Abstract In this study, we present a multi-objective optimization design for liquid cooling plates (LCPs) in electric vehicle (EV) battery packs to enhance thermal management efficiency and reduce energy consumption. Using thermo-fluid-solid coupling, we optimized flow channel distributions to maximize heat transfer and minimize pressure drop. Numerical simulations were conducted under three typical EV operating conditions, comparing the performance of conventional straight-channel LCPs with optimized topology designs. Results show that the optimized LCP reduces the maximum battery temperature by 14.6%, improves cooling rates by up to 58.3%, and decreases pressure drop by 5.36% under high-temperature fast-charging conditions, demonstrating significant improvements in thermal uniformity and energy efficiency.
Keywords: electric vehicle battery; thermal management; liquid cooling plate; topology optimization; thermo-fluid-solid coupling
1. Introduction
Electric vehicle batteries, particularly lithium-ion cells, are widely adopted for their high energy density and long lifespan. However, heat accumulation during operation poses critical challenges, including reduced capacity, shortened lifespan, and safety risks. Effective thermal management is therefore essential to maintain optimal operating temperatures (20–45°C) and ensure uniform temperature distribution across battery packs.
Liquid cooling has emerged as a leading thermal management solution due to its high efficiency. The performance of liquid cooling plates (LCPs), which facilitate heat transfer between the battery and coolant, is critical. Traditional LCP designs with straight channels often suffer from uneven flow distribution and high pressure drop, limiting their effectiveness. Topology optimization offers a data-driven approach to design efficient flow channels, automatically determining optimal layouts to balance heat transfer and fluid dynamics.
This study aims to optimize LCP flow channels using topology optimization, targeting both heat transfer enhancement and pressure drop reduction. We conducted numerical simulations under three typical EV 工况 (operating conditions) to validate the performance of the optimized design against conventional straight-channel LCPs.
2. Topology Optimization of Liquid Cooling Channels
2.1 Design Problem
We considered a battery pack composed of 18650 lithium-ion cells with intercalated LCPs. The LCP design domain (Figure 1) features an inlet at the top-left and an outlet at the bottom-right, with a rectangular design domain (100 mm × 70 mm). The coolant (50% ethylene glycol-water mixture) flows at a laminar velocity of 0.01 m/s, with an inlet temperature of 25°C and adiabatic side boundaries. The volume fraction constraint was set to 0.5, allowing 50% of the design domain to be occupied by solid material.
2.2 Governing Equations
Navier-Stokes Equations For incompressible laminar flow, the momentum equation is:\(\rho \frac{du}{dt} = -\nabla p + \mu \nabla^2 u + \rho f \quad (1)\) with continuity equation:\(\nabla \cdot u = 0 \quad (2)\) where \(\rho\) is density, u is velocity, p is pressure, \(\mu\) is dynamic viscosity, and f is body force.
Brinkman Penalty Model To simulate fluid flow through porous media, the volume force F is expressed as:\(F = -\alpha u \quad (4)\) where \(\alpha\) is the permeability, linked to the design variable \(\gamma\).
Energy Conservation For conjugate heat transfer:\(\begin{cases} \rho C_p (u \cdot \nabla) T = \nabla \cdot (k_f \nabla T) & \text{(fluid domains)} \\ 0 = \nabla \cdot (k_s \nabla T) & \text{(solid domains)} \end{cases} \quad (5)\) Unified during topology optimization:\(\gamma \rho C_{pf} (u \cdot \nabla) T = \left( (1-\gamma) k_s + \gamma k_f \right) \nabla^2 T + (1-\gamma) Q \quad (6)\) where Q is the heat source.
2.3 Optimization Mathematical Model
Objective Functions
- Maximize heat transfer:\(J_{th} = \int_{\Omega} (1-\gamma) h (T_Q – T) d\Omega \quad (7)\) where h is the heat transfer coefficient.
- Minimize pressure drop:\(J_f = \mu \int_{\Omega} \nabla u \cdot \nabla u d\Omega + \int_{\Omega} \alpha(\gamma) u \cdot u d\Omega \quad (8)\)
Normalization and Multi-Objective Formulation Normalized objectives:\(J’_{th} = \frac{J_{th} – J_{th,\text{min}}}{J_{th,\text{max}} – J_{th,\text{min}}}, \quad J’_f = \frac{J_f – J_f_{\text{min}}}{J_f_{\text{max}} – J_f_{\text{min}}} \quad (9, 10)\) Weighted objective function:\(J = -\omega_1 J’_{th} + \omega_2 J’_f \quad (11)\) with \(\omega_1 + \omega_2 = 1\). Here, \(\omega_1 = \omega_2 = 0.5\).
Constraints:\(\int_{\Omega} \gamma d\Omega \leq V_f \cdot V, \quad 0 \leq \gamma \leq 1\) where \(V_f\) is the volume fraction constraint.
2.4 Optimization Results
The optimized flow channel topology features a hierarchical structure with main branches and sub-branches, resembling leaf veins (Figure 2). This design enhances flow uniformity, reduces resistance, and maximizes heat exchange by distributing coolant evenly across the battery pack.
3. Numerical Simulation Setup
3.1 Geometric Model
The battery pack includes 20 × 18650 cells (diameter 18 mm, length 65 mm) with aluminum LCPs. The conventional LCP has straight channels with dimensions listed in Table 1. The optimized LCP is a 3D extrusion of the 2D topology result, ensuring full contact with each cell via curvature-matched surfaces.
Table 1: Geometric Parameters of Straight-Channel LCP
| Parameter | L1 (mm) | L2 (mm) | L3 (mm) | L4 (mm) | L5 (mm) | L6 (mm) | L7 (mm) |
|---|---|---|---|---|---|---|---|
| Value | 3 | 5 | 5 | 6 | 77 | 6.4 | 6 |
3.2 Material Properties
- Coolant: 50% ethylene glycol-water mix (density = 1073.35 kg/m³, specific heat = 3281 J/kg·K, thermal conductivity = 0.38 W/m·K, viscosity = 0.00394 Pa·s).
- Battery: 18650 lithium-ion cells (density = 2900 kg/m³, specific heat = 1100 J/kg·K, thermal conductivity: \(k_x = k_y = 1.8 \, \text{W/m·K}, k_z = 28 \, \text{W/m·K}\)).
- LCP: Aluminum (density = 2700 kg/m³, specific heat = 900 J/kg·K, thermal conductivity = 200 W/m·K).
3.3 Boundary Conditions
Battery Heat Generation The ohmic resistance \(R_0\) is modeled as a function of temperature (T), state of charge (SOC), and current (I):\(R_0 = -0.000041 \cdot \text{SOC}^3 + 0.009286 \cdot \text{SOC}^2 – 0.827470 \cdot \text{SOC} + 60.665193 \, (\text{m}\Omega) \quad (15)\) Heat generation rate q is calculated using the Bernardi model, neglecting reversible heat:\(q = \frac{1}{V_b} i^2 R_0 \quad (17)\) where \(V_b\) is the battery volume and i is the current.
Operating Conditions Three typical EV 工况 were simulated (Table 2), with an ambient temperature of 43°C, initial battery temperature of 38°C, and coolant inlet temperature of 25°C.
Table 2: EV Operating Conditions
| 工况 (Case) | Description | Duration (s) | Charge/Discharge Rate |
|---|---|---|---|
| 1 | 120 km/h cruise + fast charge (20–95% SOC), 2 cycles | 4050 | 2C discharge + 4C charge |
| 2 | High-temperature fast charge (30–80% SOC) | 450 | 4C charge |
| 3 | High-temperature fast charge (10–100% SOC) | 810 | 4C charge |
3.4 Simulation Setup
- Turbulence Model: \(k-\epsilon\) standard wall function (Reynolds number > 2200 indicating turbulent flow).
- Solver: Pressure-based coupled algorithm for momentum and energy equations.
- Time Step: 1 s, transient analysis.
4. Results and Discussion
4.1 Maximum Temperature
Table 3: Maximum Temperature Comparison
| 工况 (Case) | LCP Type | Maximum Temperature (°C) | Thermal Equilibrium Temperature (°C) |
|---|---|---|---|
| 1 | Straight-channel | 39.31 | N/A |
| Optimized | 38.35 | 33.27 | |
| 2 | Straight-channel | 38.41 | 33.27 |
| Optimized | 38.38 | 28.61 | |
| 3 | Straight-channel | 38.42 | 33.26 |
| Optimized | 38.35 | 28.40 |
Under high-temperature fast-charging (工况 2–3), the optimized LCP reduces the maximum temperature by 14.6% compared to the straight-channel design (Figure 3). Thermal equilibrium temperatures with the optimized LCP (28.40–28.61°C) fall within the optimal operating range, whereas the straight-channel LCP exceeds 33°C.
4.2 Cooling Rate
Table 4: Cooling Rate Comparison
| 工况 (Case) | LCP Type | Max Cooling Rate (°C/min) | Min Cooling Rate (°C/min) | Improvement (%) |
|---|---|---|---|---|
| 1 | Straight-channel | 8.61 | 1.21 | – |
| Optimized | 12.44 | 1.50 | 44.5 (max) | |
| 2 | Straight-channel | 9.80 | 1.17 | – |
| Optimized | 15.49 | 1.55 | 58.1 (max) | |
| 3 | Straight-channel | 7.84 | 1.19 | – |
| Optimized | 12.41 | 1.49 | 58.3 (max) |
The optimized LCP achieves up to 58.3% higher cooling rates under fast-charging conditions (Figure 4), demonstrating superior heat dissipation efficiency.
4.3 Temperature Uniformity
Temperature standard deviation (\(T_{\sigma}\)) was used to evaluate uniformity:\(T_{\sigma} = \sqrt{\frac{\int_{V_b} (T_b – T_{b,\text{avg}})^2 dV_b}{\int_{V_b} dV_b}} \quad (22)\) In 工况 3, the optimized LCP reduced \(T_{\sigma}\) by 50% compared to the straight-channel design (Figure 5), ensuring more uniform temperature distribution across cells.
4.4 Pressure Drop
Table 5: Inlet-Outlet Pressure Drop
| LCP Type | Pressure Drop (Pa) | Reduction (%) |
|---|---|---|
| Straight-channel | 964.42 | – |
| Optimized | 912.72 | 5.36 |
The optimized topology reduces pressure drop by 5.36%, lowering pump energy consumption and improving system efficiency.
5. Conclusion
This study demonstrates the effectiveness of topology optimization in enhancing the thermal performance of EV battery pack LCPs. Key findings include:
- The optimized LCP reduces maximum battery temperature by 14.6% and maintains thermal equilibrium within the optimal range (28–30°C).
- Cooling rates are improved by 44.5–58.3%, enhancing heat dissipation under high-demand conditions.
- Pressure drop is reduced by 5.36%, leading to lower energy consumption.
- Temperature uniformity is significantly improved, with standard deviation reduced by up to 50%.
These results highlight topology optimization as a powerful tool for designing efficient LCPs, addressing critical challenges in EV battery thermal management and supporting the development of safer, more reliable electric vehicles.