In the pursuit of advancing electric vehicle and energy storage technologies, I have focused on addressing the critical thermal challenges associated with cylindrical battery packs. During charging and discharging cycles, these batteries generate substantial heat, which can lead to accelerated capacity degradation and even thermal runaway if not properly managed. Traditional air-cooling systems often fall short in dissipation efficiency, while cold-plate liquid cooling introduces significant thermal resistance. Immersion liquid cooling, where batteries are directly submerged in a dielectric coolant, offers a promising alternative due to its superior heat transfer capabilities. However, key issues such as coolant selection, flow channel design, and circulation strategies require further optimization to achieve a balance between safety, performance, and cost-effectiveness. In this study, I investigate the design and optimization of an immersion liquid cooling-based battery management system (BMS) for cylindrical battery packs, employing finite element method simulations to analyze the impacts of coolant flow rate, coolant type, and circulation patterns on thermal performance. The goal is to develop a robust thermal management solution that ensures battery operation within optimal temperature ranges, thereby enhancing lifespan and safety.
The effectiveness of a battery management system hinges on its ability to maintain uniform temperature distribution and prevent hotspots. My approach integrates theoretical models with computational simulations to evaluate various design parameters. I begin by establishing the foundational principles of heat transfer and battery heat generation, which guide the development of the numerical model. Subsequently, I construct a detailed system model representing the immersion cooling setup, including battery pack geometry, coolant properties, and flow pathways. Through systematic experimental designs, I simulate different operating conditions to assess thermal behavior. The results are analyzed using temperature contours, flow fields, and quantitative metrics such as maximum temperature, average temperature, and temperature differentials. Key findings indicate that a coolant flow rate of 1.0 L/min, coupled with fluorinated liquid as the coolant and a “two-inlet-one-outlet” circulation pattern, yields significant improvements in cooling performance and temperature uniformity. This optimized configuration not only mitigates thermal runaway risks but also aligns with industry standards for battery safety. Below, I present a comprehensive account of this research, enriched with tables, formulas, and discussions to elucidate the underlying mechanisms and outcomes.
The theoretical framework underpinning this study encompasses heat transfer phenomena and battery electrothermal behavior. In an immersion liquid cooling system, heat is primarily dissipated through conduction and convection, with radiation playing a minor role. For conductive heat transfer within the battery pack, I employ Fourier’s law of heat conduction to model heat flow through solid components such as battery casings and electrodes. The effective thermal conductivity in three dimensions can be derived from composite structure parameters, as expressed by the following equations:
$$ \lambda_x = \frac{\sum_i k_i d_i x_i}{a} = \frac{k_r d_{xr} + k_s d_{xs} + k_t d_{xt}}{a} $$
$$ \lambda_y = \frac{\sum_i k_i d_i y_i}{b} = \frac{k_r d_{yr} + k_s d_{ys} + k_t d_{yt}}{b} $$
$$ \lambda_z = \frac{\sum_i k_i d_i z_i}{c} = \frac{k_r d_{zr} + k_s d_{zs} + k_t d_{zt}}{c} $$
Here, \( k \) represents the thermal conductivity of each structural layer, \( d_x, d_y, d_z \) denote thickness parameters in respective directions, and \( a, b, c \) are geometric coefficients. Convective heat transfer between the battery surface and coolant involves both forced and natural convection. For forced convection, the heat transfer coefficient can be estimated using empirical correlations like the Dittus-Boelter equation, which relates fluid velocity, properties, and channel geometry. Natural convection, driven by density variations due to temperature differences, is modeled using the Boussinesq approximation, with its intensity linked to the Grashof number. Although radiative heat transfer is less significant, it is accounted for via the Stefan-Boltzmann law:
$$ q = \varepsilon \sigma (T^4 – T_{\text{sur}}^4) $$
where \( \varepsilon \) is emissivity, \( \sigma \) is the Stefan-Boltzmann constant, \( T \) is battery surface temperature, and \( T_{\text{sur}} \) is ambient temperature. The heart of the thermal analysis lies in the battery heat generation model. During charge-discharge cycles, lithium-ion batteries produce heat from irreversible (joule) and reversible (entropic) processes. I utilize the Bernardi equation to calculate the volumetric heat generation rate:
$$ q = \frac{I}{V_{\text{cell}}} \left[ (U – E_e) + T \frac{dE_e}{dT} \right] $$
In this equation, \( q \) is the heat generation rate per unit volume, \( I \) is the current, \( V_{\text{cell}} \) is the cell volume, \( U \) is the operating voltage, \( E_e \) is the open-circuit voltage, \( T \) is temperature, and \( \frac{dE_e}{dT} \) is the temperature coefficient. This model is integral to simulating thermal behavior under various loads, forming the basis for evaluating the battery management system’s performance.
To simulate the immersion liquid cooling system, I developed a finite element model that captures the geometry and physics of the battery pack and cooling apparatus. The system comprises a cylindrical battery pack submerged in a coolant-filled enclosure, with inlet and outlet pipes connected to a pump and a radiator-fan assembly for heat rejection. The battery pack consists of 50 cylindrical cells, each with a diameter of 10 mm and length of 70 mm, arranged in a structured array with 3 mm gaps between cells to allow coolant flow. Key material properties and parameters are summarized in Table 1, which are essential for accurate thermal and fluid dynamics simulations. These parameters include battery density, specific heat capacity, thermal conductivities, internal resistance, and operating conditions. The coolant properties vary depending on the type—mineral oil, ethylene glycol, or fluorinated liquid—with their thermophysical characteristics detailed in Table 2. The model assumes steady-state conditions for simplicity, but transient effects are considered through iterative simulations to reflect real-world operating scenarios.
| Parameter | Value |
|---|---|
| Number of Batteries | 50 |
| Battery Diameter (mm) | 10 |
| Battery Length (mm) | 70 |
| Inter-cell Gap (mm) | 3 |
| Battery Density (kg/m³) | 2523 |
| Specific Heat Capacity (J/(kg·K)) | 1145 |
| Radial Thermal Conductivity (W/(m·K)) | 1.2 |
| Axial Thermal Conductivity (W/(m·K)) | 34.4 |
| Internal Resistance (mΩ) | 15 |
| Operating Current (A) | 3.2 |
| Discharge Rate (C) | 2 |
| Electrolyte Thermal Conductivity (W/(m·K)) | 0.143 |
| Separator Thermal Conductivity (W/(m·K)) | 0.034 |
| Heat Dissipation per Cell (W) | 0.614 |
| Coolant Type | Density (g/mL) | Specific Heat Capacity (kJ/(kg·K)) | Thermal Conductivity (W/(m·K)) |
|---|---|---|---|
| Mineral Oil | 0.8 | 1.8 – 2.2 | 0.13 – 0.17 |
| Ethylene Glycol | 1.1 | 3.3 – 3.5 | 0.45 – 0.50 |
| Fluorinated Liquid | 1.5 | 1.0 – 1.4 | 0.08 – 0.12 |
The experimental design phase involves varying key parameters to assess their impact on the battery management system’s thermal performance. I focus on three primary variables: coolant flow rate, coolant type, and circulation pattern. For flow rate analysis, I simulate five conditions ranging from 0.6 to 1.4 L/min at intervals of 0.2 L/min, while maintaining other factors constant. This range is selected to cover low to high flow scenarios, enabling observation of trends in temperature reduction and uniformity. Higher flow rates generally enhance convective heat transfer but may increase pressure drops and energy consumption. The coolant type study compares mineral oil, ethylene glycol, and fluorinated liquid at a fixed flow rate of 1.0 L/min, evaluating their cooling efficiency based on thermophysical properties and safety attributes. Mineral oil offers good insulation but moderate heat capacity; ethylene glycol has high thermal conductivity but toxicity concerns; fluorinated liquid provides excellent safety (non-flammable, insulating) though with lower thermal conductivity. Lastly, I investigate circulation patterns by contrasting traditional “single-inlet-single-outlet” flow with an optimized “two-inlet-one-outlet” configuration. The latter aims to reduce coolant travel distance and improve temperature uniformity by introducing coolant from both ends of the battery pack and exiting from the center. All simulations are conducted using finite element software, with results analyzed through temperature contours, flow velocity fields, and quantitative metrics like maximum temperature (\( T_{\text{max}} \)), minimum temperature (\( T_{\text{min}} \)), average temperature (\( T_{\text{avg}} \)), and maximum temperature difference (\( \Delta T_{\text{max}} \)).
Evaluation criteria for the battery management system are derived from industry standards, particularly GB 38031-2020, which outlines safety requirements for electric vehicle traction batteries. Key benchmarks include: (1) Maximum cell surface temperature should not exceed 45°C under extreme operating conditions, with an absolute limit of 50°C to prevent thermal runaway; (2) Maximum temperature difference within the battery pack should be kept below 5°C to ensure uniform aging and performance consistency; (3) Optimal operating temperature range for lithium-ion batteries is 20–40°C to maximize energy output, cycle life, and efficiency. These criteria guide the interpretation of simulation results and the selection of optimal design parameters. By adhering to these standards, the proposed immersion cooling system can be validated for practical applications in electric vehicles and energy storage systems.
Simulation results for coolant flow rate variations reveal significant insights into thermal management performance. As shown in Table 3, increasing the flow rate from 0.6 to 1.4 L/min leads to a gradual decrease in average temperature and maximum temperature, indicating enhanced cooling capacity. However, the maximum temperature difference exhibits a non-linear trend: it decreases from 5.5°C at 0.6 L/min to 4.2°C at 1.0 L/min, then rises to 4.6°C at 1.4 L/min. This suggests that while higher flow rates improve overall heat removal, excessive flow can cause uneven coolant distribution and increased hydraulic resistance, compromising temperature uniformity. At 1.0 L/min, the battery pack achieves the lowest \( \Delta T_{\text{max}} \) of 4.2°C, along with a reasonable \( T_{\text{avg}} \) of 44.46°C, striking a balance between cooling efficacy and energy efficiency. Temperature contour plots visually confirm this, displaying more homogeneous temperature fields at 1.0 L/min compared to lower or higher rates. Thus, for the battery management system, a flow rate of 1.0 L/min is identified as optimal, minimizing thermal gradients while maintaining adequate heat dissipation.
| Flow Rate (L/min) | Minimum Temperature (°C) | Maximum Temperature (°C) | Maximum Temperature Difference (°C) | Average Temperature (°C) |
|---|---|---|---|---|
| 0.6 | 42.2 | 47.7 | 5.5 | 45.56 |
| 0.8 | 42.0 | 46.9 | 4.9 | 44.89 |
| 1.0 | 42.5 | 46.7 | 4.2 | 44.46 |
| 1.2 | 42.1 | 46.5 | 4.4 | 44.34 |
| 1.4 | 41.9 | 46.5 | 4.6 | 44.23 |
The choice of coolant type profoundly influences the battery management system’s thermal behavior and safety. Table 4 summarizes simulation results for mineral oil, ethylene glycol, and fluorinated liquid at 1.0 L/min. Ethylene glycol yields the lowest \( \Delta T_{\text{max}} \) of 3.7°C due to its high thermal conductivity, but it results in a higher \( T_{\text{avg}} \) of 44.64°C and poses toxicity risks. Mineral oil offers moderate performance with \( T_{\text{avg}} = 44.46°C \) and \( \Delta T_{\text{max}} = 4.6°C \), yet its cooling capacity is limited. Fluorinated liquid, despite having a higher \( \Delta T_{\text{max}} \) of 5.3°C, achieves the lowest \( T_{\text{avg}} \) of 44.16°C and boasts superior safety characteristics such as non-flammability and electrical insulation. These attributes make fluorinated liquid particularly suitable for high-risk applications where battery management system reliability is paramount. The temperature contours further illustrate that fluorinated liquid maintains lower overall temperatures but exhibits greater end-to-end gradients, highlighting a need for circulation pattern optimization to improve uniformity.
| Coolant Type | Minimum Temperature (°C) | Maximum Temperature (°C) | Maximum Temperature Difference (°C) | Average Temperature (°C) |
|---|---|---|---|---|
| Mineral Oil | 42.5 | 46.7 | 4.2 | 44.46 |
| Ethylene Glycol | 42.1 | 45.8 | 3.7 | 44.64 |
| Fluorinated Liquid | 42.1 | 47.4 | 5.3 | 44.16 |
To address the temperature uniformity issue with fluorinated liquid, I propose and test an optimized circulation pattern: “two-inlet-one-outlet”. In this configuration, coolant enters from both ends of the battery pack and exits from a central outlet, reducing flow path length and promoting symmetric cooling. Simulation results, compared to the baseline “single-inlet-single-outlet” pattern, demonstrate remarkable improvements. As detailed in Table 5, the optimized design reduces \( T_{\text{max}} \) from 47.4°C to 42.6°C (a 10.12% decrease), \( T_{\text{avg}} \) from 44.16°C to 42.31°C (a 4.18% decrease), and \( \Delta T_{\text{max}} \) from 5.3°C to 0.6°C (an 88.67% reduction). This drastic enhancement in temperature homogeneity stems from balanced coolant distribution, which mitigates end-to-end temperature disparities. The temperature contour plot for the optimized system shows a tightly clustered temperature range of 42.0–42.6°C, confirming effective thermal management. These findings underscore the importance of circulation design in maximizing the performance of an immersion cooling-based battery management system.
| Circulation Pattern | Minimum Temperature (°C) | Maximum Temperature (°C) | Maximum Temperature Difference (°C) | Average Temperature (°C) |
|---|---|---|---|---|
| Single-Inlet-Single-Outlet (Baseline) | 42.1 | 47.4 | 5.3 | 44.16 |
| Two-Inlet-One-Outlet (Optimized) | 42.0 | 42.6 | 0.6 | 42.31 |
The underlying fluid dynamics and heat transfer mechanisms can be further elucidated through analytical models. For forced convection in the immersion cooling system, the Nusselt number (\( Nu \)) correlates with Reynolds (\( Re \)) and Prandtl (\( Pr \)) numbers, governing convective heat transfer coefficients. A simplified relationship for turbulent flow in channels is given by:
$$ Nu = 0.023 \, Re^{0.8} \, Pr^{0.4} $$
where \( Re = \frac{\rho v D}{\mu} \) and \( Pr = \frac{c_p \mu}{k} \), with \( \rho \) being coolant density, \( v \) velocity, \( D \) hydraulic diameter, \( \mu \) dynamic viscosity, \( c_p \) specific heat, and \( k \) thermal conductivity. This equation helps explain why increasing flow rate (and thus \( Re \)) enhances cooling, but also why excessive flow may lead to inefficiencies due to elevated pressure drops. The pressure drop \( \Delta P \) in the system can be estimated using the Darcy-Weisbach equation:
$$ \Delta P = f \frac{L}{D} \frac{\rho v^2}{2} $$
Here, \( f \) is the friction factor, and \( L \) is pipe length. Higher flow rates increase \( \Delta P \), raising pump power requirements and potentially causing uneven flow distribution. Therefore, optimizing flow rate is crucial for the battery management system to achieve energy-efficient operation.
In addition to thermal metrics, I evaluate the battery management system based on energy consumption and cost implications. The pump power \( P_{\text{pump}} \) required to circulate coolant is proportional to flow rate and pressure drop:
$$ P_{\text{pump}} = \frac{\Delta P \cdot Q}{\eta} $$
where \( Q \) is volumetric flow rate and \( \eta \) is pump efficiency. At 1.0 L/min, \( P_{\text{pump}} \) is relatively low compared to higher rates, contributing to overall system efficiency. Moreover, fluorinated liquid, while potentially more expensive than mineral oil or ethylene glycol, offers long-term benefits through enhanced safety and reduced risk of thermal incidents. A holistic assessment of the battery management system must consider these trade-offs to ensure practical viability.
To generalize the findings, I derive a comprehensive optimization framework for immersion liquid cooling systems. The objective function aims to minimize both maximum temperature and temperature difference while constraints include flow rate limits, coolant properties, and geometric parameters. Mathematically, this can be formulated as:
$$ \text{Minimize: } \alpha T_{\text{max}} + \beta \Delta T_{\text{max}} $$
subject to:
$$ Q_{\text{min}} \leq Q \leq Q_{\text{max}} $$
$$ T_{\text{max}} \leq 45^\circ \text{C} $$
$$ \Delta T_{\text{max}} \leq 5^\circ \text{C} $$
where \( \alpha \) and \( \beta \) are weighting factors reflecting the relative importance of temperature reduction versus uniformity. Using simulation data, I can solve this optimization problem to identify Pareto-optimal designs. For instance, the combination of 1.0 L/min flow rate, fluorinated liquid, and two-inlet-one-outlet circulation represents one such optimal point, balancing multiple performance criteria. This framework can be adapted for different battery pack configurations, making it a valuable tool for battery management system designers.
Further discussions delve into the implications of these results for real-world applications. In electric vehicles, where space and weight are constraints, an efficient battery management system is critical for maximizing range and longevity. The proposed immersion cooling system, with its optimized parameters, can be integrated into vehicle designs to handle high-power charging and discharging scenarios. For energy storage systems, such as grid-scale batteries, thermal management ensures stability and prevents catastrophic failures. The use of fluorinated liquid aligns with safety regulations, while the two-inlet-one-outlet pattern simplifies piping layouts and reduces material costs. Additionally, the simulation methodology developed here can be extended to other battery formats (e.g., prismatic or pouch cells) by adjusting geometric and thermal parameters accordingly.
Potential limitations of this study include assumptions made in the finite element model, such as idealized coolant properties and neglect of transient thermal effects during rapid load changes. Future work could involve experimental validation through prototype testing, incorporation of advanced coolants like nanofluids, and exploration of hybrid cooling strategies combining immersion with phase-change materials. Moreover, integrating the thermal management system with battery management system algorithms for real-time control could further enhance performance. For example, adaptive flow rate modulation based on temperature feedback could optimize energy use while maintaining thermal limits.
In conclusion, this research demonstrates the effectiveness of immersion liquid cooling as a thermal management solution for cylindrical battery packs. Through systematic simulation and analysis, I have identified key design parameters that optimize cooling performance and temperature uniformity. The optimal configuration—comprising a coolant flow rate of 1.0 L/min, fluorinated liquid as the coolant, and a two-inlet-one-outlet circulation pattern—significantly reduces maximum temperature, average temperature, and temperature differences, meeting safety standards and operational requirements. These findings provide a theoretical and technical foundation for developing advanced battery management systems in electric vehicles and energy storage applications. By prioritizing safety, efficiency, and cost-effectiveness, this approach contributes to the advancement of sustainable energy technologies and underscores the critical role of thermal management in battery performance and longevity.
The battery management system, as explored here, is not merely a supplementary component but a core enabler of battery reliability. As energy densities continue to rise and charging speeds accelerate, innovative thermal management strategies like immersion cooling will become increasingly vital. I hope that this work inspires further research and development in this field, ultimately leading to safer, more efficient, and longer-lasting battery systems for a greener future.