Lithium-ion batteries are widely adopted in electric vehicles due to their high energy density, long cycle life and low self-discharge rate, yet their performance, durability and safety are strongly dependent on temperature. For an EV battery pack, the optimal working window is generally considered to be 15–35°C, and the largest temperature difference within a pack should be kept below 5°C. Excessive temperature accelerates impedance growth, capacity degradation and may trigger thermal runaway, while low temperature reduces available power and causes lithium plating during charging. Therefore, a well-designed liquid cooling system is essential for EV battery thermal management. In this work, I investigate the cooling performance and temperature uniformity of a liquid-cooled EV battery pack by combining numerical simulation, HPPC experiments and multi-objective optimization. The main novelty is a staggered rib-groove cold plate placed between cells, which strengthens heat transfer without increasing pumping power compared with a conventional harmonica-style side cold plate.
1. Background and Research Motivation
Several thermal management approaches exist for EV battery packs, including air cooling, phase-change material cooling, heat-pipe cooling, liquid cooling and direct refrigerant cooling. Air cooling is simple but insufficient for high-rate charging and high-power discharging. Phase-change materials offer large latent heat but suffer from leakage and difficult heat rejection. Heat pipes show excellent conductivity but are hard to integrate with vehicle thermal systems. Liquid cooling is therefore the mainstream solution for modern EV battery packs because of the high specific heat and thermal conductivity of the coolant. In liquid-cooled EV battery packs, the cold plate is usually placed either beneath the cells or between the cell modules. The underside configuration is easy to assemble and widely used, but the cell temperature gradient in the vertical direction remains large, and the upper part of the cell often becomes the hot spot. Side-mounted cold plates increase the effective heat-transfer area and can better utilize the in-plane conductivity of the cell, leading to lower maximum temperatures and better uniformity.
Previous studies on EV battery liquid cooling have mainly focused on flow-channel layout, inlet/outlet arrangements and geometric parameters such as channel width, channel depth and flow path shape. Serpentine and parallel mini-channel cold plates have been extensively compared. Serpentine designs produce good temperature uniformity but are accompanied by higher pressure drop, whereas parallel straight channels cause uneven flow distribution. More recently, heat-transfer enhancement structures, including pin fins, airfoil-shaped fins, convex ribs and concave grooves, have been introduced into cold plates. The convex ribs disturb the thermal boundary layer and enhance convection, but they inevitably increase pressure drop. Concave grooves enlarge the flow cross-section locally, reduce friction loss and provide a lower pressure drop; however, the trapped fluid in the grooves weakens local heat transfer. The key design challenge is to exploit the advantages of both ribs and grooves in one cold plate structure without exceeding the pressure-drop budget. Therefore, I design a side cold plate in which circular convex ribs and circular concave grooves are arranged alternately along the flow direction, and I optimize this structure to improve the cooling performance and uniformity of the EV battery pack.
2. Thermal Characterization of the Lithium-Ion Cell
2.1 Cell Geometry and Thermophysical Properties
The investigated EV battery cell is a prismatic NCM lithium-ion cell with a nominal capacity of 190 Ah, nominal voltage of 3.8 V, dimensions of 146 mm × 80 mm × 103 mm and a mass of 1.8 kg. The cell is shown schematically in the figure below.
Since the internal structure of the cell is complex, an equivalent homogeneous solid model was adopted in the simulation. The equivalent density and specific heat capacity were calculated by weighting the constituent layer properties, while the thermal conductivities in the in-plane and through-plane directions were obtained by series and parallel thermal-resistance formulations. Table 1 summarizes the thermophysical properties used in the simulation.
| Property | Value |
|---|---|
| Density / kg m−3 | 2478.5 |
| Specific heat / J kg−1 K−1 | 1100 |
| Thermal conductivity x direction / W m−1 K−1 | 18.2 |
| Thermal conductivity y direction / W m−1 K−1 | 2.0 |
| Thermal conductivity z direction / W m−1 K−1 | 18.2 |
2.2 Heat-Generation Model of the EV Battery
The total heat generated by a lithium-ion EV battery during charge and discharge comprises reaction heat, ohmic heat, polarization heat and side-reaction heat. Under normal operating conditions, the side-reaction heat can be neglected. The volumetric heat generation rate can be expressed using an equivalent model based on internal resistance:
$$q_{b}=\frac{1}{V_{b}}\left[I^{2}\left(R_{e}+R_{p}\right)-IT\frac{\partial E_{oc}}{\partial T}\right]$$
where \(V_{b}\) is the cell volume, \(I\) is the current, \(R_{e}\) is the ohmic resistance, \(R_{p}\) is the polarization resistance, \(T\) is temperature, and \(\partial E_{oc}/\partial T\) is the entropic heat coefficient. I determined the internal resistance at different states of charge (SOC) through hybrid pulse power characterization (HPPC) tests. A series of 30 s discharge pulses and 30 s charge pulses were applied at 10% SOC increments between 10% and 90% SOC. The resulting discharge resistances at 0.5C, 1C and 2C are listed in Table 2, and the charge resistances are listed in Table 3.
| SOC | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 | 0.9 |
|---|---|---|---|---|---|---|---|---|---|
| 0.5C | 0.59 | 0.42 | 0.32 | 0.28 | 0.28 | 0.33 | 0.37 | 0.35 | 0.34 |
| 1C | 0.45 | 0.33 | 0.25 | 0.23 | 0.25 | 0.31 | 0.33 | 0.32 | 0.28 |
| 2C | 0.37 | 0.27 | 0.22 | 0.20 | 0.23 | 0.28 | 0.29 | 0.25 | 0.24 |
| SOC | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 | 0.9 |
|---|---|---|---|---|---|---|---|---|---|
| 0.5C | 0.39 | 0.29 | 0.24 | 0.24 | 0.26 | 0.30 | 0.32 | 0.31 | 0.32 |
| 1C | 0.30 | 0.23 | 0.20 | 0.21 | 0.24 | 0.27 | 0.28 | 0.28 | 0.29 |
| 2C | 0.23 | 0.18 | 0.17 | 0.18 | 0.20 | 0.24 | 0.25 | 0.26 | 0.26 |
The measured internal resistance decreases with increasing charge/discharge rate and increases sharply when SOC drops below 0.2. Charge resistance is generally lower than discharge resistance for the same SOC and current rate. The cell heat-generation rate was calculated from the equivalent internal-resistance model and then fitted as a sixth-order polynomial as a function of discharge time:
$$\dot{q}(t)=A_{1}t^{6}+A_{2}t^{5}+A_{3}t^{4}+A_{4}t^{3}+A_{5}t^{2}+A_{6}t+A_{7}$$
The fitted coefficients are listed in Table 4 for the three discharge current rates.
| Coefficient | 0.5C | 1C | 2C |
|---|---|---|---|
| A1 | −4.76 × 10−18 | −3.50 × 10−16 | −2.02 × 10−13 |
| A2 | 9.97 × 10−14 | 3.94 × 10−12 | 9.99 × 10−10 |
| A3 | −7.86 × 10−10 | −1.62 × 10−8 | −1.77 × 10−6 |
| A4 | 2.90 × 10−6 | 3.03 × 10−5 | 1.34 × 10−3 |
| A5 | −4.87 × 10−3 | −2.37 × 10−2 | 0.382 |
| A6 | 2.41 | 2.48 | 9.23 |
| A7 | 4001 | 12004 | 40084 |
Before building the battery-pack model, I validated the heat-generation model with single-cell temperature-rise tests. The cell was placed in a constant-temperature chamber at 25°C, and surface temperatures were recorded with thermocouples during 0.5C, 1C and 2C constant-current discharges. The three-dimensional finite-volume model of the cell was solved in Fluent with the same boundary conditions. The simulated average surface temperatures agree with the measured data within 8% for all three discharge rates. At the end of the 0.5C, 1C and 2C discharges, the measured temperatures reach approximately 29.5°C, 33.3°C and 54°C. The result confirms that the 2C high-rate discharge causes serious overheating without active liquid cooling.
3. Cold Plate Arrangement in the EV Battery Pack
3.1 Simulation Model
The full EV battery pack has an energy capacity of 139.2 kWh and uses an 88-series, 2-parallel configuration. The pack is divided into upper and lower layers, and each layer is studied separately because of computational cost. In this section, I analyze one single-layer battery group consisting of eight modules. Two cold-plate arrangements are compared: bottom cooling and side cooling. In both schemes, each module is cooled by a harmonica-type aluminum cold plate with identical parallel mini-channels. The heat-conduction pad of 2 mm thickness is inserted between the cell module and the cold plate to reduce contact resistance and absorb assembly tolerances. The cooling liquid is a 50% ethylene glycol/water mixture at 25°C, and the total volume flow rate of the battery group is set to 21.78 L/min. Table 5 lists the properties of the materials used in the simulation.
| Material | Density / kg m−3 | Specific heat / J kg−1 K−1 | Thermal conductivity / W m−1 K−1 | Dynamic viscosity / kg m−1 s−1 |
|---|---|---|---|---|
| Aluminum 6061 | 2719 | 871 | 180 | — |
| 50% EG/water | 1071.1 | 3300 | 0.384 | 0.017 |
| Thermal pad | 2150 | 1200 | 2 | — |
The CFD model solves the incompressible Navier–Stokes equations together with the energy equation. A poly-hexcore mesh was generated in Fluent. Three mesh densities were tested for the side-cooled EV battery group, and the intermediate mesh was selected because the difference in maximum temperature between the medium and fine meshes was below 0.1% while the pressure-drop difference was only about 0.21%. The final mesh counts are about 3.23 million cells for the side-mounted cold plate battery group.
3.2 Bottom-Placed and Side-Placed Cold Plates
The simulation results at the end of the 2C discharge are summarized in Table 6. With the bottom cold plate, the highest temperature of the EV battery pack reaches 39.67°C, while the maximum temperature difference inside one cell is 12.15°C and the pack-level difference is 13.27°C. Such a large temperature difference is caused mainly by the vertical temperature gradient along the cell height. The side-mounted cold plate reduces the highest temperature to 35.6°C, the intra-cell temperature difference to 6.9°C and the pack-level difference to 10.46°C. The side arrangement significantly enlarges the effective heat-transfer area and takes advantage of the higher in-plane thermal conductivity of the layered electrode structure. Nevertheless, the maximum temperature remains above 35°C and the temperature difference still exceeds 5°C, which indicates that further improvement is necessary.
| Configuration | Pack Tmax / °C | Cell ΔT / °C | Pack ΔT / °C |
|---|---|---|---|
| Bottom harmonica cold plate | 39.67 | 12.15 | 13.27 |
| Side harmonica cold plate | 35.60 | 6.90 | 10.46 |
3.3 Inlet and Outlet Arrangement
For the side-cooled battery group, the inlet and outlet can be placed on the same side or on opposite sides. The temperature field of the same-side arrangement shows a clear gradient from the coolant inlet to the outlet. To make the flow direction more uniform over the whole pack, an alternating inlet/outlet arrangement was considered. The inlet and outlet positions of neighboring cold plates are reversed, changing the effective flow direction relative to the cell modules. Table 7 compares the two arrangements.
| Inlet/outlet arrangement | Pack Tmax / °C | Cell ΔT / °C | Pack ΔT / °C |
|---|---|---|---|
| Same side | 35.60 | 6.90 | 10.46 |
| Staggered sides | 34.50 | 6.93 | 8.50 |
The staggered inlet/outlet arrangement reduces the pack-level maximum temperature from 35.6°C to 34.5°C and lowers the pack temperature difference from 10.46°C to 8.5°C. The cell-level maximum temperature difference increases only slightly from 6.9°C to 6.93°C. Thus, the staggered side-mounted harmonica cold plate is chosen as the baseline for further structural improvement.
4. Rib-Groove Structure Design and Parametric Analysis
4.1 Design Concept and Evaluation Criteria
To further improve the EV battery cooling performance, I modified the harmonica cold plate by adding convex ribs and concave grooves inside every parallel mini-channel. The aim is to interrupt the thermal boundary layer with convex ribs while using concave grooves to reduce flow resistance. The ribs and grooves may have different cross-sectional shapes, including circular, diamond, forward water-drop and backward water-drop shapes. For a fair comparison, the rib height and groove depth are first fixed to 2 mm, the separation between adjacent ribs/grooves is 25 mm, and the diameter of the circular structures is 10 mm unless otherwise stated. A single side cold plate between two adjacent cell modules was extracted as the test model, and the EV battery module was treated as a heat source generating heat according to the 2C discharge profile. The coolant flow rate was set to 2.42 L/min when the effect of flow rate was not being investigated.
The performance of the cold plate is evaluated from the cooling performance, temperature uniformity, pressure drop and overall thermo-hydraulic performance. The Reynolds number, friction factor, Nusselt number and PEC performance evaluation criterion are defined as:
$$Re=\frac{\rho_{f}u_{in}D_{h}}{\mu_{f}},\qquad D_{h}=\frac{2H_{ch}W_{ch}}{H_{ch}+W_{ch}}$$
$$f=\frac{2D_{h}\Delta p}{\rho_{f}u_{aver}^{2}L_{ch}}$$
$$h_{con}=\frac{q_{eff}A_{c}}{A_{con}\left(T_{w,aver}-T_{f,aver}\right)},\qquad Nu=\frac{h_{aver}D_{h}}{\lambda_{f}}$$
$$PEC=\frac{Nu/Nu_{0}}{\left(f/f_{0}\right)^{1/3}}$$
where \(Nu_0\) and \(f_0\) are the Nusselt number and friction factor of the original harmonica cold plate. A PEC value larger than unity indicates that the modified cold plate has a better trade-off between enhanced heat transfer and increased friction loss compared with the baseline.
4.2 Influence of Rib and Groove Shape
Four shapes were examined: circular, diamond, forward water-drop and backward water-drop. For each shape, two versions were considered: convex ribs protruding into the channel and concave grooves carved into the channel wall. The simulation results indicate that all rib and groove configurations perform better than the original harmonica structure in terms of heat transfer. Convex ribs generally give lower cold-plate surface temperature than concave grooves because the ribs accelerate the coolant and periodically suppress the thermal boundary layer. By contrast, concave grooves produce a low-velocity recirculation region that weakens local heat transfer. Among all shapes, the circular convex rib has the lowest surface maximum temperature and the highest Nu/Nu0 ratio. The circular concave groove also gives the highest PEC among all groove configurations because of its very small pressure-drop penalty. The overall comparison is summarized in Table 8.
| Shape | Rib behavior | Groove behavior |
|---|---|---|
| Circular | Lowest Tmax, highest Nu/Nu0, highest pressure-drop penalty among ribs, best rib PEC | Good Nu enhancement, moderate temperature uniformity, lowest friction among grooves, best overall PEC |
| Diamond | Highest Tmax among ribs, lowest Nu/Nu0 and lowest rib PEC | Good temperature uniformity, lowest pressure drop |
| Forward water-drop | Medium Tmax and Nu/Nu0 | Lower pressure drop than circular |
| Backward water-drop | Medium Tmax and Nu/Nu0 | Lower pressure drop than circular |
Since the circular convex rib provides the best heat-transfer enhancement and the circular concave groove provides the best overall thermo-hydraulic performance, I selected circular ribs and circular grooves for the final design.
4.3 Influence of Volume Flow Rate
With fixed geometric parameters, the coolant volume flow rate was varied from 1.21 L/min to 3.62 L/min. As the flow rate increases, both the maximum surface temperature and the surface-temperature standard deviation decrease significantly. The convex-rib cold plate decreases the maximum temperature from about 35.15°C at 1.21 L/min to about 30.20°C at 3.62 L/min, while the concave-groove cold plate decreases it from about 35.32°C to about 30.35°C in the same range. The highest temperature reduction, however, gradually levels off beyond 2.42 L/min. The pressure drop increases rapidly with flow rate, which is unfavorable for pump energy consumption. The groove structure always exhibits lower pressure drop than the harmonica baseline, while the rib structure shows higher pressure drop. The PEC value remains greater than unity for both ribs and grooves over the whole flow-rate range, but it decreases when the flow rate increases. Therefore, the flow rate of 2.42 L/min was chosen as a compromise between heat-transfer improvement and pump-power consumption.
| Volume flow rate / L min−1 | Rib Tmax / °C | Groove Tmax / °C | Rib friction ratio f/f0 | Groove friction ratio f/f0 |
|---|---|---|---|---|
| 1.21 | 35.15 | 35.32 | 1.21 | 0.76 |
| 3.62 | 30.20 | 30.35 | 1.24 | 0.79 |
4.4 Influence of Rib-Groove Spacing
The spacing between adjacent rib/groove structures was then changed from 35 mm to 25 mm while the flow rate was fixed at 2.42 L/min. Reducing the spacing increases the number of interruptions of the thermal boundary layer and therefore improves heat transfer. The maximum cold-plate surface temperature of the rib cold plate drops from about 31.76°C at 35 mm spacing to about 31.64°C at 25 mm spacing. The Nu/Nu0 ratio of the convex rib increases from about 1.46 to 1.60, while that of the concave groove increases from about 1.30 to 1.44 in the same range. The friction-factor ratio of the convex rib rises modestly from 1.18 to 1.22, whereas that of the concave groove decreases from 0.81 to 0.78. The PEC value of both structures increases as the spacing decreases. Hence, the smaller spacing of 25 mm is selected in the subsequent optimization.
4.5 Influence of Rib-Groove Diameter
The circular diameter was varied from 6 mm to 10 mm with a fixed spacing of 25 mm. The maximum surface temperature of the convex-rib cold plate decreases from 31.81°C at 6 mm to 31.65°C at 10 mm, while the concave-groove structure shows only a slight temperature reduction. The pressure drop of the convex-rib structure increases continuously with the diameter and reaches about 394.7 Pa at 10 mm; in contrast, the pressure drop of the concave-groove cold plate decreases slowly and is about 258.8 Pa at 10 mm. This is because larger grooves increase the local flow area and reduce wall friction. The friction-factor ratio \(f/f_0\) of the convex rib increases from about 1.04 to 1.23 from 6 mm to 10 mm, while that of the concave groove decreases from about 0.86 to 0.78. The PEC of both rib and groove structures improves as the diameter increases. Thus, the diameter of 10 mm is retained for the final design.
| Diameter / mm | Rib Tmax / °C | Rib Δp at 10 mm / Pa | Groove Δp at 10 mm / Pa | Rib f/f0 | Groove f/f0 |
|---|---|---|---|---|---|
| 6 | 31.81 | — | — | 1.04 | 0.86 |
| 10 | 31.65 | 394.7 | 258.8 | 1.23 | 0.78 |
5. Multi-Objective Optimization of the Staggered Rib-Groove Cold Plate
5.1 Design Variables and Optimization Model
On the basis of the single-factor analysis, a staggered rib-groove cold plate was constructed by placing convex circular ribs and concave circular grooves alternately along each mini-channel. The heights of the ribs and the depths of the grooves are not uniform along the flow direction, because the thermal boundary layer develops continuously and the coolant temperature rises from inlet to outlet. I therefore defined the first-column and last-column rib heights as \(h_1\) and \(h_{19}\), and the first-column and last-column groove depths as \(d_1\) and \(d_{18}\). The intermediate columns vary linearly between these two values. Since the groove depth is a depression below the channel wall, it is represented by a negative value. The optimization design variables and their ranges are listed in Table 11.
| Variable | Parameter | Lower bound / mm | Upper bound / mm |
|---|---|---|---|
| x1 | h1 | 0 | 2 |
| x2 | h19 | 0 | 2 |
| x3 | d1 | −2 | 0 |
| x4 | d18 | −2 | 0 |
The linear distribution of the rib heights and groove depths is expressed as:
$$\Delta_{h}=\frac{h_{19}-h_{1}}{18},\qquad h_{i}=h_{1}+\Delta_{h}\left(i-1\right),\quad i=1,2,\ldots,19$$
$$\varepsilon_{d}=\frac{d_{18}-d_{1}}{17},\qquad d_{j}=d_{1}+\varepsilon_{d}\left(j-1\right),\quad j=1,2,\ldots,18$$
The response variables are the maximum cold-plate surface temperature \(T_{\max}\), the surface-temperature standard deviation \(T_{\mathrm{sd}}\), and the inlet/outlet pressure drop \(\Delta p\). The optimization model is written as:
$$\mathrm{Minimize}\left\{f_{1}\left(\mathbf{x}\right),\,f_{2}\left(\mathbf{x}\right),\,f_{3}\left(\mathbf{x}\right)\right\}$$
subject to:
$$\Delta p\left(\mathbf{x}\right)\leq 300.4\,\mathrm{Pa},\qquad 0\leq x_{1},x_{2}\leq2,\qquad -2\leq x_{3},x_{4}\leq0$$
5.2 Surrogate Model Construction
Because direct CFD simulation is computationally expensive, I used the optimal Latin hypercube design to generate 84 sample points in the four-dimensional design space. The samples were parameterized automatically, and the responses were evaluated by CFD. A radial basis function (RBF) surrogate model was then fitted to map the design variables to the three responses. The coefficient of determination \(R^2\) of the RBF model is 0.9009 for the maximum temperature, 0.9291 for the temperature standard deviation and 0.9624 for the pressure drop. Since all three values are above 0.90, the surrogate model is considered accurate enough for optimization. Part of the sample set and corresponding responses is listed in Table 12.
| h1 / mm | h19 / mm | d1 / mm | d18 / mm | Tmax / °C | Tsd / °C | Δp / Pa |
|---|---|---|---|---|---|---|
| 1.30 | 2.00 | −0.80 | −0.40 | 31.769 | 1.308 | 302.44 |
| 1.10 | 0.40 | 0.00 | −1.40 | 31.913 | 1.290 | 264.19 |
| 0.70 | 0.10 | −1.60 | −0.50 | 31.935 | 1.308 | 257.32 |
| 0.30 | 0.90 | −1.70 | −1.80 | 31.857 | 1.278 | 262.29 |
| 1.60 | 0.70 | −1.40 | −0.10 | 31.912 | 1.326 | 276.76 |
| 0.80 | 0.30 | −0.40 | −0.20 | 31.915 | 1.298 | 259.51 |
| 2.00 | 1.40 | −1.30 | −1.00 | 31.847 | 1.325 | 305.81 |
| 1.90 | 0.20 | −0.70 | −0.90 | 31.974 | 1.337 | 277.51 |
| 1.20 | 1.80 | −1.50 | −1.70 | 31.798 | 1.305 | 294.68 |
| 0.40 | 1.30 | −1.00 | 0.00 | 31.866 | 1.290 | 267.33 |
5.3 NSGA-II Optimization and Verification
The non-dominated sorting genetic algorithm II (NSGA-II) was applied to the RBF surrogate model with a population size of 20, evolution generations of 100, crossover probability of 0.8 and mutation probability of 0.1. The Pareto front in the three-objective space shows that the cold-plate surface temperature decreases with increasing pressure drop, while the temperature standard deviation also decreases slightly with higher pump power. I selected a compromise solution that ensures a low maximum temperature and temperature standard deviation without imposing too much pressure-drop penalty. The selected optimal design variables are \(h_1 = 0\ \mathrm{mm}\), \(h_{19} = 2\ \mathrm{mm}\), \(d_1 = -0.8\ \mathrm{mm}\) and \(d_{18} = -2\ \mathrm{mm}\). This means that the convex rib height increases gradually from zero near the inlet to 2 mm near the outlet, and the concave groove depth also increases along the flow direction. The predicted response values for this point are \(T_{\max}=31.726\,^{\circ}\mathrm{C}\), \(T_{\mathrm{sd}}=1.258\,^{\circ}\mathrm{C}\) and \(\Delta p=276.7\,\mathrm{Pa}\). After rounding and rebuilding the CAD model, the CFD verification yields \(T_{\max}=31.712\,^{\circ}\mathrm{C}\), \(T_{\mathrm{sd}}=1.261\,^{\circ}\mathrm{C}\) and \(\Delta p=273.4\,\mathrm{Pa}\), which agrees well with the surrogate prediction.
| Quantity | Optimal design | Rounded design | CFD verification |
|---|---|---|---|
| x1 (h1) / mm | 1.226 × 10−4 | 0 | 0 |
| x2 (h19) / mm | 1.9987 | 2 | 2 |
| x3 (d1) / mm | −0.8214 | −0.8 | −0.8 |
| x4 (d18) / mm | −1.9967 | −2 | −2 |
| Tmax / °C | 31.726 | 31.712 | 31.712 |
| Tsd / °C | 1.258 | 1.261 | 1.261 |
| Δp / Pa | 276.71 | 273.40 | 273.40 |
The optimized rib-groove cold plate was then applied to the full single-layer EV battery pack with staggered inlet/outlet arrangement. The performance is compared with the baseline side-mounted harmonica cold plate in Table 14. The optimized staggered rib-groove cold plate reduces the pack maximum temperature from 34.5°C to 33.46°C, which corresponds to a 3% reduction. The maximum temperature difference inside one cell decreases from 6.93°C to 6.23°C, i.e., by 10.1%. The pack-level temperature difference decreases from 8.5°C to 7.74°C, i.e., by 8.94%. At the same time, the pressure drop of the cooling system decreases from 2703.6 Pa to 2460.6 Pa, a reduction of about 8.99%. This improvement is particularly valuable because the enhanced heat transfer is obtained without increasing pumping power.
| Configuration | Pack Tmax / °C | Cell ΔT / °C | Pack ΔT / °C | Pressure drop / Pa |
|---|---|---|---|---|
| Harmonica side cold plate | 34.50 | 6.93 | 8.50 | 2703.6 |
| Optimized staggered rib-groove side cold plate | 33.46 | 6.23 | 7.74 | 2460.6 |
| Improvement / % | −3.01 | −10.10 | −8.94 | −8.99 |
6. Typical Operating-Condition Analysis
After obtaining the optimized staggered rib-groove cold plate, I evaluated the final EV battery pack liquid cooling system under three representative operating conditions: fast charging, low-temperature heating and high-temperature high-speed cruising.
6.1 Fast-Charging Condition
Fast charging is one of the most demanding conditions for an EV battery thermal management system because the vehicle is stationary and there is less auxiliary air flow to reject heat. A stepped-current charging strategy was adopted: 2C charging from 0 to 0.6 SOC, 1C charging from 0.6 to 0.9 SOC, and 0.5C charging from 0.9 to 1.0 SOC. The total charging time is 2880 s, and about 80% SOC is restored within 30 minutes. The highest temperature and maximum temperature difference during this process both occur near the end of the 2C charging stage at about 1080 s, with values of 30.13°C and 4.53°C, respectively. At the end of the whole charging process, the maximum temperature is 26.45°C and the pack temperature difference is only 1.3°C. Therefore, the optimized cooling system successfully maintains the EV battery pack within the recommended operating window during fast charging.
6.2 Low-Temperature Heating Condition
In cold regions, the EV battery must be heated before fast charging. The cell, thermal pads and battery-pack components were initialized at −20°C, and the coolant inlet temperature was set to 15°C. The coolant flow velocity was 2 m/s. The cell minimum temperature reaches 0°C after about 620 s, allowing low-rate charging, and exceeds 10°C after about 1210 s, at which point the charging/discharging capability is considered sufficient and the heating process is stopped. The average heating rate of the EV battery pack is about 1.5°C/min, which is higher than the typical requirement of 0.3°C/min. When the minimum temperature reaches 10°C, the maximum cell temperature is 15.03°C and the minimum is 10.23°C. The temperature difference remains within an acceptable range for subsequent charging.
6.3 High-Temperature High-Speed Cruising Condition
Finally, the EV battery cooling system was tested in a hot summer environment followed by high-speed cruising at 120 km/h. The initial temperature of the battery and environment is 40°C, the coolant inlet temperature is 25°C, and the coolant velocity is 2 m/s. By solving the vehicle longitudinal dynamics equation:
$$P_{e}=\frac{1}{\eta_{T}}\left(\frac{G f u_{a}}{3600}+\frac{C_{D} A u_{a}^{3}}{76140}\right)$$
the approximate power demand of the vehicle at 120 km/h is about 65 kW, which corresponds to roughly 0.5C discharge from the double-parallel EV battery configuration. The battery temperature decreases rapidly from 40°C and drops below 35°C after about 390 s. The pack temperature difference falls below 5°C after about 770 s. At steady state, the maximum battery temperature is 25.77°C and the maximum temperature difference is 0.66°C, demonstrating that the optimized staggered rib-groove liquid cooling structure has strong cooling capacity and excellent temperature uniformity under severe ambient conditions.
7. Conclusions
In this work, I have proposed and optimized a staggered rib-groove side-mounted liquid cold plate for EV battery thermal management. The main conclusions are as follows:
First, the HPPC-based heat-generation model was validated by single-cell temperature-rise experiments within an error of 8%, which enables accurate prediction of battery temperature in subsequent simulations.
Second, the thermal performance of the EV battery pack is significantly affected by the cold plate position and inlet/outlet arrangement. A side-mounted cold plate reduces the pack maximum temperature from 39.67°C to 35.60°C compared with a bottom-mounted cold plate. The staggered inlet/outlet arrangement further reduces the pack maximum temperature to 34.50°C and the pack temperature difference from 10.46°C to 8.50°C.
Third, the single-factor parametic study shows that circular ribs provide the strongest heat-transfer enhancement, whereas circular grooves provide the best overall PEC. The maximum temperature decreases with increasing flow rate, decreasing rib-groove spacing and increasing rib-groove diameter, but these changes affect pressure drop in different ways. The rib structure increases pressure drop while the groove structure decreases pressure drop, which motivates the staggered rib-groove design.
Fourth, multi-objective optimization via the RBF surrogate model and NSGA-II algorithm gives the optimal rib heights and groove depths as \(h_1 = 0\ \mathrm{mm}\), \(h_{19} = 2\ \mathrm{mm}\), \(d_1 = -0.8\ \mathrm{mm}\) and \(d_{18} = -2\ \mathrm{mm}\). Compared with the original harmonica side cold plate, the optimized EV battery pack exhibits a 3% lower maximum temperature, 10.1% lower cell-level temperature difference, 8.94% lower pack-level temperature difference and 8.99% lower pressure drop.
Fifth, the optimized cooling system satisfies the requirements for fast charging, low-temperature heating and high-temperature high-speed cruising. The solution provides a promising route for high-power EV battery liquid cooling systems that need improved heat transfer without an additional pumping-power burden.