1. Introduction and Research Motivation
The rapid advancement of electric vehicle (EV) technology has fundamentally transformed the global automotive industry, with traction battery systems standing at the core of this transition. As the primary energy storage device in EVs, the performance, range, and safety of traction battery packs are critically dependent on effective thermal management. The temperature behavior of traction battery systems directly influences charge-discharge efficiency, cycle life, and operational safety, making thermal management a key research direction in battery management systems (BMS).
According to recent market data, the penetration rate of new energy vehicles in China has surged from 0.3% in 2014 to 36% in 2023, with the total number of traction battery-powered vehicles reaching approximately 20 million. This explosive growth, however, brings significant technical challenges. With increasing energy density and faster charging rates, traction battery packs generate substantial heat during operation. Under high-power-density conditions, if heat within the battery pack cannot be dissipated efficiently and promptly, temperatures may rise sharply, leading to rapid performance degradation, thermal runaway, or severe safety incidents.
Research indicates that approximately 70% of battery safety accidents are directly related to the failure of battery thermal management systems. Maintaining traction battery operating temperatures within the optimal range of 20–40°C can significantly enhance energy output efficiency and extend cycle life. Moreover, thermal management systems must address extreme temperature conditions during fast charging scenarios, necessitating robust and efficient cooling solutions.
2. Battery Thermal Management Technologies: A Comprehensive Review
Battery thermal management systems (BTMS) are essential for maintaining optimal operating temperatures of traction battery packs. Various cooling technologies have been developed over the years, each with distinct advantages and limitations. Table 1 summarizes the comparative characteristics of mainstream cooling approaches for traction battery thermal management.
| Cooling Method | Advantages | Limitations | Typical Application Scenarios |
|---|---|---|---|
| Air Cooling | Simple structure, low cost, no complex piping | Low heat dissipation efficiency, poor temperature uniformity | Low-power battery modules, compact installations |
| Liquid Cooling | High heat dissipation efficiency, precise temperature control, excellent uniformity | Complex system, higher cost, energy consumption | High-power EV battery packs |
| Phase Change Material (PCM) Cooling | High latent heat storage, passive operation, no parasitic power | Low thermal conductivity, leakage concerns | Pulse load conditions, thermal runaway prevention |
| Heat Pipe Cooling | Ultra-high effective conductivity, compact design, passive operation | Limited heat rejection capability alone | Space-constrained applications |
| Hybrid Cooling (Liquid+Heat Pipe) | Synergistic effect, superior heat transfer, improved uniformity | System complexity, higher initial investment | High energy density traction battery packs |
2.1 Air Cooling Technology
Air cooling technology has been widely adopted in early traction battery thermal management due to its structural simplicity and cost-effectiveness. However, as traction battery energy density continues to rise, the limited heat transfer capability of air cooling has become increasingly problematic. Research by Dinesh Kumar Sharma and colleagues indicates that forced air cooling can be significantly improved through optimized inlet/outlet configurations, flow channel topology, and control strategies.
Key developments in air cooling include:
Research by Li and colleagues demonstrated that lateral air inlet strategies achieve approximately 5K temperature reduction compared to conventional front-side cooling approaches. Chen and co-workers proposed a symmetric air-cooled system with non-uniform battery spacing, achieving a 43% reduction in maximum temperature difference and 33% energy savings compared to asymmetric configurations. Fan placement and spoiler configurations have also shown promise; Zhang’s research team demonstrated that an optimized spoiler configuration with an 80-degree inclination angle could reduce battery pack maximum temperature by 3.97K and maximum temperature difference by 5.28K.
2.2 Liquid Cooling Technology
Liquid cooling has emerged as the dominant thermal management approach for modern traction battery systems, particularly for high-capacity prismatic cells. Its superior heat transfer coefficients, precise temperature regulation, and better thermal uniformity make it particularly suitable for high-power traction battery applications. Recent advances focus on channel structure optimization, contact surface enhancement, and multi-goal design optimization.
The flow channel design significantly influences liquid cooling performance. Researchers have explored numerous configurations:
Xiong and colleagues developed a biomimetic spider-web flow channel structure, achieving maximum temperature differences of 3.726K and pressure drops of 29.69 Pa in traction battery packs. Yang’s group applied variable density topology optimization to design tree-like flow channels, achieving a 490% reduction in pressure drop and 13.2% reduction in temperature difference. Luo and colleagues proposed a square spiral ring microchannel liquid cooling plate that maintained maximum temperatures below 33.63°C during 2C discharge operations.
2.3 Heat Pipe Technology in Traction Battery Cooling
Heat pipes represent an advanced heat transfer technology characterized by exceptionally high effective thermal conductivity—typically thousands of times greater than conventional metals. These devices operate on the principles of phase-change heat transfer, utilizing the evaporation and condensation of an internal working fluid to transfer heat efficiently between source and sink regions.
For traction battery thermal management, heat pipes offer several distinct advantages: ultra-high thermal conductivity, compact and flexible geometry, passive operation without parasitic power consumption, and excellent temperature uniformity characteristics. When integrated with liquid cooling systems, heat pipes create a synergistic cooling architecture that addresses the challenges of internal heat extraction within traction battery packs.
The coupling mechanism involves placing the heat pipe’s evaporator section in direct contact with traction battery cell surfaces or inter-cell spaces, while the condenser section interfaces with liquid cooling channels. This configuration enables efficient heat extraction from internal battery regions that are typically difficult to cool using conventional bottom-plate liquid cooling alone.
3. Theoretical Framework for Traction Battery Thermal Analysis
3.1 Classification of Traction Battery Chemistries and Formats
Lithium-ion batteries dominate the current traction battery market due to their high energy density, long cycle life, and mature manufacturing technology. According to different cathode materials, lithium-ion traction battery cells can be classified into several categories:
| Battery Type | Advantages | Disadvantages | Application |
|---|---|---|---|
| Lithium Iron Phosphate | High safety, long cycle life, low cost | Lower energy density | BYD, mainstream Chinese EVs |
| Ternary (NCM/NCA) | High energy density | Thermal runaway risk, higher cost | Tesla, premium European EVs |
| Lithium Manganese Oxide | Good rate capability | Moderate energy density, degradation | Early generation EVs |
| Lithium Cobalt Oxide | High energy density | High cost, thermal stability concerns | Portable electronics |
In terms of cell formats, prismatic cells have gained significant market share in traction battery applications due to their superior space utilization, structural rigidity, and thermal management compatibility. This study specifically focuses on prismatic lithium iron phosphate (LiFePO₄) cells, which offer an excellent balance of safety, cycle life, and cost-effectiveness for EV traction battery systems.
3.2 Heat Generation Mechanisms in Traction Battery Cells
The heat generation within a traction battery cell during operation arises from multiple coupled mechanisms. The total heat generation can be expressed as:
$$Q_{total} = Q_r + Q_{\Omega} + Q_P + Q_s$$
where \(Q_r\) represents the electrochemical reaction heat, \(Q_{\Omega}\) denotes the ohmic heat, \(Q_P\) is polarization heat, and \(Q_s\) represents side reaction heat, which is typically negligible for normal operating conditions of traction battery systems.
The electrochemical reaction heat is expressed as:
$$Q_r = \frac{nFI}{M}\frac{\partial E}{\partial T}$$
where \(n\) is the number of transferred electrons, \(F\) is Faraday’s constant, \(I\) is the operating current, and \(\frac{\partial E}{\partial T}\) is the temperature coefficient.
The ohmic heat generation follows Joule’s law:
$$Q_{\Omega} = I^2 R_o$$
The polarization heat is given by:
$$Q_P = I\eta$$
Note that during charging, the electrochemical reaction heat becomes endothermic (negative), providing a slight cooling effect, whereas during discharge all heat generation terms are positive, requiring effective thermal management for traction battery packs. The heat generation levels intensify with increasing C-rates during fast charging applications.
3.3 Heat Transfer Mechanisms
Heat transfer in traction battery systems occurs through three fundamental mechanisms. Internal heat transfer within battery cells primarily occurs through conduction, following Fourier’s law:
$$\psi = -\lambda\frac{\partial T}{\partial x}$$
External heat exchange with the environment includes both convective and radiative components. Convective heat transfer is expressed by Newton’s law of cooling:
$$Q = hA(T_s – T_f)$$
Radiative heat transfer follows the Stefan-Boltzmann law:
$$Q = \varepsilon\sigma AT^4$$
Effective thermal management of traction battery packs requires optimization of all these heat transfer pathways to maintain uniform and safe operating temperatures.
3.4 Heat Pipe Operating Principles
Heat pipes are passive heat transfer devices that operate on the principles of phase-change heat transfer and capillary action. A typical heat pipe consists of three sections: an evaporator section, an adiabatic section, and a condenser section. The internal structure includes a sealed metallic enclosure, a wick structure, and a small quantity of working fluid.
The operating cycle proceeds as follows: when the evaporator section is heated by the traction battery cells, the working fluid within the wick structure evaporates, absorbing the latent heat of vaporization. The vapor, carrying the thermal energy, travels through the adiabatic section toward the condenser section due to the pressure differential created by the temperature difference. In the condenser section, the vapor releases its latent heat and condenses back to liquid form. The condensed liquid returns to the evaporator section through capillary action in the wick structure. This continuous evaporation-transport-condensation cycle enables remarkably efficient heat transfer with minimal temperature gradients.
For numerical simulation purposes, heat pipes can be treated as solid materials with extremely high effective thermal conductivity. Based on validated literature values, this study adopts an effective thermal conductivity of 5000 W/(m·K) for the heat pipe numerical model, representing a significant enhancement over conventional metallic conductors used in traction battery thermal management.
4. Numerical Modeling of Prismatic LiFePO₄ Battery Packs
4.1 Geometric Model Specifications
This study employs a prismatic LiFePO₄ battery with specifications of 3.2V/180Ah. The cell dimensions are 207 mm (height) × 174 mm (length) × 72 mm (width). The traction battery module configuration consists of 24 cells arranged in a 3×8 array with a 1P24S (1 parallel, 24 series) electrical connection scheme. The geometric model is developed using SpaceClaim CAD software, with simplifications applied to the actual cell features, including the removal of fillets, terminal connections, and module mounting frames. The simplified model retains the essential components: cell bodies, positive and negative terminal posts, and busbars for electrical interconnection.
4.2 NTGK Electrochemical Model
The battery thermal behavior is simulated using the NTGK (Newman-Thermal-Governing-Kinetics) electrochemical model, implemented through the Multi-Scale Multi-Domain (MSMD) solution method within ANSYS Fluent. The NTGK model couples electrochemical kinetics with thermal physics to accurately predict heat generation and temperature distribution within traction battery cells.
The energy conservation equation governing the temperature field is:
$$\frac{\partial(\rho h_e)}{\partial t} + \nabla \cdot (V \cdot \rho \cdot h_e) = \nabla(k \cdot \nabla T) + S_h$$
The volumetric current transfer rate, describing the rate of charge transfer in the electrochemical reactions, is expressed as:
$$J_{ech} = Y\left[U – (\phi_+ – \phi_-)\right]$$
where parameters \(U\) and \(Y\) are functions of depth of discharge (DOD) and temperature:
$$U = \sum_{n=0}^{5} a_n \times (DOD)^n$$
$$Y = \sum_{n=0}^{5} b_n \times (DOD)^n$$
The DOD is calculated as:
$$DOD = \frac{vol}{3600 \times Q_{ah}} \times I \cdot dt$$
The electrochemical heat generation is expressed as:
$$Q_{ech} = J_{ech}\left[(\phi_+ – \phi_-) – T\frac{\partial U}{\partial T}\right]$$
Key physical property parameters used in the battery thermal model are presented in Table 5.
| Parameter | Value |
|---|---|
| Cell Chemistry | LiFePO₄ / Graphite |
| Cell Dimensions (mm) | 207×174×72 |
| Nominal Capacity (Ah) | 180 |
| Nominal Voltage (V) | 3.22 |
| Density (kg/m³) | 2248 |
| Specific Heat [J/(kg·K)] | 850 |
| Thermal Conductivity (H/L/W) [W/(m·K)] | 15/15/1 |
| Maximum Discharge Rate | 3C |
| Operating Temperature Range | -34°C to 65°C |
| Contact Resistance | Neglected |
The simulation setup includes transient-state analysis with 180 time steps at 20-second intervals, totaling 3600 seconds for a complete 1C discharge cycle. The ambient temperature is set to 298K, with a natural convection heat transfer coefficient of 5 W/(m²·K) applied to the battery pack external surfaces. The initial temperature condition is:
$$t=0, \quad T(x, y, z) = T_0 = 298K$$
The adiabatic boundary condition is expressed as:
$$-k_b\frac{\partial T}{\partial y} = 0$$
4.3 Mesh Independence Verification
Grid independence verification is essential to ensure numerical accuracy while maintaining reasonable computational costs. Eight different mesh configurations were evaluated, ranging from 5.14×10⁵ to 1.21×10⁸ elements. The verification utilized two key metrics: maximum battery temperature and pressure drop across the cooling channels. Table 6 presents the mesh independence study results in summary form.
| Mesh Number | Max Temperature (K) | Temperture Change (%) | Pressure Drop (Pa) | Pressure Change (%) |
|---|---|---|---|---|
| 5.14×10⁵ | 330.59 | — | 394.51 | — |
| 7.06×10⁵ | 337.19 | 1.96% | 405.86 | 2.80% |
| 1.44×10⁶ | 327.46 | -2.97% | 416.45 | 2.61% |
| 2.15×10⁶ | 327.49 | 0.01% | 406.74 | -2.33% |
| 3.81×10⁶ | 326.33 | -0.35% | 412.33 | 1.37% |
| 7.67×10⁶ | 323.61 | -0.85% | 411.16 | -0.28% |
| 2.11×10⁷ | 321.72 | -0.59% | 400.41 | -2.62% |
| 1.21×10⁸ | 321.46 | -0.08% | 400.37 | -0.01% |
Analysis of the mesh independence results confirms that when the mesh count reaches 2.11×10⁷, the maximum temperature variation drops below 0.08%, and the pressure variation remains within 0.01%, both satisfying grid independence criteria. Therefore, a mesh count of 2.11×10⁷ is selected for subsequent simulations as the optimal balance between computational accuracy and efficiency.
4.4 Model Validation
Experimental validation was conducted to ensure the reliability and accuracy of the numerical model. The model was validated using conditions consistent with published experiments on a prismatic LiFePO₄ battery system under liquid cooling. The validation utilized a water-cooled flat tube configuration under 1C discharge conditions with a water flow rate of 0.5 L/min and an inlet temperature of 20°C.
| Metric | Experimental Value (°C) | Simulation Value (°C) | Error (%) |
|---|---|---|---|
| Battery Temperature at 1C | 36.31 | 36.72 | 1.13% |
| Coolant Temperature Rise | 32.37 | 33.02 | 2.01% |
The maximum error between the numerical simulation and experimental results is 2.01%, confirming that the numerical model developed in this study accurately captures the thermal behavior of prismatic LiFePO₄ cells in a traction battery cooling system. This error level is well within acceptable ranges for engineering analysis purposes.
5. Cooling System Design for Traction Battery Packs
5.1 System Architecture
Based on the comprehensive analysis of various cooling technologies for traction battery thermal management, this study proposes a liquid cooling system coupled with heat pipes to achieve enhanced heat dissipation performance. The system architecture is schematically illustrated in Figure 5, showing the strategic placement of components within the traction battery module.
The thermal management architecture for traction battery packs consists of three key elements: prismatic LiFePO₄ battery cells, L-shaped heat pipes, and liquid cooling flow channels. The heat pipes, each with a thickness of 5mm and width of 20mm, are designed with L-shaped geometry—the long section corresponds to the cell width (207mm), and the short section corresponds to the cell depth (174mm). Two heat pipes are assigned to each battery cell in a staggered arrangement to maximize internal heat extraction from the traction battery module.
The heat pipe evaporator section interfaces directly with the battery cell surfaces. The condenser section is embedded within and contacts the liquid cooling plate. The heat transfer chain from traction battery cells to ambient can be represented as follows:
Battery internal heat \(\rightarrow\) Heat pipe evaporation \(\rightarrow\) Heat transport through adiabatic section \(\rightarrow\) Heat pipe condensation \(\rightarrow\) Cooling plate conduction \(\rightarrow\) Coolant convection \(\rightarrow\) Ambient
The heat pipe in this study is modeled as a solid structure with a very high effective thermal conductivity value of 5000 W/(m·K), as validated in literature. This simplified approach captures the fundamental thermal behavior of heat pipes as heat super-conductors for traction battery thermal management.
5.2 Coolant Selection and Flow Characteristics
The coolant selected for the liquid cooling system is a 50% ethylene glycol-water solution for traction battery thermal management. This concentration provides an optimal balance between freezing point depression and thermal performance. At this concentration, the freezing point is -33.8°C and the boiling point is 107.2°C, providing a broad operating temperature window suitable for traction battery applications across various climatic conditions.
| Material | Density (kg/m³) | Specific Heat [J/(kg·K)] | Thermal Conductivity [W/(m·K)] | Dynamic Viscosity (Pa·s) |
|---|---|---|---|---|
| 50% Ethylene Glycol Solution | 1069 | 3494 | 0.419 | 0.00315 |
| Aluminum (Cooling Plate) | 2702 | 903 | 237 | — |
| Copper (Busbar) | 8978 | 381 | 387.6 | — |
| Aluminum (Terminals) | 2719 | 871 | 202.4 | — |
For the fluid flow assessment in the liquid cooling structure, the Reynolds number is calculated to characterize the flow regime. The Reynolds number equation for round-tube channels is adapted as follows:
$$Re = \frac{\rho_w v_w \cdot 2ab}{\mu(a+b)}$$
where \(\rho_w\) is the coolant density, \(v_w\) is the flow velocity, \(\mu\) is the dynamic viscosity, and \(a\), \(b\) are the dimensions of the channel cross-section. In our case, the maximum coolant velocity studied is 0.6 m/s, which yields a maximum Reynolds number of 1364.25—well below the turbulent transition threshold of 2300. The flow is therefore classified as laminar for all tested conditions in the liquid cooling system of the traction battery module.
5.3 Governing Equations for Fluid Flow
The fluid flow and heat transfer in the liquid cooling system must satisfy the fundamental conservation laws: conservation of mass, momentum, and energy.
Mass Conservation (Continuity Equation):
$$\frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \vec{u}) = 0$$
Momentum Conservation:
$$\frac{\partial (\rho \vec{u})}{\partial t} + \nabla \cdot (\rho \vec{u}\vec{u}) = -\nabla p + \nabla \cdot \tau + \rho \vec{F}_i$$
Energy Conservation:
$$\frac{\partial (\rho e)}{\partial t} + \nabla \cdot [\rho \vec{u}(e + \frac{1}{2}u^2)] = -\nabla \cdot (k\nabla T) + \Phi + Q$$
where \(\Phi\) represents the viscous dissipation function, and \(Q\) is the volumetric heat source term representing heat generation from the traction battery cells.
5.4 Heat Transfer Modeling
The coupled heat transfer in the traction battery cooling system involves conjugate heat transfer between the battery cell, heat pipes, cold plates, and coolant. The governing equation for solid heat conduction regions is:
$$\frac{\partial (\rho_s c_{p,s} T)}{\partial t} = \nabla \cdot (k_s \nabla T) + S_h$$
The boundary conditions for the coupled simulation are set as follows. The initial condition for all regions is set to the ambient temperature:
$$T(x, y, z, 0) = T_0 = 298K$$
At the interface between the battery cell and heat pipe surfaces, perfect thermal contact is assumed:
$$-k_b\frac{\partial T}{\partial n} = -k_s\frac{\partial T}{\partial n}$$
The heat transfer from the cooling plate surface to the coolant follows:
$$h_c(T_w – T_f) = -k_s\frac{\partial T}{\partial n}$$
A constant heat transfer coefficient is imposed at the outer boundaries of the traction battery pack to represent natural convection with ambient air at 5 W/(m²·K).
6. Performance Analysis of Traditional Flow Channel Configurations
6.1 Parallel Flow Channel Configuration
The parallel flow channel design distributes coolant through multiple parallel straight channels beneath the heat pipe condenser sections. This configuration offers advantages in terms of low flow resistance and simple manufacturing. The following analysis examines the performance of the parallel flow channel layout in the traction battery thermal management system.
Table 9 presents the numerical simulation results for the cooling system with and without coupling heat pipes at various coolant velocities for the traction battery pack.
| Velocity (m/s) | Without Heat Pipe | With Heat Pipe | ||
|---|---|---|---|---|
| Max Temp (K) | ΔT (K) | Max Temp (K) | ΔT (K) | |
| 0.1 | 323.30 | 3.68 | 317.14 | 1.87 |
| 0.2 | 322.33 | 3.77 | 315.04 | 1.63 |
| 0.3 | 321.91 | 3.93 | 314.98 | 3.77 |
| 0.4 | 321.63 | 4.09 | 314.28 | 3.67 |
| 0.5 | 321.41 | 4.12 | 312.13 | 2.38 |
| 0.6 | 321.25 | 4.19 | 313.49 | 3.64 |
The simulation results reveal several important performance characteristics of the parallel flow channel cooling system for traction battery thermal management:
First, in the flowing coolant system without heat pipes, increasing the velocity from 0.1 m/s to 0.6 m/s causes the pressure drop to rise dramatically from 20.15 Pa to 585.01 Pa. While simultaneously reducing the maximum battery temperature from 323.30 K to 321.25 K. However, the temperature difference within the traction battery pack degrades from 3.68 K to 4.19 K, indicating that higher flow rates create a more non-uniform temperature field across the battery surfaces.
Second, after integrating heat pipes into the liquid cooling system, at the coolant velocity of 0.5 m/s, the maximum temperature shows a remarkable reduction from 321.41 K to 312.13 K (a drop of 9.28 K). Additionally, the best temperature uniformity is achieved at 0.2 m/s with a temperature difference of only 1.63 K, demonstrating that heat pipes effectively redistribute and extract the heat from within the traction battery cells to enhance overall thermal uniformity.
6.2 Effect of Inlet Temperature on Parallel Flow Channel Performance
The coolant inlet temperature serves as another critical operational parameter affecting traction battery thermal management in liquid cooling systems. Table 10 summarizes the modeling results for different coolant inlet temperatures at a fixed velocity of 0.5 m/s.
| Inlet Temperature (K) | Without HP | With HP | ||
|---|---|---|---|---|
| Max Temp (K) | Temperature Difference (K) | Max Temp (K) | ΔT (K) | |
| 298 | 321.41 | 4.12 | 313.49 | 3.64 |
| 293 | 320.40 | 7.53 | 308.95 | 2.48 |
| 288 | 318.26 | 7.77 | 305.80 | 2.53 |
| 283 | 316.00 | 7.81 | 304.10 | 3.58 |
| 278 | 313.71 | 7.25 | 300.88 | 3.38 |
These results demonstrate that when the coolant inlet temperature is reduced from 298 K to 278 K, in the system without heat pipes, the maximum battery temperature decreases from 321.41 K to 313.71 K. However, the temperature difference within the traction battery pack expands noticeably from 4.12 K to about 7.25 K due to the increased temperature gradient at the entrance region of the cells.
After adding heat pipes to the liquid cooling structure, the maximum temperature of the traction battery module is reduced by 11 to 13 K under identical inlet temperature settings. The temperature difference is simultaneously suppressed to less than 3.6 K, confirming that the heat pipe integration improves both the heat dissipation performance and thermal uniformity of the liquid cooling architecture.
6.3 S-shaped Flow Channel Configuration
The S-shaped (serpentine) flow channel configuration increases the coolant flow path length and introduces multiple directional changes, enhancing turbulent mixing and heat transfer. Table 11 gives the simulation results for this configuration in a traction battery module for different flow velocities.
| Velocity (m/s) | Without Heat Pipe | With Heat Pipe | ||
|---|---|---|---|---|
| Max Temp (K) | ΔT (K) | Max Temp (K) | ΔT (K) | |
| 0.1 | 323.29 | 4.82 | 316.04 | 2.10 |
| 0.2 | 322.09 | 4.98 | 314.03 | 3.78 |
| 0.3 | 321.57 | 5.06 | 313.08 | 3.70 |
| 0.4 | 321.27 | 5.11 | 312.54 | 3.65 |
| 0.5 | 321.07 | 5.15 | 312.20 | 3.64 |
| 0.6 | 320.93 | 5.17 | 311.96 | 3.62 |
The S-shaped flow channel configuration exhibits significantly higher pressure drops compared to the parallel flow channel design. The pressure drop increases dramatically from 223.75 Pa at 0.1 m/s to 8874.06 Pa at 0.6 m/s. This substantial pressure increase introduces a significant parasitic power burden on the cooling system. The heat pipe coupling with the S-shaped flow channel achieves a maximum temperature reduction of up to 8–9 K across the range of flow velocities tested.
The following table summarizes the pressure drop values for the two classic flow configurations when the coolant is driven at different velocities in the traction battery cooling structure:
| Velocity (m/s) | Parallel Channel ΔP (Pa) | S-shaped Channel ΔP (Pa) |
|---|---|---|
| 0.1 | 20.15 | 223.75 |
| 0.2 | 71.31 | 942.64 |
| 0.3 | 149.08 | 2174.33 |
| 0.4 | 262.60 | 3945.49 |
| 0.5 | 418.50 | 6054.63 |
| 0.6 | 585.01 | 8874.07 |
The detailed analysis of heat pipe coupling with liquid cooling in these configurations confirms that the temperature of the traction battery pack can be effectively regulated by altering coolant velocity or inlet temperature. However, the S-shaped flow path suffers from excessive pressure drops, while the parallel flow configuration shows limited heat transfer enhancement. This trade-off motivates the development of the novel series-parallel flow channel design described in the following sections.
7. Design and Multi-Objective Optimization of Series-Parallel Flow Channels
7.1 Design Concept
Based on the comparative analysis of the parallel and S-shaped flow configurations presented in the preceding section, a novel series-parallel flow channel design is proposed. The design philosophy is to combine the advantages of both configurations: extending the coolant path over the heat pipe condenser sections to maximize heat extraction, while simultaneously maintaining a moderate pressure drop to avoid excessive energy consumption in the pumping system. The resulting design achieves the efficient utilization of the heat pipe condensation segments while reducing the total hydraulic resistance below the level of the S-shaped architecture.
In this innovative series-parallel flow channel layout, the coolant passes through a series arrangement of branch flow channels connected in a sequence that forms a combined overall flow path. Each branch channel contacts a section of the heat pipe condenser, allowing improved thermal communication between the coolant and the heat pipe system. The flow paths of coolant through the series-parallel layout achieve an effective balance between heat transfer area, flow resistance, and temperature uniformity across the traction battery module.
7.2 Determination of Optimal Operating Parameters
Before the channel structure optimization, the optimal operating parameters (coolant inlet velocity and inlet temperature) are first identified using a control-variable approach to isolate the effects of the channel-structure parameters from the operating-condition variables.
Selection of coolant inlet velocity. A parametric sweep of coolant velocity from 0.1 m/s to 0.6 m/s is conducted for the series-parallel channel structure. The thermal and hydraulic results of the coupled system are summarized below:
| Velocity (m/s) | Temperature Difference (K) | Max Temperature (K) | Pressure Drop (Pa) |
|---|---|---|---|
| 0.1 | 4.89 | 321.36 | 111.78 |
| 0.2 | 6.93 | 319.61 | 481.07 |
| 0.3 | 6.86 | 318.53 | 1106.89 |
| 0.4 | 6.81 | 317.90 | 1995.40 |
| 0.5 | 6.78 | 317.21 | 3165.14 |
| 0.6 | 6.77 | 317.50 | 4582.90 |
From these results, the minimum battery maximum temperature of 317.21 K is achieved at a coolant velocity of 0.5 m/s. Increasing the velocity beyond this point to 0.6 m/s yields a slightly higher maximum temperature because the shorter residence time of the coolant in the heat transfer zone reduces thermal exchange effectiveness despite the larger mass flow. Meanwhile, the pressure drop continues to grow rapidly at higher flow velocities. Therefore, 0.5 m/s is identified as the preferred operating flow velocity for the series-parallel channel configuration.
Selection of coolant inlet temperature. With the velocity fixed at 0.5 m/s, the inlet temperature is varied from 298 K down to 278 K to evaluate the influence of the inlet temperature on the maximum temperature and temperature uniformity of the traction battery.
| Inlet Temperature (K) | Max Temperature (K) | Temperature Difference (K) |
|---|---|---|
| 298 | 317.50 | 6.78 |
| 293 | 313.85 | 6.68 |
| 288 | 310.21 | 6.24 |
| 283 | 306.58 | 6.51 |
| 278 | 303.65 | 7.52 |
The minimum temperature difference of 6.24 K is achieved when the inlet temperature equals 288 K. Although decreasing the inlet temperature to 278 K further reduces the absolute maximum temperature of the traction battery pack, the temperature uniformity is degraded. Consequently, 288 K is selected as the appropriate coolant inlet temperature that provides the best temperature uniformity while maintaining adequate cooling capability.
7.3 Taguchi Experimental Design
The Taguchi experimental design method provides a structured approach to investigate the influence of multiple design parameters on the system performance of traction battery cooling while minimizing the total number of experiments or simulations required. This method uses orthogonal arrays to systematically vary design factors at different levels and statistically analyzes the resulting signal-to-noise (S/N) ratios to identify optimal parameter settings.
Figure 6 and the values listed in Table 15 illustrate the four geometric design parameters considered for the series-parallel flow channel: number of branch channels (N), branch channel width (D1), branch channel spacing (D2), and channel thickness (D3).
| Level | N (Number of Branch Channels) | D1 (Width, mm) | D2 (Spacing, mm) | D3 (Thickness, mm) |
|---|---|---|---|---|
| 1 | 2 | 15 | 30 | 2 |
| 2 | 3 | 20 | 36 | 3 |
| 3 | — | 25 | 44 | 4 |
| 4 | — | 30 | 50 | 5 |
To accommodate one factor at two levels and three factors at four levels, the mixed-level orthogonal array L32 (2¹ × 4³) is constructed, yielding 32 distinct configurations for numerical simulation. Each configuration is modeled, meshed, and solved. The simulation output includes the maximum battery temperature, battery temperature difference, and pressure drop, as summarized in Table 16:
| Run | N | D1 (mm) | D2 (mm) | D3 (mm) | T_max (K) | ΔT (K) | ΔP (Pa) |
|---|---|---|---|---|---|---|---|
| 1 | 2 | 15 | 30 | 2 | 308.04 | 4.42 | 3150.66 |
| 2 | 2 | 15 | 36 | 3 | 306.25 | 3.57 | 3159.78 |
| 3 | 2 | 15 | 44 | 4 | 305.47 | 3.31 | 3719.57 |
| 4 | 2 | 15 | 50 | 5 | 305.25 | 3.23 | 3603.73 |
| 5 | 2 | 20 | 30 | 2 | 309.48 | 5.28 | 2933.53 |
| 6 | 2 | 20 | 36 | 3 | 306.09 | 3.48 | 3152.66 |
| 7 | 2 | 20 | 44 | 4 | 306.30 | 3.93 | 3105.48 |
| 8 | 2 | 20 | 50 | 5 | 305.69 | 3.69 | 2746.01 |
| 9 | 2 | 25 | 30 | 3 | 307.81 | 4.28 | 2548.24 |
| 10 | 2 | 25 | 36 | 2 | 312.28 | 6.93 | 2179.57 |
| 11 | 2 | 25 | 44 | 5 | 310.08 | 4.20 | 2678.60 |
| 12 | 2 | 25 | 50 | 4 | 305.33 | 3.23 | 1962.44 |
| 13 | 2 | 30 | 30 | 3 | 306.08 | 3.32 | 2661.06 |
| 14 | 2 | 30 | 36 | 2 | 305.95 | 3.36 | 2390.11 |
| 15 | 2 | 30 | 44 | 5 | 307.86 | 4.11 | 2376.79 |
| 16 | 2 | 30 | 50 | 4 | 306.06 | 3.77 | 927.75 |
| 17 | 3 | 15 | 30 | 5 | 307.21 | 3.76 | 2912.72 |
| 18 | 3 | 15 | 36 | 4 | 306.04 | 4.33 | 2786.14 |
| 19 | 3 | 15 | 44 | 3 | 305.42 | 3.48 | 2390.25 |
| 20 | 3 | 15 | 50 | 2 | 306.46 | 3.90 | 1665.56 |
| 21 | 3 | 20 | 30 | 5 | 308.55 | 4.43 | 2910.49 |
| 22 | 3 | 20 | 36 | 4 | 305.57 | 3.85 | 2633.19 |
| 23 | 3 | 20 | 44 | 3 | 305.69 | 3.58 | 1968.11 |
| 24 | 3 | 20 | 50 | 2 | 307.32 | 4.02 | 939.55 |
| 25 | 3 | 25 | 30 | 4 | 309.21 | 4.09 | 2795.90 |
| 26 | 3 | 25 | 36 | 5 | 305.40 | 3.13 | 2440.17 |
| 27 | 3 | 25 | 44 | 2 | 306.70 | 4.73 | 854.02 |
| 28 | 3 | 25 | 50 | 3 | 309.07 | 4.00 | 606.99 |
| 29 | 3 | 30 | 30 | 4 | 308.51 | 4.06 | 2309.17 |
| 30 | 3 | 30 | 36 | 5 | 305.71 | 3.37 | 828.45 |
| 31 | 3 | 30 | 44 | 2 | 308.09 | 4.77 | 694.73 |
| 32 | 3 | 30 | 50 | 3 | 310.08 | 4.60 | 590.94 |
From the 32 simulation results shown in the table, the geometric configuration affects the maximum traction battery temperature only weakly (a total variation of about 1.5% across all runs), while the temperature difference changes by approximately 27% and the pressure drop varies by more than 84%. This indicates that the main optimization opportunities for the series-parallel structure reside in the minimization of both the thermal non-uniformity and the hydraulic resistance.
7.4 Signal-to-Noise Ratio Analysis for Single Targets
Using the Taguchi method, a signal-to-noise (S/N) ratio analysis with the smaller-is-better characteristic is applied for both the battery temperature difference and the coolant pressure drop. The S/N ratio is calculated as:
$$SNR = -10\log_{10}\left[\frac{1}{n}\sum_{i=1}^{n} y_i^2\right]$$
where \(y_i\) is the measured response of the i-th experimental trial.
The S/N response tables for both optimization targets, respectively, are obtained:
| Optimization Target | Level | N (Branch Count) | D1 (Width, mm) | D2 (Spacing, mm) | D3 (Thickness, mm) |
|---|---|---|---|---|---|
| ΔT (Battery Temperature Difference) | 1 | -16.26 | -16.29 | -16.49 | -17.03 |
| 2 | -16.50 | -16.49 | -16.50 | -16.22 | |
| 3 | — | -16.34 | -16.32 | -15.83 | |
| 4 | — | -16.38 | -16.20 | -16.43 | |
| Range | 0.24 | 0.20 | 0.30 | 1.20 | |
| ΔP (Pressure Drop) | 1 | -68.29 | -69.09 | -68.84 | -64.13 |
| 2 | -63.88 | -67.62 | -67.22 | -65.14 | |
| 3 | — | -65.03 | -65.78 | -67.50 | |
| 4 | — | -62.06 | -62.51 | -67.58 | |
| Range | 4.41 | 6.48 | 6.33 | 3.46 |
The S/N analysis indicates that the channel thickness D3 has the most significant influence on the temperature difference, with a range of 1.20, while the branch channel width D1 has the largest influence on the pressure drop, with a range of 6.48. When the optimization targets are treated independently, minimizing the temperature difference suggests selecting D1=15 mm, D2=50 mm, D3=4 mm with N=2, whereas minimizing the pressure drop suggests selecting D1=30 mm, D2=50 mm, D3=2 mm with N=3. These conflicting recommendations confirm the need for a multi-objective formulation that trades off the two quality targets.
7.5 Grey Relational Multi-Quality Analysis
To reconcile the conflicting requirements of the temperature uniformity and hydraulic resistance inside the traction battery liquid cooling system, grey relational analysis is implemented as a multi-objective optimization technique. This approach normalizes the multiple quality attributes and computes a composite grey relational grade representing the overall closeness of each candidate design to an ideal reference.
The grey relational analysis proceeds through the following steps:
Step 1: Establish the reference sequence. For smaller-is-better quality characteristics, the reference sequence Y is set as the minimum values observed among all experiments:
$$Y = \{y_1^{min}, y_2^{min}\} = \{3.13, 590.99\}$$
Step 2: Normalize the experimental sequences. The original sequence X is normalized to eliminate dimensional differences among the various design factors and quality attributes. The normalized comparison sequence for the smaller-is-better criterion is obtained by:
$$x_i^*(k) = \frac{\max\{x_i(k)\} – x_i(k)}{\max\{x_i(k)\} – \min\{x_i(k)\}}$$
Step 3: Compute the grey relational coefficient. The grey relational coefficient for each trial is calculated as follows:
$$\gamma_i(k) = \frac{\Delta_{min} + \zeta \Delta_{max}}{\Delta_i(k) + \zeta \Delta_{max}}$$
where \(\Delta_i(k) = |y^*(k) – x_i^*(k)|\) is the absolute difference between the reference and comparison sequences, \(\Delta_{max}\) and \(\Delta_{min}\) are respectively the maximum and minimum absolute differences across all trials, and the distinguishing coefficient \(\zeta\) is typically set to 0.5.
Step 4: Calculate the grey relational grade. The grey relational grade for the two quality targets—temperature difference and pressure drop—is aggregated as:
$$\gamma_i = \sqrt{\frac{\gamma_{i,\Delta T}^2 + \gamma_{i,\Delta P}^2}{2}}$$
This composite grade provides a single dimensionless index that quantifies the overall desirability of each candidate flow-channel configuration. A higher grey relational grade indicates better simultaneous attainment of both low temperature difference and low pressure drop in the traction battery cooling system.
The computed grey relational coefficients for the 32 trial configurations are:
| Run | γ | Run | γ | Run | γ | Run | γ |
|---|---|---|---|---|---|---|---|
| 1 | 0.52 | 9 | 0.71 | 17 | 0.66 | 25 | 0.84 |
| 2 | 0.57 | 10 | 0.59 | 18 | 0.69 | 26 | 0.72 |
| 3 | 0.56 | 11 | 0.59 | 19 | 0.70 | 27 | 0.71 |
| 4 | 0.51 | 12 | 0.68 | 20 | 0.64 | 28 | 0.82 |
| 5 | 0.56 | 13 | 0.70 | 21 | 0.69 | 29 | 0.82 |
| 6 | 0.60 | 14 | 0.58 | 22 | 0.72 | 30 | 0.71 |
| 7 | 0.59 | 15 | 0.58 | 23 | 0.73 | 31 | 0.71 |
| 8 | 0.54 | 16 | 0.68 | 24 | 0.67 | 32 | 0.83 |
Table 19 lists the average grey relational grades for each design factor at its different levels, revealing the level of each factor that yields the optimal overall performance. The grey relational grade response table is as follows:
| Level | N (Number of Branch Channels) | D1 (Width, mm) | D2 (Spacing, mm) | D3 (Thickness, mm) |
|---|---|---|---|---|
| 1 | 0.500 | 0.428 | 0.777 | 0.453 |
| 2 | 1.000 | 0.566 | 0.586 | 0.814 |
| 3 | — | 0.850 | 0.598 | 0.791 |
| 4 | — | 0.834 | 0.745 | 0.468 |
From the grey relational analysis, the parameter ranking according to influence on the overall multi-objective grade is: N (number of branch channels) > D1 (branch width) > D3 (thickness) > D2 (spacing). The combination that yields the maximum grey relational coefficient corresponds to 3 branch channels (N=3), a branch width D1 of 25 mm, a spacing D2 of 30 mm, and a flow channel thickness D3 of 3 mm.
8. Verification and Performance Evaluation of the Optimized Cooling Structure
8.1 Numerical Validation of Optimized Series-Parallel Channels
Based on the multi-objective grey relational analysis, the optimum set of design parameters is obtained for the series-parallel flow channel. The geometry is reconstructed with these parameter values and evaluated numerically at the selected operating conditions of 0.5 m/s coolant velocity and 288 K inlet temperature. The simulated temperature field of the optimized channel design shows a substantially improved temperature distribution across the surfaces of the traction battery pack.
The temperature field visualization clearly illustrates that the coolant within the series-parallel channel extracts heat effectively and uniformly through the heat pipe array while maintaining a modest pressure load on the pumping system. The temperature at the coolant entry regions remains low, and the battery surface temperature distribution is far more uniform than observed in the S-shaped channel, confirming the benefits of the proposed layout.
8.2 Performance Comparison Before and After Optimization
Table 20 shows the numerical results comparing the traction battery cooling performance between the initial series-parallel channel design and the optimized design:
| Metric | Initial Design | Optimized Design | Improvement |
|---|---|---|---|
| Maximum Temperature (K) | 305.56 | 303.22 | 2.33 K reduction |
| Temperature Difference (K) | 3.45 | 3.24 | 6.10% reduction |
| Pressure Drop (Pa) | 3165.14 | 1956.16 | 38.20% reduction |
The optimized series-parallel flow channel configuration achieves simultaneous improvements in both thermal and hydraulic performance. The maximum battery temperature is reduced by 2.33 K, the temperature difference across the traction battery pack decreases by 6.10%, and the coolant pressure drop is reduced by as much as 38.20%. This outcome demonstrates that the multi-objective optimization approach is effective for achieving a sound balance between heat transfer enhancement and energy consumption reduction in the traction battery cooling circuit.
8.3 Comparative Benchmarking Against Traditional Channel Configurations
To fully appreciate the advantages of the proposed optimized design, the performance of the series-parallel channel with the integrated heat pipes is benchmarked against the basic parallel and S-shaped configurations coupled with the heat-pipe technology. Table 21 provides the results for the different cooling structures in the traction battery pack:
| Flow Channel Configuration | Maximum Temperature (K) | Temperature Difference (K) | Pressure Drop (Pa) |
|---|---|---|---|
| Parallel Channel | 305.80 | 2.53 | 6054.63 |
| S-shaped Channel | 305.05 | 3.48 | 289.74 |
| Series-Parallel (Initial) | 305.56 | 3.45 | 3165.14 |
| Series-Parallel (Optimized) | 303.22 | 3.24 | 1956.16 |
The general comparison shows that relative to the parallel flow channel, the optimized series-parallel channel arrangement lowers the maximum traction battery temperature by 2.58 K. Compared with the S-shaped channel, the temperature difference is reduced by approximately 6.94%, while the pressure drop is drastically lowered by 67.69% relative to the S-shaped configuration. This confirms that the innovative series-parallel design attains both the enhanced heat-transfer capability of the S-shaped channel and the low-flow-resistance advantage of the parallel channel arrangement.
8.4 Heat Generation Comparison
To visualize the overall thermal benefit of the optimized cooling design relative to the natural heat generation condition, the temperature evolution of the traction battery module during a complete discharge cycle was compared with the baseline model (battery pack without an active cooling system). Since the baseline battery pack temperature reaches roughly 325 K at the end of the discharge, whereas the optimized liquid-cooled heat-pipe coupled pack temperature rises to a maximum of only 303.22 K, the optimized cooling system successfully lowers the peak traction battery temperature by about 21.78 K during the nominal 1C discharge process.
This comparison underscores the critical importance of implementing a robust thermal management architecture for traction battery systems, especially as fast charging requirements push traction battery packs toward higher heat generation rates in modern electric vehicles.
9. Conclusions and Outlook
9.1 Main Conclusions
This study systematically investigated the thermal performance of prismatic LiFePO₄ traction battery systems equipped with a hybrid liquid cooling and heat pipe thermal management architecture. Through extensive numerical modeling, parametric analysis, and multi-objective structural optimization, the following conclusions are drawn:
(1) Modeling and simulation framework. A validated NTGK electrochemical-thermal model was developed that can faithfully reproduce the heat generation behavior of prismatic LiFePO₄ traction battery cells. The numerical model was confirmed to predict experimental data with an error below 2.01%, providing a reliable simulation platform for traction battery thermal analysis.
(2) Heat-pipe coupling strongly enhances basic flow-channel cooling performance. Under identical testing conditions, the coupling of heat pipes with the liquid-cooling system significantly lowered the maximum temperature of the battery module when compared with a stand-alone liquid cooling system. For the parallel flow channel, the average temperature reduction achieved by coupling heat pipes was about 7.5 K for velocity conditions and 11.5 K for inlet-temperature conditions. For the S-shaped channel, the heat-pipe coupling achieved average temperature reductions of around 8.5 K under flow-velocity sweeps and approximately 12 K under inlet-temperature sweeps.
(3) Novel series-parallel flow-channel design. The series-parallel design successfully balances the hydraulic and thermal demands of the traction battery liquid-cooling system. A Taguchi L32 experimental matrix was developed, followed by grey relational multi-quality analysis of the structural factors N, D1, D2, and D3.
Grey relational analysis identified that the structural parameters rank in terms of the influence on overall performance as: N (number of branch channels), then D1 (branch channel width), D3 (channel thickness), and finally D2 (branch spacing). The optimal parameter combination is N=3, D1=25 mm, D2=30 mm, D3=3 mm.
(4) The optimized structure achieves simultaneous thermal and hydraulic improvements. The optimized series-parallel channel coupled with heat pipes achieves a maximum battery temperature of 303.22 K and a temperature difference of only 3.24 K while producing a pressure drop of 1956 Pa. Relative to the initial series-parallel design, this corresponds to a maximum temperature reduction of 2.33 K, temperature difference reduction of 6.10%, and pressure drop reduction of 38.20%. With respect to the original battery heat generation model, the test system lowers the maximum traction battery temperature by approximately 21.78 K.
(5) Overall performance comparisons with traditional alternates. The optimized series-parallel flow channel improves the maximum temperature by 2.58 K relative to the parallel channel, improves the temperature uniformity by 6.94% relative to the S-shaped channel, and at the same time reduces the pressure drop in the flow channel by 67.69%. These results confirm the effectiveness of the proposed heat-pipe-assisted series-parallel cooling system for traction battery applications, showing that it achieves a practical balance between battery thermal control and pumping energy consumption.
9.2 Future Research Directions
Although the present research has contributed to the design and optimization of traction battery liquid cooling systems, several limitations open avenues for further investigation:
(1) Experimental validation of the optimized flow channel. Future work should include constructing an experimental test bench for the series-parallel flow channel coupled with heat pipes, enabling empirical validation of the numerical predictions for traction battery modules under realistic driving conditions.
(2) Detailed heat pipe modeling. In this study, the heat pipe was represented as a solid with high effective conductivity. More advanced modeling approaches—including multiphase flow, the evaporation and condensation kinetics, and the influence of the wick structure—could provide more accurate design guidance for optimizing heat pipe geometry in the traction battery system.
(3) Higher discharge rates. The simulations were limited to 1C discharge conditions. With the emergence of fast-charging and high-discharge-rate applications, future research should investigate the thermal performance of this cooling architecture under 2C, 3C, or even higher C-rate operating conditions for traction battery packs.
(4) Pack-level integration. Future design should integrate the optimized cooling channels and heat pipes into a fully packaged traction battery system including structural supports, busbar connections, and battery management system components. This would provide a complete engineering validation of the thermal management concept under real vehicle constraints.
In summary, this research offers a systematic methodology and theoretical foundation for designing efficient liquid-cooled, heat pipe-assisted thermal management systems for prismatic LiFePO₄ traction battery modules in electric vehicles. Future improvements in heat-pipe design, multi-rate discharge capability, and full-scale pack integration will facilitate the safe and efficient deployment of next-generation traction battery systems.