Thermal management stands as a critical challenge for the widespread adoption and safe operation of high-power li ion battery packs, particularly in demanding applications like electric vehicles. The electrochemical processes within a li ion battery during charge and discharge cycles generate substantial heat. If this heat is not effectively removed, it can lead to elevated operating temperatures and significant temperature gradients across the battery module. Prolonged operation at high temperatures accelerates the degradation of battery components, leading to permanent capacity fade and reduced cycle life. More critically, excessive heat can trigger thermal runaway—a dangerous, self-perpetuating reaction that may result in fire or explosion. Furthermore, a large temperature differential (ΔT) between cells causes uneven aging and stress, further compromising the pack’s longevity and reliability. Therefore, an efficient Battery Thermal Management System (BTMS) is indispensable for maintaining the li ion battery within its optimal temperature window (typically 25–40°C) and ensuring a minimal temperature difference (preferably below 5°C).
Among various cooling techniques, indirect liquid cooling using cold plates offers a compelling balance of effectiveness, compactness, and reliability. The core of this approach lies in the design of the coolant flow channel embedded within the cold plate. While conventional designs like straight or serpentine channels are simple, they often struggle to achieve uniform cooling, leading to localized hot spots and high ΔT in large-format li ion battery packs. Inspired by nature’s efficient transport networks, bio-inspired channel designs, such as spider-web, leaf-vein, or capillary patterns, have shown promise in improving temperature uniformity by providing more distributed flow paths. However, even these advanced designs can sometimes fall short of the stringent ΔT requirement under high discharge rates. To address this limitation, this work introduces a novel approach: integrating spoilers (also called turbulators or vortex generators) into a bio-inspired spider-web channel cold plate. The primary objective is to enhance the convective heat transfer coefficient by perturbing the flow, disrupting the thermal boundary layer, and promoting fluid mixing, thereby simultaneously lowering the maximum temperature ($T_{max}$) and ΔT of the li ion battery module.
Design of the Spider-Web Channel with Spoilers
The thermal management system is designed for a module comprising multiple pouch-type li ion battery cells. Each cell has dimensions of 150 mm (length) × 240 mm (height) × 7.2 mm (thickness) and a nominal capacity of 24 Ah. A representative module configuration is analyzed, where cells are arranged with thermally conductive aluminum interlayer plates (2 mm thick) between them. Two identical aluminum cold plates are attached on the outer sides of the module.
The cold plate features a spider-web inspired channel geometry, chosen for its radial flow distribution characteristics which mimic efficient natural systems for nutrient transport. The key dimensions of the cold plate (204.4 mm × 240 mm × 6 mm) and its channel network are summarized in the table below. The channel consists of primary inlets/outlets, bifurcating into secondary and tertiary branches, creating a web-like structure that covers the plate area corresponding to the battery surface.
| Design Parameter | Symbol | Value (mm) |
|---|---|---|
| Cold Plate Length | L | 204.4 |
| Cold Plate Height | H | 240 |
| Cold Plate Thickness | D | 6 |
| Channel Wall Thickness | $d_1$ | 2 |
| Channel Depth | $d_2$ | 2 |
| Branch Channel Angle | $\alpha$ | 80° |
| Primary Inlet/Outlet Width | $w$ | 30 |
| Secondary Inlet/Outlet Width | $w_3$ | 20 |
| Tertiary/Branch Channel Width | $w_1$, $w_2$, $w_4$ | 10, 19, 10 |
The innovation lies in incorporating cylindrical spoilers within these channels. The spoilers are designed with three key geometric parameters: diameter ($\phi$), height ($h$), and longitudinal spacing ($d_3$). Two primary arrangements are investigated: a vertical alignment, where spoilers in opposite channel walls are directly facing each other, and a staggered alignment, where spoilers on opposite walls are offset. The coolant flow direction for the two side cold plates is configured in a counter-flow manner to promote a more uniform temperature field across the li ion battery module.
Numerical Modeling and Methodology
A three-dimensional coupled thermal-fluid model is established to simulate the heat dissipation performance. The model encompasses the li ion battery cells, the aluminum interlayer plates, the aluminum cold plates with the spider-web channels, and the coolant (water) domain.
Governing Equations for Heat Conduction
For the solid domains (battery, interlayer, cold plate), energy conservation is governed by the transient heat conduction equation. For the li ion battery, the equation accounts for internal heat generation ($q_i$):
$$ \rho_b C_{p,b} \frac{\partial T_b}{\partial t} = \lambda_{b,x} \frac{\partial^2 T_b}{\partial x^2} + \lambda_{b,y} \frac{\partial^2 T_b}{\partial y^2} + \lambda_{b,z} \frac{\partial^2 T_b}{\partial z^2} + q_i $$
where $\rho_b$, $C_{p,b}$, and $T_b$ are the density, specific heat capacity, and temperature of the li ion battery, respectively. $\lambda_{b,x}$, $\lambda_{b,y}$, $\lambda_{b,z}$ are the anisotropic thermal conductivities. The internal heat generation rate $q_i$ is a critical input, derived from the Bernardi model:
$$ q_i = \frac{I}{V} \left[ (U – U_0) + T_b \frac{dU_0}{dT_b} \right] = \frac{I}{V} \left[ I R_{internal} + T_b \frac{dU_0}{dT_b} \right] $$
Here, $I$ is the discharge current, $V$ is the cell volume, $U$ is the open-circuit voltage, $U_0$ is the terminal voltage, and $R_{internal}$ is the internal resistance. The term $T_b (dU_0/dT_b)$ represents the reversible entropic heat. For a 3C discharge rate (72A) from an initial State of Charge (SOC) of 100%, the internal resistance variation with SOC is fitted to a polynomial function based on experimental data at 25°C. The instantaneous heat generation $q_i(t)$ is then computed as a function of time. The heat conduction in the aluminum interlayer and cold plate is modeled without the heat generation term:
$$ \rho_{Al} C_{p,Al} \frac{\partial T_{Al}}{\partial t} = \lambda_{Al} \left( \frac{\partial^2 T_{Al}}{\partial x^2} + \frac{\partial^2 T_{Al}}{\partial y^2} + \frac{\partial^2 T_{Al}}{\partial z^2} \right) $$
Governing Equations for Fluid Flow and Heat Transfer
The coolant flow is assumed to be incompressible, Newtonian, and turbulent due to the spoiler-induced disturbances. The Reynolds-Averaged Navier-Stokes (RANS) equations with a suitable turbulence model (e.g., k-ε realizable) are solved. The governing equations for mass, momentum, and energy conservation are:
Continuity: $$ \nabla \cdot \vec{u} = 0 $$
Momentum: $$ \rho_f \left( \frac{\partial \vec{u}}{\partial t} + \vec{u} \cdot \nabla \vec{u} \right) = -\nabla p + \mu \nabla^2 \vec{u} + \rho_f \vec{g} $$
Energy: $$ \rho_f C_{p,f} \left( \frac{\partial T_f}{\partial t} + \vec{u} \cdot \nabla T_f \right) = \lambda_f \nabla^2 T_f $$
where $\rho_f$, $C_{p,f}$, $\lambda_f$, $\mu$, $T_f$, $\vec{u}$, and $p$ are the density, specific heat, thermal conductivity, dynamic viscosity, temperature, velocity vector, and pressure of the coolant, respectively.
Boundary Conditions, Material Properties, and Mesh
The initial temperature for the entire system (batteries, plates, coolant) is set to 25°C. The external surfaces of the module are subjected to natural convection with air (heat transfer coefficient of 2 W/m²·K). The interfaces between different solid components (battery-interlayer, interlayer-cold plate) are assumed to be perfect thermal contacts. At the solid-fluid interface (channel walls), a no-slip condition is applied, and the convective heat transfer is implicitly coupled. Coolant inlets are defined as mass-flow inlets at 25°C, and outlets are defined as pressure outlets. The material properties used in the simulation are listed below.
| Material | Density (kg/m³) | Specific Heat (J/kg·K) | Thermal Conductivity (W/m·K) | Viscosity (kg/m·s) |
|---|---|---|---|---|
| Li-ion Battery | 1929 | 1200 | $\lambda_x=\lambda_y=32$, $\lambda_z=1$ | – |
| Aluminum (Plate) | 2719 | 871 | 202.4 | – |
| Coolant (Water) | 998.2 | 4182 | 0.6 | 0.001003 |
A mesh independence study was conducted, refining the tetrahedral cells, particularly near the spoilers and channel walls, until the solution for $T_{max}$, ΔT, and pressure drop ($\Delta P$) became invariant. The final computational mesh consisted of approximately 2.5 million elements, ensuring both accuracy and computational efficiency.
Results and Discussion
Effect of Spoiler Arrangement
The first analysis compares the vertical and staggered spoiler alignments. With spoiler parameters fixed ($\phi=6$ mm, $h=2$ mm, $d_3=15$ mm) and a coolant mass flow rate of 0.04 kg/s, the staggered configuration demonstrates superior cooling performance for the li ion battery module.
| Performance Metric | Vertical Alignment | Staggered Alignment | Improvement |
|---|---|---|---|
| Maximum Temperature, $T_{max}$ (°C) | 32.23 | 31.25 | -0.98 °C |
| Temperature Difference, ΔT (°C) | 5.33 | 4.31 | -1.02 °C |
| Pressure Drop, $\Delta P$ (Pa) | 1459.63 | 1691.10 | +231.47 Pa |
The staggered arrangement reduces both $T_{max}$ and ΔT significantly, bringing ΔT below the 5°C threshold. The corresponding temperature contour on the li ion battery surface shows a more uniform distribution. This enhancement is attributed to the flow field. In the vertical alignment, the spoilers create a more channelized, high-velocity flow near the walls, leaving the core fluid relatively stagnant. In contrast, the staggered spoilers create a sinuous, mixing flow path, effectively disrupting the thermal boundary layer across the entire channel width and enhancing the overall convective heat transfer coefficient. The associated increase in pressure drop is moderate, indicating a favorable trade-off between cooling performance and pumping power for the staggered design.
Effect of Spoiler Diameter ($\phi$)
Using the superior staggered arrangement, the spoiler diameter was varied from 2 mm to 10 mm. The results reveal a non-monotonic relationship between spoiler size and cooling performance.
| Spoiler Diameter, $\phi$ (mm) | $T_{max}$ (°C) | ΔT (°C) | $\Delta P$ (Pa) |
|---|---|---|---|
| 2 | 32.02 | 5.01 | 1152.21 |
| 4 | 31.12 | 4.05 | 1420.55 |
| 6 | 30.64 | 3.62 | 1778.23 |
| 8 | 30.98 | 3.95 | 2880.15 |
| 10 | 31.41 | 4.21 | 4139.77 |
As the diameter increases from 2 mm to 6 mm, both $T_{max}$ and ΔT decrease, reaching an optimum at $\phi = 6$ mm. This is because larger spoilers create stronger vortices and more significant flow blockage, increasing turbulence and heat transfer. However, beyond this point ($\phi > 6$ mm), the spoilers occupy excessive volume, substantially reducing the effective flow area and contact surface area between the coolant and the channel wall. This leads to a higher flow velocity but reduced effective heat exchange, causing $T_{max}$ and ΔT to rise again. Concurrently, the pressure drop increases dramatically with diameter due to increased form drag. Therefore, an optimal spoiler diameter exists that maximizes heat transfer enhancement without causing excessive flow restriction for the li ion battery cooling application.
Effect of Spoiler Height ($h$)
The height of the spoiler, which determines its protrusion into the flow, was varied from 0.5 mm to 2 mm (channel depth is 2 mm).
| Spoiler Height, $h$ (mm) | $T_{max}$ (°C) | ΔT (°C) | $\Delta P$ (Pa) |
|---|---|---|---|
| 0.5 | 31.68 | 4.41 | 1278.65 |
| 1.0 | 31.05 | 3.92 | 1485.30 |
| 1.5 | 30.78 | 3.75 | 1635.12 |
| 2.0 | 30.64 | 3.62 | 1778.23 |
The results show a consistent improvement in cooling performance with increasing spoiler height. Taller spoilers interact more aggressively with the bulk flow, generating stronger secondary flows and vortices that enhance mixing and heat transfer from the channel walls to the coolant core. This leads to a continuous reduction in both $T_{max}$ and ΔT for the li ion battery. The pressure drop increases as well, but the rate of increase is less severe compared to increasing the diameter. The full-height spoiler ($h = 2$ mm) provides the best thermal performance, though the choice may be constrained by manufacturing and pressure drop considerations.
Effect of Spoiler Spacing ($d_3$)
The longitudinal spacing between consecutive spoilers along the channel length influences the flow development and periodicity of disturbance. The spacing was varied from a dense 10 mm to a sparse 35 mm.
| Spoiler Spacing, $d_3$ (mm) | $T_{max}$ (°C) | ΔT (°C) | $\Delta P$ (Pa) |
|---|---|---|---|
| 10 | 30.34 | 3.31 | 2256.24 |
| 15 | 30.64 | 3.62 | 1778.23 |
| 20 | 31.05 | 4.15 | 1550.98 |
| 25 | 31.52 | 4.78 | 1401.33 |
| 30 | 31.92 | 5.32 | 1305.40 |
| 35 | 32.13 | 5.71 | 1258.12 |
A clear trade-off is observed. Denser spoiler placement ($d_3 = 10$ mm) provides the most frequent flow agitation, resulting in the lowest $T_{max}$ and ΔT for the li ion battery. However, this comes at the cost of the highest pressure drop due to the cumulative flow resistance. As the spacing increases, the cooling performance gradually deteriorates because the flow has more distance to re-laminarize between disturbances, reducing the average heat transfer enhancement. Conversely, the pressure drop decreases significantly with increased spacing. The choice of optimal spacing thus depends on the system’s priority: maximizing cooling uniformity or minimizing pumping power. A spacing of 15-20 mm appears to be a balanced point, maintaining ΔT well below 5°C while offering a substantially lower $\Delta P$ than the densest configuration.
Effect of Coolant Flow Rate and Comparison with Smooth Channel
The performance of the optimized spoiler-equipped channel (staggered, $\phi=6$ mm, $h=2$ mm, $d_3=15$ mm) was evaluated across a range of coolant mass flow rates (0.02 to 0.10 kg/s) and compared against a traditional smooth spider-web channel (no spoilers).
| Flow Rate (kg/s) | $T_{max}$ (°C) | ΔT (°C) | $\Delta P$ (Pa) | |||
|---|---|---|---|---|---|---|
| With Spoiler | Smooth | With Spoiler | Smooth | With Spoiler | Smooth | |
| 0.02 | 32.01 | 33.44 | 5.10 | 7.09 | 512.3 | 210.5 |
| 0.04 | 30.64 | 31.94 | 3.62 | 5.75 | 1778.2 | 580.1 |
| 0.06 | 30.01 | 30.96 | 3.25 | 4.89 | 3685.1 | 1150.8 |
| 0.08 | 29.62 | 30.41 | 3.08 | 4.50 | 6250.7 | 1920.3 |
| 0.10 | 29.34 | 30.09 | 2.97 | 4.32 | 9455.9 | 2885.0 |
The key finding is that the spoiler-enhanced channel consistently outperforms the smooth channel at every flow rate. Crucially, the spoiler channel meets the dual criteria ($T_{max} < 40°C$, ΔT < 5°C) at a flow rate of just 0.04 kg/s, whereas the smooth channel requires a higher flow rate of approximately 0.06 kg/s to achieve a similar ΔT. This represents a potential 33% reduction in the required coolant flow rate for the same thermal performance, which can translate to lower pump power and system size. The enhanced mixing from the spoilers is responsible for this superior performance. The trade-off, as expected, is a higher system pressure drop for the spoiler channel due to the added flow resistance. However, at the target operating point of 0.04 kg/s, the absolute pressure drop (1778 Pa) remains within a manageable range for typical liquid cooling systems.
Conclusion
This investigation demonstrates that integrating spoilers into a bio-inspired spider-web channel cold plate is a highly effective strategy for enhancing the thermal management of li ion battery packs. The numerical analysis leads to the following key conclusions:
- Spoiler Arrangement is Critical: A staggered alignment of spoilers is markedly superior to a vertical alignment. It promotes better fluid mixing across the entire channel width, leading to a more uniform temperature distribution and lower maximum temperature and temperature difference in the li ion battery module.
- Optimal Spoiler Geometry Exists: The spoiler diameter has a non-linear effect. An optimal diameter (6 mm in this study) maximizes heat transfer enhancement by creating strong turbulence without excessively blocking the flow. Increasing spoiler height consistently improves cooling performance, with full-height spoilers providing the best results.
- Spoiler Spacing Presents a Trade-off: Denser spoiler placement yields the best thermal performance but at the cost of high pressure drop. A balanced spacing (e.g., 15 mm) can maintain excellent temperature uniformity (ΔT < 4°C) while significantly reducing pumping power requirements compared to the densest configuration.
- Significant Performance Gain Over Smooth Channels: The optimized spoiler-equipped channel allows the li ion battery pack to meet stringent thermal safety criteria ($T_{max} \approx 30.6°C$, ΔT \approx 3.6°C) at a lower coolant flow rate (0.04 kg/s) compared to an equivalent smooth channel. This enhances system-level efficiency.
The proposed design offers a practical pathway to achieve more uniform and effective cooling for high-power li ion battery systems. Future work could explore spoilers with different cross-sectional shapes (elliptical, winglet), advanced bio-inspired channel patterns, and multi-objective optimization to simultaneously minimize temperature, temperature difference, and pressure drop for specific li ion battery module geometries and operating conditions.