Chapter 1. Introduction and Research Significance
My research focuses on the thermal management of a traction battery pack, which is one of the most critical subsystems in modern electric vehicles. The performance, lifespan, and safety of lithium-ion batteries are strongly dependent on operating temperature. Excessive heat accumulation during high-rate charging or high-speed cruising can lead to capacity degradation and even thermal runaway, while excessively low temperatures reduce the available power and may cause irreversible internal damage.
The significance of this work is rooted in the ever-increasing demand for higher energy density and faster charging capability in electric vehicles. As the energy source of such vehicles, the traction battery pack must be maintained within its optimal temperature window. According to established engineering guidelines, the cell temperature should remain between 15°C and 35°C, while the maximum temperature difference across the entire traction battery pack should not exceed 5°C. When these limits are exceeded, the cycle life of the cells deteriorates, and the risk of safety incidents increases markedly.
I first reviewed the state-of-the-art in battery thermal management literature. In the existing body of research, liquid cooling has become the dominant approach for high-power applications because of the superior heat capacity and thermal conductivity of coolants compared with air. Many researchers have investigated the flow channel geometry of cold plates. Bottom-mounted liquid-cooled plates with serpentine channels or parallel channels are widely used in the industry. However, a common shortcoming is the large temperature gradient along the height direction of the cell, because the upper portion of the cell is not in direct contact with the cooling plate. To overcome this deficiency, side-mounted cold plates have been proposed by placing the plate between adjacent cells or modules, thereby increasing the effective heat transfer area.
A number of studies also explored enhanced heat transfer structures inside the coolant channels, such as pin fins, ribs, grooves, and various wing-like turbulators. These structures can effectively disturb the thermal boundary layer and improve convective heat transfer. Yet, most of these enhancements inevitably lead to an increase in pressure drop and pumping power. A trade-off between thermal performance and hydraulic performance exists in almost every design. Therefore, I was motivated to seek a new configuration that can provide a higher heat transfer rate without significantly increasing pumping loss.
My objective became clear: design a liquid-cooled plate for a traction battery pack, incorporating both convex ribs and concave grooves in an alternating arrangement, that would produce a better balance between cooling performance and energy consumption. I planned to accomplish this through numerical simulation, single-factor analysis, surrogate modeling and multi-objective optimization.
Chapter 2. Thermal Characteristics of the Lithium-Ion Cell
2.1 Cell Structure and Working Principle
The lithium-ion cells used in the traction battery pack under study are of prismatic format. A prismatic cell consists of stacked electrode pairs, an aluminum housing, current collectors, and a safety vent. The positive electrode material is a nickel-cobalt-manganese (NCM) ternary compound, while the negative electrode is graphite-based. During discharge, lithium ions are deintercalated from the graphite anode and inserted into the NCM cathode. The reverse process occurs during charging. These electrochemical reactions are accompanied by heat generation that can be classified into four categories: reaction heat \(Q_r\), Joule heat \(Q_j\), polarization heat \(Q_p\), and side-reaction heat \(Q_s\). Under normal operating conditions, the side-reaction heat is negligible.
The total heat generation rate of the cell can be expressed as follows:
$$
Q_t = Q_r + Q_j + Q_p
$$
where:
$$
Q_j + Q_p = I^2(R_e + R_p)
$$
Here, \(I\) is the current, \(R_e\) represents the ohmic resistance and \(R_p\) represents the polarization resistance.
2.2 Heat Generation Rate Model
To predict the cell temperature accurately under various discharge rates, I adopted the equivalent heat generation model proposed by Bernardi. The volumetric heat generation rate is given by:
$$
q = \frac{I}{V_b}\left[(U_{oc} – U) – T\frac{\partial E_{oc}}{\partial T}\right]
$$
In this equation, \(V_b\) is the cell volume, \(U_{oc}\) is the open-circuit voltage, \(U\) is the terminal voltage, \(T\) is the cell temperature, and \(\partial E_{oc}/\partial T\) is the entropic heat coefficient. The term \((U_{oc} – U)\) can be replaced by the product of current and total internal resistance.
To obtain the internal resistance as a function of the state of charge (SOC), I conducted a hybrid pulse power characterization (HPPC) test on the 190 Ah prismatic cell. The cell was placed inside a temperature-controlled chamber at 25°C. The HPPC procedure consisted of repeated discharge and charge pulses at various depths of discharge, from 10% to 90% SOC. For each SOC level, the cell was subjected to a 30-second discharge pulse, followed by a rest period and a 30-second charge pulse. The resulting voltage responses were recorded to calculate the ohmic and polarization resistances.
The measured discharge internal resistance values at different SOC and current rates are summarized in the following table:
| 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 |
The following table presents the charge internal resistance values measured under the same conditions:
| 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 |
Based on these resistance data, the heat generation rate at each SOC value was calculated using the equivalent heat generation model. To express the heat generation rate as a function of discharge time, I converted the SOC axis into time using:
$$
SOC(t) = SOC_0 – \frac{It}{3600 C_R}
$$
where \(C_R\) is the rated capacity in ampere-hours. The heat generation rate curves were then fitted with a sixth-order polynomial:
$$
q(t) = A_1 t^6 + A_2 t^5 + A_3 t^4 + A_4 t^3 + A_5 t^2 + A_6 t + A_7
$$
The fitting coefficients are listed below:
| Coefficient | A1 | A2 | A3 | A4 | A5 | A6 | A7 |
|---|---|---|---|---|---|---|---|
| 0.5C | -4.76e-18 | 9.97e-14 | -7.86e-10 | 2.9e-6 | -4.87e-3 | 2.41 | 4001 |
| 1C | -3.5e-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 |
2.3 Thermal Property Determination
Because the commercial software used for simulation treats the cell as a homogeneous solid with equivalent thermal properties, I needed to compute the anisotropic thermal conductivity, equivalent specific heat, and average density of the cell. The directional thermal conductivities are expressed as:
$$
\lambda_y = \frac{\sum_{i=1}^{n} L_{yi}}{\sum_{i=1}^{n} L_{yi} / \lambda_i}
$$
for the through-plane direction, and:
$$
\lambda_{x,z} = \frac{\sum_{i=1}^{n} L_{xi,zi} \lambda_i}{\sum_{i=1}^{n} L_{xi,zi}}
$$
for the in-plane directions. The equivalent specific heat capacity is:
$$
C_p = \frac{\sum_{i=1}^{n} m_i C_i}{\sum_{i=1}^{n} m_i}
$$
The average density was obtained from the mass and volume of the cell components. These parameters are summarized below:
| Parameter | 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 |
2.4 Temperature Rise Experiment and Model Validation
I performed temperature rise experiments on a single cell at discharge rates of 0.5C, 1C and 2C. Five thermocouples were attached to the large surface of the cell, and the average temperature was recorded as a function of time. The cell was placed inside a chamber maintained at 25°C. After each test, the cell was fully recharged and allowed to rest until thermal equilibrium was achieved.
The experimental results show a non-linear temperature rise during discharge. At the early stage, the temperature rises rapidly. During the middle portion, the temperature rise becomes more gradual. Near the end of discharge, the temperature again increases quickly. At the end of the 2C discharge, the cell surface temperature reached 54°C, which is beyond both the optimal operating window and the allowable limit for sustained operation. This observation clearly justifies the necessity of a liquid cooling system in the traction battery pack.
In parallel with the experiments, I built a simplified geometric model of the cell with dimensions 146 mm × 80 mm × 103 mm. The heat generation rate was specified according to the polynomial fits described above. The outer surfaces were subjected to convective boundary conditions with a heat transfer coefficient of 5 W/(m²·K). The simulation results were compared with the measured temperatures. The maximum error between the simulation and experimental data was less than 8% for all three discharge rates. Thus, the thermal model was deemed sufficiently accurate for further investigations of the traction battery pack cooling system.
Chapter 3. Influence of Cold Plate Placement on the Traction Battery Pack Cooling Performance
3.1 Cold Plate Configurations
The full-size traction battery pack studied in this thesis has a total capacity of 139.2 kWh and is arranged in a 2-parallel by 88-series configuration. The pack is split into two layers, and each layer consists of eight modules. Due to the large size of the full model, I selected one module layer for detailed investigation. Each module contains a number of prismatic cells connected in series.
Two different cold plate placements were compared. The first scheme placed the liquid-cooled plates beneath the modules, which is the conventional bottom cooling arrangement commonly seen in the automotive industry. In this design, thermal interface material pads were inserted between the battery module housings and the cold plates to reduce the contact resistance and to provide mechanical compliance. The second scheme placed the liquid-cooled plates between the modules. In this side-mounted arrangement, each cold plate served two adjacent modules, except for the two outermost plates, which each served one module. This configuration significantly increased the heat transfer area and utilized the high in-plane thermal conductivity of the cell.
The cold plate used in both configurations was a commercially available accordion-type plate with multiple parallel micro-channels. A cross-section view of the plate reveals a series of straight rectangular channels through which the coolant flows from the inlet header to the outlet header.
| Material or component | Property | Value |
|---|---|---|
| Aluminum alloy 6061 | Density (kg m⁻³) | 2719 |
| Specific heat (J kg⁻¹ K⁻¹) | 871 | |
| Thermal conductivity (W m⁻¹ K⁻¹) | 180 | |
| 50% ethylene glycol-water | Density (kg m⁻³) | 1071.1 |
| Specific heat (J kg⁻¹ K⁻¹) | 3300 | |
| Thermal conductivity (W m⁻¹ K⁻¹) | 0.384 | |
| Dynamic viscosity (kg m⁻¹ s⁻¹) | 0.017 | |
| Thermal pad | Density (kg m⁻³) | 2150 |
| Specific heat (J kg⁻¹ K⁻¹) | 1200 | |
| Thermal conductivity (W m⁻¹ K⁻¹) | 2 |
3.2 Numerical Model Setup
I generated the computational grids in the Fluent meshing environment. A poly-hexcore approach was adopted, which creates hexahedral cells in the interior region and polyhedral cells near the boundaries. Inflation layers were added on the fluid-solid interfaces to resolve the near-wall gradient. The total element count for the bottom-cooling configuration was about 2.49 million, while the side-cooling configuration required approximately 3.23 million elements.
I performed a grid independence check using the side-cooled arrangement as a representative case. Three grid densities were tested: a coarse mesh with about 2.05 million cells, a medium mesh with approximately 3.23 million cells, and a fine mesh with about 4.07 million cells. The predicted maximum temperature differed by only 0.6% between the coarse and fine meshes, while the difference in pressure drop was approximately 1.3%. The discrepancy between the medium and fine meshes was less than 0.1% for temperature and 0.21% for pressure drop. Based on this analysis, the medium mesh was used for all subsequent simulations.
The governing equations for the fluid domain consist of the continuity equation:
$$
\nabla \cdot \vec{U} = 0
$$
and the momentum equation:
$$
\rho_f (\vec{U} \cdot \nabla) \vec{U} = -\nabla P + \mu_f \nabla^2 \vec{U}
$$
The energy equation for the fluid is written as:
$$
\rho_f c_{p,f}(\vec{U} \cdot \nabla T) = \lambda_f \nabla^2 T
$$
while for the solid regions:
$$
\lambda_s \nabla^2 T_s = 0
$$
I assumed steady incompressible flow with temperature-independent material properties. The inlet boundary condition was a mass flow corresponding to a volume flow rate of 21.78 L/min for the entire module layer. The inlet temperature was fixed at 25°C. The outlet boundary was set to atmospheric pressure. All external surfaces exposed to ambient air were assigned a natural convection heat transfer coefficient of 5 W/(m²·K). The cell heat generation rate was specified using the polynomial fit for the 2C discharge condition.
3.3 Results and Discussion
The key performance indicators I evaluated were the maximum temperature of the traction battery pack, the maximum temperature difference across any single cell, and the maximum temperature difference across the entire pack. The results for the two mounting arrangements are summarized in the following table:
| Cooling scheme | T_max pack (℃) | ΔT single cell (℃) | ΔT pack (℃) |
|---|---|---|---|
| Bottom-mounted accordion plate | 39.67 | 12.15 | 13.27 |
| Side-mounted accordion plate | 35.60 | 6.90 | 10.46 |
The side-mounted cooling scheme outperformed the bottom-mounted scheme in all aspects. The maximum temperature was reduced by 4.07°C, while the maximum temperature difference in the pack decreased by 2.81°C. More significantly, the maximum temperature difference within a single cell dropped by 5.25°C. This improvement can be attributed to the larger effective heat transfer area of the side-mounted plate and the fact that the plate is in direct contact with the large face of the cell, where the in-plane thermal conductivity is about nine times higher than the through-plane conductivity.
However, even with the side-mounted arrangement, the peak temperature still exceeded 35°C. The maximum temperature difference across the pack remained high at approximately 10.46°C. Therefore, further improvements were necessary.
3.4 Effect of Inlet and Outlet Positions
In order to address the temperature gradient observed along the coolant flow direction, I compared two inlet and outlet configurations for the side-mounted plates. The first configuration placed the inlet and outlet on the same side of the plate. The second configuration positioned the inlet and outlet on opposite sides, creating a diagonal flow pattern through the channels. The purpose of the staggered layout was to equalize the temperature distribution in the plane of the plate.
The simulation results under identical operating conditions are listed below:
| Inlet/outlet configuration | T_max pack (℃) | ΔT single cell (℃) | ΔT pack (℃) |
|---|---|---|---|
| Same side | 35.60 | 6.90 | 10.46 |
| Staggered sides | 34.50 | 6.93 | 8.50 |
The staggered configuration produced a 1.1°C reduction in the maximum temperature and a 1.96°C reduction in the pack temperature difference. The single-cell temperature difference remained essentially unchanged. Despite these gains, the peak temperature was still close to 34.5°C, which left limited margin for ambient temperature variations. This motivated me to improve the internal structure of the side-mounted cold plate itself.
Chapter 4. Structural Design and Simulation of the Side-Mounted Cold Plate with Rib-Groove Features
4.1 Design Concept
To enhance the heat transfer capability of the side-mounted cold plate without an excessive increase in pumping power, I proposed to introduce convex ribs and concave grooves into the flow channels. The convex ribs protrude into the coolant flow and act as turbulators. They accelerate the fluid locally and promote mixing, thereby reducing the thermal boundary layer thickness. The concave grooves, on the other hand, enlarge the local flow area and reduce the velocity of the fluid, creating recirculation zones that can also improve heat transfer but with a lower pressure drop penalty than ribs.
In my study, I selected one individual side-mounted cold plate from the module layer as the representative object for the parametric analysis. The cold plate is 298 mm long and 103 mm wide. It cools the two battery modules attached to its two major surfaces. The coolant enters from the bottom header, passes through the vertical channels, and exits from the top header. The baseline flow rate per plate was set to 2.42 L/min, which corresponds to the nominal operating condition of the traction battery pack.
The key performance indicators for the cold plate evaluation were the maximum surface temperature of the plate, the surface temperature standard deviation, the pressure drop across the plate, and a comprehensive performance criterion called the PEC factor.
4.2 Evaluation Methodology
I defined the Reynolds number as:
$$
Re = \frac{\rho_f u_{in} D_h}{\mu_f}
$$
The hydraulic diameter \(D_h\) for a rectangular channel of height \(H_{ch}\) and width \(W_{ch}\) is:
$$
D_h = \frac{2H_{ch} W_{ch}}{H_{ch} + W_{ch}}
$$
The surface friction factor is given by:
$$
f = \frac{2\Delta p D_h}{\rho_f L_{ch} u_{aver}^2}
$$
The heat transfer coefficient is calculated from:
$$
h_{con} = \frac{q_{eff} A_c}{A_{con}(T_{w,aver} – T_{f,aver})}
$$
The average Nusselt number is:
$$
Nu_{aver} = \frac{h_{aver} D_h}{\lambda_f}
$$
The comprehensive performance evaluation criterion proposed by Gee and Webb is defined as:
$$
PEC = \frac{Nu / Nu_0}{(f / f_0)^{1/3}}
$$
where \(Nu_0\) and \(f_0\) correspond to the baseline accordion plate. A PEC value greater than unity indicates better overall thermal-hydraulic performance compared with the baseline.
4.3 Effect of Rib and Groove Shape
I designed four distinct shapes for the convex ribs and concave grooves: circular, diamond, forward water-drop and backward water-drop. For each shape, the cross-section was extruded along the thickness direction of the flow channel. The convex ribs occupied the region between the opposing walls of the channel, effectively splitting the flow. The concave grooves were recessed into the wall of the channel, producing a cavity that locally expanded the cross-sectional area.
The simulation results for these shapes are organized in the following table:
| Structure | T_max (℃) | Tsd (℃) | Δp (Pa) | Nu/Nu₀ | f/f₀ | PEC |
|---|---|---|---|---|---|---|
| Baseline accordion | 32.45 | 1.08 | 317.2 | 1.00 | 1.00 | 1.00 |
| Circular rib | 31.64 | 1.31 | 394.7 | 1.59 | 1.22 | 1.48 |
| Diamond rib | 31.95 | 1.28 | 368.5 | 1.47 | 1.17 | 1.39 |
| Forward drop rib | 31.77 | 1.29 | 381.2 | 1.52 | 1.19 | 1.43 |
| Backward drop rib | 31.82 | 1.30 | 376.8 | 1.50 | 1.18 | 1.42 |
| Circular groove | 31.88 | 1.24 | 258.8 | 1.44 | 0.78 | 1.56 |
| Diamond groove | 32.05 | 1.18 | 241.3 | 1.33 | 0.72 | 1.48 |
| Forward drop groove | 31.94 | 1.21 | 245.6 | 1.38 | 0.73 | 1.53 |
| Backward drop groove | 31.99 | 1.22 | 248.1 | 1.36 | 0.74 | 1.50 |
The convex ribs reduced the maximum surface temperature more effectively than the concave grooves. Among all shapes, the circular rib achieved the lowest maximum temperature of 31.64°C. The concave grooves, however, exhibited lower pressure drops and better temperature uniformity. The circular groove had the highest PEC value among all candidates of 1.56 because its pressure drop penalty was quite small while its heat transfer enhancement remained meaningful.
I selected the circular geometry for both the convex ribs and the concave grooves, due to the combination of favorable thermal performance and the highest comprehensive PEC metrics.
4.4 Effect of Volume Flow Rate
In this phase, I fixed the geometric parameters as follows: rib-groove spacing of 25 mm, circular diameter of 10 mm, and rib height/groove depth of 2 mm. The volume flow rate was varied from 1.21 L/min to 3.62 L/min. The trends can be summarized from the following table:
| Flow rate (L/min) | T_max rib (℃) | T_max groove (℃) | Δp rib (Pa) | Δp groove (Pa) | PEC rib | PEC groove |
|---|---|---|---|---|---|---|
| 1.21 | 35.15 | 35.32 | 102.4 | 66.5 | 1.53 | 1.60 |
| 1.81 | 32.98 | 33.12 | 201.8 | 132.4 | 1.51 | 1.58 |
| 2.42 | 31.64 | 31.88 | 394.7 | 258.8 | 1.48 | 1.56 |
| 3.02 | 30.78 | 31.02 | 645.3 | 423.5 | 1.45 | 1.53 |
| 3.62 | 30.20 | 30.35 | 952.1 | 625.8 | 1.42 | 1.50 |
The results show that increasing the flow rate improved the heat transfer and reduced the maximum temperature. However, the magnitude of improvement weakened gradually. The pressure drop, in contrast, increased almost quadratically with flow rate. The PEC value decreased with increasing flow rate, which indicates that excessive flow rates compromise the overall energy efficiency of the traction battery pack cooling system. Based on this trade-off, I selected 2.42 L/min as a balanced operating condition.
4.5 Effect of Rib-Groove Spacing
The spacing between the centers of adjacent ribs or grooves was varied from 35 mm to 25 mm. The results are shown in the table below:
| Spacing (mm) | T_max rib (℃) | T_max groove (℃) | Δp rib (Pa) | Δp groove (Pa) | PEC rib | PEC groove |
|---|---|---|---|---|---|---|
| 35 | 31.76 | 31.98 | 382.5 | 261.3 | 1.47 | 1.54 |
| 30 | 31.70 | 31.93 | 389.2 | 259.6 | 1.47 | 1.55 |
| 25 | 31.64 | 31.88 | 394.7 | 258.8 | 1.48 | 1.56 |
A decrease in spacing means a larger number of the rib-groove features along the channel. The maximum temperatures declined as the spacing was reduced. The pressure drop of the ribbed plate increased, whereas the groove plate showed a slight decrease in pressure drop due to the additional cavity volume. The PEC improved for both configurations as the spacing decreased. Therefore, I chose the 25 mm spacing for the final design.
4.6 Effect of Rib and Groove Diameter
The diameter of the circular ribs and grooves was varied from 6 mm to 10 mm while the spacing was fixed at 25 mm and the depth or height was fixed at 2 mm. The following table summarizes the effects:
| Diameter (mm) | T_max rib (℃) | T_max groove (℃) | Δp rib (Pa) | Δp groove (Pa) | PEC rib | PEC groove |
|---|---|---|---|---|---|---|
| 6 | 31.81 | 31.94 | 320.5 | 282.4 | 1.38 | 1.48 |
| 7 | 31.77 | 31.92 | 341.2 | 273.9 | 1.42 | 1.51 |
| 8 | 31.73 | 31.90 | 359.8 | 268.2 | 1.44 | 1.53 |
| 9 | 31.68 | 31.89 | 378.1 | 262.7 | 1.46 | 1.54 |
| 10 | 31.64 | 31.88 | 394.7 | 258.8 | 1.48 | 1.56 |
I observed that increasing the diameter enhanced the heat transfer performance. For the ribbed plate, the pressure drop increased significantly with the diameter. For the grooved plate, the pressure drop was reduced because of the enlargement of the cavity volume. The PEC values increased monotonically for both types. In light of all the analyzed indicators, I selected the largest tested diameter of 10 mm for both ribs and grooves.
Chapter 5. Multi-Objective Optimization of the Staggered Rib-Groove Cold Plate
5.1 Design Variables and Responses
Having determined the shape, spacing, diameter and flow rate of the rib-groove features, I then proposed a staggered arrangement in which the convex ribs and concave grooves appear alternately along the flow path. The convex ribs are marked as rib columns 1 through 19 and the concave grooves as groove columns 1 through 18.
To further enhance the performance, I decided to optimize the height of the ribs and the depth of the grooves at different longitudinal positions. Instead of fixing all rib heights at a single value, I allowed the first column and the last column of ribs to take independent values. The intermediate rib heights were linearly interpolated:
$$
\delta = \frac{h_{19} – h_1}{18}
$$
$$
h_i = h_1 + (i-1)\delta, \quad i = 1,2,\ldots,19
$$
Similarly, for the grooves:
$$
\varepsilon = \frac{d_{18} – d_1}{17}
$$
$$
d_j = d_1 + (j-1)\varepsilon, \quad j = 1,2,\ldots,18
$$
The four design variables are \(h_1\), \(h_{19}\), \(d_1\) and \(d_{18}\). The allowed ranges are 0 to 2 mm for the rib height and -2 mm to 0 for the groove depth. The three responses are the maximum surface temperature of the cold plate, \(T_{max}\), the surface temperature standard deviation, \(T_{sd}\), and the pressure drop, \(\Delta p\).
The general mathematical formulation of the optimization problem can be written as:
$$
\text{find} \quad \mathbf{x} = [h_1, h_{19}, d_1, d_{18}]
$$
to minimize:
$$
f_1(\mathbf{x}) = T_{max}(\mathbf{x})
$$
$$
f_2(\mathbf{x}) = T_{sd}(\mathbf{x})
$$
$$
f_3(\mathbf{x}) = \Delta p(\mathbf{x})
$$
subject to:
$$
0 \leq h_1, h_{19} \leq 2 \ \text{mm}
$$
$$
-2 \leq d_1, d_{18} \leq 0 \ \text{mm}
$$
5.2 Optimal Latin Hypercube Sampling
I used the optimal Latin hypercube design method to generate 84 sample points uniformly distributed within the four-dimensional design space. For each sample point, I built the geometric model of the cold plate and imported it into the CFD solver. The boundary conditions corresponded to a 2C discharge of the adjacent battery modules, with a coolant volume flow rate of 2.42 L/min and an inlet temperature of 25°C. The response data collected from these simulations served as the training dataset for surrogate modeling. A portion of the sampling results is shown in the table below:
| No. | h₁ (mm) | h₁₉ (mm) | d₁ (mm) | d₁₈ (mm) | T_max (℃) | T_sd (℃) | 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 |
5.3 Surrogate Model Construction and Validation
I compared several types of surrogate models for this task. The radial basis function model was found to be particularly attractive due to its flexibility in capturing non-linear relationships and its high computational efficiency. Hence, I chose the RBF model to approximate each response as a function of the four design variables.
After training the surrogate models on the 84 CFD samples, I evaluated their accuracy by computing the coefficient of determination \(R^2\) between the model predictions and the CFD results. The obtained values were 0.90091 for \(T_{max}\), 0.92914 for \(T_{sd}\), and 0.96244 for \(\Delta p\). Since all the \(R^2\) values exceeded 0.9, the surrogate models were considered sufficiently reliable for the subsequent optimization step.
5.4 NSGA-II Multi-Objective Optimization
The non-dominated sorting genetic algorithm II was employed to solve the optimization problem. I set the population size to 20, the number of generations to 100, the crossover probability to 0.8, and the mutation rate to 0.1. During the optimization, a penalty was imposed if the pressure drop exceeded the baseline value of 300.4 Pa, in order to ensure that the final design does not consume more pumping power than the original accordion plate.
The Pareto front obtained from the optimization shows a clear trade-off relationship among the three objectives. In general, a lower maximum surface temperature tends to be accompanied by a higher pressure drop. The selected optimal solution from the Pareto front corresponds to a maximum surface temperature of 31.726°C, a surface temperature standard deviation of 1.258°C, and a pressure drop of 273.4 Pa. The design variables of the selected point are summarized below:
| Variable | Value before rounding | Value after rounding |
|---|---|---|
| h₁ (mm) | 0.0001 | 0 |
| h₁₉ (mm) | 1.9987 | 2 |
| d₁ (mm) | -0.8214 | -0.8 |
| d₁₈ (mm) | -1.9967 | -2 |
| T_max (℃) | 31.726 | 31.712 |
| T_sd (℃) | 1.258 | 1.261 |
| Δp (Pa) | 276.7 | 273.4 |
The optimized geometry displays a progressive increase in rib height from the inlet side to the outlet side, and a similar increase in groove depth. This means that the heat transfer enhancement is intensified toward the downstream region where the coolant has already absorbed more heat and the fluid temperature is higher. The gradual strengthening of the turbulation activity toward the downstream region compensates for the loss of temperature difference between the fluid and the wall, thereby producing a more uniform wall temperature distribution.
I then inserted the optimized staggered rib-groove cold plates into the module-level model of the traction battery pack. The simulation was run under the same 2C discharge conditions as before. The comparison between the optimized staggered rib-groove cold plate and the original side-mounted accordion plate for the traction battery pack is shown below:
| Configuration | T_max pack (℃) | ΔT cell (℃) | ΔT pack (℃) | Δp (Pa) |
|---|---|---|---|---|
| Original accordion plate side-mounted | 34.50 | 6.93 | 8.50 | 2703.6 |
| Optimized staggered rib-groove plate | 33.46 | 6.23 | 7.74 | 2460.6 |
| Improvement | -3.0% | -10.1% | -8.94% | -8.99% |
The optimized plate reduced the maximum temperature of the traction battery pack by 3%. The maximum temperature difference across a single cell dropped by 10.1%, while the pack-level temperature difference was reduced by 8.94%. Remarkably, the pressure drop also decreased by approximately 9% compared with the baseline. Thus, the staggered rib-groove configuration managed to achieve simultaneous improvements in thermal performance and hydraulic performance, which is rarely seen in the literature.
The underlying mechanism can be explained as follows: the convex ribs generate strong local acceleration and flow separation that strip away the thermal boundary layer. The concave grooves create gentle recirculation zones that promote transverse mixing. When these two types of structures are alternated, the beneficial effects are compounded but the flow resistance introduced by the ribs is partly mitigated by the expansion volumes of the grooves. Consequently, the overall pressure drop remains lower than that of an equivalent ribbed channel, while the heat transfer enhancement is higher than that of a pure groove channel.
Chapter 6. Performance Evaluation under Typical Operating Conditions
In order to ensure that the optimized cold plate is suitable for real-world applications, I evaluated the thermal performance of the complete traction battery pack liquid cooling system under three representative operating scenarios.
6.1 Fast Charging Condition
Fast charging is one of the most demanding scenarios for the thermal management system of the traction battery pack. While the vehicle is stationary, there is little assistance from the airflow passing over the vehicle body. In addition, the charging current is high during the initial stage. I simulated a stepped charging strategy in which the battery is 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 duration is 2880 seconds, corresponding to a 30-minute charge from empty to 80% SOC.
The simulation results indicate that the maximum temperature of the traction battery pack reaches a peak of 30.13°C near the end of the 2C charging phase. The maximum temperature difference rises to 4.53°C at the same time. When the charging process is complete, the maximum temperature drops back to 26.45°C, and the temperature difference reduces to 1.3°C. All these values remain comfortably within the allowable ranges.
6.2 Low Temperature Heating Condition
In cold regions, the temperature of the traction battery pack can fall well below the minimum allowable temperature for charging. Under such conditions, the coolant itself can be used as a heating medium to warm the cells before charging. I simulated a condition where the initial temperature of the battery modules, the thermal pads, and the cold plates is -20°C. The coolant entering the cold plate is maintained at 15°C, which is a typical temperature that can be provided by the vehicle heat pump system.
The simulation reveals that the cell temperature rises quickly in the initial phase. The minimum cell temperature reaches 0°C after 620 seconds, at which point the cells are able to accept a low-rate charge. After 1210 seconds, the minimum temperature reaches 10°C, and the heating process can be terminated. The average heating rate is approximately 1.5°C/min throughout the process, which satisfies the commonly accepted engineering requirement of at least 0.3°C/min.
6.3 High Temperature Highway Cruising Condition
The third scenario simulates the traction battery pack after prolonged exposure to high ambient temperatures, followed by high-speed driving. The initial temperature of the battery pack is set to 40°C. The vehicle is driven at a constant speed of 120 km/h, and the required discharge power is about 65 kW as calculated from the vehicle dynamics equation:
$$
P_{motor} = \frac{u_a}{3600 \eta} \left( G f u_a \cos\alpha + \frac{C_D A u_a^2}{21.15} + G u_a \sin\alpha \right)
$$
This power demand translates to approximately 0.5C discharge per cell. The coolant enters the cold plate at 25°C with a flow velocity of 2 m/s.
The simulation results show that the maximum temperature of the traction battery pack decreases quickly from the initial 40°C. It drops below 35°C after 390 seconds, and the temperature difference drops below 5°C after 770 seconds. At steady state, the maximum temperature is 25.77°C, and the temperature difference is only 0.66°C. These results confirm that the optimized liquid cooling system is entirely capable of protecting the traction battery pack under severe summer driving conditions.
The following table summarizes the key outcomes for the three typical operating conditions of the traction battery pack:
| Operating condition | Maximum temperature (℃) | Maximum temperature difference (℃) | Requirement satisfied |
|---|---|---|---|
| Fast charging (2C to 0.6 SOC) | 30.13 | 4.53 | Yes |
| Low temperature heating at -20℃ initial | 15.03 (final) | 4.80 | Yes |
| Highway cruise at 40℃ ambient | 25.77 (stable) | 0.66 | Yes |
Conclusions
In this thesis, I have systematically investigated the liquid cooling system for a traction battery pack and proposed a novel cold plate design with staggered convex ribs and concave grooves. The major findings and contributions of my work can be summarized as follows.
First, I experimentally characterized the thermal behavior of a 190 Ah prismatic lithium-ion cell using HPPC tests and temperature-rise experiments. The heat generation rate polynomial functions for 0.5C, 1C and 2C discharge rates were obtained by curve fitting, and the thermal property parameters were calculated using equivalent medium theory. The single-cell thermal model was validated by comparing the simulated surface temperatures with the experimental measurements, with a maximum error below 8%.
Second, I compared the bottom-mounted and side-mounted liquid-cooled plates for the traction battery pack. The side-mounted arrangement reduced the maximum pack temperature by 4.07°C and the cell-level temperature difference by 5.25°C compared with the bottom-mounted arrangement. In addition, the staggered inlet and outlet positions further reduced the pack temperature difference by 1.96°C compared with the same-side arrangement.
Third, I conducted a comprehensive single-factor analysis on the shape, spacing, diameter and flow rate of the convex ribs and concave grooves. Among the four shapes evaluated, circular ribs and grooves exhibited the most favorable combination of heat transfer enhancement and pressure drop. A flow rate of 2.42 L/min, a rib-groove spacing of 25 mm and a diameter of 10 mm were selected as the most balanced parameters.
Fourth, I developed an staggered arrangement of the ribs and grooves with linearly varying height and depth along the flow direction. A surrogate-assisted optimization framework combining optimal Latin hypercube sampling, RBF surrogate models and NSGA-II was used to find the optimal parameter combination. The optimized cold plate achieved reductions of 3% in maximum temperature, 10.1% in the single-cell temperature difference, 8.94% in the pack temperature difference, and 8.99% in the pressure drop compared with the original accordion side-mounted plate. This is a rare accomplishment because both thermal and hydraulic performances are improved simultaneously.
Finally, I verified the feasibility of the optimized cooling system under three typical operating scenarios. In all scenarios, the maximum temperature and temperature difference of the traction battery pack remained well within the required limits. The optimized liquid cooling system was proven to be effective for fast charging, low-temperature heating, and high-temperature highway driving.
In future work, I plan to extend the present single-layer module analysis to a full-scale three-dimensional model of the entire traction battery pack, including the manifold pipes, connectors and supporting structures. I would also like to experimentally validate the optimized cold plate by constructing a test bench that replicates the operating conditions of the traction battery pack. Moreover, the control strategy of the cooling system can be further refined by incorporating the thermal model into an energy management framework that balances cooling demand against energy consumption.