My research focuses on a critical challenge in the advancement of energy storage technology: ensuring the safety and efficiency of lithium-ion batteries under high-power operations. The thermal behavior of lithium-ion batteries is paramount; during charging and discharging, especially at high rates, significant heat is generated. If this heat is not managed effectively, it can lead to elevated temperatures, accelerated degradation, and in severe cases, thermal runaway—a dangerous chain reaction. Therefore, developing efficient thermal management systems (TMS) is essential for the reliable application of lithium-ion batteries in electric vehicles and large-scale energy storage.
While air cooling has been widely used, its limited heat dissipation capacity often falls short for high-density lithium-ion battery modules. Liquid cooling, utilizing coolants with high thermal conductivity and specific heat capacity, offers a superior solution. My work explores the design of advanced cooling plates, drawing inspiration from nature—a field known as biomimetics. Biological systems, such as circulatory networks in animals or vascular structures in leaves, have evolved highly efficient pathways for fluid transport and heat exchange. By emulating these principles, I aim to create liquid cooling plates that optimize temperature uniformity and peak temperature suppression in a lithium-ion battery pack.
The core of my analysis is based on a three-dimensional, multi-physics model that couples electrochemical reactions with heat generation and fluid dynamics. This coupled model is crucial for accurately simulating the complex behavior of a lithium-ion battery under load.
Electrochemical-Thermal Coupling Model
The electrochemical model describes the internal processes of the lithium-ion battery. It is based on the porous electrode theory and accounts for lithium-ion diffusion in the solid active materials, ion migration in the electrolyte, and the electrochemical reactions at the electrode-electrolyte interfaces. The primary governing equations are summarized below.
Solid-Phase Diffusion (in spherical particles):
$$ \frac{\partial c_s}{\partial t} = \frac{D_s}{r^2} \frac{\partial}{\partial r} \left( r^2 \frac{\partial c_s}{\partial r} \right) $$
where \( c_s \) is the lithium concentration in the solid particle, \( D_s \) is the solid-phase diffusion coefficient, \( r \) is the radial coordinate, and \( t \) is time.
Liquid-Phase Mass Conservation:
$$ \epsilon_2 \frac{\partial c_2}{\partial t} = \frac{\partial}{\partial x} \left( D_2 \frac{\partial c_2}{\partial x} \right) + \frac{(1 – t_{+}) S_a j_{ioc}}{F} $$
where \( c_2 \) is the electrolyte concentration, \( \epsilon_2 \) is the electrolyte volume fraction, \( D_2 \) is the liquid-phase diffusion coefficient, \( t_{+} \) is the lithium-ion transference number, \( S_a \) is the specific surface area, \( j_{ioc} \) is the pore wall flux of lithium ions, and \( F \) is Faraday’s constant.
Charge Conservation:
In the solid phase:
$$ \frac{\partial}{\partial x} \left( -\sigma_1 \frac{\partial \phi_1}{\partial x} \right) = -S_a j_{ioc} $$
In the liquid phase:
$$ \frac{\partial}{\partial x} \left( -\sigma_2 \frac{\partial \phi_2}{\partial x} \right) + \frac{\partial}{\partial x} \left[ \frac{2RT}{F} \left( 1 + \frac{\partial \ln f_{\pm}}{\partial \ln c_2} \right) (1 – t_{+}) \sigma_2 \frac{\partial \ln c_2}{\partial x} \right] = S_a j_{ioc} $$
where \( \phi_1 \) and \( \phi_2 \) are potentials in the solid and liquid phases, \( \sigma_1 \) and \( \sigma_2 \) are effective conductivities, \( R \) is the ideal gas constant, \( T \) is temperature, and \( f_{\pm} \) is the mean molar activity coefficient.
Butler-Volmer Kinetics:
$$ j_{ioc} = i_0 \left[ \exp\left(\frac{\alpha_a F}{RT}\eta\right) – \exp\left(-\frac{\alpha_c F}{RT}\eta\right) \right] $$
where \( i_0 \) is the exchange current density, \( \eta \) is the overpotential, and \( \alpha_a \), \( \alpha_c \) are the anodic and cathodic charge transfer coefficients.
The heat generation within the lithium-ion battery arises from three main sources: reaction heat \( Q_R \), polarization heat \( Q_P \), and ohmic heat \( Q_\Omega \). The total volumetric heat generation rate \( Q \) is:
$$ Q = Q_R + Q_P + Q_\Omega $$
This heat diffuses through the battery materials. The energy conservation equation governing the temperature field \( T \) in the lithium-ion battery is:
$$ \rho C_p \frac{\partial T}{\partial t} = \lambda_x \frac{\partial^2 T}{\partial x^2} + \lambda_y \frac{\partial^2 T}{\partial y^2} + \lambda_z \frac{\partial^2 T}{\partial z^2} + Q $$
where \( \rho \) is the density, \( C_p \) is the specific heat capacity, and \( \lambda_x, \lambda_y, \lambda_z \) are the thermal conductivities in different directions. Heat dissipation from the battery surface to the cooling plate or ambient air follows Newton’s law of cooling.
System Configuration and Simulation Setup
I constructed a module consisting of six parallel-connected lithium-ion battery cells. Each cell has dimensions of 140 mm (height) × 40 mm (width) × 9 mm (thickness). To manage the heat from this lithium-ion battery module, two identical liquid cooling plates are attached to its largest lateral surfaces.
The core of this study is the design of four distinct biomimetic cooling plate structures, all having the same total heat exchange area of 3120 mm². Their flow channel designs are as follows:
- Serpentine: A single, continuous winding channel.
- Direct: Multiple straight, parallel channels.
- Leaf-Vein: A branched network inspired by plant vasculature, with a central inlet and outlet.
- Spider-Web: A radial network inspired by spider webs, with a peripheral inlet and central outlet.
The coolant employed is a mixture with the following properties: density \( \rho_c = 1071 \, \text{kg/m}^3 \), specific heat \( C_{p,c} = 3300 \, \text{J/(kg·K)} \), thermal conductivity \( k_c = 0.384 \, \text{W/(m·K)} \), and dynamic viscosity \( \mu_c = 0.00339 \, \text{Pa·s} \). The cooling plate material is aluminum.
Key simulation parameters and boundary conditions are listed in the table below.
| Parameter | Value / Setting |
|---|---|
| Battery Initial Temperature | 298.15 K |
| Coolant Initial Temperature | 293.15 K |
| Coolant Inlet Velocity (Baseline) | 0.1 m/s |
| Discharge Rate | 10C |
| Battery Surface Heat Transfer Coefficient | 5 W/(m²·K) |
| Cooling Plate Thickness (Baseline) | 5 mm |
| Flow Channel Cross-Section (Baseline) | 4 mm (width) × 3 mm (height) |
| Flow Regime | Laminar (Re < 2300) |
The performance of the thermal management system for the lithium-ion battery module is evaluated based on two critical metrics at the end of the 10C discharge: the maximum temperature (\(T_{max}\)) within the battery module and the maximum temperature difference (\(\Delta T_{max}\)) across the module. A lower \(T_{max}\) indicates better heat dissipation, while a lower \(\Delta T_{max}\) indicates better temperature uniformity, which is crucial for the longevity and safety of the lithium-ion battery.
Results Analysis: Effect of Coolant Flow Rate
The flow rate of the coolant is a primary operational parameter. I investigated its impact by varying the inlet velocity from 0.05 m/s to 0.2 m/s. The results for \(T_{max}\) and \(\Delta T_{max}\) are consolidated in the table below and analyzed thereafter.
| Flow Velocity (m/s) | Structure | \(T_{max}\) (K) | \(\Delta T_{max}\) (K) |
|---|---|---|---|
| 0.05 | Serpentine | 307.1 | 5.2 |
| Direct | 307.9 | 7.6 | |
| Leaf-Vein | 307.8 | 8.5 | |
| Spider-Web | 307.8 | 7.1 | |
| 0.10 | Serpentine | 304.2 | 5.1 |
| Direct | 305.2 | 7.8 | |
| Leaf-Vein | 305.0 | 8.6 | |
| Spider-Web | 305.1 | 7.2 | |
| 0.15 | Serpentine | 302.8 | 5.0 |
| Direct | 304.0 | 8.0 | |
| Leaf-Vein | 303.7 | 8.8 | |
| Spider-Web | 303.9 | 7.3 | |
| 0.20 | Serpentine | 302.0 | 5.0 |
| Direct | 303.4 | 8.1 | |
| Leaf-Vein | 303.1 | 8.9 | |
| Spider-Web | 303.3 | 7.4 |
The data clearly shows that increasing the flow rate improves cooling performance for all structures, lowering \(T_{max}\). However, the Serpentine structure consistently outperforms the others, achieving the lowest \(T_{max}\) at every flow rate. At 0.2 m/s, the \(T_{max}\) for the Serpentine design is 1.4 K lower than the next best (Leaf-Vein). This is attributed to its single, uninterrupted channel which maintains a high coolant velocity throughout its path, maximizing convective heat transfer from the lithium-ion battery surface.
Conversely, the multi-channel designs (Direct, Leaf-Vein, Spider-Web) inherently distribute the flow, reducing the velocity in individual branches and thus their local heat transfer coefficients. Among these, the Leaf-Vein structure exhibits the largest \(\Delta T_{max}\), indicating poor temperature uniformity. This is likely due to its central inlet/outlet layout creating uneven flow path lengths and potentially stagnant zones in peripheral branches. The Spider-Web design shows better uniformity than the Leaf-Vein and Direct designs, thanks to its radial symmetry which promotes more balanced flow distribution. Interestingly, for the Direct channel, the \(\Delta T_{max}\) increases with flow rate. This can be explained by the formation of enhanced localized vortices or recirculation zones at the sharp 90-degree bends at higher Reynolds numbers, which impede efficient heat exchange in those areas, exacerbating temperature gradients in the lithium-ion battery module.
Results Analysis: Effect of Coolant Inlet Temperature
The inlet temperature of the coolant directly sets the baseline for heat absorption. I evaluated three inlet temperatures: 288.15 K, 293.15 K, and 298.15 K. The results are summarized in Table 3.
| Coolant Inlet Temp (K) | Structure | \(T_{max}\) (K) | \(\Delta T_{max}\) (K) |
|---|---|---|---|
| 288.15 | Serpentine | 300.9 | 5.8 |
| Direct | 301.9 | 8.9 | |
| Leaf-Vein | 301.7 | 9.8 | |
| Spider-Web | 301.8 | 8.3 | |
| 293.15 | Serpentine | 304.2 | 5.1 |
| Direct | 305.2 | 7.8 | |
| Leaf-Vein | 305.0 | 8.6 | |
| Spider-Web | 305.1 | 7.2 | |
| 298.15 | Serpentine | 307.5 | 4.4 |
| Direct | 308.5 | 6.7 | |
| Leaf-Vein | 308.3 | 7.6 | |
| Spider-Web | 308.4 | 6.3 |
As expected, a lower coolant temperature significantly reduces the maximum temperature of the lithium-ion battery module. On average, a 5 K decrease in coolant temperature reduces \(T_{max}\) by approximately 3.3–3.5 K across all structures. The Serpentine design again provides the greatest absolute cooling, achieving the lowest \(T_{max}\) at each coolant temperature level.
A counter-intuitive trend observed is that while \(T_{max}\) drops with cooler coolant, the temperature uniformity within the lithium-ion battery module often worsens (\(\Delta T_{max}\) increases). For instance, with the Serpentine plate, \(\Delta T_{max}\) increases from 4.4 K to 5.8 K as the coolant temperature drops from 298.15 K to 288.15 K. This suggests that a very cold coolant may extract heat so rapidly from the regions closest to the inlet and main flow paths that other areas cannot equilibrate quickly enough, leading to larger gradients. This highlights a trade-off in thermal management design for lithium-ion batteries: aggressive cooling can reduce peak temperature but may necessitate more sophisticated flow designs to maintain uniformity.
Results Analysis: Effect of Cooling Plate Thickness
The thickness of the cooling plate influences its structural mass, flow volume, and thermal mass. I analyzed thicknesses of 4 mm, 5 mm (baseline), and 6 mm, keeping the channel height proportional. The performance data is shown in Table 4.
| Plate Thickness (mm) | Structure | \(T_{max}\) (K) | \(\Delta T_{max}\) (K) |
|---|---|---|---|
| 4 | Serpentine | 305.9 | 6.4 |
| Direct | 306.9 | 9.8 | |
| Leaf-Vein | 306.6 | 10.6 | |
| Spider-Web | 306.8 | 9.1 | |
| 5 | Serpentine | 304.2 | 5.1 |
| Direct | 305.2 | 7.8 | |
| Leaf-Vein | 305.0 | 8.6 | |
| Spider-Web | 305.1 | 7.2 | |
| 6 | Serpentine | 302.2 | 5.0 |
| Direct | 303.3 | 7.8 | |
| Leaf-Vein | 303.2 | 8.6 | |
| Spider-Web | 303.3 | 7.1 |
Increasing the cooling plate thickness from 4 mm to 6 mm consistently improves thermal performance for all designs applied to the lithium-ion battery module. The \(T_{max}\) drops significantly (e.g., by ~3.7 K for the Serpentine design). This improvement stems from two factors: (1) increased cross-sectional area for coolant flow, which reduces flow resistance and can enhance flow distribution in multi-channel designs, and (2) greater thermal mass of the plate itself, which can act as a transient heat sink, smoothing out temperature spikes. Furthermore, a thicker plate improves temperature uniformity, as evidenced by the notable reduction in \(\Delta T_{max}\), particularly for the thinner 4 mm case. This is because a more substantial plate facilitates lateral heat conduction, helping to equalize temperatures across the surface in contact with the lithium-ion battery. However, this benefit comes at the cost of increased weight and volume of the thermal management system, which is a critical consideration for mobile applications like electric vehicles.
Discussion and Conclusion
Through a comprehensive simulation study of a lithium-ion battery module with biomimetic liquid cooling, several key insights emerge for thermal management system design. The single-channel Serpentine design proved to be the most effective in minimizing the maximum temperature of the lithium-ion battery under high discharge rates, primarily due to its maintenance of high coolant velocity. However, its pressure drop would be higher than parallel-channel designs, implying a greater pumping power requirement—a factor to be optimized in a full system design.
The multi-channel biomimetic designs (Leaf-Vein, Spider-Web) offer alternative paradigms. Their performance is more sensitive to inlet/outlet placement and internal flow distribution. The Spider-Web structure demonstrated better temperature uniformity than the Leaf-Vein structure, suggesting that radial symmetry and peripheral-to-central (or central-to-peripheral) flow can be advantageous for the thermal management of a flat lithium-ion battery module. The poor uniformity of the Leaf-Vein design calls for optimization of its branching angles and channel widths to prevent flow stagnation.
The study also quantified the effects of key parameters:
- Coolant Flow Rate: Higher flow rates improve cooling but with diminishing returns and potential adverse effects on uniformity in designs with sharp bends (e.g., Direct channel). The relationship between heat removal and pumping power is non-linear and crucial for system efficiency.
- Coolant Temperature: A lower temperature is highly effective for peak temperature suppression but may worsen temperature gradients, indicating that the cooling strategy must balance absolute cooling with uniformity needs for the health of the lithium-ion battery.
- Plate Thickness: Increasing thickness improves both peak temperature and uniformity but adds mass. An optimal thickness exists that balances thermal performance with system-level weight and volume constraints.
In conclusion, the effective thermal management of lithium-ion batteries is a multi-dimensional optimization problem involving structure, operation, and packaging. Biomimetic designs offer a rich avenue for innovation. The Serpentine structure stands out for peak performance, while optimized branched networks hold promise for excellent uniformity. Future work will involve multi-objective optimization that simultaneously minimizes the maximum temperature and temperature difference of the lithium-ion battery module while accounting for pumping power and system weight, potentially leading to novel, high-performance hybrid cooling plate architectures.