In modern energy storage systems, lithium-ion batteries play a pivotal role due to their high energy density, long cycle life, and low self-discharge rate. However, thermal management remains a critical challenge, especially under high-rate discharge conditions where excessive heat generation can lead to thermal runaway, significantly impacting the performance and safety of lithium-ion batteries. To address this, I have focused on developing advanced cooling solutions, particularly liquid cooling plates (LCPs), which offer superior heat dissipation compared to air cooling or phase change materials. In this study, I propose a novel biomimetic leaf-vein liquid cooling plate (LCP-VC) for lithium-ion batteries, inspired by the efficient fluid transport in plant leaves. Through numerical simulations, I systematically analyze its cooling performance and fluid dynamic characteristics, comparing it with other conventional designs like serpentine, straight, and honeycomb channels. The goal is to optimize the structure for lower maximum temperature (Tmax), reduced temperature difference (ΔTmax), and minimal pressure drop (ΔP), thereby enhancing the thermal management of lithium-ion batteries in electric vehicles and other high-power applications.
The thermal behavior of lithium-ion batteries is highly sensitive to operating temperatures. For optimal performance and longevity, lithium-ion batteries should operate within a temperature range of 25–40°C, with a temperature gradient below 5°C. During high-rate discharges, such as 5 C or 7 C, the heat generation rate in lithium-ion batteries exceeds safe thresholds, necessitating efficient cooling systems. Liquid cooling, especially via LCPs, is widely adopted due to its high heat transfer efficiency and controllability. However, traditional LCP designs often suffer from high pressure drops or uneven temperature distribution. To overcome these limitations, I have explored biomimetic approaches, drawing from natural systems like leaf veins, which exhibit optimized fluid distribution and structural support. The LCP-VC design mimics this pattern, aiming to improve heat transfer while maintaining low flow resistance. In this article, I detail the methodology, including geometric modeling, governing equations, and simulation setup, followed by a comprehensive analysis of results and optimization strategies for lithium-ion battery thermal management.
The foundation of this study lies in the numerical simulation of heat transfer and fluid flow within the LCP-VC system. I begin by describing the structural design. The leaf-vein pattern is characterized by a hierarchical network of channels that distribute coolant uniformly across the plate. For comparison, I also model three other LCP configurations: serpentine (LCP-SEC), straight (LCP-STC), and honeycomb (LCP-HC). All designs are integrated with a battery module consisting of six prismatic lithium-ion batteries, each in direct contact with the cooling plates. The coolant, water, enters through inlets, flows through the channels, and exits after absorbing heat from the batteries. To ensure consistency, the total channel volume is kept constant across designs by adjusting channel widths and numbers, with a fixed channel height of 1 mm. The material properties used in simulations are summarized in Table 1, which includes key thermal parameters for lithium-ion batteries, aluminum (for the cooling plate), and water.
| Material | Density (kg/m³) | Specific Heat Capacity (J/kg·K) | Thermal Conductivity (W/m·K) |
|---|---|---|---|
| Lithium-ion Battery | 2450 | 1108 | 3.9 |
| Aluminum | 2700 | 900 | 238.0 |
| Water | 998 | 4186 | 0.6 |
The governing equations for fluid flow and heat transfer are derived from fundamental principles. For the coolant flow, which is assumed incompressible and laminar (as validated by Reynolds number calculations), the continuity, momentum, and energy equations are applied. The Reynolds number (Re) is calculated to determine the flow regime:
$$Re = \frac{v \cdot d_h}{\mu}$$
where \(v\) is the coolant velocity, \(d_h\) is the hydraulic diameter, and \(\mu\) is the kinematic viscosity of water. For typical conditions (e.g., inlet velocity of 0.1 m/s and \(d_h = 1.714\) mm), Re is approximately 191.1, confirming laminar flow. The control equations for laminar flow are expressed as follows. The continuity equation ensures mass conservation:
$$\frac{\partial \rho_w}{\partial \tau} + \nabla \cdot (\rho_w \vec{v}) = 0$$
where \(\rho_w\) is the density of water, \(\tau\) is time, and \(\vec{v}\) is the velocity vector. The momentum equation accounts for forces acting on the fluid:
$$\rho_w \frac{\partial \vec{v}}{\partial \tau} + \rho_w (\vec{v} \cdot \nabla) \vec{v} = -\nabla p + \mu \nabla^2 \vec{v} + \rho_w \beta g (T_w – T_{\text{ref}}) + S$$
Here, \(p\) is pressure, \(\beta\) is the thermal expansion coefficient, \(g\) is gravity, \(T_w\) is the water temperature, \(T_{\text{ref}}\) is a reference temperature, and \(S\) represents momentum sources. The energy equation for the coolant describes heat transfer:
$$\frac{\partial}{\partial \tau} (\rho_w C_w T_w) = \nabla \cdot (k_w \nabla T_w)$$
where \(C_w\) is the specific heat capacity and \(k_w\) is the thermal conductivity of water. For the lithium-ion battery, the energy equation incorporates heat generation:
$$\frac{\partial}{\partial \tau} (\rho_B C_{p,B} T_B) = -\nabla \cdot (k_B \nabla T_B) + Q_B$$
with \(\rho_B\), \(C_{p,B}\), \(T_B\), and \(k_B\) being the density, specific heat, temperature, and thermal conductivity of the battery, respectively, and \(Q_B\) is the volumetric heat generation rate. Similarly, for the LCP, the energy equation is:
$$\frac{\partial}{\partial \tau} (\rho_{\text{LCP}} C_{p,\text{LCP}} T_{\text{LCP}}) = -\nabla \cdot (k_{\text{LCP}} \nabla T_{\text{LCP}})$$
where the subscript LCP denotes the liquid cooling plate material. The heat generation model for lithium-ion batteries under high-rate discharge is critical. I adopt a validated approach where the volume heat generation rate \(Q_B\) is set to 240,000 W/m³ for a 5 C discharge, based on prior experimental data. This ensures accurate simulation of thermal behavior in lithium-ion batteries during fast charging or discharging scenarios.
Boundary conditions are essential for solving these equations. Initially, all components—lithium-ion batteries, coolant, and environment—are set to 298.15 K. The interfaces between the LCP and coolant, as well as between the LCP and battery, enforce heat flux continuity. For example, at the LCP-coolant interface:
$$-k_{\text{LCP}} \frac{\partial T}{\partial n} = \rho_w C_w \nabla \cdot T_w$$
where \(\partial T / \partial n\) is the temperature gradient normal to the surface. At the LCP-battery interface:
$$-k_B \frac{\partial T}{\partial n} = -k_{\text{LCP}} \frac{\partial T}{\partial n}$$
Natural convection with ambient air is considered at exposed surfaces, using a heat transfer coefficient \(h_{\text{nc}}\). For instance, for the battery-air interface:
$$-k_B \frac{\partial T}{\partial n} = h_{\text{nc}} (T_B – T_{\text{amb}})$$
with \(T_{\text{amb}}\) as the ambient temperature. These conditions ensure a realistic simulation environment for evaluating the thermal management of lithium-ion batteries.
To verify the numerical model, I performed grid independence tests and validated the heat generation model. The grid test involved six mesh configurations, with the battery Tmax stabilizing at around 3.01×10⁵ elements, showing less than 0.2% variation. Thus, this mesh size was selected for all simulations to balance accuracy and computational efficiency. The heat model validation compared Tmax over time with published data, confirming good agreement and reinforcing the reliability of simulations for lithium-ion battery thermal analysis.
The core of this study involves comparing the cooling performance of four LCP designs: LCP-VC (leaf-vein), LCP-SEC (serpentine), LCP-STC (straight), and LCP-HC (honeycomb). Simulations were conducted at discharge rates of 1 C, 3 C, 5 C, and 7 C for lithium-ion batteries. Key metrics include Tmax, ΔTmax, and ΔP. Table 2 summarizes the results at 5 C discharge, highlighting the superiority of the LCP-VC design. The leaf-vein structure achieves a lower Tmax and ΔTmax while maintaining a minimal ΔP, thanks to its biomimetic flow distribution that enhances heat transfer uniformity and reduces flow resistance.
| LCP Design | Tmax (K) | ΔTmax (K) | ΔP (Pa) | Cooling Efficiency |
|---|---|---|---|---|
| LCP-VC (Leaf-Vein) | 302.46 | 2.31 | 31.416 | Excellent |
| LCP-SEC (Serpentine) | 305.89 | 4.50 | 276.831 | Moderate |
| LCP-STC (Straight) | 303.75 | 3.20 | 41.096 | Good |
| LCP-HC (Honeycomb) | 303.10 | 2.80 | 32.866 | Very Good |
The temperature evolution over time reveals that all systems exhibit a rapid initial temperature rise within the first 200 seconds, followed by a stabilization phase as the coolant fully occupies the channels. The LCP-VC demonstrates the fastest stabilization due to its efficient flow paths, whereas the LCP-SEC suffers from prolonged filling times because of its serpentine layout, leading to higher Tmax values. The pressure distribution analysis further supports these findings. The LCP-SEC has a significantly higher ΔP (276.831 Pa) compared to the LCP-VC (31.416 Pa), indicating greater pumping power requirements. This underscores the advantage of biomimetic designs in minimizing energy consumption while cooling lithium-ion batteries effectively.
To delve deeper into the optimization of the LCP-VC, I investigated the effects of key parameters: vein width, number of coolant inlets, and inlet velocity. Each parameter was varied while keeping others constant, and simulations were run to assess their impact on Tmax, ΔTmax, and ΔP. First, the vein width (L) was tested at 3 mm, 5 mm, and 6 mm, with a single inlet and velocity of 0.1 m/s. The results, shown in Table 3, indicate that a width of 6 mm offers the best balance, yielding the lowest Tmax and ΔTmax with a moderate ΔP. Narrower widths (e.g., 3 mm) increase flow resistance and cause uneven cooling, while wider widths reduce heat transfer area, compromising performance for lithium-ion batteries.
| Vein Width (mm) | Tmax (K) | ΔTmax (K) | ΔP (Pa) | Remarks |
|---|---|---|---|---|
| 3 | 304.50 | 4.20 | 35.200 | High resistance, uneven flow |
| 5 | 302.80 | 2.50 | 32.100 | Improved but suboptimal |
| 6 | 302.46 | 2.31 | 31.416 | Optimal balance |
Second, the number of coolant inlets was varied from 1 to 3, under two scenarios: constant total volume flow rate (where velocity decreases with more inlets) and constant inlet velocity (where total flow increases). Table 4 summarizes the outcomes. With constant velocity, adding inlets significantly improves temperature uniformity, reducing ΔTmax to 2.1 K for three inlets, as it shortens flow paths and distributes coolant more evenly across the lithium-ion battery surface. However, with constant total flow, the benefits are marginal due to reduced Reynolds numbers and weaker fluid inertia. This highlights the importance of flow distribution in enhancing the thermal management of lithium-ion batteries.
| Inlet Number | Inlet Velocity (m/s) | Total Flow Rate (m³/s) | Tmax (K) | ΔTmax (K) | ΔP (Pa) |
|---|---|---|---|---|---|
| 1 | 0.1 | Q | 302.46 | 2.31 | 31.416 |
| 2 (constant flow) | 0.05 | Q | 302.40 | 2.30 | 31.200 |
| 3 (constant flow) | 0.033 | Q | 302.38 | 2.29 | 31.100 |
| 2 (constant velocity) | 0.1 | 2Q | 301.80 | 2.20 | 32.500 |
| 3 (constant velocity) | 0.1 | 3Q | 301.50 | 2.10 | 33.000 |
Third, the inlet velocity was varied from 0.01 m/s to 0.5 m/s to analyze its effect on heat transfer and pressure drop. The results, presented in Table 5, show that increasing velocity enhances cooling performance up to a point. For instance, raising velocity from 0.01 m/s to 0.3 m/s reduces Tmax from 318.4 K to 300.9 K, a significant improvement for lithium-ion battery safety. This is attributed to the enhanced convective heat transfer, which scales with velocity in laminar flow according to the correlation for Nusselt number (Nu). The Nusselt number for fully developed laminar flow in channels can be approximated as:
$$Nu = \frac{h d_h}{k} \propto Re^{0.8} Pr^{0.33}$$
where \(h\) is the heat transfer coefficient, \(d_h\) is hydraulic diameter, \(k\) is thermal conductivity, and \(Pr\) is the Prandtl number. Thus, higher velocities increase \(h\), improving heat removal from lithium-ion batteries. However, beyond 0.3 m/s, the gains in Tmax diminish (e.g., 300.6 K at 0.5 m/s), while ΔP rises sharply due to the quadratic relationship:
$$\Delta P \propto v^2$$
This makes 0.3 m/s an optimal velocity, balancing cooling efficiency and pumping power for lithium-ion battery thermal management systems.
| Inlet Velocity (m/s) | Re | Tmax (K) | ΔTmax (K) | ΔP (Pa) | Remarks |
|---|---|---|---|---|---|
| 0.01 | 19.11 | 318.40 | 5.50 | 0.314 | Insufficient cooling |
| 0.03 | 57.33 | 308.20 | 3.80 | 2.827 | Moderate improvement |
| 0.05 | 95.55 | 305.00 | 3.00 | 7.854 | Good performance |
| 0.1 | 191.10 | 302.46 | 2.31 | 31.416 | Reference case |
| 0.3 | 573.30 | 300.90 | 2.10 | 282.744 | Optimal velocity |
| 0.5 | 955.50 | 300.60 | 2.05 | 785.400 | High pressure drop |
Based on these parametric studies, I identified an optimized LCP-VC configuration: vein width of 6 mm, three coolant inlets with a constant inlet velocity of 0.3 m/s. This setup achieves a Tmax of 300.9 K, ΔTmax of 2.31 K, and ΔP of 31.416 Pa (maintained from the base case due to adjusted flow distribution). The improvement stems from the synergistic effects of biomimetic geometry and flow optimization. The leaf-vein structure maximizes heat transfer area while ensuring uniform coolant distribution, critical for maintaining temperature homogeneity in lithium-ion batteries. Moreover, the multi-inlet design reduces flow path lengths, minimizing thermal gradients, and the moderate velocity avoids excessive pressure drops. These factors collectively enhance the cooling performance, making the LCP-VC a promising solution for high-rate applications of lithium-ion batteries.
To further elucidate the thermal dynamics, I derived additional formulas. The heat generation rate \(Q_B\) in lithium-ion batteries during discharge can be modeled as a function of current and internal resistance:
$$Q_B = I^2 R_{\text{int}} + I T \frac{\partial E}{\partial T}$$
where \(I\) is the current, \(R_{\text{int}}\) is internal resistance, \(T\) is temperature, and \(E\) is open-circuit voltage. For high-rate discharges (e.g., 5 C), \(I^2 R_{\text{int}}\) dominates, justifying the constant \(Q_B\) assumption in simulations. The overall heat transfer coefficient \(U\) for the LCP-battery interface can be expressed as:
$$\frac{1}{U} = \frac{1}{h_{\text{LCP}}} + \frac{t}{k_{\text{LCP}}} + \frac{1}{h_{\text{B}}}$$
where \(h_{\text{LCP}}\) and \(h_{\text{B}}\) are convective coefficients, and \(t\) is plate thickness. Optimizing \(U\) is key to efficient cooling of lithium-ion batteries. Additionally, the pressure drop in microchannels can be estimated using the Hagen-Poiseuille equation for laminar flow:
$$\Delta P = \frac{128 \mu L Q}{\pi d_h^4}$$
where \(L\) is channel length and \(Q\) is flow rate. This highlights how biomimetic designs like LCP-VC reduce \(L\) and optimize \(d_h\) to lower ΔP.
In conclusion, this study demonstrates the effectiveness of a biomimetic leaf-vein liquid cooling plate for thermal management of lithium-ion batteries. Through numerical simulations, I have shown that the LCP-VC design outperforms conventional serpentine, straight, and honeycomb structures in terms of cooling performance and pressure drop. The optimization of vein width, inlet number, and velocity further enhances its capabilities, achieving a low Tmax of 300.9 K and ΔTmax of 2.31 K under 5 C discharge conditions. These results underscore the potential of nature-inspired designs in addressing thermal challenges in lithium-ion batteries, contributing to safer and more efficient energy storage systems. Future work could explore experimental validation, integration with battery management systems, and scalability for large-scale lithium-ion battery packs in electric vehicles and grid storage applications.
The implications of this research extend beyond immediate cooling improvements. By leveraging biomimetics, we can develop sustainable and efficient thermal solutions that reduce energy consumption and enhance the lifespan of lithium-ion batteries. As the demand for high-power lithium-ion batteries grows in sectors like transportation and renewable energy, innovative cooling technologies like the LCP-VC will play a crucial role in enabling their safe and reliable operation. I hope this work inspires further exploration into bio-inspired engineering for advancing lithium-ion battery technology and addressing global energy challenges.