A coupled thermal resistance network and finite element method for lithium-ion battery module expansion modeling

Abstract

The present invention discloses a method for modeling the expansion of a lithium-ion battery module by coupling a thermal resistance network and a finite element method, and relates to the technical field of lithium-ion battery model construction and simulation methods. The specific steps are as follows: (1) selecting a lithium-ion battery module and obtaining measurable battery electrochemical parameters, material thermophysical parameters and geometric characteristic parameters of the battery module; (2) establishing a three-dimensional geometric model and dividing the grid according to initial parameters and simulation working conditions, and setting boundary conditions; (3) establishing a lumped parameter model of a single battery node and calculating the heat generation, gas production and pressure accumulation inside the single battery; (4) connecting adjacent battery nodes through thermal resistance to establish a thermal resistance network model of the battery module and solve the heat transfer and thermal runaway propagation process between batteries; (5) using the battery temperature and internal pressure parameters obtained by the thermal resistance network calculation as dynamic boundary conditions and applying them to the physical boundary of the battery shell; (6) solving a mechanical model based on the finite element to obtain the stress and strain of the battery and simulate the battery expansion behavior during the thermal runaway propagation process. The present invention can calculate the expansion behavior of a lithium-ion battery module caused by increased internal pressure during the propagation of thermal runaway, providing a calculation basis for the safety design of the battery module.

Description

Technical Field

[0001] The present invention belongs to the technical field of lithium-ion battery model construction and simulation methods, and particularly relates to a lithium-ion battery module expansion modeling method that couples a thermal resistance network and a finite element method. Background Art

[0002] With the widespread adoption of lithium-ion batteries in electric vehicles, renewable energy storage, and portable electronic devices, their safety has attracted increasing attention. Thermal runaway, the rapid release of heat and flammable gases due to uncontrolled internal reactions in lithium-ion batteries at high temperatures, is one of the most serious safety hazards facing batteries. This process can not only cause the battery to catch fire or explode, but can also trigger serious chain reactions, posing significant safety risks to users and the surrounding environment.

[0003] To effectively prevent thermal runaway accidents, expansion force modeling is crucial. Expansion force is a direct manifestation of the mechanical stresses caused by gas generation and temperature rise during thermal runaway. Accurately modeling expansion force can provide crucial information about the battery's internal state, helping to monitor and predict early signs of thermal runaway. Compared to other physical signals, expansion force offers advantages such as fast response, strong transmissibility, and low sensor requirements, making it an ideal early warning indicator. During the propagation of thermal runaway, the expansion behavior of individual cells not only affects their own safety but also the state of other cells within the battery module. As thermal runaway progresses, the expansion force between cells gradually accumulates within the module, amplifying the expansion force signal. Furthermore, this accumulation of expansion force can reduce the contact thermal resistance between adjacent cells, increase the heat transfer rate, and accelerate the propagation of thermal runaway. Therefore, in-depth research on the propagation behavior of expansion force and its interaction with thermal runaway, as well as elucidating the evolution of the expansion force signal within the battery module during thermal runaway propagation, is crucial for developing effective early warning technologies, optimizing battery module design, and improving battery module safety.

[0004] Currently, research on battery thermal runaway behavior is mostly focused on the behavior of single cells. However, as the basic unit in practical applications, the battery module has complex internal heat conduction and mechanical response characteristics that require a more comprehensive modeling method. The traditional thermal resistance network model can effectively describe the overall characteristics of heat transfer inside the battery, but often ignores the subtle structure and local changes inside the battery. The finite element model can provide a more detailed mechanical behavior analysis, but the computational cost is high and the efficiency is low when dealing with large-scale battery modules. Therefore, there is an urgent need for a new modeling method that can combine the advantages of thermal resistance networks and finite element analysis to more accurately simulate the expansion propagation process in battery modules. By coupling the thermal resistance network and the finite element model, it is possible to dynamically predict the battery expansion behavior during the thermal runaway propagation process and deeply analyze the cumulative effect of the expansion force within the module.

[0005] The proposed method for modeling lithium-ion battery module expansion by coupling a thermal resistance network and finite element analysis aims to describe heat conduction by establishing a thermal resistance network for the battery module, while simultaneously combining it with a finite element model to analyze the battery's expansion behavior during thermal runaway. This method not only effectively captures the interplay between different batteries during the propagation of thermal runaway but also provides an important basis for battery module safety design and abnormal condition monitoring. This invention is expected to provide more comprehensive theoretical support and practical guidance for improving the safety of lithium-ion battery modules. Summary of the Invention

[0006] The purpose of the present invention is to address the above-mentioned defects in the prior art and to propose a lithium-ion battery module expansion modeling method that couples thermal resistance network and finite element.

[0007] Its technical solution is: a lithium-ion battery module expansion modeling method that couples thermal resistance network and finite element, including the following steps: S1, select a lithium-ion battery module, obtain measurable battery electrochemical parameters, material thermophysical parameters and geometric characteristic parameters of the battery module; S2, establish a three-dimensional geometric model and divide the grid according to the initial parameters and simulation conditions, and set boundary conditions; S3, establish a lumped parameter model of a single battery node, calculate the heat generation, gas production and pressure accumulation inside a single battery; S4, connect adjacent battery nodes through thermal resistance, establish a thermal resistance network model of the battery module, and solve the heat transfer and thermal runaway propagation process between batteries; S5, use the battery temperature and internal pressure parameters calculated by the thermal resistance network as dynamic boundary conditions, and apply them to the physical boundary of the battery shell; S6, solve the mechanical model based on finite elements, obtain the stress and strain of the battery, and simulate the battery expansion behavior during the thermal runaway propagation process.

[0008] Furthermore, the lumped parameter model of a single battery node in S3 uses an electrochemical reaction model to calculate the heat generation inside the battery and a jet dynamics model to calculate the gas production and pressure accumulation process inside the battery. The basic theory and establishment process include:

[0009] During battery thermal runaway, heat is generated inside the battery. Therefore, in the lumped model, each battery is treated as a single node with mass, heat capacity, and heat source. First, the lumped transient energy conservation equation based on the Arrhenius formula is used to describe the battery's electrochemical reactions and heat release process:

[0010]

[0011]

[0012] where ρ is the density, C p is the specific heat capacity, T is the node temperature, Tneigh is the temperature of the adjacent node, t is the time, Q TR is the heat released by the side reaction during thermal runaway, ΔH i is the enthalpy of the thermal abuse reaction, c i is the dimensionless concentration of active material. dc i / dt can be solved by the Arrhenius formula, and the relevant control equations are listed in Table 1.

[0013] Table 1 Control equations of thermal runaway heat generation kinetic model

[0014]

[0015] During thermal runaway, electrochemical reactions generate gas, causing the internal pressure of the battery to rise. When the internal pressure of the battery increases to a set critical value, the safety valve will open and release the generated gas. A jet dynamics model coupled with the thermal runaway process is used to calculate the internal pressure and gas flow rate of the battery. The specific calculation method includes:

[0016] The gas production process inside lithium-ion batteries includes electrolyte evaporation and side reaction release. The evaporation rate of the electrolyte is determined by the following formula:

[0017]

[0018] where α l is the volume fraction of the electrolyte in the coil, l1 and l2 are the geometric parameters of the battery, C is the evaporation coefficient; M e is the molar mass of the electrolyte, ρ v is the vapor density inside the battery, Δ vap H is the enthalpy of vaporization, T sat is the saturation temperature of the electrolyte, which can be calculated as:

[0019]

[0020] Where P represents the pressure inside the battery. For the reaction gases, hydrogen, carbon monoxide, carbon dioxide and methane are mainly considered, and their generation rates are considered to be linear functions of the electrochemical reaction rates and are calculated according to the following formula:

[0021]

[0022] where ω i is the gas generation coefficient, which is obtained by experimentally measuring the total amount of gas generated.

[0023] Furthermore, the internal pressure and jet dynamics model in step 3 is calculated using a lumped parameter model represented by ordinary differential equations, where the governing equation representing the pressure change is expressed as:

[0024]

[0025] Where R is the molar gas constant, V h is the volume of free space inside the battery, and n is the molar mass of gas molecules. For a single gas component, its molar change rate depends on the generation rate and the outflow rate, which can be given by the following formula:

[0026]

[0027] in represents the blocking coefficient, C d is the gas emission coefficient, A v is the battery safety valve area, ρ is the gas density, and u is the gas jet velocity. The jet velocity is calculated by the internal pressure of the battery and can be given by the following equation:

[0028]

[0029]

[0030]

[0031] Where γ represents the heat capacity ratio of the exhaust gas mixture, P v is the pressure at the battery safety valve, P a is the ambient pressure; Ma is the Mach number.

[0032] Furthermore, thermal runaway of a single battery will release a large amount of heat, which will be transferred to adjacent batteries through heat conduction and other means, causing the thermal runaway to propagate. In S4, adjacent battery nodes are connected through thermal resistance to establish a thermal resistance network model of the battery module to solve the heat transfer and thermal runaway propagation process between batteries. The basic theory and establishment process include:

[0033] For a battery module containing n cells, the energy conservation equation corresponding to the i-th cell can be expressed as:

[0034] In the above formula, each item from left to right represents: battery internal energy change, side reaction heat release, conductive heat flux between adjacent batteries, conductive heat flux between the battery and the shell, and convective heat flux between the air and the battery. cell,i-1 、T cell,i and T cell,i+1 represents the temperature of the i-th battery and its adjacent i-1 and i+1 batteries, T wall Indicates the temperature of the module housing, which is assumed to be equal to the ambient temperature. cod,bb Represents the equivalent heat transfer resistance between batteries, R bc Represents the equivalent thermal resistance between the battery and the shell, R cov,tis the convection thermal resistance between the airflow and the top surface of the battery. R cod,bb 、R bc and R cov,t This can be calculated using the following equation:

[0035]

[0036]

[0037]

[0038]

[0039]

[0040] Where δ represents the length along the heat transfer direction, S represents the heat transfer surface area; R rad,bc and R cod,bc is the radiation thermal resistance and conduction thermal resistance between the battery and the shell; ε cell is the surface emissivity of the cell, and σ is the Stefan-Boltzmann constant. bb and κ bc is the equivalent thermal conductivity after considering the contact thermal resistance, h is the convective heat transfer coefficient, and l1, l2, and l3 are the length, width, and height of the battery.

[0041] Furthermore, the basic theories based on the finite element model in S5 include:

[0042]

[0043] F is the yield stress of the material, B is the strain hardening coefficient. ε is the strain, and i is the strain hardening exponent. C n is the strain rate sensitivity coefficient. ε' is the strain rate. T is the battery temperature, obtained through the lumped parameter model in step 3. r is the ambient temperature, T m is the melting point temperature of the battery casing, and j is the temperature effect index.

[0044] Furthermore, the interaction effect between two adjacent batteries is obtained through contact analysis, and the normal force on each contact node or unit is obtained by iterative calculation in the contact area. The calculation method includes: (1) defining the boundary conditions and contact type of the contact area (such as frictionless, friction contact, etc.); (2) performing nonlinear iterative calculations and solving the normal force distribution on the contact area through the contact mechanics algorithm; (3) calculating the contact pressure; (4) since the normal force in the contact area is not uniformly distributed on the contact surface, the normal force of each contact node is calculated, and then the area between adjacent nodes is used to approximate the contact area of ​​each node, thereby calculating the local contact pressure on each node. The contact pressure can be expressed as:

[0045]

[0046] F normal is the normal contact force in the contact area obtained by finite element model calculation; A contact is the area of ​​the contact region.

[0047] Furthermore, the increase in contact pressure between adjacent batteries will lead to a decrease in contact thermal resistance, which in turn increases the heat transfer rate and accelerates the propagation of thermal runaway. Therefore, the equivalent thermal conductivity κ between batteries bb It is expressed as a function of contact pressure, specifically:

[0048]

[0049] η is the empirical coefficient, κ c is the equivalent thermal conductivity inside the battery core, which can be obtained by experimental measurement.

[0050] Furthermore, the coupling process of this method is as follows: the electrochemical reaction inside the battery can cause the battery to generate heat and gas, which in turn causes the internal pressure to increase and expand; the heat released by the thermal runaway of a single battery can heat the adjacent batteries, causing the temperature of the adjacent batteries to rise and thermal runaway to spread and expand; the expansion force accumulates as the thermal runaway propagates, causing the thermal resistance between batteries to decrease and accelerating the thermal runaway propagation. This process is reproduced in the open source computational fluid dynamics software OpenFOAM. The coupling process and calculation process are shown in the attached manual. Figure 1 .

[0051] The advantages of the present invention compared with the prior art are: (1) it makes up for the lack of research on the thermal runaway propagation model of the existing lithium-ion battery module that fails to consider the battery expansion process; (2) the modeling method can study the temperature and internal pressure changes of the lithium-ion battery module under different abuse conditions by changing a series of parameters, and at the same time can obtain the evolution characteristics and laws of the expansion force and volume deformation of the battery module during the thermal runaway process, and can provide data support for the thermal runaway early warning system based on force signals; (3) the modeling method provides a model framework for lithium-ion battery model developers and simulation researchers, which can provide a basis and guidance for subsequent model development. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Attachment Figure 1 It is an operational flow chart of a method for modeling lithium-ion battery module expansion by coupling thermal resistance network and finite element;

[0053] Attachment Figure 2 This is the coupling process and calculation flow of the battery module expansion modeling method in the present invention;

[0054] Attachment Figure 3is a schematic diagram of the model geometry and mesh in an embodiment of the present invention;

[0055] Attachment Figure 4 is a battery temperature change curve during the thermal runaway propagation process calculated in an embodiment of the present invention;

[0056] Attachment Figure 5 It is the battery expansion behavior during thermal runaway predicted in the embodiment of the present invention. DETAILED DESCRIPTION

[0057] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0058] Example

[0059] Taking a square lithium-ion battery module with lithium iron phosphate as the positive electrode material and graphite as the negative electrode material as an example, the expansion behavior of the battery module during the propagation of thermal runaway is simulated to fully and detailedly describe the present invention. This method is not limited to the modeling of lithium iron phosphate-graphite square lithium-ion battery modules, but is applicable to the expansion behavior of all lithium-ion battery modules. The method is mainly divided into the following steps: S1, select a lithium-ion battery module, obtain measurable battery electrochemical parameters, material thermal physical parameters and geometric characteristic parameters of the battery module; S2, establish a three-dimensional geometric model and divide the grid according to the initial parameters and simulation conditions, and set boundary conditions; S3, establish a lumped parameter model of a single battery node, calculate the heat generation, gas production and pressure accumulation inside a single battery; S4, connect adjacent battery nodes through thermal resistance, establish a thermal resistance network model of the battery module, and solve the heat transfer and thermal runaway propagation process between batteries; S5, use the battery temperature and internal pressure parameters obtained by the thermal resistance network calculation as dynamic boundary conditions, and apply them to the physical boundary of the battery shell; S6, solve the finite element-based mechanical model, obtain the stress and strain of the battery, and simulate the battery expansion behavior during the thermal runaway propagation process.

[0060] S1, selecting a lithium-ion battery module and obtaining the electrochemical parameters, material physical parameters, and geometric characteristic parameters of the battery module. The specific steps include:

[0061] Step 1: obtaining the geometric characteristic parameters of the battery module by measurement method;

[0062] Step 2: Obtain the physical properties and reaction kinetic parameters of the single cell according to the literature research method, and use them as input parameters for the thermal resistance network model and the finite element model.

[0063] S2, based on the initial parameters and simulation conditions, establish a 3D geometric model, divide the mesh, and set boundary conditions. The specific steps include:

[0064] Step 1: Establish the geometric model. According to the specifications and dimensions of the battery, build the geometric model and divide the mesh. Model geometry and mesh are shown in Figure 3 The size of the entire calculation area is 148mm×134mm×162mm. The boundary of the calculation model includes the outer surface of the battery and the contact surface between adjacent batteries.

[0065] Step 2: Set the mechanical boundaries of the battery. The outer surface of the battery is set as a displacement boundary condition, and the contact surface between adjacent batteries is set as a normal contact condition to prevent the two batteries from penetrating on the contact surface.

[0066] S3: Establish a lumped parameter model for a single battery node to calculate the heat generation, gas production, and pressure accumulation inside the battery. The specific steps include:

[0067] In step 1, the lumped transient energy conservation equation based on the Arrhenius formula is used to describe the electrochemical reaction and heat release process of the battery.

[0068] In the second step, the jet dynamics model of the coupled thermal runaway process is used to calculate the internal pressure and gas flow rate of the battery.

[0069] S4, connects adjacent battery nodes through thermal resistance, establishes a thermal resistance network model of the battery module, and solves the heat transfer and thermal runaway propagation process between batteries. The specific steps include:

[0070] The control equations involved in the thermal resistance network model are constructed using C++ code and compiled in OpenFOAM, and the discrete ordinary differential equations are solved through iteration.

[0071] To verify the effectiveness of the thermal resistance network model in predicting thermal runaway propagation, the simulation results were compared with experimental data (Applied Energy, 2015, 154:74-91). In the experiment, the battery module consisted of six series-connected cells, each composed of two pouch cells. Therefore, a micro-thermocouple could be inserted inside the battery to measure the internal temperature during the experiment. Figure 4A comparison of experimental and simulated battery temperatures is shown. It can be seen that during the needle-puncture triggering experiment, the temperature of the first battery instantly rises sharply to 845°C, while the simulated peak temperature is approximately 885°C. Due to the heating of the thermal runaway battery, the temperature of the second battery gradually rises and enters thermal runaway at approximately 241 seconds. Thereafter, the remaining four batteries experience a similar process. The simulated peak thermal runaway temperature and trigger time for each battery are close to the measured values, verifying the validity of the calculations.

[0072] S5, applying the battery temperature and internal pressure parameters obtained by thermal resistance network calculation as dynamic boundary conditions to the physical boundary of the battery housing. The specific steps include:

[0073] like Figure 2 As shown in the figure, the thermal resistance network model calculates the battery temperature and internal pressure respectively, outputs and records them every 1 second, and stores them in the specified text document in the case folder; the time series data in the document is read in the finite element model and used as dynamic parameters to set boundary conditions.

[0074] S6, solve the mechanical model based on finite elements, obtain the stress and strain of the battery, and simulate the battery expansion behavior during the thermal runaway propagation process, such as Figure 5 As shown in the figure, it can be found that as the battery electrochemical reaction occurs and the internal pressure of the battery increases, the battery module will continue to expand, and the simulation results can well simulate this process.

[0075] Based on the above analysis of the calculation results such as the evolution of characteristic parameters during thermal runaway, it can be seen that the lithium-ion battery module expansion modeling method of coupling thermal resistance network and finite element described in the present invention can calculate the expansion behavior of the battery module caused by the increase in internal pressure during the propagation of thermal runaway, and can accurately predict the key parameters of thermal runaway propagation, which can provide a basis for the safety warning design of lithium-ion battery modules and energy storage systems.

Claims

1. A method for modeling lithium-ion battery module expansion by coupling thermal resistance network and finite element, characterized in that: The following steps are involved: S1, select a lithium-ion battery module and obtain measurable battery electrochemical parameters, material thermophysical parameters, and geometric characteristic parameters of the battery module; S2, based on the initial parameters and simulation conditions, a three-dimensional geometric model is established and meshed, and boundary conditions are set; S3, establish a lumped parameter model of a single battery node to calculate the heat generation, gas generation and pressure accumulation inside a single battery; S4, connects adjacent battery nodes through thermal resistance, establishes a thermal resistance network model of the battery module, and solves the heat transfer and thermal runaway propagation process between batteries; S5, applying the battery temperature and internal pressure parameters obtained by thermal resistance network calculation as dynamic boundary conditions to the physical boundary of the battery housing; S6, solves the finite element-based mechanical model to obtain the stress and strain of the battery and simulates the battery expansion behavior during the thermal runaway propagation process; The temperature evolution of each battery in the battery module is calculated using the thermal resistance network model in S4, and the stress distribution and deformation of the battery module are calculated using the finite element model in S6. The two models are coupled through the internal pressure of the battery. Equivalent thermal conductivity κ between batteries bb Expressed as a function of contact pressure, the calculation method is as follows: Where η is the empirical coefficient, κ c is the equivalent thermal conductivity inside the battery core, F normal is the normal contact force in the contact area calculated by the finite element model, A contact is the area of ​​the contact region between cells.

2. The method for modeling lithium-ion battery module expansion by coupling thermal resistance network and finite element method according to claim 1, characterized in that: Through model calculation, the expansion characteristics of the battery module during the propagation of thermal runaway and the temperature evolution curve of each single battery in the module can be obtained simultaneously.

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