Lithium ion battery thermal runaway propagation modeling method coupled with semi-empirical flame radiation model

Abstract

The invention discloses a lithium ion battery thermal runaway propagation modeling method coupled with a semi-empirical flame radiation model, and belongs to the technical field of battery thermal safety. According to the method, thermal runaway jet parameters of the battery are obtained, a single-point source method is adopted to calibrate flame radiation fractions, a solid flame radiation model with a cylinder and a cuboid combined is established, and a radiation heat source is coupled to a three-dimensional thermal runaway propagation model to solve temperature distribution. According to the method, the technical problem that a traditional method cannot give consideration to calculation efficiency and precision is solved, through innovative combination of special geometric simplification and a semi-empirical radiation model, the calculation efficiency is remarkably improved while the model precision is guaranteed, and an efficient and reliable simulation tool is provided for thermal safety design of the lithium ion battery module.

Description

Technical Field

[0001] This invention belongs to the field of lithium-ion battery thermal safety simulation technology, specifically involving a lithium-ion battery thermal runaway propagation modeling method coupled with a semi-empirical flame radiation model, which is particularly suitable for thermal runaway propagation prediction and safety design at the battery module level. Background Technology

[0002] With the widespread application of lithium-ion batteries in electric vehicles and large-scale energy storage systems, their thermal safety has become a key factor restricting the industry's development. In high-density energy clusters composed of numerous closely packed cells, once a single cell triggers thermal runaway due to abuse conditions such as internal short circuits or overheating, the enormous energy released can rapidly propagate to surrounding cells, triggering a catastrophic chain reaction. Therefore, developing effective strategies to suppress thermal runaway propagation is crucial. In this process, numerical simulation, with its advantages of low cost, no risk, and the ability to provide detailed physical field distributions, has become an important tool for studying thermal runaway propagation mechanisms and evaluating containment schemes. However, in the actual enclosed space of a battery pack, thermal runaway can cause high-temperature flammable gas to be ejected from the safety valve, forming a jet flame. When the flame impacts the top plate or obstacles above the battery pack, it can transform into a top plate flame that spreads along the top plate. This flame heats the upper surface of the battery module below through intense radiative heat transfer, creating a significant longitudinal temperature gradient. This gradient interacts with the transverse temperature gradient formed between the batteries through thermal conduction, jointly accelerating the propagation of thermal runaway. This makes many barrier strategies designed based solely on traditional models of thermal conduction less effective in practical applications.

[0003] To more realistically simulate this physical process, existing technologies attempt to couple computational fluid dynamics (CFD) with thermal runaway models to characterize the heating effect of jet fires. However, these full-order CFD models require solving complex Navier-Stokes equations and rigid multi-component chemical reaction conservation equations. This not only consumes enormous computational resources and makes convergence extremely difficult, but also, due to the incomplete understanding of the mechanism of gas generation during battery thermal runaway, many assumptions are still made regarding key parameters such as real-time changing jet composition, velocity, and temperature, resulting in limited model accuracy and requiring repeated experimental calibration. These factors collectively lead to severely low computational efficiency of coupled CFD methods, making rapid iterative application in engineering design difficult. Therefore, the current technological field faces a prominent contradiction:

[0004] On the one hand, ignoring flame radiation will distort the model and make it unable to guide actual safety design;

[0005] On the other hand, the introduction of full-order flame simulation makes the computational cost prohibitive.

[0006] Against this backdrop, there is an urgent need for an innovative modeling method that can achieve a good balance between computational efficiency and simulation accuracy. It must be able to reasonably reflect the accelerating effect of flame radiation on thermal runaway propagation under the confined space of the top plate, while avoiding getting caught up in the complexity of full-order fluid calculations. This would provide an efficient and reliable theoretical tool and simulation method for the thermal safety design of battery modules. Summary of the Invention

[0007] This invention aims to address the technical problem that existing technologies cannot simultaneously balance computational efficiency and simulation accuracy in roof-constrained environments, particularly overcoming the technical shortcomings of high computational cost of full-order CFD models and the neglect of flame radiation effects by traditional heat conduction models. To solve these problems, this invention provides a lithium-ion battery thermal runaway propagation modeling method coupled with a semi-empirical flame radiation model, the specific scheme of which is as follows:

[0008] S1. Select a lithium-ion battery and obtain the gas composition, jet velocity fluid parameters, material properties and geometric characteristics after thermal runaway of a single cell.

[0009] S2. Based on the gas composition and jet velocity fluid parameters, simulate pure gas phase jet fire under different nozzle diameters and flow rates, and obtain the flame radiation fraction using the single-point source method;

[0010] S3. Obtain the jet fire height and heat release rate input parameters under the top plate constraint, and establish a solid flame radiation model in combination with the flame radiation fraction, wherein the solid flame radiation model geometrically equates the jet fire to a combination of cylindrical flame and cuboid flame.

[0011] S4. Use a semi-empirical radiation model to integrate and obtain the radiative heat transfer of the flame on the top surface of the battery, obtain the radiative heat source, and couple it to the heat source term of the three-dimensional thermal runaway propagation model.

[0012] S5. Solve the heat transfer model based on the finite volume method to obtain the three-dimensional temperature distribution including flame heat transfer.

[0013] Preferably, in step S2, when obtaining the flame radiation fraction using the single-point source method, the horizontal distance between the radiant heat flow meter and the center of the burner is not less than 5 times the burner diameter, and the flame radiation fraction is calculated using the following formula:

[0014] ;

[0015] in, For radiative heat flow, Fuel mass flow rate, The calorific value of the fuel. The flame height was determined through preliminary experiments. and These represent the axial and radial distances of the heat flow meter from the center of the burner, respectively. The radiation fraction function, The flame radiation fraction and , This indicates the distance between the heat flow meter and the center of the flame.

[0016] Preferably, in step S3, the viewing angle coefficient of the cylindrical flame is calculated using the following formula:

[0017] ;

[0018] in, The angular coefficient of the cylindrical flame relative to the horizontal plane. , , , , This represents the equivalent diameter of a cylindrical flame. and These represent the height and diameter of the cylindrical flame, respectively.

[0019] Preferably, in step S3, the viewing angle coefficient of the cuboid flame is calculated using the following formula:

[0020] ;

[0021] ;

[0022] in, denoted as the viewing angle coefficient of the cuboid flame relative to its vertical surface. For the first The visual coefficient components of a cuboid flame. and The first The width and height of the rectangular flame The distance from the target to the cuboid flame.

[0023] Preferably, in step S4, the radiant heat source Calculated by the following integral:

[0024] ;

[0025] in, As a time-varying radiative heat source, It is the radiative heat flux density and is a function of time and space. Let be the normal vector of the top surface of the battery. To the radiation source point To the target point Viewpoint coefficient, Let be the area of ​​a micro-element on the top surface of the battery. The top area of ​​the battery is divided into regions.

[0026] Preferably, in step S4, the governing equations of the three-dimensional thermal runaway propagation model include:

[0027] ;

[0028] in, It's battery density. It is the specific heat capacity of the battery. It's the battery temperature. It is time. This represents the transient change in internal energy per unit volume of a battery. The thermal conductivity of the battery. It is the sum of the heat sources of the side reactions during battery thermal runaway. For the equivalent convection loss source term, For heating plate source item, For flame radiation source term, This indicates the contribution to characterizing heat conduction. Let be the Laplace operator, representing the gradient of the physical quantity associated with it.

[0029] Preferably, the reaction heat source Calculated using the Arrhenius equation, and the progress variable of the thermal runaway side reaction. Follow the following transport equations:

[0030] ;

[0031] By disabling the convection and diffusion flux terms, the transient term is obtained as follows: And source item Described by the following formula:

[0032] ;

[0033] ;

[0034] in, For convection velocity, The turbulent diffusion coefficient is... Where is the thermal diffusivity, This represents the source term for the temperature-dependent thermal runaway reaction rate. Representative reaction The pre-exponential factor, Representative reaction activation energy, Let be the ideal gas constant. Representative and The relevant functions, Representative reaction The enthalpy of the reaction.

[0035] Preferably, in step S5, the solution of the heat transfer model based on the finite volume method is implemented in the OpenFOAM framework, and implicit Euler discretization is used to process the Arrhenius-type reaction source terms.

[0036] Preferably, in step S3, the jet fire height under the constraint of the top plate satisfies the condition that the height of the top plate is much smaller than the size of the top plate, approximating a radial relationship between infinitely large planes, and the height of the cylindrical flame is... It equals the height of the top plate.

[0037] This invention cleverly replaces full-order computational fluid dynamics simulation with a semi-empirical radiation model, thus avoiding the solution of complex Navier-Stokes equations and rigid chemical reaction source terms. This allows the computational task to focus solely on solid-state heat transfer, resulting in an order-of-magnitude speedup in practical applications, significantly meeting the rapid iterative design requirements in engineering. Furthermore, this invention ensures model accuracy by introducing an innovative geometric simplification method. Specifically, for the first time in the specific scenario of a confined top plate, the complex jet flame morphology is represented as a combination of cylinders and cuboids, with a dedicated formula for calculating the closed-view coefficient. This unique approach enables the model to efficiently and accurately describe the complex radiative heat transfer relationship between the flame and the battery surface, providing solid technical support and theoretical basis for the barrier safety design of lithium-ion battery modules. Attached Figure Description

[0038] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below.

[0039] Figure 1 This is a flowchart illustrating the overall operation of the method of the present invention;

[0040] Figure 2 This is a schematic diagram of the coupled modeling and calculation process for thermal runaway propagation with coupled flame radiation heat transfer in this invention;

[0041] Figure 3 This is a curve showing the change in radiation fraction obtained from experiments in an embodiment of the present invention;

[0042] Figure 4 This is a schematic diagram comparing the radiative heat flux density curves obtained from experiments and thermal radiation models in an embodiment of the present invention, wherein:

[0043] Figure 4 (a) in the figure is a schematic diagram comparing the experimentally measured values ​​of internal radiative heat flow with the model predictions during thermal runaway at a top height of 0.05m.

[0044] Figure 4 (b) in the figure is a schematic diagram comparing the experimentally measured values ​​of internal radiative heat flow and the model prediction values ​​during thermal runaway at a top plate height of 0.10m;

[0045] Figure 4 (c) in the figure is a schematic diagram comparing the experimental measured value of internal radiative heat flow and the model prediction value during thermal runaway at a top plate height of 0.15m;

[0046] Figure 5 This is a schematic diagram of the geometric model and mesh generation in an embodiment of the present invention, wherein:

[0047] Figure 5 (a) in the diagram is a schematic diagram of the fixed gradient boundary conditions set on the upper surface of the battery, the thermal insulation walls set on the side and bottom surfaces of the battery, and the coupling surface set between adjacent batteries.

[0048] Figure 5 (b) in the diagram is a detailed feature diagram of the grid division of the battery computation region;

[0049] Figure 6 This is a schematic diagram comparing the battery thermal runaway propagation temperature evolution curves obtained from experiments and simulations in the embodiments of the present invention;

[0050] Figure 7 The thermal runaway propagation temperature distribution cloud map obtained by simulation in an embodiment of the present invention, wherein:

[0051] Figure 7 (a) in the figure is a schematic diagram comparing the three-dimensional temperatures predicted based on the heat conduction model and the coupled flame heat transfer model within the time range of 4000s to 6000s;

[0052] Figure 7 (b) is a comparative schematic diagram of the thermal runaway propagation front predicted based on the heat conduction model and the coupled flame heat transfer model within the time range of 4000s to 6000s;

[0053] Figure 8 This is a schematic diagram comparing the curves of different thermal runaway prevention strategies obtained from simulation in the embodiments of the present invention. Detailed Implementation

[0054] The following examples are used to illustrate the present invention, but are not intended to limit the scope of the invention.

[0055] like Figure 1 As shown, this embodiment provides a method for modeling the thermal runaway propagation of lithium-ion batteries coupled with a semi-empirical flame radiation model, which first requires obtaining accurate basic parameters. In this embodiment, we select a 280Ah lithium iron phosphate square lithium-ion battery as the modeling object, such as... Figure 5The battery module shown comprises three individual cells, each with geometric dimensions of 173mm × 72mm × 207.5mm. The heating plate's calculated area measures 148mm × 134mm × 162mm. Basic battery parameters were obtained through a combination of systematic literature review and experimental measurements, with the battery density set at 2118 kg / m³. 3 The specific heat capacity is 1029 J / (kg·K), and the thermal conductivity values ​​along the three principal axes are 21 W / (m·K), 21 W / (m·K), and 5 W / (m·K), respectively. The accuracy of these fundamental physical properties directly affects the reliability of subsequent models, therefore, cross-validation through multiple methods is necessary.

[0056] To obtain the jet characteristics parameters after battery thermal runaway, a thermal runaway experiment was conducted in a specially designed sealed pressure vessel. During the experiment, thermal runaway of a single cell was triggered by heating. The mixed gas ejected from the safety valve was collected, and the gas sample was immediately and precisely analyzed using gas chromatography-mass spectrometry to obtain the volume percentages of major components, including carbon monoxide, carbon dioxide, hydrogen, and methane. Simultaneously, a Pitot tube and an anemometer were placed directly in front of the safety valve outlet to record the transient changes in jet velocity.

[0057] After obtaining sufficient basic parameters, the precise calibration stage of flame radiation fraction begins. This stage utilizes existing jet fire experimental equipment, replacing the gas source with the real mixed gas obtained from the aforementioned thermal runaway experiment. The gas flow rate is adjusted using a mass flow controller to simulate pure gas-phase jet fires under different nozzle diameter conditions. It is particularly important to emphasize that the experimental setup strictly adheres to the measurement requirements of the single-point source method, ensuring that the horizontal distance between the radiative heat flux meter and the burner center is no less than five times the burner diameter. Furthermore, the flame height at different flow velocities is determined through preliminary experiments. .

[0058] The specific formula for calculating the flame radiation fraction based on the single-point source method is as follows. This formula establishes the radiative heat flux. Quantitative relationship with fuel characteristic parameters:

[0059] ;

[0060] ;

[0061] ;

[0062] in, Indicates fuel mass flow rate, The calorific value of the fuel. and These represent the axial and radial distances of the heat flow meter from the center of the burner, respectively. The value is the radiation fraction function, and in this embodiment it is taken as 0.85. The flame radiation fraction and , This indicates the distance between the heat flow meter and the center of the flame. During the experiment, the distance was fixed. and By adjusting the geometric proportions of the nozzle and the gas flow rate, the system measures the radiation fraction under different operating conditions.

[0063] like Figure 3 As shown, the radiation fraction is calculated under nozzle diameters of 4 mm, 6 mm, and 8 mm. The values ​​fluctuate within the range of 0.1 to 0.3. To ensure the stability of the model input, the measured radiation fraction data are time-averaged, and the final average value, such as 0.18, is used as the key input parameter for the solid flame radiation model.

[0064] After completing the radiation fraction calibration, the next step is to establish a solid flame radiation model for a confined environment with a roof. The geometric parameters of the roof structure are one of the key inputs to this model, especially the roof height. (i.e., the vertical distance from the lower surface of the top plate to the upper surface of the battery) and the dimensions of the top plate (i.e., the length of the top plate) With width When the height of the top plate Much smaller than the length of the top plate or width In radiation calculations, this can be approximated as a radiative heat transfer problem between infinitely large parallel planes. This simplification is a crucial prerequisite for the efficient calculation of the semi-empirical radiation model in this embodiment. The core of this step lies in simplifying the complex geometry of the roof jet fire into a combination of cylindrical and cuboid flames. Key input parameters such as the roof flame height and heat release rate are extracted through thermal runaway experiments, where the diameter of the cylindrical flame is... The height of the cylindrical flame is set to 0.08m. The height is equal to the height of the top plate, specifically 0.15m in this embodiment. The length and width of the cuboid flame are directly taken from the actual dimensions of the top plate. and ,thickness Based on the flame morphology experiment, the value is determined to be 0.02m in this embodiment.

[0065] For these two simplified geometries, their surface area and volume need to be calculated separately to provide a basis for subsequent heat release rate calculations. Surface area of ​​a cuboid flame. Calculated using the following formula:

[0066] ;

[0067] Volume of a cuboid flame Calculated using the following formula:

[0068] ;

[0069] Surface area of ​​a cylindrical flame Calculated using the following formula:

[0070] ;

[0071] Volume of a cylindrical flame Calculated using the following formula:

[0072] ;

[0073] in, The height of the flame after it crosses the top plate;

[0074] The heat release rate distribution of the top plate flame follows the following proportional relationship:

[0075] ;

[0076] in, This refers to the flame radiation power. This represents the total heat release rate; The volume of the flame on the top plate.

[0077] For these two simplified geometries, radiative heat transfer analysis is performed using closed-form view coefficient calculation formulas. View coefficient of a cylindrical flame relative to a horizontal plane. Calculated using the following formula:

[0078] ;

[0079] in, , , , For intermediate calculation variables, specifically defined as , , , , This represents the equivalent diameter of a cylindrical flame. and These represent the height and diameter of the cylindrical flame, respectively.

[0080] The angular coefficient of a cuboid flame on its vertical face Then it is calculated using the following formula:

[0081] ;

[0082] ;

[0083] This embodiment uses a summation method with four cuboid components, and the viewing angle coefficient of each component... The width of the cuboid flame ,high And the distance from the target to the cuboid flame. A joint decision.

[0084] After obtaining the solid flame radiation model, it needs to be deeply coupled with the three-dimensional thermal runaway propagation model. For example... Figure 2 The coupled computational process shown first calculates the spatiotemporal distribution of radiative heat flux density using a semi-empirical radiation model. Then, apply the following formula to the upper surface of the battery. With viewpoint coefficient By performing an area integral on the product, we obtain the time-varying radiative heat source. :

[0085] ;

[0086] in, For radiative heat flux density, Let be the normal vector of the top surface of the battery. To the radiation source point To the target point Viewpoint coefficient, Let be the area of ​​a micro-element on the top surface of the battery. The top area of ​​the battery is divided into regions.

[0087] This radiant heat source As a new heat source item Add to the energy conservation equation of the three-dimensional thermal runaway propagation model:

[0088] ;

[0089] In the formula, It's battery density. It is the specific heat capacity of the battery. It's the battery temperature. It is time. This represents the transient change in internal energy per unit volume of a battery. The thermal conductivity of the battery. This represents the sum of heat sources from side reactions during multiple battery thermal runaway events. For the equivalent convection loss source term, For heating plate source item, For flame radiation source term, This indicates the contribution to characterizing heat conduction. Let be the Laplace operator, representing the gradient of the physical quantity associated with it.

[0090] Among them, the equivalent convection loss source term The calculation formula is:

[0091] ;

[0092] In the formula, Indicates surface emissivity; This represents the Stefan-Boltzmann constant; Indicates ambient temperature; This represents the convective heat transfer coefficient.

[0093] like Figure 2 As shown in the calculation cycle, the simulation of the battery thermal runaway side reactions adopts a kinetic model based on the Arrhenius equation, with each side reaction... progress variables Follow the following transport equations:

[0094] ;

[0095] By disabling the convection and diffusion flux terms, the rate of change of the progress variable simplifies to:

[0096] ;

[0097] Among them, source terms Described by the Arrhenius equation:

[0098] ;

[0099] To ensure numerical stability, an implicit Euler discretization scheme is used to handle the drastic changes in the reaction source term.

[0100] ;

[0101] The heat generated by the side reaction is calculated using the following formula:

[0102] ;

[0103] In the above formula, For convection velocity, The turbulent diffusion coefficient is... Where is the thermal diffusivity, This represents the source term for the temperature-dependent thermal runaway reaction rate. Representative reaction The pre-exponential factor, Representative reaction activation energy, Let be the ideal gas constant. Representative and The relevant functions, Representative reaction enthalpy of reaction Indicates a time range. Indicates a time step.

[0104] These thermal runaway reaction kinetic calculations require precise kinetic parameters as input. These parameters were obtained through systematic experimental measurements and literature review, and the specific values ​​are shown in Table 1 below. Table 1 provides the key kinetic parameters for three major thermal runaway side reactions, including the negative electrode SEI film decomposition reaction, the negative electrode-electrolyte reaction, and the positive electrode material decomposition reaction.

[0105] Table 1: Reaction Parameters

[0106]

[0107] The accuracy of these kinetic parameters directly determines the reliability of the model's predictions of thermal runaway triggering and propagation processes. These are optimized values ​​determined through fitting and verification of a large amount of experimental data. In actual calculations, these parameters can be directly substituted into the above formulas to calculate the reaction rates and heat generation power of each side reaction, thereby accurately describing the complex chain reaction process inside the battery.

[0108] like Figure 5 The geometric model and mesh generation shown in (a) and (b) are used to complete the model coupling before proceeding to the solution calculation stage. The entire solution process is implemented in the open-source computational fluid dynamics software OpenFOAM framework, using the finite volume method to spatially discretize and time-progress the governing equations. The computational mesh adopts a hexahedral-dominated structured mesh, with appropriate refinement at the battery surface and key regions, and the total number of meshes can be controlled within 1.5 × 10⁻⁶. 6 Up to 2.0×10 6 between. Figure 5 The fixed gradient boundary conditions, adiabatic walls, and coupling surfaces shown in (a) fully consider the actual physical conditions. The upper surface of the battery is set as a fixed heat flux gradient boundary condition, the sides and bottom of the battery are set as adiabatic walls, and the contact surfaces between adjacent batteries are set as coupling surfaces. During the solution process, considering the strong rigidity of the Arrhenius-type reaction source term, the implicit Euler discretization method is used to effectively avoid numerical instability. An adaptive control strategy can be adopted for the time step, with the initial time step set to 0.01s, which is automatically shortened to 0.001s during the intense reaction phase.

[0109] Finally, the accuracy of the model was verified through a thermal runaway roof jet fire experiment. Figure 4The comparison of radiative heat flux density at three different top plate heights shown in (a), (b), and (c) reveals that the maximum errors in the model's predicted heat flux are 10.8%, 7.1%, and 9.7% for top plate heights of 0.15m, 0.10m, and 0.05m, respectively. To better evaluate the model's predictive performance, we calculated the overall accuracy of the model, finding that the average error between the model and experimental results is less than 11% within a given thermal runaway period. This demonstrates that the combination of the "cylinder + cuboid" solid flame model and the thermal radiation model presented in this embodiment can effectively reproduce the measured heat flux.

[0110] like Figure 6 The temperature evolution curves shown further confirm the effectiveness of the model. The temperature curves at different monitoring locations all show good consistency between the simulated values ​​and the experimental measurements, proving that the model can match the thermal runaway propagation experiment under the top plate flame very well and can reproduce the acceleration effect of thermal runaway propagation under the top plate flame.

[0111] Figure 7 The three-dimensional temperature distribution cloud map visually demonstrates the comparison results between the coupled flame heat transfer model and the heat conduction-based model within the time range of 4000s to 6000s. Figure 7 As can be clearly observed in (a) of the model, the three-dimensional temperature distribution in the coupled flame heat transfer model exhibits significant temperature gradients in both the transverse (direction of thermal runaway propagation) and vertical (perpendicular to the direction of thermal runaway propagation). In contrast, the temperature gradient shown in the heat conduction-based model exists only in the transverse direction. To more accurately quantify the thermal runaway propagation process, 450℃ was selected as the threshold temperature of the thermal runaway propagation front. Figure 7 As can be clearly seen in (b), the thermal runaway propagation front given by the coupled flame heat transfer model is significantly ahead of the traditional heat conduction-based model. At the same time point, the coupled model predicts a wider range and faster propagation speed of thermal runaway, highlighting the necessity of coupled flame heat transfer.

[0112] In addition, through Figure 8 The comparison of temperature responses under different thermal resistance layer configurations demonstrates the value of this model in practical engineering applications. When the thermal conductivity of the insulation material is 1.0 W / (m·K), both models block thermal runaway propagation, and the temperature responses are almost identical. However, when the thermal conductivity is 1.5 W / (m·K), the thermal runaway propagation model with a flame heat transfer term significantly accelerates thermal runaway propagation, advancing the thermal runaway occurrence time from 5310 s to 12850 s, while the traditional model overestimates the insulation layer's barrier capability.

[0113] The modeling method provided in this embodiment forms a complete simulation solution for thermal runaway propagation in lithium-ion batteries through systematic parameter acquisition, radiation fraction calibration, geometric simplification modeling, multiphysics coupling, and rigorous verification. This method innovatively combines a semi-empirical radiation model with a three-dimensional thermal runaway propagation model, accurately considering the impact of flame radiation in a confined environment while ensuring computational efficiency, thus providing a reliable technical tool for the thermal safety design of battery modules. This method can accurately predict thermal runaway propagation behavior under different insulation configurations, and its computational efficiency is more than an order of magnitude higher than that of full-order CFD methods, demonstrating promising engineering application prospects.

Claims

1. A method for modeling the thermal runaway propagation of lithium-ion batteries coupled with a semi-empirical flame radiation model, characterized in that, Includes the following steps: S1. Select a lithium-ion battery and obtain the gas composition, jet velocity fluid parameters, material properties and geometric characteristics after thermal runaway of a single cell. S2. Based on the gas composition and jet velocity fluid parameters, simulate pure gas phase jet fire under different nozzle diameters and flow rates, and obtain the flame radiation fraction using the single-point source method; S3. Obtain the jet fire height and heat release rate input parameters under the top plate constraint, and establish a solid flame radiation model in combination with the flame radiation fraction, wherein the solid flame radiation model geometrically equates the jet fire to a combination of cylindrical flame and cuboid flame. S4. Use a semi-empirical radiation model to integrate and obtain the radiative heat transfer of the flame on the top surface of the battery, obtain the radiative heat source, and couple it to the heat source term of the three-dimensional thermal runaway propagation model. S5. Solve the heat transfer model based on the finite volume method to obtain the three-dimensional temperature distribution including flame heat transfer.

2. The lithium-ion battery thermal runaway propagation modeling method coupled with a semi-empirical flame radiation model as described in claim 1, characterized in that, In step S2, when obtaining the flame radiation fraction using the single-point source method, the horizontal distance between the radiant heat flow meter and the burner center is not less than 5 times the burner diameter, and the flame radiation fraction is calculated using the following formula: ； in, For radiative heat flow, Fuel mass flow rate, The calorific value of the fuel. The flame height was determined through preliminary experiments. and These represent the axial and radial distances of the heat flow meter from the center of the burner, respectively. The radiation fraction function, The flame radiation fraction and , This indicates the distance between the heat flow meter and the center of the flame.

3. The lithium-ion battery thermal runaway propagation modeling method coupled with a semi-empirical flame radiation model as described in claim 1, characterized in that, In step S3, the viewing angle coefficient of the cylindrical flame is calculated using the following formula: ； in, The angular coefficient of the cylindrical flame relative to the horizontal plane. , , , , This represents the equivalent diameter of a cylindrical flame. and These represent the height and diameter of the cylindrical flame, respectively.

4. The lithium-ion battery thermal runaway propagation modeling method coupled with a semi-empirical flame radiation model as described in claim 1, characterized in that, In step S3, the viewing angle coefficient of the cuboid flame is calculated using the following formula: ； ； in, denoted as the viewing angle coefficient of the cuboid flame relative to its vertical surface. For the first The visual coefficient components of a cuboid flame. and The first The width and height of the rectangular flame The distance from the target to the cuboid flame.

5. The lithium-ion battery thermal runaway propagation modeling method coupled with a semi-empirical flame radiation model as described in claim 1, characterized in that, In step S4, the radiant heat source Calculated by the following integral: ； in, As a time-varying radiative heat source, It is the radiative heat flux density and is a function of time and space. Let be the normal vector of the top surface of the battery. To the radiation source point To the target point Viewpoint coefficient, Let be the area of ​​a micro-element on the top surface of the battery. The top area of ​​the battery is divided into regions.

6. The lithium-ion battery thermal runaway propagation modeling method coupled with a semi-empirical flame radiation model as described in claim 1, characterized in that, In step S4, the governing equations of the three-dimensional thermal runaway propagation model include: ； in, It's battery density. It is the specific heat capacity of the battery. It's the battery temperature. It is time. This represents the transient change in internal energy per unit volume. The thermal conductivity of the battery. It is the sum of the heat sources of the side reactions during battery thermal runaway. For the equivalent convection loss source term, For heating plate source item, For flame radiation source term, This indicates the contribution to characterizing heat conduction. Let be the Laplace operator, representing the gradient of the physical quantity associated with it.

7. The lithium-ion battery thermal runaway propagation modeling method coupled with a semi-empirical flame radiation model as described in claim 6, characterized in that, The sum of the side reaction heat sources during battery thermal runaway Calculated using the Arrhenius equation, and the progress variable of the thermal runaway side reaction. Follow the following transport equations: ； By disabling the convection and diffusion flux terms, the transient term is obtained as follows: And source item Described by the following formula: ； ； in, For convection velocity, The turbulent diffusion coefficient is... Where is the thermal diffusivity, This represents the source term for the temperature-dependent thermal runaway reaction rate. Representative reaction The pre-exponential factor, Representative reaction activation energy, Let be the ideal gas constant. Representative and The relevant functions, Representative reaction The enthalpy of the reaction.

8. The lithium-ion battery thermal runaway propagation modeling method coupled with a semi-empirical flame radiation model as described in claim 1, characterized in that: In step S5, the solution of the heat transfer model based on the finite volume method is implemented in the OpenFOAM framework, and implicit Euler discretization is used to handle the Arrhenius-type reaction source terms.

9. The lithium-ion battery thermal runaway propagation modeling method coupled with a semi-empirical flame radiation model as described in claim 1, characterized in that: In step S3, the height of the cylindrical flame It equals the height of the top plate.

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