In the rapidly evolving landscape of electric car technology, efficient thermal management of power battery packs is critical for ensuring safety, longevity, and performance. As the demand for China EV solutions grows, addressing heat dissipation challenges becomes paramount. Lithium-ion batteries, widely used in electric car applications, generate significant heat during operation, which can lead to temperature imbalances, reduced efficiency, and potential hazards. Liquid cooling systems, particularly those incorporating optimized cooling plates, offer a promising approach to mitigate these issues. In this study, we focus on the topology optimization of liquid cooling plates for electric car battery packs, aiming to enhance heat transfer while minimizing energy consumption. By leveraging multi-objective optimization under thermo-fluid-structure coupling, we derive an innovative flow channel distribution. Through numerical simulations of typical electric car operating scenarios, including high-temperature fast-charging conditions, we compare the performance of traditional straight-channel cooling plates with our optimized designs. The results demonstrate substantial improvements in temperature control, cooling rates, and pressure drop reduction, underscoring the potential of topology optimization in advancing China EV thermal management systems.
The proliferation of electric car technologies, especially in the China EV market, has intensified the need for reliable battery thermal management. Lithium-ion batteries, favored for their high energy density and longevity, are susceptible to heat-related degradation. During charging and discharging cycles, internal resistance variations cause non-uniform heat generation, leading to localized hotspots. If unaddressed, this can accelerate aging, reduce capacity, and compromise safety. Liquid cooling systems, which indirectly transfer heat via cooling plates, provide an effective solution. However, the design of these plates significantly influences overall performance. Traditional approaches, such as straight-channel configurations, often fall short in achieving optimal heat distribution and low flow resistance. Thus, we explore topology optimization to automatically generate flow channel layouts that maximize heat exchange and minimize pressure drops, catering to the dynamic demands of electric car operations.
Topology optimization, a computational method that determines the optimal material distribution within a design domain, is well-suited for fluid flow and heat transfer applications. For electric car battery packs, we consider a cooling plate model where the flow channels are optimized to enhance thermal performance. The design domain, as illustrated in previous studies, includes inlet and outlet boundaries, with the central region serving as the optimization area. We assume laminar flow conditions and incorporate a heat source representing battery heat generation. The optimization objectives are twofold: maximize heat transfer and minimize the pressure drop between the inlet and outlet. This multi-objective approach ensures that the cooling system not only dissipates heat effectively but also operates with minimal energy expenditure, a crucial factor for China EV sustainability.
The governing equations for fluid flow and heat transfer form the basis of our optimization model. For incompressible, steady-state laminar flow, the Navier-Stokes equations are employed. The continuity equation and momentum conservation are expressed as:
$$ \nabla \cdot \mathbf{u} = 0 $$
$$ \rho (\mathbf{u} \cdot \nabla) \mathbf{u} = -\nabla p + \mu \nabla^2 \mathbf{u} + \mathbf{F} $$
Here, \( \mathbf{u} \) represents the velocity vector, \( p \) is the pressure, \( \rho \) is the fluid density, \( \mu \) is the dynamic viscosity, and \( \mathbf{F} \) denotes the volume force. To model flow resistance in porous media, we use the Brinkman penalty approach, where the volume force is proportional to the velocity:
$$ \mathbf{F} = -\alpha \mathbf{u} $$
Here, \( \alpha \) is the permeability, linked to the design variable \( \gamma \). For conjugate heat transfer, the energy conservation equation is unified as:
$$ \gamma \rho C_{p,f} (\mathbf{u} \cdot \nabla) T = [(1 – \gamma) k_s + \gamma k_f] \nabla^2 T + (1 – \gamma) Q $$
where \( C_{p,f} \) is the specific heat capacity, \( k_s \) and \( k_f \) are the thermal conductivities of the solid and fluid, respectively, and \( Q \) is the heat source term. This formulation allows us to simulate the thermal behavior of both the fluid and solid domains seamlessly.
The optimization problem is formulated to maximize heat transfer capacity while minimizing flow resistance. The heat transfer objective \( J_{th} \) is defined as:
$$ J_{th} = \int_{\Omega} (1 – \gamma) h (T_Q – T) \, d\Omega $$
where \( h \) is the heat transfer coefficient, \( T_Q \) is a reference temperature, and \( \Omega \) is the design domain. The flow resistance objective \( J_f \), representing the pressure drop, is given by:
$$ J_f = \mu \int_{\Omega} \nabla \mathbf{u} \cdot \nabla \mathbf{u} \, d\Omega + \int_{\Omega} \alpha(\gamma) \mathbf{u} \cdot \mathbf{u} \, d\Omega $$
To handle the multi-objective nature, we normalize these functions:
$$ J’_{th} = \frac{J_{th} – J_{th,\min}}{J_{th,\max} – J_{th,\min}} $$
$$ J’_{f} = \frac{J_{f} – J_{f,\min}}{J_{f,\max} – J_{f,\min}} $$
The combined objective function is then:
$$ J = -\omega_1 J’_{th} + \omega_2 J’_{f} $$
with \( \omega_1 + \omega_2 = 1 \). For this study, we set \( \omega_1 = 0.5 \) and \( \omega_2 = 0.5 \) to balance both objectives. The optimization problem is subject to a volume constraint:
$$ \int_{\Omega} \gamma \, d\Omega \leq V_f \cdot V $$
where \( V_f \) is the volume fraction, set to 0.5, and \( V \) is the total volume. Solving this yields an optimized flow channel topology that resembles natural branching patterns, such as leaf veins, enhancing fluid distribution and heat exchange.
To validate the optimized design, we conduct numerical simulations using a 3D model of a battery pack composed of 18650 lithium-ion cells, typical in electric car applications. The cooling plate, made of aluminum alloy, is integrated between cells, with a 50% ethylene glycol-water mixture as the coolant. Key geometric parameters are summarized in Table 1, and material properties are provided in Table 2. The China EV context emphasizes the need for robust thermal management under varied operating conditions.
| Parameter | Symbol | Value (mm) |
|---|---|---|
| Battery Radius | R1 | 3 |
| Cooling Plate Thickness | D1 | 14 |
| Channel Width | L2 | 5 |
| Design Domain Length | D3 | 100 |
| Design Domain Width | D4 | 70 |
| 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 | – |
Boundary conditions are defined based on typical electric car scenarios. The battery heat generation rate is modeled using the Bernardi equation, which accounts for ohmic losses:
$$ q = \frac{1}{V_b} \left[ i^2 R_0 + i T \frac{\partial U_0}{\partial T} \right] $$
where \( i \) is the current, \( R_0 \) is the ohmic resistance, \( V_b \) is the battery volume, and the reversible heat term is neglected for simplicity. The ohmic resistance varies with the state of charge (SOC), as fitted from experimental data:
$$ R_0 = -0.000041 \times \text{SOC}^3 + 0.009286 \times \text{SOC}^2 – 0.827470 \times \text{SOC} + 60.665193 $$
We consider three operational scenarios relevant to China EV usage: (1) 120 km/h cruising followed by fast charging (20% to 95% SOC), (2) high-temperature fast charging (30% to 80% SOC), and (3) high-temperature fast charging (10% to 100% SOC). The ambient temperature is set to 43°C, with an initial battery temperature of 38°C and coolant inlet temperature of 25°C. The coolant flow rate is 10 L/min, and transient simulations are performed with a time step of 1 second. Turbulent flow is modeled using the k-ε standard wall function, given the Reynolds number exceeds 2200.
Simulation results highlight the superiority of the topology-optimized cooling plate. Under high-temperature fast-charging conditions, the optimized design reduces the maximum battery temperature by 14.6% compared to the straight-channel plate. For instance, in Scenario 3, the maximum temperature drops from 33.26°C to 28.40°C, maintaining the battery within the optimal 20-30°C range. The cooling rate, defined as \( v_b = \frac{Q}{C} \), where \( Q \) is the散热 power and \( C \) is the battery heat capacity, shows significant improvement. The散热 power is calculated as \( Q = v_c \cdot c_{p,c} \cdot \Delta T \), with \( v_c = \rho_c \cdot q_c \) being the mass flow rate. As shown in Table 3, the maximum cooling rate increases by up to 58.3% in Scenario 3, enhancing heat dissipation efficiency.
| Scenario | Straight-Channel Max Rate (°C/min) | Optimized Max Rate (°C/min) | Improvement (%) |
|---|---|---|---|
| Scenario 1 | 8.61 | 12.44 | 44.5 |
| Scenario 2 | 9.80 | 15.49 | 58.1 |
| Scenario 3 | 7.84 | 12.41 | 58.3 |
Temperature uniformity is assessed using the standard deviation of battery temperatures:
$$ T_\sigma = \sqrt{ \frac{ \int_{V_\sigma} (T_b – T_{b,avg})^2 \, dV_b }{ \int_{V_\sigma} dV_b } } $$
where \( T_{b,avg} \) is the average battery temperature. For individual cells, such as #1 in Scenario 3, the standard deviation with the optimized plate remains below 1.5°C initially, stabilizing around 0.5°C, whereas the straight-channel plate reaches up to 3°C. This demonstrates better temperature homogeneity, crucial for prolonging battery life in electric car systems.
Pressure drop across the cooling plate is another critical metric, as it directly impacts energy consumption. The optimized design reduces the inlet-outlet pressure drop by 5.36%, from 964.42 Pa to 912.72 Pa. This reduction lowers pumping power requirements, contributing to overall energy efficiency in China EV applications. The results are summarized in Table 4.
| Design | Inlet-Outlet Pressure Drop (Pa) | Change (%) |
|---|---|---|
| Straight-Channel | 964.42 | – |
| Optimized | 912.72 | -5.36 |
In conclusion, topology optimization offers a transformative approach to designing liquid cooling plates for electric car battery packs. By maximizing heat transfer and minimizing flow resistance, we achieve significant improvements in thermal management, aligning with the demands of the growing China EV market. The optimized flow channels enhance cooling performance, ensure temperature uniformity, and reduce energy consumption, supporting the sustainable development of electric car technologies. Future work could explore dynamic operating conditions and integration with other thermal management strategies to further advance electric car efficiency.