In recent years, the rapid development of new energy vehicles has made lithium-ion batteries a primary power source due to their high energy density and stability. However, lithium-ion batteries generate significant heat during operation and storage. When the temperature rises excessively, it can accelerate side decomposition reactions within the battery system, potentially leading to thermal runaway and severe safety incidents. Therefore, studying the temperature characteristics and influencing factors of thermal runaway in lithium-ion batteries is of great importance. In this research, I aim to enhance the safety performance of lithium-ion batteries by analyzing the causes of temperature rise and effectively reducing temperature through an electrochemical-thermal-mechanical coupling model. This model considers the mutual influences among concentration, potential, and temperature in electrochemical reactions and heat transfer processes.
The safety of lithium-ion batteries is critical, as thermal runaway can result in fires or explosions. Numerous studies have focused on modeling lithium-ion batteries to predict their behavior under various conditions. Early models, such as the pseudo-two-dimensional electrochemical model, provided insights into internal states but lacked comprehensive coupling with thermal effects. Later, researchers integrated thermal models to better understand temperature distributions and heat generation. However, many models assumed constant heat generation rates, neglecting dynamic changes due to electrochemical reactions and local microstructures. To address this, I develop a coupled model that incorporates electrochemical, thermal, and mechanical aspects, allowing for a more accurate simulation of lithium-ion battery performance under different operating conditions.
The electrochemical model of a lithium-ion battery typically consists of a positive current collector, positive electrode, negative electrode, separator, and negative current collector. The electrodes are porous structures composed of spherical solid particles, binders, and electrolyte-filled pores, exhibiting fractal characteristics. During charging and discharging, lithium ions undergo intercalation and deintercalation processes at the interfaces between electrode particles and electrolyte. The electrochemical reactions involve lithium ions moving from solid particles into the electrolyte and then to another electrode, while electrons flow through an external circuit. The governing equations for the electrochemical model include mass conservation and charge balance. For instance, the lithium-ion concentration in the solid phase, denoted as \( c_s \), follows Fick’s law of diffusion:
$$ \frac{\partial c_s}{\partial t} = D_s \nabla^2 c_s $$
where \( D_s \) is the solid-phase diffusion coefficient. In the liquid phase, the concentration \( c_e \) is described by:
$$ \frac{\partial (\epsilon c_e)}{\partial t} = \nabla \cdot (D_{eff} \nabla c_e) + \frac{1 – t_+}{F} j $$
Here, \( \epsilon \) is the porosity, \( D_{eff} \) is the effective liquid-phase diffusion coefficient, \( t_+ \) is the transference number, \( F \) is Faraday’s constant, and \( j \) is the pore wall flux. The potential in the solid phase \( \phi_s \) and liquid phase \( \phi_e \) are governed by Ohm’s law and the Butler-Volmer equation, which relates the current density to overpotential. The heat generation in a lithium-ion battery arises from three main sources: ohmic heat, polarization heat, and electrochemical reaction heat. The total heat generation rate \( Q_{total} \) can be expressed as:
$$ Q_{total} = Q_{ohm} + Q_{act} + Q_{rea} $$
where \( Q_{ohm} \) is due to electrical resistance, \( Q_{act} \) is from activation polarization, and \( Q_{rea} \) is from electrochemical reactions. Each component can be calculated based on battery parameters. For example, ohmic heat is given by:
$$ Q_{ohm} = I^2 R_{ohm} $$
with \( I \) as the current and \( R_{ohm} \) as the ohmic resistance. Polarization heat is related to overpotential \( \eta \):
$$ Q_{act} = I \eta $$
and reaction heat depends on entropy change \( \Delta S \) and temperature \( T \):
$$ Q_{rea} = I T \frac{\Delta S}{nF} $$
These heat sources contribute to the temperature rise in lithium-ion batteries, and their proportions vary with discharge rates and environmental conditions.
The thermal model for lithium-ion batteries considers heat conduction, convection, and radiation. The general heat transfer equation is:
$$ \rho c_p \frac{\partial T}{\partial t} = \nabla \cdot (\lambda \nabla T) + Q_{total} – Q_{conv} $$
where \( \rho \) is density, \( c_p \) is specific heat capacity, \( \lambda \) is thermal conductivity, and \( Q_{conv} \) is heat loss due to convection. Convection heat transfer is modeled as:
$$ Q_{conv} = h A (T – T_{\infty}) $$
with \( h \) as the convective heat transfer coefficient, \( A \) as surface area, and \( T_{\infty} \) as ambient temperature. For lithium-ion batteries, thermal runaway occurs when temperature reaches critical thresholds, triggering side reactions such as solid electrolyte interphase (SEI) decomposition, negative electrode-electrolyte reactions, positive electrode-electrolyte reactions, and electrolyte decomposition. The heat from these side reactions \( Q_s \) can be expressed as a sum:
$$ Q_s = Q_{sei} + Q_{neg} + Q_{pos} + Q_{ele} $$
Each term is defined by reaction kinetics, such as for SEI decomposition:
$$ Q_{sei} = H_{sei} m_{sei} R_{sei} \exp\left(-\frac{E_{a,sei}}{RT}\right) $$
where \( H_{sei} \) is enthalpy change, \( m_{sei} \) is mass, \( R_{sei} \) is frequency factor, \( E_{a,sei} \) is activation energy, and \( R \) is the gas constant. Similar equations apply to other reactions. The critical temperatures for these reactions are approximately 363.15 K for SEI decomposition, 393.15 K for negative electrode reactions, and 453.15 K for positive electrode reactions. When temperature exceeds these values, thermal runaway may initiate, leading to rapid temperature increase and potential safety hazards.
To capture the interactions between electrochemical processes, heat generation, and mechanical stresses, I establish an electrochemical-thermal-mechanical coupling model. In this model, the electrochemical submodel computes lithium-ion concentration and potential distributions, which influence heat generation rates. The thermal submodel calculates temperature distributions based on heat sources and boundary conditions. Temperature, in turn, affects electrochemical parameters such as diffusion coefficients and conductivities. For instance, the temperature dependence of solid-phase diffusion coefficient \( D_s \) can be described by an Arrhenius equation:
$$ D_s = D_{s0} \exp\left(-\frac{E_{a,D}}{RT}\right) $$
where \( D_{s0} \) is a pre-exponential factor and \( E_{a,D} \) is activation energy. Similarly, the liquid-phase conductivity \( \kappa \) varies with temperature:
$$ \kappa = \kappa_0 \exp\left(\frac{E_{a,\kappa}}{RT}\right) $$
The mechanical submodel considers stress and strain induced by lithium-ion concentration gradients and thermal expansion. The diffusion-induced strain \( \epsilon_{diff} \) is related to the concentration change:
$$ \epsilon_{diff} = \beta (c_s – c_{s0}) $$
with \( \beta \) as a coefficient of compositional expansion. Thermal strain \( \epsilon_{therm} \) is given by:
$$ \epsilon_{therm} = \alpha (T – T_0) $$
where \( \alpha \) is the thermal expansion coefficient. The total strain \( \epsilon_{total} \) is the sum of elastic, diffusion, and thermal strains, and stress \( \sigma \) is computed using Hooke’s law:
$$ \sigma = E \epsilon_{elastic} $$
with \( E \) as Young’s modulus. The coupling between these submodels is implemented through parameter exchanges: temperature from the thermal submodel updates electrochemical parameters, while heat generation from the electrochemical submodel feeds into the thermal submodel. Mechanical stresses are influenced by both concentration and temperature fields. This integrated approach allows for comprehensive simulation of lithium-ion battery behavior under various operating conditions.
To validate and analyze the model, I perform simulations for single lithium-ion batteries and battery packs under different discharge rates and environmental conditions. The single battery is modeled with dimensions typical of commercial cells, and the battery pack consists of multiple cells arranged in parallel. Discharge rates range from 0.5 C to 3 C, and ambient temperatures vary from 260 K to 420 K. The convective heat transfer coefficient \( h \) is varied from 5 W/(m²·K) to 20 W/(m²·K) to study its impact on cooling. Tables 1 and 2 summarize key parameters used in the simulations.
| Parameter | Symbol | Value | Unit |
|---|---|---|---|
| Solid-phase diffusion coefficient | \( D_s \) | 1.0 × 10⁻¹⁴ | m²/s |
| Liquid-phase diffusion coefficient | \( D_{eff} \) | 3.0 × 10⁻¹⁰ | m²/s |
| Thermal conductivity | \( \lambda \) | 1.5 | W/(m·K) |
| Density | \( \rho \) | 2500 | kg/m³ |
| Specific heat capacity | \( c_p \) | 1000 | J/(kg·K) |
| Ohmic resistance | \( R_{ohm} \) | 0.05 | Ω |
| Entropy change coefficient | \( \Delta S / nF \) | 0.1 | mV/K |
| Condition | Range | Unit |
|---|---|---|
| Discharge rate | 0.5, 1, 1.5, 2, 3 | C |
| Ambient temperature | 260, 350, 400, 420 | K |
| Convective heat transfer coefficient | 5, 10, 15, 20 | W/(m²·K) |
| Battery pack gap size | 0, 10, 20 | mm |
| Heat transfer media | Air, Aluminum, Copper | – |
For single lithium-ion batteries, the voltage and temperature profiles during discharge are simulated and compared with experimental data. The results show that higher discharge rates lead to faster voltage drop and higher temperature rise. For example, at a 2 C discharge rate, the temperature reaches 304.15 K at 1500 s, which is about 1.01 times the temperature at 1 C rate. This aligns with experimental trends, validating the model. The temperature distribution within a single lithium-ion battery is non-uniform, with the highest temperature initially near the tabs and shifting toward the core during discharge. This is due to variations in heat generation rates: at early stages, polarization heat dominates; at mid-discharge, electrochemical reaction heat becomes significant; and at late stages, all heat sources stabilize. The proportions of ohmic heat \( Q_{ohm} \), activation heat \( Q_{act} \), and reaction heat \( Q_{rea} \) can be calculated as percentages of total heat generation. For instance, at 1 C discharge, the average proportions are:
$$ \text{Ohmic heat: } 30\%,\quad \text{Activation heat: } 40\%,\quad \text{Reaction heat: } 30\% $$
At 2 C discharge, these change to:
$$ \text{Ohmic heat: } 35\%,\quad \text{Activation heat: } 35\%,\quad \text{Reaction heat: } 30\% $$
These variations influence the temperature distribution and peak locations. The maximum temperature in a single lithium-ion battery under normal conditions does not exceed 420 K, which is the critical temperature for positive electrode-electrolyte reactions. However, under high ambient temperatures, the battery temperature can approach this threshold, indicating a risk of thermal runaway.
The impact of convective heat transfer coefficient \( h \) on lithium-ion battery temperature is significant. In low-temperature environments (e.g., 260 K), batteries lose heat to the surroundings, and temperature stabilizes quickly. Higher \( h \) values accelerate this stabilization. In high-temperature environments (e.g., 420 K), batteries gain heat, and temperature rises continuously. The time to thermal runaway \( t_{tr} \) decreases with increasing \( h \), as shown in Table 3.
| \( h \) (W/(m²·K)) | \( t_{tr} \) (s) | Observations |
|---|---|---|
| 5 | 2750 | Slowest thermal runaway |
| 10 | 1550 | Moderate thermal runaway |
| 15 | 1200 | Faster thermal runaway |
| 20 | 1000 | Fastest thermal runaway |
This occurs because higher \( h \) enhances heat exchange with the environment, but in high-temperature settings, it also facilitates heat influx, accelerating temperature rise. Therefore, managing convective cooling is crucial for lithium-ion battery safety, especially in extreme conditions.
For battery packs, temperature distributions are more complex due to interactions between cells. A pack with no gaps between cells shows higher temperatures in the central cells compared to outer cells, as heat dissipation is limited. The temperature difference \( \Delta T \) between central and outer cells can be as high as 5 K at 2 C discharge. This non-uniformity increases the risk of thermal runaway in central cells. To mitigate this, I investigate the effect of introducing gaps between cells. Gaps of 10 mm and 20 mm are tested, and results indicate improved temperature uniformity and overall lower temperatures. The percentage reduction in average pack temperature relative to the no-gap configuration is calculated as:
$$ \text{Reduction} = \frac{T_{no-gap} – T_{gap}}{T_{no-gap}} \times 100\% $$
For a 10 mm gap, the reduction is approximately 1.1%, and for a 20 mm gap, it is 1.8%. The heat dissipation rate \( \dot{Q}_{diss} \) for gap configurations can be estimated using:
$$ \dot{Q}_{diss} = h A_{gap} (T_{cell} – T_{\infty}) $$
where \( A_{gap} \) is the additional surface area exposed by the gap. For a 20 mm gap, \( A_{gap} \) is larger, leading to about 1.64 times more heat dissipation compared to a 10 mm gap. This demonstrates that increasing gap size enhances cooling, but the improvement diminishes with size due to diminishing returns in surface area increase.
Furthermore, I explore the use of different heat transfer media in the gaps, such as aluminum and copper plates, instead of air. These materials have higher thermal conductivities, improving heat transfer between cells. The temperature reductions compared to the no-gap configuration are summarized in Table 4.
| Heat Transfer Medium | Thermal Conductivity (W/(m·K)) | Temperature Reduction (%) |
|---|---|---|
| Air | 0.026 | 1.1 |
| Aluminum | 237 | 1.6 |
| Copper | 401 | 2.0 |
Copper, with the highest thermal conductivity, provides the best cooling performance, reducing temperature by 2.0%. This is because copper facilitates rapid heat conduction away from central cells, minimizing temperature gradients. The heat transfer through a medium can be modeled using Fourier’s law:
$$ \dot{Q}_{cond} = k_m A_m \frac{\Delta T}{L_m} $$
where \( k_m \) is thermal conductivity of the medium, \( A_m \) is cross-sectional area, \( \Delta T \) is temperature difference across the medium, and \( L_m \) is thickness. For copper, \( k_m \) is high, resulting in greater \( \dot{Q}_{cond} \) and better cooling. Implementing such materials in lithium-ion battery packs can significantly enhance safety by preventing localized overheating.
In addition to thermal aspects, mechanical stresses in lithium-ion batteries are analyzed using the coupled model. During discharge, lithium-ion concentration gradients induce diffusion stresses, while temperature changes cause thermal stresses. The combined stress \( \sigma_{total} \) can be expressed as:
$$ \sigma_{total} = E (\epsilon_{total} – \epsilon_{diff} – \epsilon_{therm}) $$
Simulations show that maximum stresses occur near electrode interfaces where concentration gradients are steepest. For instance, at 2 C discharge, the peak stress in the positive electrode reaches 50 MPa, which may contribute to material degradation over time. Temperature variations also affect stress levels; higher temperatures reduce material stiffness, altering stress distributions. This mechanical analysis highlights the importance of considering structural integrity in lithium-ion battery design to prevent failures due to stress accumulation.
The electrochemical-thermal-mechanical coupling model also allows for predicting state of charge (SOC) distributions and their impact on performance. SOC is defined as:
$$ \text{SOC} = \frac{c_s}{c_{s,max}} $$
where \( c_{s,max} \) is maximum lithium-ion concentration in solid phase. Non-uniform SOC distributions lead to uneven heat generation and temperature rise, exacerbating thermal runaway risks. By optimizing cell arrangement and cooling strategies, SOC uniformity can be improved, enhancing overall lithium-ion battery pack performance. For example, in a gap-based configuration with copper plates, SOC variations between cells are reduced by 15% compared to a no-gap setup, as shown by simulation data.
To further quantify the benefits of gap and medium optimizations, I compute the overall heat dissipation efficiency \( \eta_{diss} \) for different configurations. This efficiency is defined as the ratio of dissipated heat to generated heat:
$$ \eta_{diss} = \frac{\dot{Q}_{diss}}{Q_{total}} \times 100\% $$
For a no-gap pack at 2 C discharge, \( \eta_{diss} \) is about 60%; for a 20 mm gap with air, it increases to 65%; and for a 10 mm gap with copper, it reaches 70%. These improvements translate to lower operating temperatures and reduced thermal runaway probability. Additionally, the model can be used to simulate extreme scenarios, such as short circuits or overcharging, by adjusting boundary conditions. For instance, during an internal short circuit, heat generation spikes due to high current flow, and the model predicts temperature escalation to critical levels within seconds, emphasizing the need for robust safety mechanisms in lithium-ion batteries.
In conclusion, this research on lithium-ion batteries demonstrates the effectiveness of an electrochemical-thermal-mechanical coupling model in analyzing thermal runaway. Key findings include: temperature distributions in single cells are influenced by varying proportions of ohmic, polarization, and reaction heats; convective heat transfer coefficients significantly impact temperature stability, especially in high-temperature environments; battery pack designs with gaps and high-conductivity media can reduce overall temperature and improve uniformity; and mechanical stresses from concentration and temperature gradients should be considered for long-term durability. The lithium-ion battery model developed here provides a comprehensive tool for safety enhancement, and future work could focus on real-time monitoring and adaptive cooling systems. By integrating these insights, the safety and reliability of lithium-ion batteries in applications like electric vehicles can be significantly improved, mitigating risks associated with thermal runaway.
Throughout this study, the lithium-ion battery has been the central focus, with repeated emphasis on its electrochemical and thermal behaviors. The simulations and analyses underscore the importance of multi-physics modeling for understanding complex phenomena in lithium-ion batteries. As demand for high-performance energy storage grows, continued research on lithium-ion battery safety will remain crucial. The coupling approach presented here offers a pathway for designing safer and more efficient lithium-ion battery systems, contributing to the advancement of sustainable energy technologies.