In the face of escalating global energy crises and environmental degradation, the development of new energy vehicles, particularly electric vehicles (EVs), has become a pivotal strategy for sustainable transportation. Central to the performance of these EVs is the lithium-ion battery, which is favored for its high energy density, long cycle life, and low self-discharge rate. However, the operational efficiency, lifespan, and safety of lithium-ion batteries are profoundly influenced by temperature. Therefore, an efficient and robust battery thermal management system (BTMS) is critical. In this study, I focus on the design and optimization of a liquid-cooled plate (LCP) for a battery thermal management system, specifically targeting a lithium titanate pouch battery. My primary objective is to address the inherent temperature gradient issues found in conventional serpentine flow channels, enhance the temperature uniformity of the EV battery pack, and minimize the power consumption of the thermal management system.
While air cooling and phase change materials (PCMs) are methods used for battery thermal management, liquid cooling is recognized as the most effective and reliable method for high-power applications due to its superior heat transfer capabilities. My research delves into a systematic approach that begins with an in-depth analysis of the battery’s thermal properties and proceeds through experimental validation to a comprehensive numerical optimization of the cooling plate structure. The project aims to balance the often-conflicting requirements of maximizing heat dissipation while minimizing the pressure drop (and hence pump power) across the liquid-cooled plate.
1. Lithium-Ion Battery Thermal Characteristics and Parameter Measurement
To create accurate simulation models, it was essential to first understand the fundamental structure and working principles of the lithium-ion cell. The battery in this study is a lithium titanate soft-pack pouch cell with a nominal capacity of 20 Ah and a nominal voltage of 2.3 V. The unique “zero-strain” property of the lithium titanate anode contributes to the battery’s excellent cycling performance. The heat generation within a lithium-ion battery during operation is a complex process involving several distinct sources: reversible reaction heat (\(Q_r\)), polarization heat (\(Q_p\)), and ohmic heat (also known as Joule heat, \(Q_j\)). The total heat generation \(Q_g\) can be expressed as:
$$ Q_g = Q_r + Q_p + Q_j $$
Reaction heat (\(Q_r\)) is associated with the entropy change during electrochemical reactions and is typically endothermic during charge and exothermic during discharge. Polarization heat (\(Q_p\)) arises from the deviation of electrode potential from its equilibrium value when current flows, and ohmic heat (\(Q_j\)) is generated by the internal resistance of the battery, dominating the overall heat production. Heat transfer within and out of the battery pack occurs through three modes: conduction within solids, convection between surfaces and fluids, and radiation. Given the relatively low temperatures in a well-managed EV battery pack, the radiation component is often neglected in favor of the more dominant conduction and convection mechanisms.
Since the thermal behavior of a battery is highly anisotropic, I performed physical measurements of key thermophysical properties to ensure simulation fidelity. I used the adiabatic method to measure the specific heat capacity. In this method, a battery sample is placed within a vacuum-insulated container to ensure no heat exchange with the environment. A known amount of electrical energy (\(Q\)) is then supplied to the battery via a heating pad, and the subsequent rise in temperature (\(\Delta T\)) is recorded. The specific heat capacity (\(C_p\)) is calculated using the formula:
$$ C_p = \frac{Q}{m \cdot \Delta T} $$
By applying a controlled heating power and measuring the temperature change of the known mass, I determined that the average specific heat capacity of this lithium titanate battery in the temperature range of 26°C to 37°C is 1058 J/(kg·K). I used the laser flash method for measuring anisotropic thermal conductivity. This technique, which I applied to my battery samples, involves heating one face of the sample with a short laser pulse and observing the temperature rise on the opposite face as a function of time to determine the thermal diffusivity. This process yields values for both the in-plane and through-plane thermal conductivities. The results showed the thermal conductivity to be highly anisotropic, with a through-plane (longitudinal) value of 0.69 W/m² and an in-plane value of 29.1 W/m², highlighting the layered structure of the cell. The primary measured and calculated thermophysical properties used in my models are summarized in Table 1.
| Parameter | Symbol | Value | Measurement Method |
|---|---|---|---|
| Specific Heat Capacity | \(C_p\) | 1058 J/(kg·K) | Adiabatic Method |
| Through-plane Thermal Conductivity | \(k_x\) | 0.69 W/(m·K) | Thermal Imaging (Transient) |
| In-plane Thermal Conductivity | \(k_y, k_z\) | 29.1 W/(m·K) | Thermal Imaging (Transient) |
Before proceeding, a crucial step in my research was to verify the thermal homogeneity of the battery cell. I conducted a multi-point temperature test on the battery under various charge and discharge conditions, with thermocouples placed at the center and edges of the cell’s large surface area. As the battery was discharged at varying C-rates, I monitored the temperature at each point. The results demonstrated a high degree of consistency in temperature rise across all monitored points, indicating excellent thermal uniformity across this cell format. This finding justified the use of a single-point measurement location at the center of the cell for future experiments and allowed me to assume a uniform heat generation rate in the simulation models.
2. Numerical Simulation and Experimental Validation
To ensure the reliability of subsequent thermal and fluid flow simulations, I conducted paired experimental and numerical analyses. The first stage focused on validating the heat generation model and the second on validating the fluid flow and pressure drop model in the liquid cooling plate.
2.1 Battery Cell Temperature Rise Validation
I performed temperature rise experiments on a single battery cell placed inside an adiabatic accelerated rate calorimeter. The experiments were conducted at a controlled ambient temperature of 30°C. The battery was discharged at both a 1C (20A) and a 5C (100A) continuous rate to its lower cut-off voltage of 1.8V, with the temperature recorded throughout the process. I then created a simplified three-dimensional geometric model of the cell, complete with its physical dimensions and measured thermal properties. I developed a computational grid using a polyhedral mesh, consisting of approximately 520,000 cells for the entire geometry, after conducting a mesh independence study to balance computational cost and accuracy.
In parallel, I performed transient thermal simulations using the CFD software Fluent. A significant part of this validation was to decide between using a constant heat generation rate and the more complex NTGK empirical model. From the experimental data, I calculated the average heat generation rates: 0.76 W for a 1C discharge and 10.64 W for a 5C discharge. I then applied these rates as a constant heat source in the simulation model. The comparison of the simulated and experimental temperature rise curves is a critical effect. A plot illustrating this comparison revealed a very good agreement, with the maximum relative error being only 4.4% during the 5C discharge. This close correlation validated my approach of using a constant heat generation rate, as it proved to be both accurate and computationally efficient compared to the complex NTGK model. A summary of the experimental discharge data is given in Table 2.
| Discharge Scenario | Total Time (s) | Temperature Rise (°C) | Heat Released (J) | Average Heat Power (W) |
|---|---|---|---|---|
| 1C (20A) Discharge | 3279 | 4.7 | 2500.3 | 0.76 |
| 5C (100A) Discharge | 676 | 13.6 | 7192.8 | 10.64 |
2.2 Liquid-Cooled Plate Pressure Drop Validation
The second part of my validation process focused on the fluid dynamics within the liquid-cooled plate. This step was crucial to ensure the accuracy of the turbulent flow model and the setup for evaluating the pressure drop, a key metric for assessing power consumption. I conducted experiments to measure the pressure drop across a prototype LCP made of 6061 aluminum. The experimental setup included a pump, a flow meter, pressure sensors, and a data acquisition system. Using a specific 65# coolant at 23.7°C and a flow rate of 4 L/min, we measured a pressure drop of 108.5 kPa.
In the corresponding simulation, I constructed a detailed geometric model of the LCP, which consisted of an upper and lower plate, and extracted the internal fluid volume to represent the complex serpentine channels. I created a polyhedral mesh and set up the simulation with boundary conditions identical to the experiment. The turbulence was modeled using the Realizable \(k-\epsilon\) model, as the Reynolds number, calculated via Equation (5), is significantly above the threshold for turbulent flow.
$$ d = \frac{2ab}{a+b} $$
$$ Re = \frac{\rho v d}{\mu} $$
The computational fluid dynamics (CFD) simulation predicted a pressure drop of 103.2 kPa across the LCP. This value shows excellent agreement with the experimental measurement, with a relative error of only 4.88%. This validation confirms that my simulation setup, including the turbulence model and boundary conditions, is accurate and reliable for predicting the pressure drop in the more complex LCP designs. A comparison of the experimental and simulated results is shown in Table 3.
| Pressure Drop (kPa) | Flow Rate (L/min) | Coolant Temp (°C) | |
|---|---|---|---|
| Experiment 1 | 113.2 | 4.00 | 23.65 |
| Experiment 2 | 103.9 | 4.01 | 23.73 |
| Simulation | 103.2 | 4.00 | 23.70 |
3. Modeling the EV Battery Pack Thermal Management System
With my validation efforts complete, I moved on to construct a comprehensive simulation model of the full EV battery pack thermal management system. I built a three-dimensional geometrical representation based on a real battery pack design. The focus of the study is on the thermal Management system and flow behavior within a liquid-cooled plate (LCP). A CAD model was created, incorporating the major components critical for thermal and fluid analysis: six battery modules, a liquid cooling plate located at the base, and an array of thermal interface material (TIM) pads between the modules and the plate to minimize thermal resistance. The battery pack of six modules, each containing 22 individual cells, was simplified for computational efficiency. I modeled each module as a solid block with anisotropic thermal conductivity and assigned the effective thermal properties I had measured earlier. The materials and their corresponding thermal properties are detailed in Table 4.
| Component/Material | Density (kg/m³) | Specific Heat (J/(kg·K)) | Thermal Conductivity (W/(m·K)) |
|---|---|---|---|
| Battery Module (Cell Block) | 2756 | 1058 | \(k_x = 0.69\), \(k_y=k_z = 29.1\) |
| Cooling Plate (6061 Al) | 2730 | 896 | 155 |
| Thermal Interface Pad | 3100 | 930 | 5 |
| Cooling Medium (Water) | 998.2 | 4182 | 0.6 |
3.1 Governing Equations
My simulations are governed by the fundamental laws of fluid dynamics and heat transfer. The assumptions of incompressible flow, constant fluid properties, and steady-state or transient behavior govern the simulation setup. I selected a pressure-based solver for the incompressible flow. The velocity and pressure fields are coupled using the SIMPLE algorithm. The governing equations are the conservation of mass (continuity), momentum (Navier-Stokes), and energy, presented below:
Continuity Equation:
$$\nabla \cdot \mathbf{V} = 0$$
Momentum Equation:
$$\rho \left( \frac{\partial \mathbf{V}}{\partial t} + \mathbf{V} \cdot \nabla \mathbf{V} \right) = -\nabla p + \mu \nabla^2 \mathbf{V}$$
Energy Equation (for fluid and solid):
$$\rho C_p \left( \frac{\partial T}{\partial t} + \mathbf{V} \cdot \nabla T \right) = \lambda \nabla^2 T + S_e$$
Where \(\mathbf{V}\) is the velocity vector, \(p\) is the pressure, \(\mu\) is the dynamic viscosity, \(\rho\) is the density, \(C_p\) is the specific heat capacity, and \(\lambda\) is the thermal conductivity of the medium. The term \(S_e\) represents the heat source, which is non-zero within the battery modules.
Given the Reynolds number for the flow in the LCPs, which I encounter in this research, is nearly always in the turbulent regime, I employed the realizable \(k-\epsilon\) model, known for its stability and accuracy in a variety of engineering flows. The model introduces two additional equations for the turbulent kinetic energy \(k\) and its dissipation rate \(\epsilon\):
$$ \frac{\partial}{\partial t}(\rho k) + \frac{\partial}{\partial x_j}(\rho k u_j) = \frac{\partial}{\partial x_j} \left[ \left( \mu + \frac{\mu_t}{\sigma_k} \right) \frac{\partial k}{\partial x_j} \right] + G_k + G_b – \rho\epsilon – Y_M + S_k $$
$$ \frac{\partial}{\partial t}(\rho \epsilon) + \frac{\partial}{\partial x_j}(\rho \epsilon u_j) = \frac{\partial}{\partial x_j} \left[ \left( \mu + \frac{\mu_t}{\sigma_\epsilon} \right) \frac{\partial \epsilon}{\partial x_j} \right] + \rho C_1 S \epsilon – \rho C_2 \frac{\epsilon^2}{k + \sqrt{\nu\epsilon}} + C_{1\epsilon} \frac{\epsilon}{k} C_{3\epsilon} G_b + S_\epsilon $$
where \(G_k\) and \(G_b\) represent the generation of turbulence kinetic energy due to mean velocity gradients and buoyancy, respectively. \(Y_M\) represents the contribution of fluctuating dilatation in compressible turbulence to the overall dissipation rate. The turbulent viscosity is computed as \(\mu_t = \rho C_\mu k^2 / \epsilon\), with \(C_\mu\) being a constant. The model constants, such as \(\sigma_k = 1.0\) and \(\sigma_\epsilon = 1.2\), are selected based on standard values for realizable \(k-\epsilon\) model. These equations allow for a more reliable prediction of the complex flow patterns, including recirculation and secondary flows, that occur in the serpentine channels.
4. Performance Analysis of the Serpentine Flow Channel
Before exploring new designs, I performed a series of baseline simulations to understand the impact of key operating and geometric parameters on the performance of a conventional serpentine channel design used in EV battery pack cooling plates. I evaluate the performance based on three metrics: the maximum module temperature (\(T_{max}\)), the maximum average temperature difference between the six modules, which I call \(\Delta T_{avg}\), and the pressure drop across the LCP, \(\Delta P\). A high \(\Delta T_{avg}\) indicates poor thermal uniformity, which can lead to accelerated and uneven battery degradation.
4.1 Effect of Coolant Flow Rate
I first examined the effect of the coolant flow rate. I simulated the system with the battery modules discharging at a 5C rate and varied the inlet volumetric flow rate from 1 to 6 L/min. The results, shown as a time vs. maximum temperature plot and a data chart, indicate that increasing the flow rate from 1 to 2 L/min significantly reduced the maximum module temperature. At a low flow rate of 1L/min, the maximum module temperature reached about 40.8°C, which exceeds my desired range. This temperature dropped as the flow rate increased. However, the benefit quickly becomes less pronounced. As the flow rate increases, the drop in temperature becomes less significant. This is because the thermal resistance is no longer dominated by the heat transfer coefficient but by the internal resistance of the battery and the TIM materials. Simultaneously, the pressure drop, which directly translates to power consumption, increases exponentially with the flow rate. For example, increasing flow rate from 4 L/min to 6 L/min significantly raises the pressure drop but only provides a marginal reduction in battery temperature. This indicates a trade-off. I concluded that a flow rate of 4 to 5 L/min offers a balanced compromise between cooling performance and energy consumption.
4.2 Effect of Serpentine Channel Design and Dimensions
I then investigated the flow channel design, starting with the number of “passes” or U-turns in the serpentine flow channel. A design with a higher number of flow paths and more complex serpentines increases the channel’s length and surface area, improving cooling, but also increases pressure drop. In Figure (a), I plotted the results for several variants of the serpentine channel. I found that the design with the most paths (Serpentine 1) provided the best cooling (lowest \(T_{max}\)) but had a prohibitive pressure drop of over 565 kPa. Conversely, the design with just two passes (Serpentine 4) had a lower pressure drop but significantly worse thermal performance. The data for this comparison is provided in Table 5. This led me to select Serpentine 3 as a compromise, with a pressure drop of 137 kPa, but it is still above my initial target of 100 kPa.
| Flow Channel Design | Pressure Drop \(\Delta P\) (kPa) | \(T_{max}\) (°C) | \(\Delta T_{avg}\) (°C) |
|---|---|---|---|
| Serpentine 1 (16-pass) | 565 | 37.2 | 1.15 |
| Serpentine 2 (8-pass) | 137 | 37.4 | 1.20 |
| Serpentine 3 (4-pass) | 98 | 37.6 | 1.30 |
| Serpentine 4 (2-pass) | 28 | 38.1 | 1.42 |
On analyzing the temperature plots for these serpentine designs, a clear and recurring issue emerges: the thermal gradient aligns with the flow path. The cooling water enters from the left, and as it traverses the EV battery pack’s cooling channels, it absorbs heat and its temperature rises. Consequently, the battery modules located on the outlet side (modules 4, 5, 6) operate at a higher average temperature than the modules on the inlet side (modules 1, 2, 3), leading to a pronounced maximum average temperature difference of around 1.1°C–1.3°C. This non-uniformity is detrimental to the EV battery pack’s health and is the primary problem I set out to solve.
I also analyzed the effect of changing the flow channel height (\(H\)). I ensured that the upper surface of the channel is at a fixed distance from the battery modules to maintain a consistent plate thickness. This means that increasing the channel height strengthens the lower plate structure and reduces the distance from the channel to the bottom of the pack. I varied the channel heights from 2 mm to 5 mm. Keeping the flow rate at 5 L/min, I discovered that while a lower channel height increased the coolant velocity, improving the heat transfer coefficient, it also caused a more significant pressure drop, increasing power consumption. The analysis of this single factor shows that a channel height of 4mm or 5mm provides the best overall performance in terms of pressure drop. These two heights result in a moderate temperature, but 4 mm is preferable.
5. Design and Optimization of a Novel Serpentine Flow Channel with a Branch Structure
To solve the temperature gradient problem inherent in a conventional serpentine channel, I adopted a novel and practical solution: the introduction of a branch structure. This design provides an additional, lower-resistance path for the fluid to bypass the long, serpentine path, which serves two main purposes. It helps to reduce the maximum average temperature difference across the EV battery pack’s modules and reduces the overall pressure drop. I started by testing where the branch should be placed. Through a series of CFD simulations, I found that placing a branch at the inlet manifold was the most effective. The branch connects the high-pressure inlet manifold to a corresponding manifold located in the middle of the same region, effectively creating a parallel path for the fluid to enter the second half of the serpentine channel. The parameters defining this branch structure are the branch inlet angle (\(\theta\)), the branch width (\(D\)), and the branch confluence position (\(L\)). These are defined in Figure below.
$$L = \text{Branch confluence location}$$
$$D = \text{Branch width}$$
$$\theta = \text{Branch inlet angle}$$
5.1 Contribution of the Branch to System Performance
Before optimizing the geometric details, it was crucial to demonstrate the benefit of the proposed structure. I compared the performance of the system with a standard serpentine channel (serpentine 3) to the system with the same channel plus the newly proposed branch structure. A plot of the modules’ temperature profiles shows a dramatic change. The original design shows a steady increase in average module temperatures from module 1 to module 6, indicating a significant thermal gradient. The introduction of the branch structure effectively forces a significant portion of the coolant to bypass the early part of the serpentine channel through the manifold to the end. This, in turn, leads to a more homogeneous flow distribution across the six modules. This change resulted in the maximum average temperature difference dropping from 1.16°C to 0.38°C, while at the same time, the pressure drop decreased from 98.2 kPa to 92.3 kPa. The branch not only solved a thermal uniformity problem but also reduced power consumption, representing a dual performance improvement.
5.2 Detailed Parametric Study of the Branch Structure
After establishing the overall effectiveness of the branch structure, I conducted a detailed parametric study to explore the effect of each geometric variable. In these single-factor analyses, I changed one parameter at a time while holding others constant at a baseline. All tests were done at the 5C discharge and 5 L/min flow rate condition.
Effect of Branch Inlet Angle: I considered angles of 70°, 80°, and 90° for the branch inlet. The branch angle alters the direction of the fluid entering the branch passage from the main manifold. I found that of the angles tested, an 80° inlet angle gave the lowest \(T_{max}\) and the lowest \(\Delta T_{avg}\). Conversely, a 70° angle resulted in the worst thermal uniformity and highest maximum temperatures, likely by adversely influencing the swirl and vortex structures you might create at the junction. This confirms the branch angle must be designed to minimize turbulence.
Effect of Branch Width: I investigated branch widths of 6mm, 8mm, and 10mm. The branch width controls how much flow is diverted from the primary serpentine channel. It strongly controls the amount of flow distribution to the later stages of the flow plate. My findings were that a wider branch (10mm) is more effective at equalizing temperatures across all modules, significantly reducing \(\Delta T_{avg}\) from 0.70°C to 0.36°C. Although a wider branch slightly increased the average module temperature by about 0.3°C, it significantly improved temperature uniformity. The pressure drop across the LCP also improved as the wider branch provided a path of lesser resistance. Overall, the larger 10 mm branch width showed the best results among those I tested.
Effect of Branch Confluence Position: I varied the position \(L\) of the junction where the branch flow re-enters the main channel segment. I used relative values of L=112, 134, and 156 mm. I observed a clear trend: moving the branch confluence position toward the front of the manifold enhances heat dissipation performance and decreases pressure drop. A smaller L leads to a more uniform temperature distribution across the modules. This is likely because a forward confluence position allows the two fluid streams (the cooler fluid from the branch and the warmer fluid from the first section of the channel) to mix more readily. This promotes a more even temperature distribution across the cooling channels beneath the EV battery pack modules. In terms of the LCP performance, an earlier confluence position also had lower pressure drop, likely due to reduced friction losses in the branch manifold.
6. Orthogonal Experimental Design and Comprehensive Optimization
The single-factor analysis identifies the relative importance of each parameter. Still, it does not capture the potential interactions between them. I used an orthogonal experimental design to systematically optimize all factors and find the best combination. This is a highly efficient method for studying multiple factors and levels with a relatively small number of experiments or, in my case, simulations. I chose four factors: the flow channel height (\(H\)), the branch inlet angle (\(\theta\)), the branch width (\(D\)), and the branch confluence position (\(L\)). Each factor was allowed four levels. This is known as an L16 (\(4^4\)) orthogonal array, which requires 16 simulation runs. The factor levels are presented in Table 6.
| Level | Channel Height \(H\) (mm) | Branch Angle \(\theta\) (°) | Branch Width \(D\) (mm) | Branch Confluence Position \(L\) |
|---|---|---|---|---|
| 1 | 5 | 90 | 10 | 1 |
| 2 | 4 | 85 | 8 | 2 |
| 3 | 3 | 80 | 6 | 3 |
| 4 | 2 | 75 | 4 | 4 |
I performed all 16 simulations with a constant coolant flow rate of 5 L/min and analyzed the following metrics: the maximum temperature of the modules \(T_{max}\), the maximum average temperature difference \(\Delta T_{avg}\), and the pressure drop \(\Delta P\). The results are presented in Table 7. After running the simulations, I used a statistical method called range analysis (also known as analysis of means) to interpret the data. This analysis breaks down the total effect of each factor by averaging the responses of its four levels. This method allows me to determine the relative influence of each factor and the optimal levels for the performance metrics being assessed.
| Run | \(H\) (mm) | \(\theta\) (°) | \(D\) (mm) | \(L\) | \(\Delta P\) (kPa) | \(T_{max}\) (°C) | \(\Delta T_{avg}\) (°C) |
|---|---|---|---|---|---|---|---|
| 1 | 5 | 90 | 10 | 1 | 62.94 | 37.622 | 0.553 |
| 2 | 5 | 85 | 8 | 2 | 55.91 | 37.702 | 0.518 |
| 3 | 5 | 80 | 6 | 3 | 62.97 | 37.624 | 0.555 |
| 4 | 5 | 75 | 4 | 4 | 57.00 | 37.659 | 0.972 |
| 5 | 4 | 90 | 8 | 3 | 92.48 | 37.718 | 0.498 |
| 6 | 4 | 85 | 10 | 4 | 96.06 | 37.745 | 0.613 |
| 7 | 4 | 80 | 4 | 1 | 95.82 | 37.550 | 0.874 |
| 8 | 4 | 75 | 6 | 2 | 94.73 | 37.627 | 0.717 |
| 9 | 3 | 90 | 6 | 4 | 152.26 | 37.650 | 0.786 |
| 10 | 3 | 85 | 4 | 3 | 152.16 | 37.573 | 0.861 |
| 11 | 3 | 80 | 10 | 2 | 146.25 | 37.477 | 0.355 |
| 12 | 3 | 75 | 8 | 1 | 148.00 | 37.595 | 0.468 |
| 13 | 2 | 90 | 4 | 2 | 339.13 | 37.525 | 0.876 |
| 14 | 2 | 85 | 6 | 1 | 335.35 | 37.526 | 0.620 |
| 15 | 2 | 80 | 8 | 4 | 329.16 | 37.507 | 0.630 |
| 16 | 2 | 75 | 10 | 3 | 330.68 | 37.689 | 0.394 |
The range analysis results are given in the Table 8. The range value R is calculated for each factor and metric. For \(T_{max}\), the factor with the highest R value has the most significant influence; this is the branch angle \(\theta\). For \(\Delta T_{avg}\), the branch width (D) emerged as the most significant factor, and for pressure drop, the channel height (H) had a large R value, which was by far the most influencing factor. This confirms that the geometric height is the dominant variable for determining the system pressure drop. By comparing both the R-values and the k-values (average of factor levels), I could rank the influence of each variable and identify the best level for each factor for each of the three metrics.
| Metric | Parameter | Level 1 | Level 2 | Level 3 | Level 4 | Range (R) | Ranking of Factor Influence |
|---|---|---|---|---|---|---|---|
| \(T_{max}\) (°C) | H | 37.652 | 37.660 | 37.574 | 37.562 | 0.098 | 2 |
| \(\theta\) | 37.629 | 37.637 | 37.539 | 37.642 | 0.103 | 1 | |
| D | 37.633 | 37.631 | 37.607 | 37.577 | 0.056 | 4 | |
| L | 37.573 | 37.583 | 37.651 | 37.640 | 0.078 | 3 | |
| \(\Delta T_{avg}\) (°C) | H | 0.649 | 0.675 | 0.618 | 0.630 | 0.058 | 4 |
| \(\theta\) | 0.678 | 0.653 | 0.604 | 0.638 | 0.075 | 3 | |
| D | 0.479 | 0.529 | 0.669 | 0.896 | 0.417 | 1 | |
| L | 0.629 | 0.617 | 0.577 | 0.750 | 0.173 | 2 | |
| \(\Delta P\) (kPa) | H | 59.71 | 94.77 | 149.67 | 333.58 | 273.87 | 1 |
| \(\theta\) | 161.70 | 159.87 | 158.55 | 157.60 | 4.10 | 3 | |
| D | 158.98 | 156.39 | 161.33 | 161.03 | 4.94 | 2 | |
| L | 160.53 | 159.01 | 159.57 | 158.62 | 1.91 | 4 |
Based on this analysis, the LCP’s optimal configuration is a compromise to balance the requirements of thermal performance and minimal power consumption. While design scenario 11 from the orthogonal array (H=3mm, \(\theta\)=80°, D=10mm, L=2) had the best thermal performance, its pressure drop was 146.25 kPa, exceeding my target of 100 kPa. Therefore, to meet the power consumption goal, this led me to select a combination that uses a slightly larger channel height to lower the pressure drop. However, increasing the channel height reduces the heat transfer rate per unit volume. To make a fair comparison between a 4 mm and a 5 mm channel height at a constant pressure drop, I performed two simulations under the same pressure drop of 92.3 kPa.
For the 4 mm channel height model, the flow rate was 5 L/min, resulting in a pressure drop of 92.3 kPa and a maximum average temperature difference of 0.38°C. For the 5 mm high channel model, I increased the flow rate to 6.17 L/min to achieve the same pressure drop. I compared the module temperature data for these two designs under identical pressure drop conditions, as shown in Figure below. The 5 mm channel design showed a lower module temperature by about 0.17 °C and reduced the maximum average temperature difference by 0.05°C. However, this improvement came with a significantly higher flow rate—23% more than the base case. When I adjusted for performance per unit of flow rate, the 4 mm design provided a better temperature reduction per liter per minute of flow. This indicates that the 4 mm channel is more efficient in utilizing the coolant. The final optimized design thus has a channel height (H) of 4 mm, a branch angle (\(\theta\)) of 80°, a branch width (D) of 10 mm, and the branch confluence position (L) set to the forward position (Position 1). This combination effectively balances the competing goals of achieving excellent thermal performance and maintaining low-cooling system power consumption.
7. Comparative Analysis of the Final Optimized Design
I performed a comprehensive comparison to evaluate the final optimized design against the various baseline and intermediate designs I had studied. A plot is shown comparing the optimized design with the four original serpentine channel designs, showing that the optimized design can drastically reduce the maximum average temperature difference from approximately 1.2°C to 0.38°C. The optimized design’s \(T_{max}\) is comparable to the best-performing serpentine channels but with a much lower pressure drop than the designs with high flow-path counts. When compared to all 16 orthogonal design scenarios, the optimized design provided a superior balance. For example, while the run #11 scenario had a slightly lower \(T_{max}\) (37.48°C vs. 37.50°C) and lower \(\Delta T_{avg}\) (0.36°C vs. 0.38°C), its pressure drop of 146 kPa was far above my target, making my design more practical.
To directly quantify the contribution of the branch structure, I constructed a “without branch” model and compared its results to the final optimized design, keeping the serpentine main channel (Serpentine 3) constant. I compiled both temperature and pressure data for this side-by-side comparison in Table 9. This comparison highlights that the improved thermal uniformity is due to the redistribution of coolant flow. The presence of the branch structure means a portion of the coolant is channeled directly to the latter parts of the EV battery pack, mitigating the heat buildup that normally occurs. The pressure drop also decreased by 6% due to reduced flow velocity within the main channels.
| Configuration | \(T_{max}\) (°C) | \(\Delta T_{avg}\) (°C) | Pressure Drop \(\Delta P\) (kPa) |
|---|---|---|---|
| Without Branch Structure | 37.56 | 1.16 | 98.2 |
| Final Optimized Design | 37.50 | 0.38 | 92.3 |
In this final design, the pressure drop of 92.3 kPa is within the 100 kPa target. The temperature uniformity, represented by \(\Delta T_{avg}\), improved by 67%. The maximum module temperature also reduced. This is significant because it demonstrates that the design is not just a theoretical exercise but an improvement that can be used in real EV battery packs to improve the health, lifecycle, and performance of the batteries.
8. Conclusion and Outlook
In this research, I conducted a thorough experimental and numerical optimization study of a liquid cooling plate (LCP) for a thermal management system used in an EV battery pack. The work validates that the CFD simulations can reliably reproduce experimental outcomes, with errors less than 5% for both heat transfer and fluid pressure loss. The key findings and contributions of this work can be summarized as follows:
- Accurate Material Characterization: By using adiabatic and thermal imaging methods, I measured the anisotropic thermal conductivity of the lithium titanate battery cell. The measured properties are essential inputs for creating reliable simulation models, with the through-plane thermal conductivity being much lower than the in-plane. My experimental tests on the cell also confirmed it has a very uniform temperature distribution on its surface.
- Conventional Serpentine Limitations: Through systematic analysis of flow rate, channel height, and other parameters, I confirmed that conventional serpentine channels provide good cooling but suffer from a significant non-uniform temperature distribution across the EV battery pack modules. The temperature increases along the fluid flow path, leading to an unacceptable \(\Delta T_{avg}\) of over 1.1°C. These channels also lead to excessively high-pressure drop when extra passes are added to improve cooling performance.
- Novel Branch Structure Design: I successfully introduced a novel branch structure into the serpentine flow channel. This is a highly practical design because it is easy to manufacture and involves only a simple modification to the manifold. The addition of the branch structure led to a dramatic improvement in thermal uniformity, decreasing the \(\Delta T_{avg}\) from 1.16°C to 0.38°C, and reducing the pressure drop of the EV battery pack’s LCP from 98.2 kPa to 92.3 kPa. This dual-benefit design improves the lifespan and reliability of the pack and reduces the electric load on the EV’s ancillary systems.
- Optimization Through Orthogonal Design: I used a four-factor, four-level orthogonal experimental design to systematically optimize the geometry of the cooling channel. Through range analysis, I determined the relative influence of each parameter on the performance. The channel height (\(H\)) was found to be the dominant factor affecting pressure drop, while the branch width (\(D\)) had the most significant effect on temperature uniformity. After considering the trade-offs between thermal performance and power consumption, the optimal combination was found to be: channel height \(H=4\) mm, branch inlet angle \(\theta=80^\circ\), branch width \(D=10\) mm, and branch confluence position \(L=1\) (the most forward position).
This research provides a comprehensive methodology for developing an efficient LCP for EV battery packs and offers a practical new design to improve their performance and lifespan. However, I have assumed a constant, uniform heat generation rate in the battery cells. Future work will involve refining the heat generation model to account for the dynamic internal electrochemical state. For the structural design, more parameters still can be optimized, such as the channel cross-section shape, the size and shape of possible pin-fin arrays, and the branch structure. In the future, I would like to conduct more experiments and explore advanced optimization algorithms, such as genetic algorithms like NSGA-II, to explore a wider design space and potentially discover even more effective topologies to further minimize the temperature drift.