A simplified calculation method for heat transfer of particle deposition from battery thermal runaway eruptions

Abstract

The present invention discloses a simplified calculation method for the deposition and heat transfer of particles erupting from a battery due to thermal runaway. The main purpose is to solve the problem that after applying the CFD-DEM coupling method to simulate the deposition of particles erupting from a battery, the simulation time is too long due to the limitation of too small a time step. The present invention proposes a simplified method for continuous conversion of particles into a continuous medium based on the volume fraction of the particle phase, comprising the following steps: first, traverse the flow field calculation grid containing the particles and establish a particle contact index table, and for the grids whose particle volume ratio exceeds a preset threshold, perform continuous equivalent processing and update the physical properties and temperature. The contact heat transfer coefficient and contact area between the particles and the wall are calculated by the discrete element contact model, and the contact thermal resistance between the particles and the wall is calculated and applied to the contact interface between the equivalent medium and the battery wall. At the same time, the interface heat transfer conditions between the physical domains are calculated to solve the temperature field of the battery system and conduct a risk assessment of the battery system's subsequent thermal runaway accidents.

Description

Technical Field

[0001] The present application relates to the technical field of physical field coupling simulation, and in particular to a simplified calculation method for heat transfer of particle deposition caused by thermal runaway eruption of a battery. Background Art

[0002] When a lithium-ion battery is triggered into thermal runaway by external factors, the battery particles carried out by various high-temperature fumes inside the battery are diffused into the battery system along with the smoke, and after multiple collisions within the battery system, they are deposited locally. Studies have shown that the heat transfer rate of high-temperature deposited particles near the wall is higher than the heat transfer rate between the smoke and the battery wall, which has a higher risk of causing battery thermal runaway. Currently, the CFD-DEM coupling method can be used to simulate the deposition and heat transfer of battery eruption particles. The discrete element method is used to accurately calculate the force and heat transfer of each particle. The temperature changes of the flow field within the battery and the battery system are calculated based on the CFD method to assess the risk of battery thermal runaway.

[0003] However, since particulate matter is a discrete medium, a mathematical model based on the Lagrangian perspective is used to track the motion state of each particle. However, due to the Rayleigh time step, an extremely short time step must be used to accurately determine particle contact and calculate the forces acting on the particles to avoid divergence. At the same time, the CFD calculation time step also needs to be coordinated with the DEM time step. The particles emitted by batteries are mainly composed of metals and carbon elements in battery materials, and the particle size is mostly below 0.1mm, which limits the discrete element calculation time step to the order of 1e-7 to 1e-6. Each simulation requires millions of time steps of iteration, which is too time-consuming and difficult to be practical in engineering. Due to the differences in the modeling methods of flue gas and particulate matter, the time step setting has become a major problem restricting the engineering application of the model. At the same time, the heat transfer of battery particle deposition may also cause thermal runaway eruptions in other normal batteries. It is also necessary to couple the battery thermal runaway model, involving the coupling of multiple physical fields. Summary of the Invention

[0004] In response to the above-mentioned technical problems, the present invention provides a simplified method for calculating the deposition and heat transfer of particles ejected during battery thermal runaway. The specific technical solution is as follows:

[0005] In view of the operating conditions of the battery system where thermal runaway of the battery emits smoke and particulate matter at the end, and high-temperature particulate matter is deposited in large quantities, the temperature changes inside the battery system are simulated. Through CFD-DEM (computational fluid dynamics-discrete element coupling) coupled calculations, the full-domain physical field information of the battery system at the end of the thermal runaway eruption of a single battery is obtained. The CFD-DEM coupled control equation consists of two parts: the fluid dynamics equation of the flue gas flow domain and the particle dynamics equation. The fluid dynamics equation of the flue gas is as follows:

[0006] The mass conservation equation is as follows:

[0007]

[0008] In the above formula (1), ε f is the volume fraction of flue gas, ρ f is the density of smoke, is the velocity of the flue gas.

[0009] The momentum conservation equation is as follows (2):

[0010]

[0011] In the above formula (2), P is the pressure of the flue gas, is the viscous stress of flue gas, is the force exerted by the particle on the fluid, and g is the acceleration due to gravity.

[0012] The energy conservation equation is as follows (3):

[0013]

[0014] In the above formula (3), c f is the specific heat capacity of flue gas, T f is the flue gas temperature, λ f is the thermal conductivity of flue gas, q p It is the volume heat source of heat transfer from particles to flue gas.

[0015] Because there are multiple components in the flue gas, in order to reflect the diffusion of each flue gas component in the battery system, the multi-component diffusion equation is also applied as follows (4):

[0016]

[0017] In the above formula (4), Y i is the mass fraction of each component, J i is the diffusion flux of each component, R i is the composition change caused by chemical reaction, S i A mass source term generated for a component.

[0018] Based on Newton's law of motion, the particle motion equation is established as follows (5):

[0019]

[0020] The above equation (5) is the motion equation of a single particle, where m p is the mass of the particle, is the particle speed, is the force of collision between particles or between particles and the wall, which is calculated by the contact model of discrete elements. is the force exerted by the flue gas on the particles, and Equal in value but opposite in direction.

[0021] The heat transfer equation of the particles is as follows (6):

[0022]

[0023] In the above formula (6), c p is the specific heat capacity of the particle, Q c is the heat transfer between particles and between particles and the wall, Q f The heat transfer between particles and flue gas.

[0024] The above equations are solved by the CFD-DEM coupling method to simulate the deposition behavior of particles. After a large amount of particles are deposited, the velocity, temperature field, volume distribution of the flue gas flow field occupied by the particles, and the concentration of each flue gas component are obtained; for the particle discrete medium, the temperature, specific heat capacity, thermal conductivity, elastic modulus, Poisson's ratio, density, collision force, radius and center coordinates of each particle are obtained; for the solid area where the remaining uncontrolled batteries are located, the temperature distribution, thermal conductivity, density and specific heat capacity are obtained. The calculation equation of the particle volume fraction is as follows (7):

[0025]

[0026] In the above formula (7), Vp i is the volume of the particles in the flue gas flow domain, V cell Calculate the volume of the grid cell for the flue gas flow domain, the volume fraction of the flue gas ε f =1-ε p Traverse each flue gas flow domain calculation grid and calculate the volume fraction of particles and the volume fraction of flue gas in each grid to obtain the volume fraction distribution.

[0027] In the CFD-DEM coupled simulation, the contact model needs to be redeveloped in the discrete element program. Based on the geometric relationship between the particle center coordinates and the wall, the particle contact point coordinates are calculated. The particle-wall contact point information is used as the particle's own attribute. Once the particle contacts the wall, the contact point's own attribute value is updated with the new particle-wall contact point coordinates. In the CFD program, the particle's contact point's own attribute value is obtained, the battery wall calculation unit in contact with the particle is found, and a contact index table is constructed. The index table contains the particle index ID number, the wall unit index, the normal force between the particle and the collision wall, the particle's specific heat capacity, thermal conductivity, elastic modulus, Poisson's ratio, and density, and the battery wall unit's elastic modulus, Poisson's ratio, density, thermal conductivity, and specific heat capacity. If the particle does not collide with the wall, all contents except the particle's own index ID are set to 0. Each particle is traversed to establish a complete particle-wall contact index table. This table supports bidirectional search, that is, you can query the wall unit information that the particle contacts through the particle index ID, and you can also search for information on all particles that contact the wall through the wall unit index.

[0028] According to the volume fraction of particulate matter in the flue gas flow domain, the first and second volume fraction thresholds are set. The selection of the first and second thresholds depends on the thermal properties and flow state of the flue gas and particles. In actual value selection, multiple particle deposition experiments can be carried out, and the values ​​can be selected according to experimental experience, and the threshold values ​​can be adjusted according to the experimental results. The flue gas domain calculation grid cells near the battery wall area are traversed. According to the particle volume fraction in the calculation grid cells, if the particle volume fraction exceeds the first threshold, it is considered that the particles dominate the spatial area represented by the calculation grid. The calculation grid cell area mainly shows the characteristics of the particles themselves. Compared with the heat transfer between the particles and the flue gas in the grid, the heat transfer between the particles can be approximately ignored. The heat transfer between the particles is mainly considered. The calculation grid is converted from the flue gas flow domain calculation grid to the particle equivalent solid medium calculation grid. At the same time, the corresponding physical control equation is converted from the multi-component equation describing the flue gas flow to the heat conduction equation describing the particle equivalent solid medium, and then the medium properties represented by the calculation grid are updated. According to the principle of mass conservation, the equivalent solid medium thermal properties are updated as follows (8)-(10):

[0029] cp s =ε p c p +(1-ε p )c f (8)

[0030] k s =ε p λ p +(1-ε p )λf (9)

[0031] ρ s =ε p ρ p +(1-ε p )ρ f (10)

[0032] In the above formulas (8)-(10), cp s 、k s , ρ s are the specific heat capacity, thermal conductivity and density of the equivalent solid medium respectively. p is the thermal conductivity of the particles, ρ p is the density of the particles. The above formula shows that the physical properties of the equivalent solid medium are the weighted average of the physical properties of the particles and the flue gas, with the volume fraction of the particles and the flue gas as the weight.

[0033] As for the temperature of the equivalent solid, it is updated according to the principle of energy conservation, as shown in the following formula (11):

[0034]

[0035] In the above formula (11), T s Calculate the average temperature of a grid cell for the equivalent solid medium as the ratio of the total energy of all particles in the grid to the total heat capacity and total mass of all particles.

[0036] If the particle volume fraction within the computational grid cell is below the second threshold, the flue gas is considered to still dominate the spatial region represented by the computational grid, and the computational grid cell remains a flue gas flow domain computational grid cell. If the particle volume fraction is between the second and first thresholds, the flue gas and particulate matter are considered to have a significant influence within the computational cell. The porous media model demonstrates that the presence of particles hinders the flow of flue gas within the computational cell. Through this continuous transformation process, particulate matter, originally in the form of a discrete medium, is transformed into a continuous medium.

[0037] After continuous processing, the interfacial heat transfer conditions between the physical regions within the battery system are obtained. Based on the particle-wall contact index table, all particle information contacting any battery wall is retrieved. The particle radius, elastic modulus, Poisson's ratio, specific heat capacity, thermal conductivity, and normal force acting on the wall are extracted and substituted into the discrete element contact model to calculate the contact thermal resistance between the particle and the wall as shown in Equation (12).

[0038]

[0039] In the above formula (12), h c k is the thermal conductivity of the contact area between the particle and the wall,p1 and k p2 are the thermal conductivity of particles and wall, F N is the normal force of the particle colliding with the wall. E * is the equivalent elastic modulus after the particle contacts the wall, r * is the geometric mean radius of the particles calculated by contact theory. In the calculation process, the wall is regarded as a particle with infinite radius.

[0040] The definition and calculation formula of the contact thermal resistance between a single particle and the wall are as follows (13) and (14):

[0041]

[0042] In the above equations (13) and (14), q is the heat transfer rate between a single particle and the wall, T i is the particle temperature, T wall is the wall temperature in contact with the particles, R p is the contact thermal resistance between the particle and the wall, which reflects the barrier to heat transfer between the particle and the wall. The closer the contact between the particle and the wall, the higher the contact thermal conductivity, the smaller the corresponding contact thermal resistance, and the better the contact heat transfer effect.

[0043] Since a battery wall may be in contact with multiple particles at the same time, the contact thermal resistance between the particles and the equivalent medium is regarded as the parallel form of the contact thermal resistance between multiple particles and the wall. The contact thermal resistance between the battery wall and the particle equivalent solid medium is calculated according to the parallel thermal resistance calculation method. The more particles in contact with the wall, the smaller the contact thermal resistance between the particle group and the wall, as shown in the following formula (15).

[0044]

[0045] In the above formula (15), R w is the total contact thermal resistance between the wall and all particles in contact with it, R p1 , R pn is the thermal resistance between a single particle and the wall, and the total number is n.

[0046] The interfacial heat transfer conditions between the battery wall and the flue gas flow domain, and between the equivalent solid medium and the flue gas flow domain, apply the interfacial heat flow continuity conditions of fluid-solid coupled heat transfer, and the flow boundary conditions apply the slip boundary conditions.

[0047] The conjugate heat transfer boundary conditions for continuous interface heat flow at the gas-solid interface between the battery wall and the flue gas flow region, and the equivalent solid medium and the flue gas flow region are as follows (16):

[0048]

[0049] In the above formula (16), represents the heat flux density of flue gas to the gas-solid interface, is the normal vector pointing to the gas-solid interface from the flue gas side, is the heat flux density of heat transfer inside the solid phase at the gas-solid interface, is the external normal vector of the solid phase pointing to the gas-solid interface. f and k st are the thermal conductivity coefficients of flue gas and solid phase near the gas-solid interface, T w is the temperature at the gas-solid interface, and Δy is the normal distance from the center of the computational grid near the wall of the gas phase and the solid phase to the gas-solid interface.

[0050] After completing the above steps, all discrete medium regions containing particles are converted into equivalent continuous media. Based on the heat transfer law of continuous media, the physical field control equations are established and solved using the finite volume method.

[0051] For the battery area, the temperature change inside the battery satisfies the heat conduction differential equation. At the same time, as the battery temperature continues to rise, the battery thermal runaway reaction is triggered, and the reaction heat is introduced, causing the battery to continue to rise in temperature uncontrollably and form thermal runaway, as shown in the following equations (17)-(19):

[0052]

[0053] Q gen =m i ΔH i κ i (18)

[0054]

[0055] In the above formulas (17), (18), and (19), ρ bat is the density of the battery, Cp bat is the specific heat capacity of the battery, λ bat is the thermal conductivity of the battery, T bat is the battery temperature, t is the time, Q gen is the heat source term. m i is the mass of reactants in the battery thermal runaway reaction, ΔH i is the enthalpy of thermal runaway reaction, κ i is the reaction rate, which is a function related to temperature through the Arrhenuis formula, A i is the pre-exponential factor of the reaction, E a,i is the activation energy of the reaction, c i is the normalized concentration of the reactant, and R is the gas constant.

[0056] For equivalent solid media, particles do not participate in chemical reactions and do not undergo phase changes, so there is no heat and mass transport process, but the heat conduction differential equation still satisfies the following equation (20):

[0057]

[0058] In the above formula (20), T s is the temperature of the equivalent solid medium area. It should be pointed out that there is a contact thermal resistance between the equivalent medium and the battery wall area. The contact heat transfer boundary conditions are as follows (21), (22), and (23):

[0059]

[0060] In the above formulas (21)-(23), n bat and n s are the normal vectors from the battery side and the equivalent medium side at the interface, and h is the joint thermal conductivity at the interface, which is the inverse of the thermal resistance of the interface. s and T bat is the temperature of the equivalent medium and battery on both sides of the contact surface, Q f is the heat generated by friction. If there is no relative displacement between the battery and the equivalent solid medium, there is no frictional heat generation. r is the distribution ratio of frictional heat on both sides of the contact surface.

[0061] For flue gas, its diffusion equation still satisfies the fluid dynamics equations for multi-component transport as follows (24):

[0062]

[0063] Similarly, the variables have the same meaning as in (1)-(3). In the flue gas flow domain, ε f =1, while in the porous medium region, ε f is a number between 0 and 1, as shown in formula (25).

[0064]

[0065] In the above formula (25), is the force exerted by particles on the flow field. In the porous medium region, The volume fraction of the particle phase is calculated using Darcy's law, and in the flue gas flow domain, this term is 0.

[0066] The energy conservation in the flue gas flow domain is as follows (26):

[0067]

[0068] The above physical field control equations and interface heat transfer conditions are combined, and the finite volume method is used to discretize the equations and solve them. The temperature field information of the entire battery system is obtained, and the temperature field changes as the simulation progresses. Based on the temperature field, it is determined whether the remaining batteries are at risk of thermal runaway. If a battery is at risk of thermal runaway, CFD-DEM coupled calculations are continued to obtain the deposition distribution relationship of particulate matter in the battery system. The above steps are repeated, and the temperature field in the battery system is re-simulated until the preset simulation time or other simulation termination conditions are reached.

[0069] The beneficial effects of the present invention are as follows:

[0070] (1) Since particles are discrete media, a solution method based on the Euler-Lagrangian framework is often used to simulate the multiphase flow process containing particles. This method requires tracking a large number of particles, and is limited by the Rayleigh time step limit of the discrete element method. The time for flow field calculation is also greatly reduced accordingly, resulting in a very time-consuming process of simulating heat transfer after particle deposition. The present invention uses a reasonable continuous transformation method. After a large amount of particles are deposited, the particles in the discrete medium are reclassified into the category of continuous media in accordance with the principles of conservation of energy, conservation of mass, and conservation of momentum. Physical field control is uniformly established based on the characteristics of the continuous medium, so that each physical field in the battery system can be solved synchronously, avoiding multiple data interactions and iterative processes between particles and flue gas, and particles and batteries, greatly improving the calculation efficiency, and meeting the accuracy requirements of engineering safety design.

[0071] (2) Through a continuous approach, the present invention avoids the potential for global computational non-convergence caused by a sudden change in volume fraction and momentum in the local flue gas domain due to the movement of a small number of particles. This overcomes the Rayleigh time step limitation, significantly increasing the simulation time step while maintaining good robustness. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] In order to more clearly illustrate the technical solutions in the embodiments of the present application or related technologies, the following briefly introduces the drawings required for use in the embodiments of the present application or related technical descriptions. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without paying any creative work.

[0073] Figure 1 A schematic diagram of the principle of constructing the particle-avoidance index table according to the present invention;

[0074] Figure 2 Schematic diagram of the principle of continuousization of a particle discrete medium based on the particle phase volume fraction according to the present invention;

[0075] Figure 3This is a flow chart of a simplified method for calculating the deposition and heat transfer of particles ejected during thermal runaway of a battery, as described in the present invention. DETAILED DESCRIPTION

[0076] In order to more clearly illustrate the purpose, technical solutions and principles of the present invention, the present invention is further described in detail below in conjunction with specific implementation examples and drawings. The schematic implementation method of the present invention and its description are only used to explain the present invention and are not intended to limit the present invention.

[0077] To address the difficulties in calculating the heat transfer and deposition of particles emitted by a battery during thermal runaway, this embodiment proposes a simplified calculation method for the heat transfer and deposition of particles emitted by a battery during thermal runaway. Specifically, the method includes:

[0078] In view of the operating conditions of the battery system where the battery thermal runaway emits smoke and particulate matter at the end stage, and high-temperature particulate matter is deposited in large quantities, the temperature changes inside the battery system are simulated. Through CFD-DEM (computational fluid dynamics-discrete element coupling) coupling calculation, the physical field information of the entire battery system at the end stage of the thermal runaway eruption of a single battery is obtained. The CFD-DEM coupling control equation consists of two parts: the fluid dynamics equation of the flue gas flow domain and the particle dynamics equation. The fluid dynamics equation of the flue gas is as follows (27):

[0079] The mass conservation equation:

[0080]

[0081] In the above formula (27), ε f is the volume fraction of flue gas, ρ f is the density of smoke, is the velocity of the flue gas.

[0082] The momentum conservation equation is as follows (28):

[0083]

[0084] In the above formula (28), P is the pressure of the flue gas, is the viscous stress of flue gas, is the force exerted by the particle on the fluid, and g is the acceleration due to gravity.

[0085] The energy conservation equation is as follows (29):

[0086]

[0087] In the above formula (29), c f is the specific heat capacity of flue gas, T f is the flue gas temperature, λ f is the thermal conductivity of flue gas, q p It is the volume heat source of heat transfer from particles to flue gas.

[0088] Because there are multiple components in the flue gas, in order to reflect the diffusion of each flue gas component in the battery system, the multi-component diffusion equation is also applied as follows (30):

[0089]

[0090] In the above formula (30), Y i is the mass fraction of each component, J i is the diffusion flux of each component, R i is the composition change caused by chemical reaction, S i A mass source term generated for a component.

[0091] Based on Newton's law of motion, the particle motion equation is established as follows (31):

[0092]

[0093] The above equation (31) is the motion equation of a single particle, where m p is the mass of the particle, is the particle speed, is the force of collision between particles or between particles and the wall, which is calculated by the contact model of discrete elements. is the force exerted by the flue gas on the particles, and Equal in value but opposite in direction.

[0094] The heat transfer equation of the particles is as follows (32):

[0095]

[0096] In the above formula (32), c p is the specific heat capacity of the particle, Q c is the heat transfer between particles and between particles and the wall, Q f The heat transfer between particles and flue gas.

[0097] The above equations are solved by the CFD-DEM coupling method to simulate the deposition behavior of particles. After a large amount of particles are deposited, the velocity and temperature field of the flue gas flow domain, the volume distribution of the particles in the flue gas flow domain, and the concentration of each flue gas component are obtained; for the discrete particle medium, the temperature, specific heat capacity, thermal conductivity, elastic modulus, Poisson's ratio, density, collision force, radius and center coordinates of each particle are obtained; for the solid area where the remaining uncontrolled batteries are located, the temperature distribution, thermal conductivity, density and specific heat capacity are obtained. The calculation equation of the particle volume fraction is as follows (33):

[0098]

[0099] In the above formula (33ws), Vp i is the volume of the particles in the flue gas flow domain, V cell Calculate the volume of the grid cell for the flue gas flow domain, the volume fraction of the flue gas ε f =1-ε p Traverse each flue gas flow domain calculation grid and calculate the volume fraction of particles and the volume fraction of flue gas in each grid to obtain the volume fraction distribution.

[0100] As attached Figure 1 As shown, in the CFD-DEM coupling simulation, it is necessary to conduct secondary development of the contact model in the discrete element program. According to the geometric relationship between the particle center coordinates and the wall surface, the particle contact point coordinates are calculated, and the particle-wall contact point information is used as the particle's own attribute. Once the particle contacts the wall surface, the contact point's own attribute value is updated with the new particle-wall contact point coordinates. In the CFD program, the particle's contact point's own attribute value is obtained, the battery wall calculation unit in contact with the particle is found, and a contact index table is constructed. Figure 1 The basic format and information of the index table are given in [1]. The index table contains the particle index ID, the wall unit index, the normal force between the particle and the collision wall, the particle's specific heat capacity, thermal conductivity, elastic modulus, Poisson's ratio, and density, and the elastic modulus, Poisson's ratio, density, thermal conductivity, and specific heat capacity of the battery wall unit. If a particle does not collide with a wall, all contents except the particle's own index ID are set to 0. A complete particle-wall contact index table is constructed by traversing each particle. This table supports bidirectional search: you can query the wall unit information that a particle contacts using the particle index ID, and you can also query all particles in contact with the wall using the wall unit index.

[0101] As attached Figure 2As shown, according to the volume fraction of particulate matter in the flue gas flow domain, the first and second volume fraction thresholds are set. The selection of the first and second thresholds depends on the thermal properties and flow state of the flue gas and particles. In actual value selection, multiple particle deposition experiments can be carried out, and the values ​​can be selected according to experimental experience, and the threshold values ​​can be adjusted according to the experimental results. The flue gas domain calculation grid cells near the battery wall area are traversed. According to the particle volume fraction in the calculation grid cells, if the particle volume fraction exceeds the first threshold, it is considered that the particles dominate the spatial area represented by the calculation grid. The calculation grid cell area mainly shows the characteristics of the particles themselves. Compared with the heat transfer between the particles and the flue gas in the grid, the heat transfer between the particles can be approximately ignored. The heat transfer between the particles is mainly considered. The calculation grid is converted from the flue gas flow domain calculation grid to the particle equivalent solid medium calculation grid. At the same time, the corresponding physical control equation is converted from the multi-component equation describing the flue gas flow to the heat conduction equation describing the particle equivalent solid medium, and then the medium properties represented by the calculation grid are updated. According to the principle of mass conservation, the equivalent solid medium thermal properties are updated as follows (34)-(36):

[0102] cp s =ε p c p +(1-ε p )c f (34)

[0103] k s =ε p λ p +(1-ε p )λ f (35)

[0104] ρ s =ε p ρ p +(1-ε p )ρ f (36)

[0105] In the above formulas (34)-(36), cp s 、k s , ρ s are the specific heat capacity, thermal conductivity and density of the equivalent solid medium respectively. p is the thermal conductivity of the particles, ρ p is the density of the particles. The above formula shows that the physical properties of the equivalent solid medium are the weighted average of the physical properties of the particles and the flue gas, with the volume fraction of the particles and the flue gas as the weight.

[0106] As for the temperature of the equivalent solid, it is updated according to the principle of energy conservation as follows (37):

[0107]

[0108] In the above formula (37), T s Calculate the average temperature of a grid cell for the equivalent solid medium as the ratio of the total energy of all particles in the grid to the total heat capacity and total mass of all particles.

[0109] If the volume fraction of particles in the computational grid unit area is lower than the second threshold, it is considered that the smoke still occupies a dominant position in the spatial area represented by the computational grid, and the computational grid unit still remains a computational grid unit for the flue gas flow domain. If the volume fraction of particles is between the second threshold and the first threshold, it is considered that both smoke and particulate matter have a considerable influence in the computational unit, and the porous media model is applied to show that the presence of particles hinders the flow of smoke in the computational unit. Through this continuous transformation process, the particulate matter originally in the form of discrete media is transformed into a continuous medium. In the attached Figure 2 In the figure, the unused shaded areas represent unused physical domains. The black shaded areas are equivalent medium solid meshes, while the areas with too small particle volume fractions are unshaded areas in the figure, which are still the original smoke areas. The gray shaded areas are porous medium areas with particle volume fractions within a certain range. Figure 2 Demonstrates how to convert a discrete granular medium into a continuous medium.

[0110] After continuous processing, the interfacial heat transfer conditions between the physical regions within the battery system are obtained. Based on the particle-wall contact index table, all particle information contacting any battery wall is retrieved. The particle radius, elastic modulus, Poisson's ratio, specific heat capacity, thermal conductivity, and normal force acting on the wall are extracted and substituted into the discrete element contact model to calculate the contact thermal resistance between the particle and the wall as shown in Equation (38).

[0111]

[0112] In the above formula (38), h c k is the thermal conductivity of the contact area between the particle and the wall, p1 and k p2 are the thermal conductivity of particles and wall, F N is the normal force of the particle colliding with the wall. E * is the equivalent elastic modulus after the particle contacts the wall, r * is the geometric mean radius of the particles calculated by contact theory. In the calculation process, the wall is regarded as a particle with infinite radius.

[0113] The definition and calculation formula of the contact thermal resistance between a single particle and the wall are as follows (39) and (40):

[0114]

[0115] In the above equations (39) and (40), q is the heat transfer rate between a single particle and the wall, T i is the particle temperature, T wall is the wall temperature in contact with the particles, R p is the contact thermal resistance between the particle and the wall, which reflects the barrier to heat transfer between the particle and the wall. The closer the contact between the particle and the wall, the higher the contact thermal conductivity, the smaller the corresponding contact thermal resistance, and the better the contact heat transfer effect.

[0116] Since a battery wall may be in contact with multiple particles at the same time, the contact thermal resistance between the particles and the equivalent medium is regarded as the parallel form of the contact thermal resistance between multiple particles and the wall. According to the parallel thermal resistance calculation method, the contact thermal resistance between the battery wall and the particle equivalent solid medium is calculated. When the number of particles in contact with the wall is greater, the contact thermal resistance between the particle group and the wall is smaller, as shown in the following formula (41).

[0117]

[0118] In the above formula (41), R w is the total contact thermal resistance between the wall and all particles in contact with it, R p1 , R pn is the thermal resistance between a single particle and the wall, and the total number is n.

[0119] The interfacial heat transfer conditions between the battery wall and the flue gas flow domain, and between the equivalent solid medium and the flue gas flow domain, apply the interfacial heat flow continuity conditions of fluid-solid coupled heat transfer, and the flow boundary conditions apply the slip boundary conditions.

[0120] The conjugate heat transfer boundary conditions for continuous interface heat flow at the gas-solid interface between the battery wall and the flue gas flow region, and the equivalent solid medium and the flue gas flow region are as follows (42):

[0121]

[0122] In the above formula (42), represents the heat flux density of flue gas to the gas-solid interface, is the normal vector pointing to the gas-solid interface from the flue gas side, is the heat flux density of heat transfer inside the solid phase at the gas-solid interface, is the external normal vector of the solid phase pointing to the gas-solid interface. f and k st are the thermal conductivity coefficients of flue gas and solid phase near the gas-solid interface, T w is the temperature at the gas-solid interface, and Δy is the normal distance from the center of the computational grid near the wall of the gas phase and the solid phase to the gas-solid interface.

[0123] After completing the above steps, all discrete medium regions containing particles are converted into equivalent continuous media. Based on the heat transfer law of continuous media, the physical field control equations are established and solved using the finite volume method.

[0124] For the battery area, the temperature change inside the battery satisfies the thermal conduction differential equation. At the same time, as the battery temperature continues to rise, the battery thermal runaway reaction is triggered, and the reaction heat is introduced, causing the battery to continue to rise in temperature uncontrollably and form thermal runaway, as shown in the following equations (43)-(45):

[0125]

[0126] Q gen =m i ΔH i κ i (44)

[0127]

[0128] In the above formulas (43)-(45), ρ bat is the density of the battery, Cp bat is the specific heat capacity of the battery, λ bat is the thermal conductivity of the battery, T bat is the battery temperature, t is the time, Q gen is the heat source term. m i is the mass of reactants in the battery thermal runaway reaction, ΔH i is the enthalpy of thermal runaway reaction, κ u is the reaction rate, which is a function related to temperature through the Arrhenuis formula, A i is the pre-exponential factor of the reaction, E a,i is the activation energy of the reaction, c i is the normalized concentration of the reactant, and R is the gas constant.

[0129] For the equivalent solid medium, the particles do not participate in chemical reactions and do not undergo phase changes, so there is no heat and mass transport process, but the heat conduction differential equation still satisfies the following equation (46):

[0130]

[0131] In the above formula (46), T s is the temperature of the equivalent solid medium area. It should be pointed out that there is a contact thermal resistance between the equivalent medium and the battery wall area. The contact heat transfer boundary conditions are as follows (47)-(49):

[0132]

[0133] In the above formulas (47)-(49), n batand n s are the normal vectors from the battery side and the equivalent medium side at the interface, and h is the joint thermal conductivity at the interface, which is the inverse of the thermal resistance of the interface. s and T bat is the temperature of the equivalent medium and battery on both sides of the contact surface, Q f is the heat generated by friction. If there is no relative displacement between the battery and the equivalent solid medium, there is no frictional heat generation. r is the distribution ratio of frictional heat on both sides of the contact surface.

[0134] For flue gas, its diffusion equation still satisfies the fluid dynamics equations for multi-component transport as follows (50):

[0135]

[0136] Similarly, the variables have the same meaning as in (1)-(3). In the flue gas flow domain, ε f =1, while in the porous medium region, ε f A number between 0 and 1.

[0137]

[0138] In the above formula (51), is the force exerted by particles on the flow field. In the porous medium region, The volume fraction of the particle phase is calculated using Darcy's law, and in the flue gas flow domain, this term is 0.

[0139] The energy conservation in the flue gas flow domain is as follows (52):

[0140]

[0141] As attached Figure 3 The calculation steps shown combine the above physical field control equations and interface heat transfer conditions, discretize the equations using the finite volume method, and solve them. The temperature field information of the entire battery system is obtained, and the temperature field changes as the simulation progresses. Based on the temperature field, it is determined whether the remaining batteries are at risk of thermal runaway. If a battery is at risk of thermal runaway, the CFD-DEM coupled calculation is continued to obtain the deposition distribution relationship of the particulate matter in the battery system. The above steps are repeated to re-simulate the temperature field in the battery system until the preset simulation time or other simulation termination conditions are reached.

Claims

1. A simplified calculation method for the deposition and heat transfer of particulate matter ejected during battery thermal runaway. This method simulates the evolution of the temperature field inside the battery system, targeting the final stage of the battery thermal runaway eruption of smoke and particulate matter, and the conditions of large-scale deposition of high-temperature particulate matter. The method is characterized by: The specific steps include: Step 1: Obtain the physical field information of the entire battery system at the end of the thermal runaway eruption of a single battery through CFD-DEM (computational fluid dynamics-discrete element coupling) coupling calculation; the battery system is a limited and enclosed space containing a battery module and a gas flow domain. The specific physical field information is: for the flue gas flow domain within the battery system, obtain the velocity, temperature field, volume distribution of the flue gas flow domain occupied by particles, and concentrations of various components of the flue gas; for the particle discrete medium, obtain the temperature, specific heat capacity, thermal conductivity, elastic modulus, Poisson's ratio, density, collision force, radius and center coordinates of each particle; for the solid area where the remaining non-runaway batteries are located, obtain the temperature distribution, thermal conductivity, density and specific heat capacity; Step 2: Based on the physical field information, each particle is traversed and the positional relationship between the particle center, particle radius and the battery surface wall unit is used to determine whether the particle is in contact with the battery surface, and a particle-wall contact index table is established. The index table includes the index of the wall unit contacted by the particle, the normal force between the particle and the wall, and the mechanical / thermal properties of the particle. By querying the index table, the particle information contacted by any battery wall unit at the current computer simulation time can be found. Step 3: Traverse each computational unit in the flue gas flow domain, find the computational grid unit in the flue gas flow domain where the particle is located based on the particle center coordinates, and calculate the volume fraction of the particle in the flue gas grid unit; re-divide the physical field based on the volume fraction of the particle in the flue gas flow domain; set a first threshold and a second threshold for the volume fraction of the flue gas flow domain where the particle is located; if the volume fraction of particulate matter in the flue gas flow domain near the battery wall is too high, exceeding the first threshold, the physical properties of the flue gas flow domain computational grid unit are dominated by particulate matter, and the flue gas flow domain computational grid unit is converted into an equivalent solid medium unit; if the particle volume fraction is lower than the second threshold, it indicates that the flue gas itself still dominates the flue gas flow domain computational grid unit, ignoring the influence of particulate matter, and the flue gas flow domain computational grid unit is still regarded as a flue gas calculation unit; if the volume fraction of particulate matter is between the second threshold and the first threshold, it indicates that both flue gas and particulate matter have a considerable influence in the flue gas flow domain computational grid unit, and the flue gas flow domain computational grid unit is converted into a porous medium computational unit; after dividing each physical domain, recalculate the temperature of the equivalent solid medium region; Step 4: After redisting the various physical fields within the battery system, calculate the heat transfer interface conditions between the various physical fields. For the contact heat transfer boundary conditions between the particles and the battery, first obtain the number of particles contacted by any battery wall and the information of each particle contacted based on the particle-wall contact index table. Calculate the contact thermal resistance between a single particle and the wall based on the discrete element contact model. Since the wall may be in contact with multiple particles at the same time, the contact thermal resistance between the particle and the equivalent medium is regarded as the parallel form of the contact thermal resistance between multiple particles and the wall. This contact thermal resistance is used as the contact thermal resistance between the battery and the equivalent solid medium formed by the particle deposition. For the battery area and the flue gas flow domain, a fluid-solid coupled heat flow continuity boundary is applied. Step 5: Convert all discrete medium regions containing particles into equivalent continuous media. Based on the heat transfer law of continuous media, establish the physical field control equations, apply the finite volume method to solve them, obtain the temperature field information of the entire battery system and the changes in the temperature field as the simulation progresses, and judge whether the remaining batteries have the risk of thermal runaway based on the temperature field. If there is a battery thermal runaway, continue to carry out CFD-DEM coupling calculations to obtain the deposition distribution relationship of particulate matter in the battery system. Repeat the above steps and re-simulate the temperature field in the battery system until the preset simulation time or other simulation termination conditions are reached.

2. The method according to claim 1, characterized in that For the implementation of step 2: first, in the discrete element program, the contact model is secondary developed. According to the geometric relationship between the particle center coordinates and the wall, the particle contact point coordinates are calculated, and the particle and wall contact point information is used as the particle's own attribute. Once the particle contacts the wall, the contact point's own attribute value is updated with the new particle and wall contact point coordinates; in the CFD program, the particle's contact point's own attribute value is obtained, the battery wall calculation unit in contact with the particle is found, and a contact index table is constructed; the index table content is the particle index ID number, the wall unit index, the particle The normal force between the particle and the wall it collides with, the particle's specific heat capacity, thermal conductivity, elastic modulus, Poisson's ratio, and density, and the elastic modulus, Poisson's ratio, density, thermal conductivity, and specific heat capacity of the battery wall unit; if the particle does not collide with the wall, all contents except the particle's own index ID are set to 0. Each particle is traversed to establish a complete particle-wall contact index table; this table supports bidirectional search, that is, you can query the wall unit information that the particle contacts through the particle index ID, and you can also search for all particles in contact with the wall through the wall unit index.

3. The method according to claim 1, characterized in that The specific implementation of step 3 is as follows: based on the pre-built CFD-DEM coupled numerical simulation model of battery thermal runaway ejection flue gas and particulate matter, the conversion of the discrete medium of particulate matter into a continuous equivalent medium is implemented; the particles are dispersed in the flue gas flow domain, and the volume fraction of the particulate matter in any flue gas flow domain calculation grid unit of the flue gas flow domain is first calculated, and then the first threshold value and the second threshold value of the volume fraction are set; the flue gas flow domain calculation grid units adjacent to the battery wall area are traversed, and according to the particle volume fraction in the flue gas flow domain calculation grid unit, if the particle volume fraction exceeds the first threshold value, it is considered that the particulate matter occupies a dominant position in the spatial area represented by the flue gas flow domain calculation grid unit area, and the characteristics of the flue gas flow domain calculation grid unit area are mainly manifested by the characteristics of the particulate matter itself, and the flue gas flow domain calculation grid is converted from the flue gas flow domain calculation grid to the particulate matter equivalent solid medium The calculation grid is constructed, and at the same time, the corresponding physical control equation is transformed from a multi-component equation describing the flue gas flow into a heat conduction equation describing the particle equivalent solid medium, and then the medium properties represented by the calculation grid are modified; if the volume fraction of the particles in the flue gas flow domain calculation grid unit area is lower than the second threshold value, it is considered that the flue gas still occupies a dominant position in the spatial area represented by the flue gas flow domain calculation grid, and the flue gas flow domain calculation grid unit still remains as a flue gas flow domain calculation grid unit; if the volume fraction of the particles is between the second threshold value and the first threshold value, it is considered that both the flue gas and the particulate matter have a considerable degree of influence in the flue gas flow domain calculation grid unit, and the porous medium model is applied to show that the existence of the particles hinders the flow of flue gas in the flue gas flow domain calculation grid unit; through this continuous transformation process, the particulate matter originally in the form of discrete media is converted into a continuous medium.

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