Simplified battery thermal runaway erupted particulate matter deposition heat transfer calculation method

Abstract

The invention discloses a simplified battery thermal runaway erupted particulate matter deposition heat transfer calculation method. The main purpose is to solve the problem that simulation time is too long due to the fact that time steps are too small after a CFD-DEM coupling method is used for simulating deposition of battery eruption particles. The invention provides a simplified method for continuously converting particles into continuous media based on particle phase volume fractions, which comprises the following steps of: firstly, traversing flow field calculation grids containing particles and establishing a particle contact index table, and for the grids of which the particle volume proportions exceed a preset threshold value, calculating the particle contact index table; and carrying out continuous equivalent treatment and updating the physical property and the temperature. The contact heat transfer coefficient and the contact area between particles and the wall surface are calculated through a discrete element contact model, the contact thermal resistance between the particles and the wall surface is calculated, and the method is applied to a contact interface between an equivalent medium and the battery wall surface. And solving the temperature field of the battery system according to the interface heat transfer conditions among the physical domains, and evaluating the risk of a battery system relay heating out-of-control accident.

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 to thermal runaway by external factors, the battery particles brought out by various high-temperature fumes inside the battery are diffused in the battery system along with the smoke, and after multiple collisions in 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, and there is a high risk of causing thermal runaway of the battery. At present, the CFD-DEM coupling method can be used to simulate the deposition and heat transfer of battery eruption particles, and the discrete element method can be used to accurately calculate the force and heat transfer of each particle. The temperature changes of the flow field in the battery and the battery system are calculated based on the CFD method to evaluate the risk of thermal runaway of the battery.

[0003] However, since particulate matter is a discrete medium, a mathematical model is established using the Lagrangian viewpoint to track the motion state of each particle. Limited by the Rayleigh time step, an extremely short time step must be used to accurately judge the contact of particles and calculate the force on particles to avoid divergence. At the same time, the CFD calculation time step also needs to be coordinated with the DEM time step. The main components of the particles erupted by the battery are metals and carbon elements in the battery materials, and the particle size is mostly below 0.1mm, which limits the calculation time step of the discrete element to the order of 1e-7 to 1e-6. Each simulation requires millions of time steps to iterate, 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 the main problem restricting the engineering application of the model. At the same time, the deposition and heat transfer of battery particles may also cause the thermal runaway eruption of 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] Based on the above-mentioned technical problems, the present invention provides a simplified calculation method for the deposition and heat transfer of particles ejected during thermal runaway of a battery, and its specific technical solution is as follows:

[0005] In view of the working conditions of large amounts of high-temperature particulate matter deposited in the final stage of thermal runaway of the battery in the battery system, the temperature changes inside the battery system are simulated, and the physical field information of the entire battery system at the final stage of thermal runaway of a single battery is obtained through CFD-DEM (computational fluid dynamics-discrete element coupling) coupling calculation. The CFD-DEM coupling control equation contains 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 smoke, ρ f is the density of smoke, is the velocity of the smoke.

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

[0010]

[0011] In the above formula (2), P is the flue gas pressure, is the viscous stress of flue gas, is the force exerted by particles 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 laws 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 and 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 It is 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 and temperature field of the flue gas flow basin, the volume distribution of the particles in the flue gas flow basin, and the concentration of each component of the flue gas 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 particle located in the flue gas flow domain calculation grid, V cell Calculate the volume of the grid cell for the smoke flow domain, and the volume fraction of the smoke ε f =1-ε p Traverse each flue gas flow 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 coupling simulation, it is necessary to carry out secondary development of the contact model in the discrete element program, calculate the coordinates of the particle contact points according to the geometric relationship between the particle center coordinates and the wall, and use the contact point information between the particle and the wall as the particle's own attribute. Once the particle contacts the wall, the contact point's own attribute value updates the new particle-wall contact point coordinates. In the CFD program, obtain the particle's own attribute value of the contact point, find the battery wall calculation unit in contact with the particle, and build a contact index table. The index table content is 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, density, battery wall unit elastic modulus, Poisson's ratio, density, thermal conductivity, specific heat capacity. If the particle does not collide with the wall, except for the particle's own index ID, the rest of the content is set to 0, traverse each particle, and 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 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 units near the battery wall area are traversed. According to the particle volume fraction in the calculation grid unit, 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 unit area mainly shows the characteristics of the particles themselves. Compared with the heat transfer between particles and flue gas in the grid, the heat transfer between particles can be approximately ignored. The heat transfer between particles is mainly considered. Then 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 )f (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 , s are the specific heat capacity, thermal conductivity and density of the equivalent solid medium respectively. p is the thermal conductivity of the particle, 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 particles and smoke with the volume fraction of particles and smoke as weights.

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

[0034]

[0035] In the above formula (11), T s The average temperature of a grid cell is calculated 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 in the computational grid unit area is lower than the second threshold, it is considered that the smoke still dominates 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 particle volume fraction 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 medium model is used 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.

[0037] After continuous processing, the interface heat transfer conditions between the physical regions in the battery system. According to the particle-wall contact index table, all the particle information contacted by any battery wall is found, and the particle radius, elastic modulus, Poisson's ratio, specific heat capacity, thermal conductivity, and normal force with 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 follows (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. * 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 particle, R p is the contact thermal resistance between the particle and the wall, which reflects the barrier effect of contact 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 condition for continuous interface heat flow is applied 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 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 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 calculation 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. According to 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 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 (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 is still satisfied as follows (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, and the contact heat transfer boundary conditions are as follows (21), (22), (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, respectively, 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 will be 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 equations (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, It is calculated using Darcy's law based on the volume fraction of the particle phase, and in the flue gas flow domain, this term is 0.

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

[0067]

[0068] Combine the above physical field control equations and interface heat transfer conditions, use the finite volume method to discretize the equations, and solve them. Obtain the temperature field information of the entire battery system and the changes in the temperature field as the simulation progresses. Based on the temperature field, determine whether the remaining batteries have the risk of thermal runaway. 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.

[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 particulate matter, 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, it follows the principles of conservation of energy, conservation of mass, and conservation of momentum to reclassify the particles of discrete media into the category of continuous media, and uniformly establishes physical field control based on the characteristics of continuous media, so that each physical field in the battery system can be solved synchronously, avoiding multiple data interactions and iterations between particles and flue gas, and between particles and batteries, greatly improving the calculation efficiency, and meeting the accuracy requirements of engineering safety design.

[0071] (2) The present invention uses a continuous scheme to avoid the sudden change of volume fraction and momentum in the local smoke domain due to the movement of a small number of particles, which may lead to the non-convergence of the global calculation. It breaks through the limitation of the Rayleigh time step, greatly increases the time step of the simulation, and has 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 drawings required for use in the embodiments of the present application or related technical descriptions will be briefly introduced below. 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 creative work.

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

[0074] Figure 2 It is a schematic diagram of the principle of continuousization of particle discrete media based on particle phase volume fraction according to the present invention;

[0075] Figure 3The present invention is a simplified flowchart of a method for calculating the deposition and heat transfer of particles ejected during thermal runaway of a battery. DETAILED DESCRIPTION

[0076] In order to more clearly explain the purpose, technical scheme and principle of the present invention, the present invention is further described in detail below in combination 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 be limiting of the present invention.

[0077] In order to solve the difficulties in calculating the heat transfer of particle deposition during battery thermal runaway eruption, this embodiment proposes a simplified calculation method for the heat transfer of particle deposition during battery thermal runaway eruption, which specifically includes:

[0078] In view of the condition of large-scale deposition of high-temperature particulate matter at the end of thermal runaway of the battery in the battery system, the temperature change inside the battery system is simulated, and the physical field information of the whole domain in the battery system at the end of thermal runaway of a single battery is obtained through CFD-DEM (computational fluid dynamics-discrete element coupling) coupling calculation. The CFD-DEM coupling control equation includes 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 smoke, ρ f is the density of smoke, is the velocity of the smoke.

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

[0083]

[0084] In the above formula (28), P is the flue gas pressure, is the viscous stress of flue gas, is the force exerted by particles 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 laws 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 and 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 It is 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 basin, the volume distribution of the particles in the flue gas flow basin, and the concentration of each component of the flue gas 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 particle located in the flue gas flow domain calculation grid, V cell Calculate the volume of the grid cell for the smoke flow domain, and the volume fraction of the smoke ε f =1-ε p Traverse each flue gas flow 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, the contact model needs to be redeveloped in the discrete element program. According to the geometric relationship between the particle center coordinates and the wall, 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, the contact point's own attribute value updates 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 form and information of the index table are given in . The content of the index table is the particle index ID number, the wall unit index, 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, 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, and each particle is traversed to establish a complete particle-wall contact index table. The 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 particle information that contacts the wall through 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 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 units near the battery wall area are traversed. According to the particle volume fraction in the calculation grid unit, 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 unit area mainly shows the characteristics of the particles themselves. Compared with the heat transfer between particles and flue gas in the grid, the heat transfer between particles can be approximately ignored. The heat transfer between particles is mainly considered. Then 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 ) 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 , s are the specific heat capacity, thermal conductivity and density of the equivalent solid medium respectively. p is the thermal conductivity of the particle, 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 particles and smoke with the volume fraction of particles and smoke as weights.

[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 The average temperature of a grid cell is calculated 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 particle volume fraction in the computational grid unit area is lower than the second threshold, it is considered that the smoke still dominates 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 particle volume fraction 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 used 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 area is the equivalent medium solid grid, and the area with too small particle volume fraction is the unshaded area in the figure, which is still the original smoke area. The gray shaded area is the porous medium area with particle volume fraction within a certain range. Figure 2 Demonstrates how to convert a discrete particle medium into a continuous medium.

[0110] After continuous processing, the interface heat transfer conditions between the physical regions in the battery system. According to the particle-wall contact index table, all the particle information contacted by any battery wall is found, and the particle radius, elastic modulus, Poisson's ratio, specific heat capacity, thermal conductivity, and normal force with 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 follows (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. * 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 particle, R p is the contact thermal resistance between the particle and the wall, which reflects the barrier effect of contact 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. 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 (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 condition for continuous interface heat flow is applied 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 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 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 calculation 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. According to 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 is still satisfied as follows (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, and 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, respectively, 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 will be 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 equations (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, It is calculated using Darcy's law based on the volume fraction of the particle phase, and in the flue gas flow domain, this term is 0.

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

[0140]

[0141] As attached Figure 3 The calculation steps shown are combined with the above physical field control equations and interface heat transfer conditions, and the finite volume method is used to discretize the equations and solve them. The temperature field information of the entire battery system and the changes in the temperature field as the simulation progresses are obtained. Based on the temperature field, it is determined whether the remaining batteries have the risk of thermal runaway. If there is a battery thermal runaway, the CFD-DEM coupling calculation is continued to obtain the deposition distribution relationship of the particles 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 particles emitted by thermal runaway batteries. This method simulates the evolution of the temperature field inside the battery system at the end of the thermal runaway emission of smoke and particles and the condition of large amounts of high-temperature particles deposited. It is characterized by: The specific steps include: Step 1, through CFD-DEM (computational fluid dynamics-discrete element coupling) coupling calculation, obtain the physical field information of the whole domain in the battery characteristic system at the end of the thermal runaway eruption of a single battery; the battery system is a limited enclosed space including a battery module and a gas flow domain, and the specific physical field information is, for the flue gas flow domain in the battery system, obtain the velocity of the flue gas flow domain, the temperature field, the volume distribution of the flue gas flow domain occupied by particles, and the concentration of each component 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, traverse each particle, determine whether the particle is in contact with the battery surface through the positional relationship between the particle center, the particle radius and the battery surface wall unit, and establish a particle-wall contact index table; the index table includes the wall unit index contacted by the particle, the normal force between the particle and the wall, and the mechanical / thermal properties of the particle (specific heat capacity, thermal conductivity, elastic modulus, Poisson's ratio, density, etc.); 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 calculation unit in the flue gas flow domain, find the calculation grid unit of the flue gas flow domain where the particle is located according to the particle center coordinates, and calculate the volume share of the particle in the flue gas grid unit; re-differentiate the physical field according to the volume share of the particle in the flue gas flow domain; set a first threshold and a second threshold for the volume share 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 area is too high and exceeds the first threshold, the physical properties in the calculation unit of the flue gas flow domain are dominated by particulate matter, and the calculation unit is converted into an equivalent solid medium unit; if the particle volume fraction is lower than the second threshold, it means that the calculation unit is still dominated by the flue gas itself, ignoring the influence of particulate matter, and it is still regarded as a unit for flue gas calculation; if the volume fraction of particulate matter is between the second threshold and the first threshold, it means that in the calculation unit, both flue gas and particulate matter have a considerable degree of influence, and the calculation unit is converted into a porous medium calculation unit; after dividing each physical domain, recalculate the temperature of the equivalent solid medium area; Step 4, after re-differentiating the physical fields in the battery system, calculate the heat transfer interface conditions between the 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 according to the particle contact index table, and calculate the contact thermal resistance between a single particle and the wall based on the discrete element contact model. Since the wall may contact 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; the contact thermal resistance is used as the contact thermal resistance between the battery and the equivalent solid medium formed by particle deposition; for the battery area and the flue gas flow domain, the fluid-solid coupled thermal flow continuous boundary is applied; Step 5: Convert all discrete medium regions containing particles into equivalent continuous media. According to the heat transfer law of continuous media, establish the physical field control equation, apply the finite volume method to solve it, obtain the temperature field information of the entire battery system and the change of the temperature field as the simulation proceeds, and judge whether the remaining batteries have the risk of thermal runaway based on the temperature field. If there is thermal runaway of the battery, continue to carry out CFD-DEM coupling calculation to obtain the deposition distribution relationship of the 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 redeveloped, and the coordinates of the particle contact points are calculated based on the geometric relationship between the particle center coordinates and the wall surface. The information of the particle-wall contact points is used as the particle's own attribute. Once the particle contacts the wall surface, the contact point's own attribute value updates 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, and the particle's contact point information. The normal force between the particle and the wall it collides with, the specific heat capacity, thermal conductivity, elastic modulus, Poisson's ratio, density of the particle, 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 index ID of the particle itself are set to 0, and each particle is traversed to establish a complete particle-wall contact index table; this table supports bidirectional search, that is, the information of the wall unit that the particle contacts can be queried through the particle index ID, and the information of all particles in contact with the wall can be searched 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-constructed CFD-DEM coupled numerical simulation model of battery thermal runaway eruption smoke and particulate matter, the particle discrete medium is transformed into a continuous equivalent medium; the particles are dispersed in the flue gas flow domain, and the volume fraction of the particles in any calculation grid in the flue gas flow domain is first calculated, and then the first threshold and the second threshold of the volume fraction are set; the flue gas domain calculation grid cells near the battery wall area are traversed, and 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, and the calculation grid unit area mainly shows the characteristics of the particles themselves, and then the calculation grid is converted from the flue gas flow domain calculation grid to the particle equivalent solid medium 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 computational grid are modified; if the volume fraction of the particles in the computational 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 computational grid, and the computational grid unit still remains as a flue gas flow domain computational 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 particles have a considerable degree of influence in the computational unit, and the porous medium model is applied to show that the existence of the particles hinders the flow of the flue gas in the computational unit; through this continuous transformation process, the particles originally in the form of discrete media are transformed into continuous media.

4. The method according to claim 1, characterized in that: The step 4 is to determine the interfacial heat transfer conditions between the physical regions in the battery system after continuous processing; according to the particle-wall contact index table described in step 2, all the particle information contacted by any battery wall is searched, and the particle radius, elastic modulus, Poisson's ratio, specific heat capacity, thermal conductivity, and normal force on the wall are extracted and substituted into the discrete element contact model to calculate the contact thermal group between the particle and the wall; since a battery 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, and the contact thermal resistance between the battery wall and the equivalent solid medium of the particle is calculated according to the parallel thermal resistance calculation method; and the contact thermal resistance between the battery wall and the flue gas flow basin, etc. The interfacial heat transfer conditions between the effective solid medium and the flue gas flow basin are applied, the interfacial heat flux continuity and heat flux density continuity conditions of fluid-solid coupled heat transfer are applied, and the flow boundary conditions apply the slip boundary conditions; finally, according to the heat transfer law of continuous media, the control equations of each physical field after continuity are established, and the finite volume method is applied to solve them, and the temperature field information of the entire battery system and the changes of the temperature field as the simulation proceeds are obtained. Based on the temperature field, it is judged whether the remaining batteries have the risk of thermal runaway. 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.

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