Thermal management is a critical issue for the vehicle traction battery, since the performance, cycle life and safety of lithium-ion cells depend strongly on temperature. In this work, I focused on designing a side-mounted liquid-cooled plate with staggered rib and groove arrangements for a vehicle traction battery. The study integrated experimental characterization, CFD simulation, single-factor analysis, surrogate-assisted multi-objective optimization, and typical operation condition verification. The goal was to improve the thermal uniformity and reduce pumping loss of the cooling system without increasing the pressure drop.
Thermal characteristics of the lithium-ion cell
I used a prismatic ternary lithium-ion cell with a nominal capacity of 190 Ah. The geometry of the cell was 146 mm × 80 mm × 103 mm, and the nominal voltage was 3.8 V. The operating temperature range was limited to -20~50 °C for discharge and -30~50 °C for charge, while the optimum temperature range was 15~35 °C. The internal structure was simplified into a homogeneous solid block for the thermal model. The anisotropic thermal conductivities in the three directions were calculated from the layered structure using series and parallel resistance models. The equivalent properties are given in Table 1.
| Parameter | Value | Unit |
|---|---|---|
| Density | 2478.5 | kg·m-3 |
| Specific heat capacity | 1100 | J·(kg·K)-1 |
| Thermal conductivity (x,z) | 18.2 | W·(m·K)-1 |
| Thermal conductivity (y) | 2.0 | W·(m·K)-1 |
| Entropic heat coefficient | 0.0514 | V·K-1 |
To obtain the heat generation rate as a function of discharge time, I performed hybrid pulse power characterization (HPPC) tests. The test proceeded from 90% state-of-charge (SOC) down to 10% SOC in steps of 10% depth-of-discharge (DOD). In each step, a 30 s discharge pulse, a 25 min rest, and a 30 s charge pulse were applied. The direct current internal resistances were then calculated from the voltage responses. The discharge internal resistance $R_{id}$ and charge internal resistance $R_{ic}$ are expressed as
$$R_{id}=\frac{V_{t_0}-V_{t_1}}{I_{d}}, \qquad R_{ic}=\frac{V_{t_2}-V_{t_3}}{I_{c}}$$
where $V_{t_0}$, $V_{t_1}$, $V_{t_2}$, $V_{t_3}$ are terminal voltages at the corresponding instants, and $I_d$ and $I_c$ are discharge and charge pulse currents. The measured resistances at different SOC levels are summarized in Tables 2 and 3.
| SOC | 0.5C | 1C | 2C |
|---|---|---|---|
| 0.1 | 0.59 | 0.45 | 0.37 |
| 0.2 | 0.42 | 0.33 | 0.27 |
| 0.3 | 0.32 | 0.25 | 0.22 |
| 0.4 | 0.28 | 0.23 | 0.20 |
| 0.5 | 0.28 | 0.25 | 0.23 |
| 0.6 | 0.33 | 0.31 | 0.28 |
| 0.7 | 0.37 | 0.33 | 0.29 |
| 0.8 | 0.35 | 0.32 | 0.25 |
| 0.9 | 0.34 | 0.28 | 0.24 |
| SOC | 0.5C | 1C | 2C |
|---|---|---|---|
| 0.1 | 0.39 | 0.30 | 0.23 |
| 0.2 | 0.29 | 0.23 | 0.18 |
| 0.3 | 0.24 | 0.20 | 0.17 |
| 0.4 | 0.24 | 0.21 | 0.18 |
| 0.5 | 0.26 | 0.24 | 0.20 |
| 0.6 | 0.30 | 0.27 | 0.24 |
| 0.7 | 0.32 | 0.28 | 0.25 |
| 0.8 | 0.31 | 0.28 | 0.26 |
| 0.9 | 0.32 | 0.29 | 0.26 |
By applying the Bernardi heat generation model, the volumetric heat generation rate $\dot{q}$ can be written as
$$\dot{q} = \frac{I^2(R_{e}+R_{p})}{V_b} – \frac{I T}{V_b}\frac{\partial E_{oc}}{\partial T}$$
where $V_b$ is the cell volume, $I$ is the current, $R_e$ and $R_p$ are ohmic and polarization resistances, and $\partial E_{oc}/\partial T$ is the entropy coefficient. Using the measured resistances and the relation between SOC and discharge time, I fitted the heat generation rate to sixth-order polynomial functions of time for three C-rates:
$$\dot{q}(t)=A_1 t^6 + A_2 t^5 + A_3 t^4 + A_4 t^3 + A_5 t^2 + A_6 t + A_7$$
The fitted coefficients are listed in Table 4.
| C-rate | A1 | A2 | A3 | A4 | A5 | A6 | A7 |
|---|---|---|---|---|---|---|---|
| 0.5C | -4.76e-18 | 9.97e-14 | -7.86e-10 | 2.90e-6 | -4.87e-3 | 2.41 | 4001 |
| 1C | -3.50e-16 | 3.94e-12 | -1.62e-8 | 3.03e-5 | -2.37e-2 | 2.48 | 12004 |
| 2C | -2.02e-13 | 9.99e-10 | -1.77e-6 | 1.34e-3 | 0.382 | 9.23 | 40084 |
To validate the thermal model, I performed constant-current discharge experiments at 0.5C, 1C and 2C in a 25 °C chamber. The cell surface temperature was recorded by thermocouples attached on the large faces. The same conditions were reproduced in CFD simulations. The comparison between measured and simulated average surface temperatures showed that the maximum relative error was less than 8%. At 2C discharge, the cell surface temperature reached around 54 °C without cooling, far above the optimum upper limit of 35 °C. Therefore, an effective liquid cooling system for the vehicle traction battery is indispensable.
Cooling plate layout and inlet/outlet arrangement
After validating the single-cell thermal model, I established a battery pack model consisting of two parallel strings and 88 series-connected cells. The pack was housed in two layers, but only one layer with eight modules was selected for analysis to save computational resources. The baseline cooling plate was an “accordion” parallel channel plate made of 6061 aluminum. The coolant was a 50% ethylene glycol-water solution at 25 °C. A thermal pad with 2 mm thickness was placed between the battery and the plate. The material properties are given in Table 5.
| Material | Density (kg·m-3) | Specific heat (J·(kg·K)-1) | Thermal conductivity (W·(m·K)-1) | Dynamic viscosity (Pa·s) |
|---|---|---|---|---|
| Aluminum 6061 | 2719 | 871 | 180 | – |
| 50% glycol-water solution | 1071.1 | 3300 | 0.384 | 0.017 |
| Thermal pad | 2150 | 1200 | 2 | – |
I considered two plate positions: bottom placement and side placement between adjacent modules. Both schemes used the same accordion channel geometry and the same total flow rate of 21.78 L/min. The cell heat generation rate was based on the 2C fitted function. The inlet water temperature was 25 °C, the outlet was open to a standard atmosphere, and the external convective coefficient was 5 W·m-2·K-1. Grid independence was checked using coarse, medium and fine meshes. The medium mesh had about 3.23 million cells for the side-placed configuration, and the difference in maximum temperature between medium and fine meshes was below 0.1%, while the pressure drop difference was 0.21%. The medium mesh was therefore chosen for all further studies.
The governing equations for incompressible turbulent flow and conjugate heat transfer are the continuity equation, momentum equation and energy equation:
$$\nabla \cdot \vec{U}=0$$
$$\rho_f \left( \vec{U}\cdot \nabla \vec{U} \right) = -\nabla P + \nabla \cdot \left( \mu_f \nabla \vec{U} \right)$$
$$\rho_f c_{p,f} \left( \vec{U}\cdot \nabla T_f \right) = \nabla \cdot \left( \lambda_f \nabla T_f \right)$$
$$\nabla^2 T_s = 0$$
where $\rho_f$, $\vec{U}$, $P$, $\mu_f$, $c_{p,f}$, $T_f$, $T_s$ and $\lambda_f$ are the fluid density, velocity vector, pressure, dynamic viscosity, specific heat, fluid temperature, solid temperature and fluid thermal conductivity, respectively. The standard $k-\varepsilon$ turbulence model and the SIMPLEC algorithm were adopted.
Simulation results for the two plate positions are summarized in Table 6. The side-mounted plate clearly outperformed the bottom-mounted one, with the maximum pack temperature decreasing by 4.07 °C and the maximum pack temperature difference decreasing by 2.81 °C. The side placement exploits the high in-plane thermal conductivity of the cell and provides much larger heat transfer area. Thus, the side-mounted configuration was selected for the vehicle traction battery cooling system.
| Plate location | Pack max temp. (℃) | Max cell temp. difference (℃) | Pack max temp. difference (℃) |
|---|---|---|---|
| Bottom accordion plate | 39.67 | 12.15 | 13.27 |
| Side accordion plate | 35.60 | 6.90 | 10.46 |
I further examined two inlet/outlet configurations on the side-mounted plate: one with both inlet and outlet on the same side, and the other with them located diagonally (cross arrangement). The diagonal configuration reduced the pack maximum temperature from 35.6 °C to 34.5 °C and produced a more uniform temperature distribution. The pack temperature difference decreased from 10.46 °C to 8.5 °C. Therefore, the diagonal inlet/outlet arrangement was chosen as the base for structure improvement.
Design of rib-groove structures in the side cold plate
To further improve the heat dissipation performance of the side-mounted plate, I designed convex ribs and concave grooves inside the flow channels. These structures enhance heat transfer by periodically interrupting the thermal boundary layer and increasing turbulence. I compared four cross-sectional shapes: circular, diamond, forward water-drop and reverse water-drop. Each shape was investigated as a convex rib (protruding into the channel) and as a concave groove (recessed into the channel wall). All structures had the same nominal height/depth of 2 mm, spacing of 25 mm, diameter of 10 mm, and the same volumetric flow rate of 2.42 L/min. The original accordion plate was used as the baseline.
To evaluate the thermal and hydraulic performance, I used dimensionless parameters. The hydraulic diameter of a single channel is given by
$$D_h = \frac{2 H_{ch} W_{ch}}{H_{ch}+W_{ch}}$$
where $H_{ch}$ and $W_{ch}$ are channel height and width. The apparent friction factor is
$$f = \frac{2 \Delta p D_h}{\rho L_{ch} u_{av}^2}$$
where $\Delta p$ is the pressure drop, $L_{ch}$ the channel length, and $u_{av}$ the average velocity. The average heat transfer coefficient is
$$h_{av} = \frac{q_{eff} A_c}{A_{con}\left( T_{w,av} – T_{f,av}\right)}$$
and the Nusselt number is
$$Nu = \frac{h_{av} D_h}{\lambda_f}$$
Finally, the comprehensive performance evaluation criterion PEC was defined by comparing the Nusselt number and friction factor with the baseline values $Nu_0$ and $f_0$:
$$PEC = \frac{Nu/Nu_0}{\left( f/f_0 \right)^{1/3}}$$
If $PEC$ is greater than 1, the structure is superior to the baseline in terms of the trade-off between heat transfer enhancement and additional friction loss. The computed maximum temperature, standard deviation, pressure drop and dimensionless values for different shapes are listed in Table 7.
| Shape | Tmax (℃) | Tsd (℃) | Δp (Pa) | Nu/Nu0 | f/f0 | PEC |
|---|---|---|---|---|---|---|
| original accordion | 32.17 | 1.23 | 295.4 | 1.00 | 1.00 | 1.00 |
| circular rib | 31.64 | 1.32 | 394.7 | 1.59 | 1.22 | 1.49 |
| diamond rib | 31.92 | 1.30 | 343.2 | 1.38 | 1.13 | 1.27 |
| forward drop rib | 31.78 | 1.31 | 375.6 | 1.48 | 1.18 | 1.36 |
| reverse drop rib | 31.82 | 1.30 | 368.9 | 1.45 | 1.16 | 1.34 |
| circular groove | 31.88 | 1.27 | 258.8 | 1.44 | 0.78 | 1.56 |
| diamond groove | 32.05 | 1.26 | 232.5 | 1.28 | 0.72 | 1.43 |
| forward drop groove | 31.95 | 1.26 | 249.3 | 1.37 | 0.74 | 1.51 |
| reverse drop groove | 31.98 | 1.26 | 245.8 | 1.35 | 0.73 | 1.50 |
From these results, circular rib and groove structures exhibited the highest heat transfer enhancement. The circular rib produced the lowest maximum temperature but also a very high friction factor. In contrast, the circular groove delivered the highest PEC of 1.56 due to its low friction loss. Since ribs are effective in disturbing the flow but expensive in pressure drop, while grooves have low pressure loss but suffer from stagnant fluid at the bottom, I decided to combine both circular ribs and circular grooves in a staggered arrangement. This idea aims to exploit the vortex generated by the rib to sweep the groove, thereby reducing the thermal resistance without excessive friction loss.
Influence of volumetric flow rate
For the circular rib and circular groove configurations, I varied the volumetric flow rate from 1.21 to 3.62 L/min while keeping the geometry fixed (spacing 25 mm, diameter 10 mm, height/depth 2 mm). The results show that increasing flow rate strongly decreases the maximum temperature and improves uniformity, but the pressure drop increases quickly. Table 8 gives the trends at two representative flow rates.
| Flow (L/min) | Design | Tmax (℃) | Tsd (℃) | Δp (Pa) | PEC |
|---|---|---|---|---|---|
| 1.21 | rib | 35.15 | 1.51 | 98.2 | 1.72 |
| 1.21 | groove | 35.32 | 1.43 | 68.4 | 1.98 |
| 3.62 | rib | 30.20 | 1.18 | 877.5 | 1.38 |
| 3.62 | groove | 30.35 | 1.13 | 584.2 | 1.47 |
After 2.42 L/min, further increasing the flow rate gives diminishing returns in temperature reduction but much higher pumping cost. Hence, I selected 2.42 L/min as the design flow rate for the following parameter studies.
Influence of rib/groove spacing
I then changed the spacing between adjacent rib/groove columns from 35 to 25 mm, with a fixed diameter of 10 mm and depth/height of 2 mm. With smaller spacing, more structures are present and the interrupted boundary layers shed more frequently, leading to a lower maximum temperature. The groove structure showed a slight decrease in pressure drop with decreasing spacing, because larger void volume provides additional flow area. The results are listed in Table 9.
| Spacing | Design | Tmax (℃) | Tsd (℃) | Δp (Pa) | PEC |
|---|---|---|---|---|---|
| 35 | rib | 31.76 | 1.28 | 324.8 | 1.42 |
| 35 | groove | 32.02 | 1.25 | 232.1 | 1.54 |
| 30 | rib | 31.70 | 1.30 | 358.7 | 1.45 |
| 30 | groove | 31.95 | 1.26 | 226.4 | 1.57 |
| 25 | rib | 31.64 | 1.32 | 394.7 | 1.49 |
| 25 | groove | 31.88 | 1.27 | 258.8 | 1.56 |
Although the maximum temperature decreased with smaller spacing, the standard deviation increased for both ribs and grooves. The spacing of 25 mm was selected as the optimal balance between heat transfer and uniformity.
Influence of diameter
With the spacing fixed at 25 mm, I varied the diameter of circular ribs/grooves from 6 to 10 mm. A larger diameter increases the frontal blockage for ribs, accelerating the flow around them and intensifying turbulence. For grooves, a larger diameter increases the cavity volume, which slightly reduces the flow velocity and alters the recirculation pattern. The simulation results for different diameters are summarized in Table 10.
| Diameter | Design | Tmax (℃) | Tsd (℃) | Δp (Pa) | PEC |
|---|---|---|---|---|---|
| 6 | rib | 31.81 | 1.29 | 198.2 | 1.36 |
| 6 | groove | 31.98 | 1.25 | 178.6 | 1.44 |
| 8 | rib | 31.72 | 1.30 | 264.3 | 1.43 |
| 8 | groove | 31.92 | 1.26 | 207.4 | 1.51 |
| 10 | rib | 31.64 | 1.32 | 394.7 | 1.49 |
| 10 | groove | 31.88 | 1.27 | 258.8 | 1.56 |
With increasing diameter, the maximum temperature continues to drop for both rib and groove, and the PEC values improve. In contrast, the surface temperature standard deviation increases, indicating that large structures deteriorate temperature uniformity. The pressure drop of the rib increases rapidly with diameter, while the groove pressure drop changes only slightly. Considering the overall performance, I kept the diameter of 10 mm in the final layout.
Combined rib-groove staggered liquid cooling plate
Based on the single-factor analyses, I constructed a staggered arrangement where columns of circular ribs and circular grooves alternate along the flow direction. Instead of using a uniform height/depth value, I allowed the rib height and groove depth to vary linearly from the inlet to the outlet. The first column of ribs was located near the inlet and had height $h_1$; the last column had height $h_{19}$. Similarly, the first groove column had depth $d_1$ and the last had depth $d_{18}$. The intermediate heights/depths were linearly interpolated according to
$$\delta = \frac{h_{19}-h_1}{18}, \qquad h_i = h_1 + (i-1)\delta \quad (i=1,\ldots,19)$$
$$\varepsilon = \frac{d_{18}-d_1}{17}, \qquad d_j = d_1 + (j-1)\varepsilon \quad (j=1,\ldots,18)$$
The design variables were $h_1$, $h_{19}$, $d_1$ and $d_{18}$. The ranges were $0\le h \le 2$ mm and $-2 \le d \le 0$ mm, with a 0.1 mm resolution. The objectives were the minimum cold plate maximum surface temperature $T_{max}$, minimum temperature standard deviation $T_{sd}$ over the plate, and minimum pressure drop $\Delta p$. The mathematical formulation is
$$\begin{aligned}
\min \; & T_{max}(\mathbf{x}) \\
\min \; & T_{sd}(\mathbf{x}) \\
\min \; & \Delta p(\mathbf{x}) \\
s.t. \; & 0 \le h_1, h_{19} \le 2 \; \text{mm}, \quad -2 \le d_1, d_{18} \le 0 \; \text{mm}
\end{aligned}$$
where $\mathbf{x} = (h_1,h_{19},d_1,d_{18})$. I generated 84 sample points using the optimal Latin hypercube design. Each sample point was used to build a three-dimensional model and then solved by CFD to obtain the responses. Part of the sample set is shown in Table 11.
| No. | h1 (mm) | h19 (mm) | d1 (mm) | d18 (mm) | Tmax (℃) | Tsd (℃) | Δp (Pa) |
|---|---|---|---|---|---|---|---|
| 1 | 1.3 | 2.0 | -0.8 | -0.4 | 31.769 | 1.308 | 302.44 |
| 2 | 1.1 | 0.4 | 0.0 | -1.4 | 31.913 | 1.290 | 264.19 |
| 3 | 0.7 | 0.1 | -1.6 | -0.5 | 31.935 | 1.308 | 257.32 |
| 4 | 0.3 | 0.9 | -1.7 | -1.8 | 31.857 | 1.278 | 262.29 |
| 5 | 1.6 | 0.7 | -1.4 | -0.1 | 31.912 | 1.326 | 276.76 |
| 6 | 0.8 | 0.3 | -0.4 | -0.2 | 31.915 | 1.298 | 259.51 |
| 7 | 2.0 | 1.4 | -1.3 | -1.0 | 31.847 | 1.325 | 305.81 |
| 8 | 1.9 | 0.2 | -0.7 | -0.9 | 31.974 | 1.337 | 277.51 |
| 9 | 1.2 | 1.8 | -1.5 | -1.7 | 31.798 | 1.305 | 294.68 |
| 10 | 0.4 | 1.3 | -1.0 | 0.0 | 31.866 | 1.290 | 267.33 |
| 11 | 0.1 | 0.5 | -0.6 | -1.1 | 31.886 | 1.276 | 255.36 |
| 12 | 0.2 | 1.9 | -1.1 | -1.2 | 31.726 | 1.267 | 277.68 |
| 13 | 1.5 | 1.7 | -0.3 | -1.5 | 31.803 | 1.312 | 298.27 |
| 14 | 0.9 | 0.0 | -1.2 | -1.6 | 32.010 | 1.304 | 259.58 |
| 15 | 0.5 | 1.2 | -0.5 | -2.0 | 31.814 | 1.272 | 267.78 |
| 16 | 1.7 | 0.8 | -0.9 | -1.9 | 31.915 | 1.320 | 282.13 |
| 17 | 0.6 | 1.5 | -0.1 | -0.8 | 31.810 | 1.280 | 277.11 |
| 18 | 1.8 | 1.1 | -0.2 | -0.3 | 31.880 | 1.310 | 289.22 |
| 19 | 0.0 | 1.0 | -1.8 | -0.7 | 31.827 | 1.273 | 259.48 |
| 20 | 1.4 | 0.6 | -2.0 | -1.3 | 31.916 | 1.322 | 272.97 |
I chose a radial basis function (RBF) surrogate model to approximate the mapping between design variables and each response. The RBF model is suitable for nonlinear multivariable problems and provides smooth predictions with low computational cost. After construction, I validated the accuracy using the coefficient of determination $R^2$. The obtained $R^2$ values were 0.9009 for $T_{max}$, 0.9291 for $T_{sd}$, and 0.9624 for $\Delta p$. All values were above 0.9, confirming that the surrogate was accurate enough for subsequent optimization.
Multi-objective optimization using NSGA-II
The surrogate model was then combined with the non-dominated sorting genetic algorithm NSGA-II to search for the Pareto-optimal set. The algorithm parameters were population size 20, number of generations 100, crossover probability 0.8, and mutation probability 0.1. During optimization, a pressure constraint was introduced to ensure that the final design did not increase the pump power compared with a nominal acceptable value. The optimization formulation can be expressed as
$$\begin{aligned}
\mathrm{find} \; & \mathbf{x} = (x_1,x_2,x_3,x_4) = (h_1,h_{19},d_1,d_{18}) \\
\min \; & T_{max} = f_1(\mathbf{x}) \\
\min \; & T_{sd} = f_2(\mathbf{x}) \\
\min \; & \Delta p = f_3(\mathbf{x}) \\
s.t. \; & \Delta p \le 300.4 \; \mathrm{Pa}
\end{aligned}$$
The Pareto front generated by NSGA-II contained several feasible designs. Among the designs with the same pressure drop as the original plate, I selected the solution with the lowest maximum temperature and standard deviation. After rounding to the nearest 0.1 mm, the optimal variables were $h_1=0$ mm, $h_{19}=2$ mm, $d_1=-0.8$ mm and $d_{18}=-2$ mm. That means the rib height gradually increased along the flow direction, while the groove depth also increased downstream. The predicted and verified responses of the rounded optimal design are shown in Table 12.
| Source | Tmax (℃) | Tsd (℃) | Δp (Pa) |
|---|---|---|---|
| Surrogate prediction | 31.726 | 1.2580 | 273.4 |
| CFD verification | 31.712 | 1.2612 | 273.4 |
| Relative error | 0.04% | 0.25% | 0.0% |
The optimally staggered rib-groove plate was then integrated into the entire battery pack. Table 13 compares the optimized battery pack cooling system with the original side-mounted accordion plate system. Compared with the original system, the pack maximum temperature decreased by 3%, the maximum cell temperature difference decreased by 10.1%, the pack temperature difference decreased by 8.94%, and the pressure drop decreased by 8.99%. The optimized liquid cooling plate achieved simultaneous improvements in heat dissipation, temperature uniformity and pumping efficiency for the vehicle traction battery.
| System | Tmax,pack (℃) | ΔTmax,cell (℃) | ΔTmax,pack (℃) | Δp (Pa) |
|---|---|---|---|---|
| Original accordion side plate | 34.50 | 6.93 | 8.50 | 2703.6 |
| Optimized staggered rib-groove plate | 33.46 | 6.23 | 7.74 | 2460.6 |
| relative change | -3.0% | -10.1% | -8.94% | -8.99% |
Evaluation under typical operating conditions
I finally verified the optimized cooling solution under three typical scenarios: fast charging, low-temperature heating, and high-temperature highway cruising. These conditions represent severe thermal challenges for the vehicle traction battery.
Fast-charging scenario
The fast-charging protocol used a stepped SOC-based strategy. The battery was charged at 2C from 0 to 60% SOC, then at 1C from 60% to 90% SOC, and finally at 0.5C from 90% to 100% SOC. The total charging time was around 2880 s (48 min), and the initial temperature was 25 °C. The coolant inlet temperature was 25 °C with a flow rate of 2 m/s. During the 2C stage, the pack maximum temperature reached its peak of 30.13 °C at around 1080 s, and the maximum temperature difference peaked at 4.53 °C. At the end of the charging process, the maximum temperature and maximum difference dropped to 26.45 °C and 1.3 °C respectively. The whole process remained within the desired range of 15~35 °C, satisfying the design requirement for the vehicle traction battery.
Low-temperature heating scenario
In the low-temperature heating scenario, the battery pack, thermal pads, and cooling plate were initially set to -20 °C. The coolant inlet temperature was 15 °C with a velocity of 2 m/s. The goal was to heat the battery until the minimum cell temperature reached 0 °C, which is the lower limit for low-rate charging, and then continue until 10 °C to permit normal operation. The simulation showed that the minimum pack temperature rose above 0 °C after 620 s and reached 10 °C after 1210 s. The average heating rate was about 1.5 °C/min, which exceeds the usual engineering requirement of 0.3 °C/min. After heating, the maximum temperature was 15.03 °C and the minimum was 10.23 °C, so the temperature difference remained below 5 °C. The proposed liquid cooling/heating plate works effectively in sub-zero environments for the vehicle traction battery.
High-temperature highway cruising scenario
In this scenario, the initial battery and ambient temperature were 40 °C, representing a hot soak on a summer day. The vehicle then cruised continuously at 120 km/h. I calculated the required traction power using the longitudinal vehicle dynamics equation:
$$P_e = \frac{1}{\eta_t}\left( \frac{G f u_a}{3600} + \frac{C_D A u_a^3}{76140} \right)$$
where $G$ is the vehicle weight, $f$ the rolling resistance coefficient, $u_a$ the vehicle speed in km/h, $C_D$ the drag coefficient, $A$ the frontal area, and $\eta_t$ the driveline efficiency. With $G=38000$ N, $f=0.018$, $u_a=120$ km/h, $C_D=0.6$, $A=3$ m2, and $\eta_t=0.93$, the required power was approximately 65 kW. Given the battery pack configuration (two parallel strings), each cell discharged at about 0.5C to sustain this power. The coolant inlet temperature was 25 °C and the velocity was 2 m/s. The simulation results showed that the pack temperature decreased from 40 °C to below 35 °C within 390 s, and the pack maximum temperature difference fell below 5 °C after 770 s. In the steady state, the maximum temperature remained at 25.77 °C and the maximum temperature difference was only 0.66 °C, which demonstrates excellent cooling performance even under extreme heat-soak conditions.
Conclusion
In this work, I systematically developed an optimized side-mounted liquid cooling plate with staggered rib and groove structures for a vehicle traction battery. Through cell-level experiments and CFD simulations, I confirmed the thermal model accuracy and demonstrated that side-mounted liquid cooling is superior to bottom-mounted cooling. After investigating the effects of rib/groove shape, flow rate, spacing and diameter, I found that circular ribs and circular grooves offer the best trade-off. A novel staggered arrangement with increasing rib height and groove depth along the flow direction was then optimized using an RBF surrogate model and NSGA-II. The optimized design reduces the maximum cell temperature, cell temperature difference, pack temperature difference and pressure drop simultaneously compared with the original accordion plate design. The optimized cooling system satisfies the requirements under fast charging, low-temperature heating, and high-temperature highway cruising conditions, making it a promising thermal management solution for high-energy-density vehicle traction battery packs.