Modeling method of thermal runaway propagation of lithium-ion battery coupled with semi-empirical flame radiation model

Abstract

The application 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. The method obtains battery thermal runaway jet parameters, calibrates a flame radiation fraction by adopting a single-point source method, establishes a solid flame radiation model of a combination of a cylinder and a cuboid, and solves a temperature distribution by coupling a radiation heat source into a three-dimensional thermal runaway propagation model. The application solves the technical problem that a traditional method cannot simultaneously consider calculation efficiency and accuracy, significantly improves calculation efficiency while ensuring model accuracy by innovative combination of special geometry simplification and a semi-empirical radiation model, and provides an efficient and reliable simulation tool for lithium ion battery module thermal safety design.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of lithium ion battery thermal safety simulation, and particularly relates to 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

[0002] With the wide application of lithium ion batteries in electric vehicles and large-scale energy storage systems, their thermal safety problems have become a key factor restricting the development of the industry. In a high-density energy cluster composed of a large number of closely arranged battery cells, once a single battery cell triggers thermal runaway due to internal short circuit, overheating or other abuse conditions, the huge energy released will quickly spread to the surrounding batteries, causing a disastrous chain reaction, so it is crucial to develop effective thermal runaway propagation suppression strategies. In this process, numerical simulation has become an important tool for studying the mechanism of thermal runaway propagation and evaluating barrier schemes due to its low cost, no risk, and the ability to provide detailed physical field distribution. However, in the actual battery package closed space, thermal runaway will eject high-temperature flammable gas from the safety valve, forming a jet flame. When the flame hits the top plate or obstacles above the battery pack, it will turn into a top plate flame that spreads along the top plate. This flame heats the upper surface of the battery module below through strong radiation heat transfer, forming a significant longitudinal temperature gradient that interacts with the transverse temperature gradient formed by heat conduction between the batteries, together accelerating the propagation of thermal runaway, which makes many barrier strategies designed based on traditional models that only consider heat conduction less effective than expected in actual application.

[0003] In order to more realistically simulate this physical process, existing technologies attempt to couple computational fluid dynamics with thermal runaway models to depict the heating effect of the jet flame. However, such full-order CFD models need to solve complex Navier-Stokes equations and stiff multi-component chemical reaction conservation equations, which not only consume huge computational resources and have extremely difficult convergence, but also, due to the incomplete understanding of the mechanism of battery thermal runaway gas production, rely on a large number of assumptions for key parameters such as jet composition, velocity and temperature that change in real time, resulting in limited model accuracy and still requiring repeated calibration through experiments. These factors together result in a serious reduction in the computational efficiency of the coupled CFD method, making it difficult to quickly iterate in engineering design. Therefore, the current technical field faces a prominent contradiction:

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

[0005] On the other hand, introducing full-order flame simulation makes the computational cost unbearable.

[0006] In this context, there is an urgent need for an innovative modeling method that can strike a good balance between computational efficiency and simulation accuracy, which can not only reasonably reflect the accelerating effect of flame radiation on thermal runaway propagation under the limited space of the roof, but also avoid falling into the complexity of full-order fluid calculation, thereby providing an efficient and reliable theoretical tool and simulation means for thermal safety design of battery modules. SUMMARY

[0007] The present application aims to solve the technical problems that the prior art cannot balance the computational efficiency and simulation accuracy under the limited environment of the roof, and in particular, to overcome the technical defects of high calculation cost of full-order CFD model and neglecting the influence of flame radiation in traditional heat conduction model. In order to solve the above problems, the present application provides a lithium ion battery thermal runaway propagation modeling method coupled with a semi-empirical flame radiation model, and the specific scheme is as follows:

[0008] S1. Selecting a lithium ion battery, obtaining gas composition, jet velocity fluid parameters, material physical parameters and geometric characteristic parameters after thermal runaway of the single battery;

[0009] S2. Simulating pure gas phase jet fire under different nozzle diameters and flow rates according to the gas composition and jet velocity fluid parameters, and obtaining flame radiation fraction by means of single-point source method;

[0010] S3. Obtaining jet fire height and heat release rate input parameters under the restriction of the roof, and establishing a solid flame radiation model combined with the flame radiation fraction, wherein the solid flame radiation model geometrically equivalent jet fire is a combination of cylindrical flame and cuboid flame;

[0011] S4. Using semi-empirical radiation model integration to obtain battery top surface flame radiation heat transfer, obtaining radiation heat source, and coupling to the heat source term of the three-dimensional thermal runaway propagation model;

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

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

[0014] ;

[0015] Wherein, is the radiation heat flow, is the fuel mass flow rate, is the fuel heat value, is the flame height and is determined by pre-experiment, and respectively represent the axial and radial distance of the heat flow meter from the center of the burner, is the radiance fraction function, is the radiance fraction of the flame and , denotes the distance between the heat flow meter and the center of the flame.

[0016] Preferably, in step S3, the view factor of the cylindrical flame is calculated by the following formula:

[0017] ;

[0018] wherein, is the view factor of the cylindrical flame to the horizontal plane, , , , , denotes the equivalent diameter of the cylindrical flame, and denote the height and diameter of the cylindrical flame, respectively.

[0019] Preferably, in step S3, the view factor of the cuboid flame is calculated by the following formula:

[0020] ;

[0021] ;

[0022] wherein, is the view factor of the cuboid flame to the vertical plane, is the view factor component of the th cuboid flame, and are the width and height of the th cuboid flame, respectively, is the distance of the target to the cuboid flame.

[0023] Preferably, in step S4, the radiative heat source is calculated by the following integral:

[0024] ;

[0025] wherein, is the time-varying radiative heat source, is the radiative heat flux density and is a function of time and space, is the normal vector of the cell top surface, is the view factor from the radiative source point to the target point , is the infinitesimal area of the cell top surface, is the battery top area.

[0026] Preferably, in step S4, the control equation of the three-dimensional thermal runaway propagation model comprises:

[0027] ;

[0028] wherein, is the battery density, is the specific heat capacity of the battery, is the battery temperature, is time, represents the transient change of energy within the battery unit volume, is the thermal conductivity of the battery, is the sum of the side reaction heat sources when the battery is in thermal runaway, is the equivalent convection loss source term, is the hot plate source term, is the flame radiation source term, represents the contribution to characterize heat conduction, is the Laplace operator, representing the gradient of the physical quantity associated therewith.

[0029] Preferably, the reaction heat source is calculated by the Arrhenius equation, and the progress variable of the thermal runaway side reaction follows the following transport equation:

[0030] ;

[0031] wherein, by disabling the convection term and the diffusion flux term, the transient term is , and the source term is described by the following formula:

[0032] ;

[0033] ;

[0034] wherein, is the convection velocity, is the turbulent diffusion coefficient, is the thermal diffusion coefficient, represents the thermal runaway reaction rate source term related to temperature, represents the pre-exponential factor of the reaction , represents the activation energy of the reaction , is the ideal gas constant, represents the function related to , represents the reaction the reaction enthalpy.

[0035] Preferably, in step S5, the solving of the heat transfer model based on the finite volume method is implemented in the OpenFOAM framework, and an implicit Euler discrete process is adopted to handle the Arrhenius type reaction source term.

[0036] Preferably, in step S3, the jet fire height under the top plate restriction satisfies that the top plate height is much smaller than the top plate size, and is approximately the radiation relationship between infinite planes, and the height of the cylindrical flame is equal to the top plate height.

[0037] The present application ingeniously replaces the full-order computational fluid dynamics simulation by adopting a semi-empirical radiation model, thereby avoiding solving complex Navier-Stokes equations and rigid chemical reaction source terms, so that the calculation task is only concentrated in the field of solid heat transfer, which in practical application means that the simulation speed is accelerated by orders of magnitude, greatly meeting the design requirements of rapid iteration in engineering. On this basis, the present application ensures the accuracy of the model by introducing an innovative geometric simplification method, which is specifically manifested in that for the first time in the specific scene of top plate restriction, the complex top plate jet flame shape is equivalent to the combination of a cylinder and a cuboid, and a dedicated closed view factor calculation formula is provided. This unique treatment enables the model to efficiently and accurately describe the complex radiation heat transfer relationship between the flame and the battery surface, thereby providing solid technical support and theoretical basis for the barrier safety design of the lithium ion battery module. BRIEF DESCRIPTION OF DRAWINGS

[0038] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, below will briefly introduce the drawings needed to be used in the embodiments or prior art description.

[0039] Figure 1 is the overall operation flowchart of the method of the present application;

[0040] Figure 2 is the thermal runaway propagation coupling modeling and calculation process diagram of the coupled flame radiation heat transfer in the present application;

[0041] Figure 3 is the radiation fraction change curve obtained by experiment in the embodiment of the present application;

[0042] Figure 4 is the comparison diagram of the radiation heat flux density curves obtained by experiment and thermal radiation model in the embodiment of the present application, wherein:

[0043] Figure 4 (a) in is the comparison diagram of the radiation heat flow experimental measurement value and the model prediction value during thermal runaway under the top plate height of 0.05m;

[0044] Figure 4 Figure 3 (c) is a comparison diagram of the experimental measured value and the model predicted value of the radiant heat flow during the thermal runaway period at a top plate height of 0.15 m;

[0045] Figure 4 Figure 3 (c) is a comparison diagram of the experimental measured value and the model predicted value of the radiant heat flow during the thermal runaway period at a top plate height of 0.15 m;

[0046] Figure 5 Figure 4 is a schematic diagram of the geometric model and meshing in the embodiment of the present application, wherein:

[0047] Figure 5 Figure 4 (a) is a schematic diagram of the fixed gradient boundary condition set on the upper surface of the battery, the adiabatic wall surface set on the side surface and the bottom surface of the battery, and the coupling surface set between adjacent batteries;

[0048] Figure 5 Figure 4 (b) is a schematic diagram of the detailed features of the meshing of the calculation region of the battery;

[0049] Figure 6 Figure 5 is a comparison diagram of the thermal runaway propagation temperature evolution curves obtained by experiment and simulation in the embodiment of the present application;

[0050] Figure 7 Figure 6 is a thermal runaway propagation temperature distribution cloud diagram obtained by simulation in the embodiment of the present application, wherein:

[0051] Figure 7 Figure 6 (a) is a comparison diagram of the three-dimensional temperature predicted based on the heat conduction model and the coupled flame heat transfer model in the time range of 4000 s to 6000 s;

[0052] Figure 7 Figure 6 (b) is a comparison diagram of the thermal runaway propagation front predicted based on the heat conduction model and the coupled flame heat transfer model in the time range of 4000 s to 6000 s;

[0053] Figure 8 Figure 7 is a comparison diagram of the curves of different thermal runaway barrier strategies obtained by simulation in the embodiment of the present application. DETAILED DESCRIPTION

[0054] The following embodiments are used to illustrate the present application, but are not used to limit the scope of the present application.

[0055] As shown in Figure 1 The embodiment provides a lithium ion battery thermal runaway propagation modeling method coupled with a semi-empirical flame radiation model, which first needs to obtain accurate basic parameters. In the embodiment, a square lithium ion battery with a capacity of 280 Ah is selected as a modeling object, and the basic parameters are obtained by experiment, as shown in Figure 5The battery module shown contains 3 single batteries, each with a geometric size of 173 mm x 72 mm x 207.5 mm, and the size of the heating plate calculation area is 148 mm x 134 mm x 162 mm. The basic parameters of the battery are obtained by combining systematic literature research and experimental measurement, among which the battery density is 2118 kg / m 3 , the specific heat capacity is 1029 J / (kg·K), and the thermal conductivity values in the three main axis directions are 21 W / (m·K), 21 W / (m·K) and 5 W / (m·K) respectively. The accuracy of these basic physical parameters is directly related to the reliability of the subsequent model, so cross-validation needs to be carried out through various means.

[0056] In order to obtain the jet characteristic parameters after the thermal runaway of the battery, a thermal runaway experiment was carried out in a specially designed sealed pressure tank. During the experiment, the thermal runaway of the single battery was triggered by heating, the mixed gas ejected from the safety valve was collected, and the gas samples were immediately analyzed accurately using gas chromatography mass spectrometry to obtain the volume fraction of main components including carbon monoxide, carbon dioxide, hydrogen and methane. At the same time, a pitot tube and an anemometer were arranged directly in front of the safety valve outlet to record the transient change process of the jet velocity.

[0057] After obtaining sufficient basic parameters, the accurate calibration stage of flame radiation fraction was entered. This stage uses the existing jet fire experiment device, replaces the gas source with the real mixed gas obtained from the aforementioned thermal runaway experiment, adjusts the gas flow through the mass flow controller, and simulates pure gas phase jet fire under different nozzle diameters. It needs to be emphasized that the experimental arrangement strictly follows the measurement requirements of the single-point source method, ensuring that the horizontal distance between the radiation heat meter and the center of the burner is not less than 5 times the diameter of the burner, and the flame height under different flow rates is determined through pre-experiment.

[0058] The specific formula for calculating the flame radiation fraction based on the basic principle of the single-point source method is as follows, which establishes the quantitative relationship between the radiation heat flow and the fuel characteristic parameters:

[0059] ;

[0060] ;

[0061] ;

[0062] wherein, represents the fuel mass flow rate, the fuel heat value, and represent the axial and radial distances of the heat meter from the center of the burner, 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 top plate height 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 The surface area of the cylindrical flame is calculated by the following equation:

[0068] ;

[0069] The surface area of the cylindrical flame is calculated by the following equation:

[0070] ;

[0071] The volume of the cylindrical flame is calculated by the following equation:

[0072] ;

[0073] where, is the height of the flame after it has passed over the ceiling;

[0074] The heat release rate distribution of the ceiling flame follows the following proportionality:

[0075] ;

[0076] where, is the radiant power of the flame; is the total heat release rate; is the volume of the ceiling flame.

[0077] For these two simplified geometries, the radiation heat transfer analysis is performed using the closed-form view factor calculation equations, respectively. The view factor of the cylindrical flame to a horizontal plane The view factor of the cylindrical flame to a horizontal plane is calculated by the following equation:

[0078] ;

[0079] where, , , , are intermediate calculation variables, defined as , , , , denotes the equivalent diameter of the cylindrical flame, and denote the height and diameter of the cylindrical flame, respectively.

[0080] The view factor of the cuboid flame to a vertical plane The view factor of the cuboid flame to a vertical plane is calculated by the following equation:

[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] The 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] where the equivalent convection loss source term is calculated as:

[0091] ;

[0092] where denotes the surface emissivity; denotes the Stefan-Boltzmann constant; denotes the ambient temperature; denotes the convective heat transfer coefficient.

[0093] As shown in the calculation cycle of Figure 2 , the simulation of battery thermal runaway side reactions adopts a kinetic model based on the Arrhenius equation, and the progress variable of each side reaction follows the following transport equation:

[0094] ;

[0095] By disabling the convection term and the diffusion flux term, the rate of change of the progress variable is simplified as:

[0096] ;

[0097] where the source term is described by the Arrhenius equation:

[0098] ;

[0099] In order to ensure numerical stability, the implicit Euler discrete format is used to deal with the characteristics of the reaction source term:

[0100] ;

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

[0102] ;

[0103] In the above formula, is the convection velocity, is the turbulent diffusion coefficient, is the thermal diffusion coefficient, represents the temperature-dependent thermal runaway reaction rate source term, represents the pre-exponential factor of the reaction , represents the activation energy of the reaction , is the ideal gas constant, represents a function related to , representing the reaction enthalpy, denotes the time range, denotes the time step.

[0104] These thermal runaway reaction kinetics calculations require accurate kinetic parameters as input, which are obtained through systematic experimental measurements and literature research, and the specific values are shown in Table 1. Table 1 provides the key kinetic parameters of the three main thermal runaway side reactions, including the decomposition reaction of the negative SEI film, the reaction between the negative electrode and the electrolyte, and the decomposition reaction of the positive electrode material.

[0105] Table 1: Reaction parameters

[0106]

[0107] The accuracy of these kinetic parameters directly determines the reliability of the model in predicting the thermal runaway triggering and propagation process, and is an optimized value determined after a large amount of experimental data fitting and verification. In actual calculation, these parameters can be directly substituted into the above formula to calculate the reaction rate and heat generation power of each side reaction, thereby accurately describing the complex chain reaction process inside the battery.

[0108] As shown in the geometric model and mesh division in (a) and (b) in Figure 5 , after coupling the model, it enters the solving calculation stage. The entire solving process is realized in the open-source computational fluid dynamics software OpenFOAM framework, using the finite volume method for spatial discretization and time advancement of the control equations. The calculation mesh uses a hexahedral-dominated structured mesh, with appropriate densification on the battery surface and key areas, and the total number of meshes can be controlled between 1.5×10 6 and 2.0×10 6 . Figure 5 The fixed gradient boundary condition, adiabatic wall, and coupled surface settings shown in (a) in fully consider the actual physical situation. The upper surface of the battery is set as a fixed heat flow gradient boundary condition, the side and bottom surfaces of the battery are set as adiabatic walls, and the contact surface between adjacent batteries is set as a coupled surface. During the solving process, due to the strong rigidity of the Arrhenius type reaction source term, the implicit Euler discretization method is used to effectively avoid numerical instability problems. The time step can use an adaptive control strategy, with an initial time step of 0.01s, which is automatically shortened to 0.001s during the reaction intensive stage.

[0109] Figure 4 Finally, the accuracy of the model is verified through the thermal runaway roof jet fire experiment. ThroughThe comparison of radiative heat flux density at three different ceiling heights (a), (b) and (c) in FIG. 11 shows that the maximum error of the model prediction is 10.8%, 7.1% and 9.7% when the ceiling height is 0.15 m, 0.10 m and 0.05 m, respectively. In order to better evaluate the prediction performance of the model, the overall accuracy of the model is calculated, and the average error between the model and the experimental results is less than 11% in the given time period of the thermal runaway. This proves that the combination of the "cylinder + cuboid" solid flame model and the thermal radiation model given in this embodiment can effectively reproduce the measured heat flux.

[0110] The comparison of temperature evolution curves as shown in FIG. 12 further proves the effectiveness of the model. The temperature curves at different monitoring positions all show good consistency between the simulation values and the experimental measured values, proving that the model can well match the thermal runaway propagation experiment under the ceiling flame and can reproduce the acceleration effect of thermal runaway propagation under the ceiling flame. Figure 6

[0111] The three-dimensional temperature distribution cloud map in FIG. 13 intuitively shows the comparison results of the coupled flame heat transfer model and the heat conduction-based model in the time range of 4000s to 6000s. Figure 7 As can be clearly observed from (a) in FIG. 13, the three-dimensional temperature distribution in the model coupled with flame heat transfer has significant temperature gradients in both the horizontal (thermal runaway propagation direction) and vertical (perpendicular to the thermal runaway propagation direction) directions. In contrast, the temperature gradient exhibited by the heat conduction-based model exists only in the horizontal direction. In order to more accurately quantify the thermal runaway propagation process, 450°C is selected as the threshold temperature of the thermal runaway propagation front, and from (b) in FIG. 13 it can be clearly found that the thermal runaway propagation front given by the coupled flame heat transfer model is obviously ahead of the traditional heat conduction-based model. At the same time node, the coupled model predicts a wider thermal runaway propagation range and a faster propagation speed, which also highlights the necessity of coupling the flame heat transfer. Figure 7 Figure 7 In addition, the comparison of temperature responses under different thermal resistance layer configurations as shown in FIG. 14 proves the value of the model in practical engineering applications. When the thermal conductivity of the insulation material is 1.0 W / (m·K), the thermal runaway propagation is blocked in both models, and the temperature responses are almost identical; when the thermal conductivity is 1.5 W / (m·K), the thermal runaway propagation model with the flame heat source term obviously accelerates the thermal runaway propagation, and the thermal runaway occurs at 12850s, which is earlier than 5310s in the traditional model, and the thermal runaway propagation model with the flame heat source term obviously accelerates the thermal runaway propagation, and the thermal runaway occurs at 12850s, which is earlier than 5310s in the traditional model.

[0112] Figure 8

[0113] ​​​The modeling method provided by the embodiment forms a complete solution for lithium-ion battery thermal runaway propagation simulation through systematic parameter acquisition, radiation fraction calibration, geometric simplified modeling, multi-physics field coupling and strict verification. The method innovatively combines the semi-empirical radiation model with the three-dimensional thermal runaway propagation model, accurately considers the influence of flame radiation in the ceiling limited environment on the premise of ensuring the calculation efficiency, and provides a reliable technical tool for the thermal safety design of the battery module. The method can accurately predict the thermal runaway propagation behavior under different heat insulation configurations, and the calculation efficiency is improved by more than one order of magnitude compared with the full-order CFD method, and has good engineering application prospect.

Claims

1. A method of modeling thermal runaway propagation in lithium-ion batteries coupled with a semi-empirical flame radiation model, characterized in that, The method comprises the following steps: S1. Selecting a lithium ion battery, obtaining gas components, jet velocity fluid parameters, material physical parameters and geometric characteristic parameters after thermal runaway of a single battery; S2. Simulating pure gas phase jet fire under different nozzle diameters and flow rates according to the gas components and jet velocity fluid parameters, and obtaining a flame radiation fraction by means of a single-point source method; S3. Obtaining jet fire height and heat release rate input parameters under a top plate restriction, and establishing 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 a cylindrical flame and a cuboid flame; In step S3, the view factor of the cylindrical flame is calculated by the following formula: ； wherein is the view factor of the cylindrical flame to the horizontal plane, , , , , represents the equivalent diameter of the cylindrical flame, and respectively represent the height and diameter of the cylindrical flame; In step S3, the view factor of the cuboid flame is calculated by the following formula: ； ； wherein, is the view factor of a cuboid fire to a vertical plane, is the view factor component of the nth cuboid fire, and are the width and height, respectively, of the nth cuboid fire, is the distance from the target to the cuboid fire; S4. Obtaining battery top surface flame radiation heat transfer by using semi-empirical radiation model integration to obtain a radiation heat source, and coupling the radiation heat source to a heat source term of a three-dimensional thermal runaway propagation model; S5. Solving a heat transfer model based on a finite volume method to obtain a three-dimensional temperature distribution containing flame heat transfer.

2. The coupled semi-empirical flame radiation model lithium-ion battery thermal runaway propagation modeling method of claim 1, wherein, In step S2, when the single-point source method is used to obtain the flame radiation fraction, the horizontal distance between a radiation heat flow meter and the center of a burner is not less than 5 times the diameter of the burner, and the flame radiation fraction is calculated by the following formula: ； where, is the radiant heat flux, is the fuel mass flow rate, is the fuel heat value, is the flame height and determined by pre-experiments, and represent the axial and radial distance of the heat flux meter from the burner center, respectively, is the radiation fraction function, is the flame radiation fraction and , denotes the distance between the heat flux meter and the flame center.

3. The coupled semi-empirical flame radiation model lithium-ion battery thermal runaway propagation modeling method of claim 1, wherein, In step S4, the radiant heat source is calculated by integration: ； wherein, is a time-varying radiant heat source, is a radiant heat flux density and is a function of time and space, is a normal vector to the top surface of the battery, is a view factor from a radiant source point to a target point , is a differential area of the top surface of the battery, is a battery top surface integration region.

4. The coupled semi-empirical flame radiation model lithium-ion battery thermal runaway propagation modeling method of claim 1, wherein, In step S4, the control equation of the three-dimensional thermal runaway propagation model comprises: ； wherein, is the battery density, is the specific heat capacity of the battery, is the battery temperature, is time, denotes the transient change of energy within a unit volume, is the thermal conductivity of the battery, is the sum of side reaction heat sources when the battery is in thermal runaway, is the equivalent convection loss source term, is the hot plate source term, is the flame radiation source term, denotes the contribution characterizing heat conduction, is the Laplace operator, denoting the gradient of the physical quantity with which it is associated.

5. The coupled semi-empirical flame radiation model lithium-ion battery thermal runaway propagation modeling method of claim 4, wherein, The sum of side reaction heat sources when the battery thermal runaway calculated by the Arrhenius equation, and the progress variable of the thermal runaway side reaction follows the following transport equation: ； where the transient term is obtained by disabling the convection and diffusion flux terms and the source term is described by the following equation: ； ； 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.

6. The coupled semi-empirical flame radiation model lithium-ion battery thermal runaway propagation modeling method of claim 1, wherein: In step S5, the heat transfer model based on the finite volume method is implemented in an OpenFOAM framework, and an implicit Euler discrete method is used to process an Arrhenius type reaction source term.

7. The coupled semi-empirical flame radiation model- lithium ion battery thermal runaway propagation modeling method of claim 1, wherein: In step S3, the height of the cylindrical flame It equals the height of the top plate.

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