In recent years, the rapid growth of the electric vehicle industry, particularly in regions like China EV markets, has highlighted the critical need for efficient thermal management systems in power battery packs. As a researcher focused on advancing energy storage technologies, I have explored topology optimization methods to enhance liquid cooling plate designs for electric vehicle applications. This approach aims to maximize heat dissipation while minimizing energy consumption, addressing key challenges in battery thermal management. The integration of multi-objective optimization under thermo-fluid-solid coupling conditions allows for the development of innovative flow channel distributions that outperform traditional designs. In this article, I will detail the methodology, numerical simulations, and comparative analyses conducted under typical electric vehicle operating scenarios, emphasizing the significance of these advancements for the future of China EV and global electric vehicle ecosystems.
The widespread adoption of lithium-ion batteries in electric vehicles is driven by their high energy density, long cycle life, and environmental benefits. However, heat generation during operation poses significant risks, including reduced battery efficiency, lifespan, and safety. Effective thermal management is essential, and liquid cooling systems have emerged as a superior solution due to their high heat transfer efficiency. In this context, I have developed a topology optimization framework for liquid cooling plates that considers both heat exchange and pressure drop objectives. This method leverages Brinkman-based models to achieve optimal flow channel layouts, resulting in structures that mimic natural patterns like leaf veins, which enhance fluid distribution and thermal performance. The following sections will elaborate on the control equations, optimization formulation, and simulation results, supported by tables and mathematical expressions to summarize key findings.
Topology optimization for liquid cooling plates involves solving a multi-objective problem where the goal is to maximize heat transfer and minimize pressure drop. The design domain, as illustrated in previous studies, includes inlet and outlet boundaries with adiabatic conditions, and the fluid flow is assumed to be laminar. The governing equations for incompressible steady-state flow are based on the Navier-Stokes equations, combined with energy conservation principles. Specifically, the momentum and continuity equations are expressed as:
$$ \rho \frac{d\mathbf{u}}{dt} = -\nabla p + \mu \nabla^2 \mathbf{u} + \rho \mathbf{f} $$
and
$$ \nabla \cdot \mathbf{u} = 0 $$
where $\rho$ is density, $\mathbf{u}$ is velocity, $p$ is pressure, $\mu$ is dynamic viscosity, and $\mathbf{f}$ represents body forces. For topology optimization, the Brinkman penalty model is applied, introducing a volume force term $\mathbf{F} = -\alpha \mathbf{u}$, where $\alpha$ is the permeability related to the design variable $\gamma$. The energy equation for conjugate heat transfer is unified as:
$$ \gamma \rho C_{p,f} (\mathbf{u} \cdot \nabla) T = \left( (1 – \gamma) k_s + \gamma k_f \right) \nabla^2 T + (1 – \gamma) Q $$
Here, $C_p$ is specific heat, $k$ denotes thermal conductivity, and $Q$ is the heat source. The optimization objectives are normalized to form a combined function:
$$ J = -\omega_1 J’_{\text{th}} + \omega_2 J’_{f} $$
with $J’_{\text{th}} = \frac{J_{\text{th}} – J_{\text{th,min}}}{J_{\text{th,max}} – J_{\text{th,min}}}$ and $J’_{f} = \frac{J_{f} – J_{f,\text{min}}}{J_{f,\text{max}} – J_{f,\text{min}}}$, where $\omega_1$ and $\omega_2$ are weight factors summing to 1. The heat transfer objective $J_{\text{th}}$ is defined as the integral of heat dissipation, while $J_{f}$ represents the pressure drop related to fluid energy dissipation. The optimization problem is constrained by a volume fraction limit, ensuring practical design feasibility.
To validate the optimized design, I conducted numerical simulations using a three-dimensional model of a battery pack comprising 18650 lithium-ion cells, as commonly used in electric vehicles. The liquid cooling plates were integrated between cells, with materials including aluminum alloy for the plates and a 50% ethylene glycol-water mixture as the coolant. The geometric parameters and material properties are summarized in the following tables:
| Parameter | Value (mm) |
|---|---|
| R1 | 3 |
| R2 | 5 |
| D1 | 14 |
| D2 | 5 |
| D3 | 100 |
| D4 | 70 |
| D5 | 5 |
| Material | Density (kg/m³) | Specific Heat (J/(kg·K)) | Thermal Conductivity (W/(m·K)) | Viscosity (mPa·s) |
|---|---|---|---|---|
| Coolant | 1073.35 | 3281 | 0.38 | 0.00394 |
| 18650 Battery | 2900 | 1100 | k_x = k_y = 1.8, k_z = 28 | – |
| Aluminum Alloy | 2700 | 900 | 200 | – |
The boundary conditions for the simulations were set to reflect real-world electric vehicle operations, including three typical scenarios: 120 km/h cruising with fast charging (20% to 95% SOC), high-temperature fast charging (30% to 80% SOC), and high-temperature fast charging (10% to 100% SOC). The ambient temperature was maintained at 43°C, with an initial battery temperature of 38°C and coolant inlet temperature of 25°C. The coolant flow rate was fixed at 10 L/min, and transient analyses were performed with a time step of 1 second. Battery heat generation was modeled using the Bernardi equation, accounting for internal resistance variations with SOC:
$$ R_0 = -0.000041 \times \text{SOC}^3 + 0.009286 \times \text{SOC}^2 – 0.827470 \times \text{SOC} + 60.665193 $$
where $R_0$ is in mΩ. The heat generation rate $q$ per unit volume is given by:
$$ q = \frac{1}{V_b} \left( i^2 R_0 + i T \frac{\partial U_0}{\partial T} \right) $$
For simplicity, the reversible heat term was neglected, focusing on ohmic losses. The thermal performance was evaluated based on maximum temperature, cooling rate, temperature uniformity, and pressure drop, comparing traditional straight-channel designs with the topology-optimized flow channels.
Simulation results demonstrated that the optimized liquid cooling plate significantly improves thermal management for electric vehicle battery packs. Under high-temperature fast charging conditions, the optimized design reduced the maximum battery temperature by 14.6% compared to the straight-channel plate. For instance, in the third operational scenario (10% to 100% SOC), the maximum temperature stabilized at 28.40°C with the optimized plate, whereas the straight-channel plate reached 33.26°C. This enhancement ensures that batteries operate within the optimal 20–30°C range, crucial for longevity and efficiency in China EV applications. The cooling rate, defined as $v_b = \frac{Q}{C}$, where $Q$ is heat dissipation power and $C$ is battery heat capacity, was also higher with the optimized design. Calculations showed a maximum cooling rate increase of up to 58.3% in high-temperature scenarios, as summarized below:
| Operating Condition | Straight-Channel Max Rate (°C/min) | Optimized Max Rate (°C/min) | Improvement (%) |
|---|---|---|---|
| 120 km/h Cruise + Fast Charge | 8.61 | 12.44 | 44.5 |
| High-Temp Fast Charge (30–80% SOC) | 9.80 | 15.49 | 58.1 |
| High-Temp Fast Charge (10–100% SOC) | 7.84 | 12.41 | 58.3 |
Temperature uniformity, assessed using the standard deviation of battery temperatures, was consistently better with the optimized plate. For example, in the third scenario, the standard deviation for individual cells remained below 1.5°C initially and stabilized around 0.5°C, outperforming the straight-channel design. This uniformity is vital for preventing localized hot spots and extending battery life in electric vehicles. Additionally, the pressure drop across the cooling plate was reduced by 5.36% in the optimized design, decreasing from 964.42 Pa to 912.72 Pa. This reduction lowers pumping power requirements, contributing to overall energy efficiency in electric vehicle systems.
The topology optimization process yielded a flow channel distribution resembling biological structures, such as leaf veins, which facilitate efficient fluid pathways. This design maximizes surface area for heat exchange while minimizing flow resistance. The mathematical formulation of the optimization problem ensured a balance between heat transfer and pressure drop, with weight factors set to 0.5 for each objective. The resultant channel layout features multiple branches that distribute coolant evenly, enhancing thermal performance compared to conventional straight channels. This innovation is particularly relevant for the evolving demands of China EV markets, where high-performance and energy-efficient solutions are prioritized.
In conclusion, the application of topology optimization to liquid cooling plates for electric vehicle battery packs offers substantial benefits in thermal management and energy savings. The optimized design achieves lower maximum temperatures, higher cooling rates, improved temperature uniformity, and reduced pressure drops, addressing key challenges in battery operation. These advancements support the sustainable growth of the electric vehicle industry, especially in regions like China EV, by enhancing battery reliability and efficiency. Future work could explore adaptive optimization under dynamic operating conditions or integration with phase change materials for further improvements. This research underscores the potential of advanced engineering methods to drive innovation in electric vehicle technologies, contributing to a greener and more efficient transportation future.