, the superiority of the sinusoidal channel over a simple straight channel was confirmed. Under identical conditions, the sinusoidal channel reduced the maximum temperature of the lithium ion battery by 0.3°C and improved its internal temperature uniformity (\(\Delta T\)) by 0.2°C. This is attributed to the increased surface area for convection, described by \(Q = h A (T_w – T_f)\), where a larger area \(A\) enhances heat removal from the lithium ion battery. Parametric studies on the sine function’s amplitude and frequency further refined the design, favoring lower values for both to minimize peak temperature and pressure drop.
A rigorous mesh independence study was conducted to ensure the reliability of the numerical solutions. The maximum temperature and pressure drop were monitored across six levels of mesh refinement. The results, summarized in Table 3, show that beyond approximately 2 million elements, the variation in both key outputs is less than 1%. Therefore, all subsequent simulations were performed with a mesh containing around 2.01 million elements.
| Mesh Size | Maximum Temperature, \(T_{max}\) (°C) | Pressure Drop, \(\Delta P\) (Pa) |
|---|---|---|
| 116,773 | 29.15 | 128.5 |
| 228,536 | 28.95 | 130.1 |
| 609,200 | 28.70 | 132.8 |
| 965,733 | 28.58 | 134.0 |
| 2,014,391 | 28.52 | 134.7 |
| 2,368,228 | 28.51 | 134.9 |
The impact of flow direction was first analyzed under different discharge rates (1C, 2C, 3C), which directly scale the heat generation within the lithium ion battery. The results, consolidated in Table 4, reveal several important trends. First, all staggered flow schemes consistently outperform the uniform flow baseline in reducing the maximum temperature (\(T_{max}\)) and improving single-cell uniformity (\(\Delta T\)). Second, the benefit is magnified at higher discharge rates. For instance, with Scheme 1 at 3C, \(T_{max}\) drops by 2.3°C compared to uniform flow, whereas at 1C the drop is only 0.51°C. This demonstrates that managing flow direction becomes increasingly critical for the thermal management of high-power lithium ion batteries.
| Flow Scheme (Staggered Count) | 1C Discharge | 2C Discharge | 3C Discharge | |||
|---|---|---|---|---|---|---|
| \(T_{max}\) (°C) | \(\Delta T\) (°C) | \(T_{max}\) (°C) | \(\Delta T\) (°C) | \(T_{max}\) (°C) | \(\Delta T\) (°C) | |
| Uniform Flow (0) | 27.41 | 2.05 | 33.12 | 4.95 | 41.15 | 9.95 |
| Scheme 4 (2) | 27.10 | 1.79 | 32.02 | 4.20 | 39.42 | 7.07 |
| Scheme 3 (3) | 26.99 | 1.65 | 31.72 | 3.83 | 38.95 | 6.30 |
| Scheme 2 (4) | 26.94 | 1.56 | 31.57 | 3.60 | 38.71 | 5.50 |
| Scheme 1 (6) | 26.90 | 1.48 | 31.45 | 3.40 | 38.85 | 3.83 |
Third, there is a clear correlation: higher staggered flow counts lead to better thermal performance. Scheme 1 (count=6) consistently yields the lowest \(T_{max}\) and \(\Delta T\). The mechanism is that alternating flow directions promote more frequent thermal mixing between channels. A channel carrying cooler fluid from the inlet passes alongside a channel carrying warmer fluid from downstream, facilitating lateral heat exchange. This process helps equalize the coolant temperature across the plate’s width, leading to a more uniform cooling effect on the adjacent lithium ion battery surface. Fourth, while pack-level consistency (\(S\)) also generally improves with staggering, the gains diminish after a certain point. The pressure drop increase due to flow direction changes was found to be negligible (under 6 Pa), indicating no significant pumping power penalty for this thermal enhancement strategy.
We further investigated the interaction between flow direction strategy and coolant inlet temperature. Simulations were run at a 3C discharge rate with inlet temperatures ranging from 15°C to 35°C. The key finding is that the percentage reduction in \(T_{max}\) achieved by staggered flow is largely independent of inlet temperature. However, the absolute thermal performance is, of course, affected. Higher inlet temperatures lead to higher absolute battery temperatures and, more critically, to significantly worse temperature uniformity (\(\Delta T\)) and pack consistency (\(S\)). This is because a smaller temperature difference between the coolant and the lithium ion battery reduces the driving force for heat transfer. Staggered flow schemes, particularly Scheme 1, are most effective at mitigating this degradation in uniformity. For a system operating near typical ambient conditions (25°C inlet), implementing a high staggered-flow scheme like Scheme 1 offers the optimal balance of peak temperature reduction and exceptional thermal uniformity for the lithium ion battery pack.
The final parameter study varied the coolant inlet velocity from 0.05 m/s to 0.2 m/s at a 3C discharge. The results, synthesized in Table 5, show expected trends: higher flow rates lower \(T_{max}\) and improve \(\Delta T\) due to increased convective cooling. However, the law of diminishing returns is evident. Doubling the velocity from 0.1 m/s to 0.2 m/s yields a much smaller incremental cooling benefit than the step from 0.05 m/s to 0.1 m/s, while the pressure drop, which is proportional to velocity squared, increases dramatically. More importantly, the relative advantage of staggered flow over uniform flow in improving \(\Delta T\) decreases at higher velocities. At very high flow rates, the coolant residence time is so short that the lateral thermal mixing effect between channels has less time to act. Consequently, while staggered flow still helps, its impact is less pronounced. This analysis suggests that combining a moderate flow rate (e.g., 0.1 m/s) with a high staggered-flow scheme (e.g., Scheme 1) is a more energy-efficient strategy for managing the temperature of a lithium ion battery than simply ramping up the pump speed.
| Inlet Velocity (m/s) | Uniform Flow | Scheme 1 (Staggered Count=6) | ||
|---|---|---|---|---|
| \(T_{max}\) (°C) | \(\Delta P\) (Pa) | \(T_{max}\) (°C) | \(\Delta P\) (Pa) | |
| 0.05 | 45.72 | ~34 | 44.03 | ~35 |
| 0.10 | 41.15 | ~135 | 38.85 | ~141 |
| 0.15 | 39.07 | ~303 | 37.12 | ~316 |
| 0.20 | 37.86 | ~540 | 36.18 | ~562 |
In conclusion, this study demonstrates that the strategic management of fluid flow direction in a sinusoidal-channel cold plate is a powerful and efficient method for enhancing the thermal management of lithium ion batteries. Key findings are:
- Staggered flow directions consistently reduce the maximum temperature and improve the temperature uniformity of a lithium ion battery compared to uniform parallel flow.
- The thermal benefits increase with the number of adjacent channels with opposing flow (staggered count), with Scheme 1 (fully alternating flow) providing the best performance.
- The advantage of this strategy is most significant under high-stress conditions, such as high discharge rates (e.g., 3C), where it can reduce peak temperature by over 2°C and dramatically slash internal temperature gradients.
- The effectiveness of flow direction control is robust across different coolant inlet temperatures and is particularly valuable at moderate flow rates (e.g., 0.1 m/s), offering superior thermal performance without a substantial penalty in pumping power.
The integration of an optimized sinusoidal geometry with an intelligent flow direction strategy presents a compelling design paradigm for next-generation liquid cooling systems, directly addressing the critical thermal challenges faced by high-performance lithium ion battery packs.