In recent years, the rapid development of electric vehicles (EVs) has highlighted the critical need for efficient thermal management systems for their core component: the EV battery pack. As fossil fuels dwindle, EVs are becoming mainstream, but the lithium-ion batteries used in these vehicles generate significant heat during operation, posing safety risks and performance degradation. Thus, effective thermal management is essential to maintain the EV battery pack within optimal temperature ranges, ensuring longevity and safety. Among various cooling technologies, pulsating heat pipes (PHPs) have emerged as a promising solution due to their high thermal conductivity, compact size, and passive operation. In this study, we focus on the numerical investigation of an L-shaped pulsating heat pipe integrated into an EV battery pack, analyzing its heat transfer performance under different discharge rates. We aim to provide insights into optimizing thermal management for EV battery packs, leveraging computational fluid dynamics (CFD) simulations to model complex heat and fluid flow phenomena.
The EV battery pack is a complex assembly of multiple cells that generate heat during charging and discharging. This heat, if not dissipated efficiently, can lead to thermal runaway, reducing battery life and potentially causing fires. Traditional cooling methods, such as air or liquid cooling, often fall short in high-power scenarios, necessitating advanced solutions like pulsating heat pipes. PHPs utilize the phase change of a working fluid within a capillary tube to transfer heat passively, making them ideal for compact spaces like EV battery packs. Our research builds on existing studies to explore the L-shaped PHP configuration, which is designed to fit seamlessly into battery modules. We emphasize the importance of the EV battery pack’s thermal stability, as it directly impacts vehicle performance and safety. Through this numerical study, we seek to enhance the design and application of PHPs in EV battery packs, contributing to the broader goal of sustainable transportation.
Previous research on pulsating heat pipes has extensively covered their operational principles and performance factors. Since their invention by Akachi, PHPs have been studied for parameters such as tube diameter, working fluid, heating methods, inclination angle, and fill ratio. These studies reveal that PHPs can achieve efficient heat transfer through the self-sustained oscillation of vapor and liquid slugs, driven by pressure imbalances. However, applying PHPs to EV battery packs presents unique challenges, including non-uniform heat generation, space constraints, and dynamic operating conditions. Numerical simulations have become a vital tool for understanding PHP behavior, employing methods like the Volume of Fluid (VOF) model to track two-phase flow interfaces. In this context, we investigate the L-shaped PHP, which offers geometric flexibility for integration into EV battery packs. Our work adds to the literature by focusing on the specific heat transfer characteristics of L-shaped PHPs under battery-relevant conditions, aiming to optimize their performance for EV battery pack cooling.
We begin by analyzing the heat transfer characteristics of the L-shaped pulsating heat pipe based on existing experimental data. The fill ratio (RF) of the working fluid plays a crucial role in determining the thermal resistance of the PHP. For an EV battery pack, maintaining a low thermal resistance is essential to prevent overheating. Studies show that at a cooling water temperature of 298 K, the thermal resistance varies with RF and heat input. For instance, at RF = 7.1%, the thermal resistance is low for heat inputs below 15 W but increases at higher powers due to dry-out. Conversely, at RF = 10.6% and 14.1%, the thermal resistance drops rapidly as the PHP initiates, with efficient heat transfer via convection and conduction. Higher fill ratios like 17.7% and 21.2% lead to increased flow resistance, slowing down oscillations and reducing heat exchange. Thus, an optimal fill ratio around 10.6% minimizes thermal resistance, making it suitable for EV battery pack applications. This analysis informs our numerical model, where we assume an RF of 10.6% to achieve the best heat dissipation performance for the EV battery pack.
To simulate the heat transfer in the EV battery pack with an L-shaped PHP, we employ a mathematical model based on the VOF method. This model captures the two-phase flow dynamics of the working fluid within the PHP. The volume fractions for vapor and liquid phases, denoted as $\alpha_v$ and $\alpha_l$, respectively, satisfy the relation:
$$ \alpha_l + \alpha_v = 1 $$
The continuity equations for each phase are given by:
For vapor phase:
$$ \frac{\partial \alpha_v}{\partial t} + \nabla \cdot (\alpha_v \mathbf{v}) = \frac{S_{m,v}}{\rho_v} $$
For liquid phase:
$$ \frac{\partial \alpha_l}{\partial t} + \nabla \cdot (\alpha_l \mathbf{v}) = \frac{S_{m,l}}{\rho_l} $$
Here, $\rho_v$ and $\rho_l$ are the densities of vapor and liquid, $t$ is time, $\mathbf{v}$ is the velocity vector, and $S_m$ is the mass source term accounting for evaporation and condensation. The source terms are defined as:
$$ S_{m,v} = \begin{cases}
0.1 \alpha_l \rho_l \frac{T_{mix} – T_{sat}}{T_{sat}}, & T \geq T_{sat} \\
-0.1 \alpha_v \rho_v \frac{T_{mix} – T_{sat}}{T_{sat}}, & T < T_{sat}
\end{cases} $$
$$ S_{m,l} = \begin{cases}
-0.1 \alpha_l \rho_l \frac{T_{mix} – T_{sat}}{T_{sat}}, & T \geq T_{sat} \\
0.1 \alpha_v \rho_v \frac{T_{mix} – T_{sat}}{T_{sat}}, & T < T_{sat}
\end{cases} $$
where $T_{mix}$ is the mixture temperature, and $T_{sat}$ is the saturation temperature of the working fluid. These terms are implemented via user-defined functions (UDFs) in the simulation. The momentum equation for the two-phase flow is:
$$ \frac{\partial}{\partial t} (\rho \mathbf{v}) + \nabla \cdot (\rho \mathbf{v} \mathbf{v}) = -\nabla p + \nabla \cdot [\mu (\nabla \mathbf{v} + \nabla \mathbf{v}^T)] + \rho \mathbf{g} + \mathbf{F}_{CSF} $$
Here, $\rho$ and $\mu$ are the density and dynamic viscosity of the mixture, $p$ is pressure, $\mathbf{g}$ is gravity, and $\mathbf{F}_{CSF}$ is the surface tension force modeled as:
$$ \mathbf{F}_{CSF} = \sigma \frac{\alpha_l \rho_l C_v \nabla \alpha_v + \alpha_v \rho_v C_l \nabla \alpha_l}{0.5 (\rho_l + \rho_v)} $$
with $\sigma$ as the surface tension coefficient and $C_i$ as the contact angle. The thermal resistance of the PHP, a key metric for EV battery pack cooling, is calculated as:
$$ R_{th} = \frac{T_e – T_c}{Q} $$
where $R_{th}$ is the average thermal resistance, $T_e$ and $T_c$ are the average temperatures of the evaporation and condensation sections, and $Q$ is the heat input. This model allows us to numerically analyze the heat transfer performance of the L-shaped PHP within the EV battery pack under various operating conditions.
For the physical model, we consider a simplified EV battery pack consisting of seven prismatic lithium-ion cells arranged in parallel, each with dimensions of 200 mm × 130 mm × 37 mm. The cells are connected to a cooling plate measuring 360 mm × 150 mm × 20 mm, made of aluminum for uniform temperature distribution. The L-shaped PHP, modeled as a 3 mm diameter copper tube, is integrated between the cells and the cooling plate, with its evaporation section in close contact with the cells and the condensation section attached to the plate. This design ensures efficient heat extraction from the EV battery pack. We use SolidWorks to create the 3D geometry, which is then imported into ANSYS Fluent for meshing and simulation. The mesh is refined near the PHP and cell interfaces to capture detailed heat transfer phenomena.
The simulation assumes several conditions to simplify the analysis while maintaining relevance to real-world EV battery pack behavior. First, we neglect auxiliary components like sensors to focus on thermal effects. Second, the current density during charging and discharging is assumed constant, reflecting typical battery operations. Third, we treat the battery as a solid block with no electrolyte flow, ignoring convection and radiation heat transfer within the cells. Fourth, the thermal properties of battery materials, such as thermal conductivity and specific heat, are considered isotropic and uniform. Fifth, these properties remain constant regardless of external factors. Lastly, we adopt the Multi-Scale Multi-Domain (MSMD) battery model for accurate electro-thermal coupling. The boundary conditions include a cooling water temperature of 25°C for the condensation section and discharge rates ranging from 1C to 3C to simulate different operating scenarios for the EV battery pack. We compare three cases: adiabatic (no cooling), convective cooling with a heat transfer coefficient of 5 W/(m²·K), and PHP cooling with an RF of 10.6%.
The numerical results reveal significant insights into the thermal management of the EV battery pack. Under a 3C discharge rate, the temperature distribution shows that hotspots primarily occur near the electrodes due to higher current density. Without cooling, the battery temperature rises rapidly, reaching up to 342 K, which is hazardous for the EV battery pack. With convective cooling, temperatures are lower but still exceed safe limits at higher discharge rates. In contrast, the L-shaped PHP maintains a more uniform temperature profile, with maximum temperatures kept below 328 K, ensuring the EV battery pack operates within the optimal range of 298 K to 318 K. The following table summarizes the maximum temperatures for the EV battery pack under different discharge rates and cooling methods:
| Discharge Rate (C) | Adiabatic Temperature (K) | Convective Cooling Temperature (K) | PHP Cooling Temperature (K) |
|---|---|---|---|
| 1 | 319 | 314 | 304 |
| 1.5 | 326 | 322 | 309 |
| 2 | 332 | 328 | 315 |
| 3 | 342 | 338 | 327 |
From this table, it is evident that the PHP cooling consistently outperforms other methods, keeping the EV battery pack temperature lower by up to 15 K. The thermal resistance of the PHP, calculated using the formula above, decreases with increasing heat input until an optimal point, after which it rises due to dry-out or flow resistance. For the EV battery pack, this implies that the PHP must be designed with an appropriate fill ratio to handle variable heat loads. We also analyze the heat generation rate of the EV battery pack, which ranges from 10 W to 30 W across discharge rates, using the energy balance equation:
$$ Q_{gen} = I^2 R_{int} + \Delta S \cdot T $$
where $Q_{gen}$ is the heat generation rate, $I$ is the current, $R_{int}$ is the internal resistance, and $\Delta S$ is the entropy change. This heat is effectively dissipated by the PHP, as shown by the temperature profiles. The simulation data further indicates that the EV battery pack’s average temperature with PHP cooling remains below 50°C, with a maximum of 55°C, which is within the safe operating range for lithium-ion batteries. This highlights the robustness of the L-shaped PHP for EV battery pack thermal management.
To deeper understand the fluid dynamics within the PHP, we examine the velocity and pressure distributions. The oscillatory flow of vapor and liquid slugs creates a pulsating motion that enhances heat transfer. The velocity magnitude $v$ can be expressed as:
$$ v = \sqrt{v_x^2 + v_y^2 + v_z^2} $$
where $v_x$, $v_y$, and $v_z$ are the velocity components. The pressure drop $\Delta p$ along the PHP is influenced by friction and acceleration terms, given by:
$$ \Delta p = f \frac{L}{D} \frac{\rho v^2}{2} + \rho g L \sin \theta $$
Here, $f$ is the friction factor, $L$ is the tube length, $D$ is the diameter, and $\theta$ is the inclination angle. For the L-shaped PHP, the bend introduces additional pressure losses, but our simulations show that this does not significantly impede performance for the EV battery pack. The heat transfer coefficient $h$ for the PHP can be estimated from the thermal resistance:
$$ h = \frac{1}{R_{th} A} $$
where $A$ is the heat transfer area. For the EV battery pack, with $A$ approximately 0.1 m², $h$ values range from 100 to 500 W/(m²·K), demonstrating the PHP’s high efficiency. Compared to convective cooling with $h \approx 5$ W/(m²·K), the PHP offers an order-of-magnitude improvement, making it ideal for high-power EV battery packs.
We also investigate the impact of environmental temperature on the EV battery pack’s thermal performance. As ambient temperature increases, the heat dissipation capacity of the PHP decreases slightly due to reduced temperature gradients. However, even at 40°C ambient, the PHP maintains the EV battery pack temperature below 60°C, which is critical for safety. The fill ratio optimization is further validated through sensitivity analysis, where we vary RF from 5% to 25% and monitor the thermal resistance. The results confirm that RF = 10.6% minimizes $R_{th}$ for the EV battery pack across all discharge rates, as summarized below:
| Fill Ratio (%) | Thermal Resistance at 1C (K/W) | Thermal Resistance at 3C (K/W) |
|---|---|---|
| 5 | 0.15 | 0.25 |
| 10.6 | 0.10 | 0.18 |
| 15 | 0.12 | 0.20 |
| 20 | 0.14 | 0.22 |
This table underscores the importance of fill ratio selection for the EV battery pack’s PHP system. Additionally, we explore the effect of PHP geometry, comparing L-shaped with straight and U-shaped configurations. The L-shaped design offers better integration into the EV battery pack, reducing space requirements while maintaining performance. The heat transfer rate $\dot{Q}$ through the PHP can be calculated as:
$$ \dot{Q} = \dot{m} \cdot h_{fg} $$
where $\dot{m}$ is the mass flow rate of the working fluid and $h_{fg}$ is the latent heat of vaporization. For the EV battery pack, with a heat load of up to 30 W, $\dot{m}$ is sufficient to ensure continuous operation without dry-out.
In discussion, we emphasize that the L-shaped PHP provides a passive, reliable cooling solution for the EV battery pack, reducing the need for external power and complex systems. Compared to active cooling methods, it lowers energy consumption and enhances the overall efficiency of the EV. The numerical model’s accuracy is validated by comparing simulated temperatures with experimental data from literature, showing good agreement within 5% error. Limitations of this study include the simplified assumptions, such as constant material properties and neglect of radiation, which could be addressed in future work. For practical implementation in EV battery packs, factors like vibration resistance, long-term durability, and cost must be considered. However, our results demonstrate that the L-shaped PHP is a viable option for next-generation EV battery pack thermal management.
In conclusion, this numerical study comprehensively analyzes the heat transfer performance of an L-shaped pulsating heat pipe for EV battery pack cooling. We develop a detailed mathematical model based on the VOF method to simulate two-phase flow and heat transfer, incorporating key equations for continuity, momentum, and thermal resistance. Through simulations under discharge rates from 1C to 3C, we show that the L-shaped PHP effectively maintains the EV battery pack temperature within safe limits, outperforming adiabatic and convective cooling methods. The optimal fill ratio of 10.6% minimizes thermal resistance, ensuring efficient heat dissipation even at high power loads. The EV battery pack’s thermal stability is crucial for vehicle safety and performance, and the L-shaped PHP offers a compact, passive solution that aligns with the evolving demands of electric mobility. Future research should focus on experimental validation and optimization for real-world EV battery pack applications, considering dynamic operating conditions and integration challenges. Overall, this work contributes to advancing thermal management technologies for sustainable transportation, highlighting the potential of pulsating heat pipes in enhancing EV battery pack reliability and longevity.