AU2021103150A4 - Method for numerical simulation of solid oxide fuel cell (sofc) under multiphysics coupling - Google Patents

Abstract

The present disclosure provides a method for numerical simulation of an SOFC under multiphysics coupling, including: establishing a single-cell multiphysics model of an SOFC; defining physical parameters required for simulating the SOFC and boundary conditions of the multiphysics model; coupling a plurality of physical fields involved in actual operation of the cell; and performing stationary and transient state calculation for a meshed multiphysics model of the SOFC, to obtain a temperature field, a stress field,agasflowfield, a substance concentration distribution field, and current density distribution inside the cell under different working conditions. The present disclosure takes into account the combined effects of many factors, and simulates distribution of the temperature field, stress field, and other physical fields inside the SOFC under multiphysics coupling in a more economical and efficient way under conditions more adapted to actual operation of the SOFC, improving the accuracy and precision of the simulation -1/5 DRAWINGS FIG. 1

Description

-1/5

DRAWINGS

FIG. 1

METHOD FOR NUMERICAL SIMULATION OF SOLID OXIDE FUEL CELL (SOFC) UNDER MULTIPHYSICS COUPLING TECHNICAL FIELD

[01] The present disclosure relates to the technical field of numerical simulation of fuel cells, and in particular, to a method for numerical simulation of a solid oxide fuel cell (SOFC) multiphysics coupling.

BACKGROUNDART

[02] An SOFC is considered to be a clean energy source that is likely to replace traditional fossil fuels in the future due to its high efficiency and low pollutant emissions. Among various types of fuel cells, a high temperature solid oxide fuel cell (HTSOFC) has many advantages compared to other conversion apparatus due to its all solid-state structure, fuel flexibility, and non-necessity of precious metal catalysts. An intermediate temperature solid oxide fuel cell (ITSOFC) has also gained considerable attentions for the alleviation of high temperature instability, reduced sealing problems and lower component costs. This is beneficial to accelerate the commercialization of the SOFC technology. A typical operating temperature of a planar ITSOFC ranges from 600°C to 800°C, which minimizes the polarization losses and increases the tolerance to poisoning of fuel impurity. However, severe thermal stress is still a concern to affect the lifetime of a single cell.

[03] A cell stack operates in a high temperature environment for a long time and has a complex structure, and internal stress-strain distribution of a cell system is affected by many factors, such as external load, temperature field loading, external air flow, and coefficients of thermal expansion (CTE) of components. Therefore, a stress field inside the SOFC presents extremely complex distribution, and key components of the SOFC will inevitably creep, damage, crack or even rupture under the long-term action of the thermal stress. To study impact of thermo-mechanical behaviors of key components of a single SOFC cell on cell performance, the coupling effect of multiple physical fields such as the temperature field, electrochemical field, flow field, concentration field, and solid mechanics field must be considered. However, optimization of cell design and operating parameters is subject to limitations such as experimental costs and laboratory conditions. Therefore, numerical simulation is becoming more important for the development and research of fuel cells, and has become one of the scientific research alternatives to experiments.

[04] At present, most researchers use computational fluid dynamics software and finite element software together to study the internal thermal stress distribution and temperature curve of the SOFC. Fluent and ABAQUS are commonly jointly used for this purpose. In this method, a temperature field generated by electrochemical reaction of an SOFC is calculated first, and then a stress field is calculated based on data of the temperature field. Although the internal stress field distribution of the SOFC can be obtained, this method ignores the reverse impact of the stress field on the temperature field. In addition, an anode part of the SOFC is subjected to creep strain under the long-term action of thermal stress, and the creep effect will cause stress relaxation. If the creep effect is ignored, a final simulation result will be greatly deviated from the actual situation.

[05] Therefore, it is necessary to design a numerical simulation method for establishing a heat transfer-structural mechanics coupling unit under the multiphysics coupling effect, to implement mutual coupling of a temperature field and a stress field inside an SOFC.

SUMMARY

[06] To resolve problems that a temperature field and a thermal stress inside an SOFC cannot be coupled with each other and stress relaxation caused by a creep effect is ignored during a traditional simulation process, the present disclosure discloses a method for numerical simulation of an SOFC under multiphysics coupling.

[07] To achieve the above objectives, the present disclosure adopts the following technical solutions:

[08] A method for numerical simulation of an SOFC under multiphysics coupling specifically includes the following steps:

[09] step 1: establishing a three-dimensional (3D) single-cell multiphysics model of an SOFC;

[10] step 2: defining physical parameters and boundary conditions of the SOFC globally;

[11] step 3: setting physical fields for the single-cell multiphysics model of the SOFC, and performing meshing;

[12] step 4: performing stationary solving on a 3D numerical model of the SOFC, to obtain a time-independent polarization curve, temperature field distribution, and stress field distribution of a single cell;

[13] step 5: using a stress and a strain obtained by the stationary solving as a prestress and a prestrain, to calculate a creep effect of a cell anode, and comparing an internal stress field of the cell, for which the anode creep effect has been considered, with a stress field obtained in step 4; and

[14] step 6: drawing a stress field distribution chart, a strain field distribution chart, a temperature field distribution chart, a gas molar fraction distribution chart, a cell polarization curve, a power curve, and their time-dependent curves based on the solving results, performing classified analysis, and performing comprehensive analysis, to obtain an optimal design for the cell under the multiphysics effect, and provide data and theoretical support for the design and optimization of the cell.

[15] Further preferably, in step 1, the multiphysics model for SOFC key components is established, where the key components include an anode flow channel, an anode electrode, an electrolyte, a cathode electrode, a cathode flow channel, and a connector material, and physical fields include mass, momentum, heat, an electrochemical reaction, and solid mechanics.

[16] Further preferably, assumptions of the SOFC model include:

[17] a. a gas mixture is composed of ideal gas;

[18] b. an electrochemical reaction occurs at a boundary interface of an electrode layer;

[19] c. a porous electrode is isotropic and macroscopically uniform;

[20] d. a connector is an excellent conductor, and its generated ohmic heat is ignored;

[21] e. a heat capacity of the gas mixture is unassociated with temperature;

[22] f. a voltage of the SOFC is equal to a voltage difference between an anode and a cathode;

[23] g. heat transferred by the connector through a radiation mechanism is ignored;

[24] h. shrinkage or expansion deformation of a porous media part of the SOFC is ignored; and

[25] i. some physical parameters of the SOFC key components do not change with temperature.

[26] Further preferably, in step 2, the physical parameters include: densities, thermal conductivities, electrical conductivities, thermal expansion coefficients, Poisson's ratios, and elasticity modulus of the anode, the cathode, the electrolyte, and the connector material, and permeability and porosity of a porous material; gas parameters include dynamic viscosities, molar masses, specific heat capacities, and thermal conductivities of fuel gas and air; creep parameters include a creep rate coefficient, a creep stress exponent, and creep activation energy; and

[27] the boundary conditions include: a pressure outlet boundary set at a flow field outlet, without slip between a fluid and a wall; a thermal insulation boundary for all parts except a fluid inlet and outlet of the cell; a boundary of rigid motion suppression applied to a solid part of the entire cell model upon solving of an internal thermal stress of the cell.

[28] Further preferably, in step 3, domain selection and parameter setting are performed for the physical fields involved in the SOFC, and multiphysics coupling is set, so that results obtained through coupling are used for the physical field parameter setting; and the entire model adopts structured meshes, boundary layer meshes are added to the anode and cathode flow channels, and finer meshes are used in a part near the electrolyte.

[29] Further preferably, in step 4, stationary solving is performed on the multiphysics model that does not involve a cell anode creep, to obtain the time-independent cell polarization curve, the temperature field distribution, and the stress field distribution, and corresponding distribution diagrams are drawn.

[30] Further preferably, in step 5, after the anode creep effect is applied, the stationary solving result obtained in step 4 is used as an initial value for transient state solving in this step, to obtain the stress field distribution of the SOFC after long-term operation with the anode creep considered.

[31] Compared with the prior art, the present disclosure achieves the following beneficial effects:

[32] (1) The present disclosure achieves a numerical model under coupling of multiple physical fields existing during actual operation of the SOFC, such as the mass, momentum, heat, electrochemical reaction, and solid mechanics fields, and can efficiently obtain how geometric mechanisms and physical parameters of the SOFC affect the internal thermal stress distribution of the cell, providing a basis for further optimizing the cell structure and design.

[33] (2) The present disclosure establishes a multiphysics model for the SOFC by using COMSOL software. With all physical modules needed to study the thermal stress of SOFC, the COMSOL software can obtain simulation results of both the temperature field and the stress field, realizing mutual coupling of the temperature field and the stress field. In addition, impact of the anode creep effect on the thermal stress is considered, further improving accuracy of the simulation.

[34] The present disclosure realizes mutual coupling of the temperature field and stress field of the SOFC in a more convenient and economical way under the premise of high-precision solving, obtains distribution of the temperature fields and stress fields with the anode creep effect considered, and achieves higher accuracy compared with the traditional SOFC thermal stress simulation method.

BRIEF DESCRIPTION OF DRAWINGS

[35] FIG. 1 is a diagram of a 3D geometric symmetry model for an anode-supported SOFC according to an embodiment of the present disclosure.

[36] FIG. 2 is a side view of FIG. 1.

[37] FIG. 3 is a schematic diagram of structured meshes of a 3D model for an anode-supported SOFC according to an embodiment of the present disclosure.

[38] FIG. 4 is a polarization curve diagram after multiphysics coupling solving is performed on a 3D model for an anode-supported SOFC according to an embodiment of the present disclosure.

[39] FIG. 5 is an effective creep strain diagram after multiphysics coupling solving is performed on a 3D model for an anode-supported SOFC according to an embodiment of the present disclosure.

DETAILED DESCRIPTION OF THE EMBODIMENTS

[40] The technical solutions in the embodiments of the present disclosure are clearly and completely described below. Apparently, the described embodiments are merely some rather than all of the embodiments of the present disclosure. All other embodiments obtained by a person of ordinary skill in the art based on the embodiments of the present disclosure without creative efforts shall fall within the protection scope of the present disclosure.

[41] The basic principle of the present disclosure is as follows: According to actual operation of a planar anode-supported SOFC, physical fields involved in the SOFC operation process are added to COMSOL software, and physical properties and boundary conditions of materials are set, to obtain distribution of temperature fields and stress fields inside the SOFC under multiphysics coupling with an anode creep effect considered.

[42] The present disclosure discloses a method for numerical simulation of an SOFC under multiphysics coupling, which specifically includes the following steps:

[43] 1. Establish a 3D single-cell multiphysics model of an SOFC.

[44] The multiphysics model for SOFC key components is established, where the key components include an anode flow channel, an anode electrode, an electrolyte, a cathode electrode, a cathode flow channel, and a connector material, and physical fields include mass, momentum, heat, electrochemical reaction, and solid mechanics fields. These physical fields are coupled with each other and act together, bringing an important and complex effect on changes of physical quantities inside the cell.

[45] Assumptions of the SOFC model include:

[46] (1) a gas mixture is composed of ideal gas;

[47] (2) an electrochemical reaction occurs at a boundary interface of an electrode layer;

[48] (3) a porous electrode is isotropic and macroscopically unifonn;

[49] (4) a connector is an excellent conductor, and its generated ohmic heat is ignored;

[50] (5) a heat capacity of the gas mixture is unassociated with temperature;

[51] (6) a voltage of the SOFC is equal to a voltage difference between an anode and a cathode;

[52] (7) heat transferred by the connector through a radiation mechanism is ignored;

[53] (8) shrinkage or expansion deformation of a porous media part of the SOFC is ignored; and

[54] (9) some physical parameters (such as elasticity modulus and Poisson's ratio) of the SOFC key components (such as the cathode, anode, and electrolyte) do not change with temperature.

[55] 2. Define physical parameters and boundary conditions of the SOFC globally.

[56] The physical parameters include: densities, thermal conductivities, electrical conductivities, thermal expansion coefficients, Poisson's ratios, and elasticity modulus of the anode, the cathode, the electrolyte, and the connector material, and permeability and porosity of a porous material; gas parameters include dynamic viscosities, molar masses, specific heat capacities, and thermal conductivities of fuel gas and air; creep parameters include a creep rate coefficient, a creep stress exponent, and creep activation energy; and

[57] the boundary conditions include: a pressure outlet boundary set at a flow field outlet, without slip between a fluid and a wall; a thermal insulation boundary for all parts except a fluid inlet and outlet of the cell; a boundary of rigid motion suppression applied to a solid part of the entire cell model upon solving of an internal thermal stress of the cell.

[58] 3. Set physical fields for the single-cell multiphysics model of the SOFC, and perform meshing.

[59] Domain selection and parameter setting are performed for the physical fields involved in the SOFC, and multiphysics coupling is set, so that results obtained through coupling are used for physical field parameter setting. For example, a temperature configured for solving the thermal stress in the solid mechanics field is a temperature obtained after coupling of the electrochemical reaction field and the heat transfer field. This also makes the model more refined and accurate. The entire model adopts structured meshes. Considering there is no slip when a fluid flows at a junction of the fluid and solid, existence of a boundary layer is conducive to capturing flow characteristics near the fluid boundary. Therefore, to improve calculation accuracy, boundary layer meshes are added to the anode and cathode flow channels, and finer meshes are used at a part close to the electrolyte.

[60] 4. Perform stationary solving on a 3D numerical model of the SOFC, to obtain a time independent polarization curve, temperature field distribution, and stress field distribution of a single cell.

[61] The stationary solving in study step 1 is performed on the multiphysics model that does not involve cell anode creep, to obtain the time-independent cell polarization curve, temperature field distribution, and stress field distribution, and corresponding distribution diagrams are drawn.

[62] 5. Use a stress and a strain obtained by the stationary solving in step 4 as a prestress and a prestrain in a new study step, to calculate an anode creep effect of the cell, and compare an internal stress field of the cell, for which the anode creep effect has been considered, with a stress field obtained in step 4.

[63] 6. Draw a stress field distribution chart, a strain field distribution chart, a temperature field distribution chart, a gas molar fraction distribution chart, a cell polarization curve, a power curve, and their time-dependent curves based on the solving results, perform classified analysis, and then comprehensive analysis, to finally obtain optimal key parameters such as a cell shape, flow channel arrangement, a flow channel length and a cross-sectional size, a fuel flow rate, a constituent material, a connection mode, and an operating temperature. After the anode creep effect is applied, the stationary solving result is used as an initial value for transient state solving at 5000h, to obtain stress field distribution of the SOFC after long-term operation with the anode creep considered. This helps further analyze the impact of the cell anode creep on the internal thermal stress of the cell.

[64] The present disclosure will be further described below in detail.

[65] (1) In COMSOL software, establish a single-cell model based on sizes of the key components of the SOFC, specify material properties, parameters, variables, and names of various parts of a geometric model of the SOFC model in Global Definitions, and add a probe needed to solve an average current density, and the like.

[66] Gas parameters of the SOFC include a gas inlet velocity, a mass fraction, a diffusion coefficient, a pressure at a gas outlet, and an initial temperature at a gas inlet. Physical parameters of solid structures (the cathode, anode, electrolyte, and connector material) include an electrical conductivity, an exchange current density, and an initial voltage required for a secondary current density interface, a thermal conductivity and a specific heat capacity required for a heat transfer in solids interface, porosity and permeability of a porous medium required for a transport of concentrated substance interface, a density, a thermal expansion coefficient, elasticity modulus, and Poisson's ratio required for a solid mechanics interface, and a creep rate coefficient, a creep stress exponent, and creep activation energy for the anode part of the SOFC.

[67] Considering the actual operation conditions of the SOFC, the initial temperature is set to 800°C and the pressure is set to 1 atm in the model.

[68] (2) In the COMSOL software, select corresponding physical field interfaces for the geometric model based on the actual operation of the SOFC: the heat transfer in solids interface in a heat transfer module, the transport of concentrated substance interface in a chemical substance transfer module, the secondary current density interface in an electrochemical module, a free and porous media flow interface in a fluid flow module, and the solid mechanics interface in a structural mechanics module.

[69] The "secondary current density distribution" interface is used for general modeling of electrochemical cells. Any kinetic expression (such as Butler-Volmer and Tafel equations) can be used to describe a relationship between charge transfer and overpotential. The "transport of concentrated substance" interface is used for multi-component diffusion, where a driving force for diffusion of each substance depends on composition, temperature, and pressure of a mixture. This physical field is used to model material transfer between the anode flow channel, the cathode flow channel, and the porous media (the anode and the cathode) in the SOFC. The "free and porous media flow" interface is used to calculate a fluid velocity and pressure a field of single-phase flow, where the free flow is connected to the porous media. In the SOFC, the anode is integrated with a fuel channel, the cathode, and an air channel. The "heat transfer in solids" interface is used to simulate heat transfer in fluids, porous media and solids by conduction, convection, and radiation in the SOFC. The "solid mechanics" interface is used to simulate the thermal stress and creep effects of the SOFC key components.

[70] The SOFC has three main components: an electrolyte and two electrodes (cathode and anode), which allow positively charged hydrogen ions (protons) to move between two sides of the SOFC. At the cathode, the fuel is oxidized, and then electrons are generated and flow from the anode to the cathode through an external load. At the cathode, hydrogen and oxygen ions react to generate water.

[71] A secondary current distribution model is used to calculate the voltage and current density produced by electrochemical reactions. The electrochemical reactions that occur on the electrodes of the planar SOFC are:

[72] Anode: H 2 +02- -+H2O+2e

[73] Cathode: 1/202 +2e- -+02 a. Secondary current distribution model

[74] The governing equations for transfer of electrons and ions of the electrolyte and porous electrode can be expressed as:

[75] at = -V (u 1V07) + Qi (1)

[76] at = -V (UsV0s) + Q, (2)

[77] pi and ps are an electron charge density and an ion charge density, respectively; ai is an effective conductivity of the electrode, and us is an ionic conductivity of the electrolyte; 01 and s are an electron voltage and an ion voltage, respectively, and Qi and Qs are an electron charge source and an ion charge source, respectively; and V is a gradient operator.

[78] Relationships between active polarization and current density in the anode and the cathode are described by the Butler-Volmer (BV) equation, in which concentration difference polarization is also considered:

[H~ ~ ~ C______ 20_ (_______

[79] Anode ia =SPB0a S [CROa 22exp aanaF(act+onc) C0 1aaF aact+c (3) RT ) CR20 PR\ Cref ref 0 acC(7ctc C 2 /~C nC

[80] Cathode ic = SPBio exp acnCF c+onc) 0e (1-accF(?cct+?7monc) (4) ref

[81] io is an exchange current density, aa and a' are electron transfer coefficients of the anode and the cathode, n is the number of electrons transferred in each electrochemical reaction, STPB (unit) is a density of a triple phase boundary (TPB) length, superscripts a and c represent the anode and the cathode, respectively, c' is a concentration of component i, and qact andqconc represent active polarization and concentration difference polarization, respectively.

[82] b. Fluid flow model

[83] Gas flows freely between the porous electrode and the gas channel. The model can also simulate the fluid flow between the porous electrode and the gas channel. The Navier-Stokes equation is widely used to describe the gas flowing in the flow channel. Considering different structures of the porous electrode and the flow channel, the Navier-Stokes equation is modified with the Darcy term, and the porosity of the porous medium is also considered:

[84] V - (pV) = Smass (5)

[85] pv - Vv = -Vp + V - [I(V + V) - pv]- (6) Smass = MH -MH

[86] Anode

[87] Cathode Smass 02 M4F (8)

[88] v is a velocity vector, Smass is a mass source term, c is a porosity, and k is a specific permeability, depending on a geometrical shape of the porous medium. In the gas flow channel, the gas flow rate is unassociated with the porosity, so the Darcy term relating to the porosity and permeability in formula (6) is ignored.

[89] The gas velocity distribution inside the SOFC can be obtained by directly solving the equation of this model.

[90] c. Mass transfer model

[91] Because electrochemical reactions occur near the electrolyte/electrode interface, to reach the reaction site, the gas must diffuse through pores of the electrode. Considering small pores in the active anode layer, which means molecules collide with the pore surface more frequently, Knudsen diffusion plays an important role in diffusion. Therefore, the mass transfer model combines Knudsen diffusion and Fick's law:

[92] ji = -p~em O _ poD mk, + poi Ek IDmkVXk (9)

[93] o is a mass fraction of substance i,ji is a mass flux of substance i, c is a volume fraction of a pore in a porous medium, M is a total molar mass, and D"k is a total diffusion coefficient of a substance, which can be calculated through Fick's diffusion coefficient D' and Knudsen diffusion coefficient D.

[94] In addition, a mass conservation equation of substances is:

[95] V - j + p(Ev - V)co = Si (10)

[96] Si is a mass source term of component i. The equation takes into account the mass changes caused by diffusion, convection and reaction. Through this model, mass fraction distribution of the gas inside the cell can be calculated based on a mass fraction at the inlet and a stoichiometric coefficient of the gas reaction in coupling with the porous electrode.

[97] d. Heat transfer model

[98] A typical heat transfer equation is:

[99] p Cv VT = V(effVT) + Q • (11)

[100] C, is a specific heat capacity, and Q is a heat source term in the cell. eff is an effective thermal conductivity, which is determined by composition of a gas in the gas flow channel.

[101] efffor the porous electrode is calculated as follows:

[102] Leff = (1 - E)s + Elg (12)

[103] *s is a thermal conductivity of a solid, and is a thermal conductivity of a gas.

[104] A key heat transfer mechanism for the electrolyte, anode interconnection and cathode interconnection components is heat conduction. Key heat transfer mechanisms for the cathode and anode porous electrodes are heat conduction and convection, respectively, and a main heat transfer mechanism in the air and fuel channels is convection. Due to the small heat transfer capacity, thermal radiation is ignored in this model. Through this model, temperature field distribution inside the cell can be obtained.

[105] It is assumed that the material of each layer of the planar SOFC satisfies the linear elastic theory, and the deformation caused by the thermal stress is very small.

[106] e. Structural mechanics model

[107] A stress-strain relationship of an elastic material under thermal load is:

[108] u=D ,j+oo(13)

[109] a is a stress vector, D is an elastic matrix, and ao is an initial stress.

[110] The elastic matrix D of an isotropic material is expressed as: 1-V 12 1 01 1 vD E1v 0

[111] D (1+)(1-2) V v 1- V 0 (14) 0 0 0 1-2 2

[112] E represents elasticity modulus, and v represents the Poisson's ratio, and satisfies the following relationship with the shear modulus G:

[113] V= 2G -_ 1 (15)

[114] A thermal strain is caused by different CTEs of various parts of the SOFC, and satisfies the following relationship:

[1151 G = a(T - Tf) (16)

[116] a represents a thermal expansion coefficient of a material, T is a physical temperature when the thermal stress is calculated, and Tf (800°C) is a reference temperature.

[117] Generally, the thermal stress of the cell is the lowest before heating. This model assumes that the thermal stress inside the cell is zero at 800°C. Through the structural mechanics model, the thermal stress distribution inside the SOFC can be obtained through segregated solving in COMSOL.

[118] When the SOFC operates for a long time in a high temperature environment, its key components will inevitably undergo creep deformation, which is irreversible. The creep deformation of the SOFC key component material can be expressed by using a Norton model: -Q

[1191 creep = A ( (Uf)n ) er (17)

[120] creep is a creep strain rate, T is a physical temperature when the thermal stress is calculated, A is a creep rate coefficient, eff is an effective stress, 0 ref is a reference stress, Q is creep activation energy, n is a stress exponent, and R is a universal gas constant. As the anode is most vulnerable, this numerical simulation method considers only the creep deformation effect of the anode part.

[121] Specifically, material properties are assigned to the SOFC multiphysics model. In the secondary current density interface, select the cathode, anode, and electrolyte of the cell in the geometric model, as shown in FIG. 1 and FIG. 2, and add the physical parameters of the electrode and electrolyte mentioned above, such as the conductivity, exchange current density, and initial polarization voltage; set one transport of concentrated species interface at the cathode and one at the anode, and add the gas viscosity coefficient, diffusion coefficient, mass fraction at the inlet, porosity, permeability, and the like; in the free and porous media flow interface, enable a porous media area, set the fluid channel and the porous medium area separately, and input physical parameters such as dynamic viscosity and pressure; in the heat transfer in solids interface, set the solids, porous media, and fluids in the cell separately, and input parameters such as the thermal conductivity, specific heat capacity, and density; set two solid mechanics interfaces, in the first solid mechanics interface, select all solid areas of the geometric model, and set the physical parameters for each area, including the elasticity modulus, thermal expansion coefficient, density, and Poisson's ratio, and apply rigid motion suppression boundary conditions to all selected solid areas, and in the second solid mechanics interface, select the anode area of the cell, set the creep parameters for the anode, and apply the rigid motion suppression boundary conditions to the anode.

[122] During the actual operation of the SOFC, mass transfer, heat transfer, momentum transfer, charge transfer, and chemical reactions are interdependent. Fluid properties and flow fields depend on temperature and substance concentration. The electrochemical reaction rate depends on temperature, substance concentration, and available surface area for the catalytic reaction. The chemical reaction generates and consumes heat, that is, temperature distribution depends on the chemical reaction rate, and solid and gas characteristics (such as the heat capacity and electrical conductivity), and the magnitude of the thermal stress depend on the temperature field distribution. All these dependencies require to be solved in a coupled way through governing equations.

[123] (3) Perform meshing for the geometric model for which the physical fields are set, where a structured mesh form is used, as shown in FIG. 3; perform multiphysics setting for the meshed geometric model; perform solver configuration for the geometric model with multiphysics set; and finally, set two study steps for the ready geometric model: study 1 and study 2. In study 1, stationary calculation of the thermal stress under multi-field coupling is performed without considering the creep effect. In study 2, a transient state solver is selected, the thermal stress and strain calculation results obtained in study 1 are used to calculate the prestress and prestrain of the creep effect, all physical field interfaces including the solid mechanics interface with the creep considered are selected to perform 5000h transient state solving, and the obtained stationary and transient state data is post-processed to obtain required distribution diagrams and curves.

[124] Specifically, during the geometric model meshing, when structured meshes are used, boundary layer meshes need to be set in the cathode and anode flow channels, and density of the meshes near the electrolyte area needs to be increased to further improve the solution accuracy.

[125] Specifically, during multiphysics setting, reacting flow is set between the transport of concentrated species interface and the free and porous media flow interface; and electrochemical heat is set between the secondary current density interface and the heat transfer in solids interface.

[126] Specifically, during solver configuration in study 1, current distribution and flow are calculated through three separate steps, and finally a series of different cell polarization voltages, as well as the temperature and thermal stress under different polarization voltages, are calculated through continuous auxiliary scanning. In the last solution step, V_pol (primary cell polarization) is set to 0.05range (0.1, 0.1, 0.8) in continuous auxiliary scanning to calculate the polarization voltage, and the last solution step is changed to segregated solving to improve the solving speed. During solver configuration in study 2, time unit is set to h, and time step is set to range (0, 1000, 5000).

[127] Specifically, the solved data is post-processed. When a 2D state curve needs to be obtained, X-axis and Y-axis variables of the curve are defined, study solution under the current node is selected as a data set, and then a curve is drawn based on solution parameters. When a 3D chart needs to be obtained, a 3D plot group is selected, a part of the geometric model for which a chart needs to be obtained is determined, physical parameter expressions described by the chart are further determined, and the required 3D chart is drawn.

[128] For example, to obtain a polarization curve from a single-cell simulation result, a user first selects a 1D plot group, selects Global under the current node, defines the X-axis as average current density of the cell and the Y-axis as cell voltage, and selects study 1 as a data set source. Then a polarization curve of the cell can be drawn, as shown in FIG. 4.

[129] For another example, the user selects study 1 as a data set source under a 3D plot group, then selects all domains of the entire model, and inputs a dependent variable T2 in the heat transfer in solids interface in Body Node Expression. Then a physical field distribution chart of the entire cell can be obtained.

[130] For another example, the users selects study 2 as a data set source under a 3D plot group, then selects all domains of the entire model, and selects a first principal stress expression from the body node expression options. Then a first-principal-stress field distribution chart of the entire cell can be obtained, with the anode creep considered.

[131] For another example, the user selects study 2 as a data set source under a 3D plot group, then selects an anode area of the cell model, and selects an effective creep strain expression in Replace Expression of Body Node Expression. Then an effective creep strain distribution chart for the anode area of the entire cell can be obtained, as shown in FIG. 5.

[132] It should be noted that the above description is not intended to limit the present disclosure, and the present disclosure is not limited to the above examples. Changes, modifications, additions or replacements made by those of ordinary skill in the art within the essential range of the present disclosure should fall within the protection scope of the present disclosure.

Claims (5)

1. A method for numerical simulation of a solid oxide fuel cell (SOFC) under multiphysics coupling, specifically comprising the following steps: step 1: establishing a three-dimensional (3D) single-cell multiphysics model of an SOFC; step 2: defining physical parameters and boundary conditions of the SOFC globally; step 3: setting physical fields for the single-cell multiphysics model of the SOFC, and performing meshing; step 4: performing stationary solving on a 3D numerical model of the SOFC, to obtain a time independent polarization curve, temperature field distribution, and stress field distribution of a single cell; step 5: using a stress and a strain obtained by the stationary solving as a prestress and a prestrain, to calculate a creep effect of a cell anode, and comparing an internal stress field of the cell, for which the anode creep effect has been considered, with a stress field obtained in step 4; and step 6: drawing a stress field distribution diagram, a strain field distribution diagram, a temperature field distribution diagram, a gas mole fraction distribution diagram, a cell polarization curve, a power curve, and their time-dependent curves, performing classified analysis, and then performing comprehensive analysis, to obtain an optimal design of the cell under the multiphysics effect.

2. The method for numerical simulation of an SOFC under multiphysics coupling according to claim 1, wherein in step 1, the multiphysics model for SOFC key components is established, wherein the key components comprise an anode flow channel, an anode electrode, an electrolyte, a cathode electrode, a cathode flow channel, and a connector material, and physical fields comprise mass, momentum, heat, an electrochemical reaction, and solid mechanics fields.

3. The method for numerical simulation of an SOFC under multiphysics coupling according to claim 2, wherein assumptions of the SOFC model comprise: a. a gas mixture is composed of ideal gas; b. an electrochemical reaction occurs at a boundary interface of an electrode layer; c. a porous electrode is isotropic and macroscopically uniform; d. a connector is an excellent conductor, and its generated ohmic heat is ignored; e. a heat capacity of the gas mixture is unassociated with temperature; f. a voltage of the SOFC is equal to a voltage difference between an anode and a cathode; g. heat transferred by the connector through a radiation mechanism is ignored; h. shrinkage or expansion deformation of a porous media part of the SOFC is ignored; and i. some physical parameters of the SOFC key components do not change with temperature.

4. The method for numerical simulation of an SOFC under multiphysics coupling according to claim 1, wherein in step 2, the physical parameters comprise: densities, thermal conductivities, electrical conductivities, thermal expansion coefficients, Poisson's ratios, and elasticity modulus of the anode, the cathode, the electrolyte, and the connector material, and permeability and porosity of a porous material; gas parameters comprise dynamic viscosities, molar masses, specific heat capacities, and thermal conductivities of fuel gas and air; creep parameters comprise a creep rate coefficient, a creep stress exponent, and creep activation energy; and the boundary conditions comprise: a pressure outlet boundary set at a flow field outlet, without slip between a fluid and a wall; a thermal insulation boundary for all parts except a fluid inlet and outlet of the cell; a boundary of rigid motion suppression applied to a solid part of the entire cell model upon solving of an internal thermal stress of the cell.

5. The method for numerical simulation of an SOFC under multiphysics coupling according to claim 1, wherein in step 3, domain selection and parameter setting are performed for the physical fields involved in the SOFC, and multiphysics coupling is set, so that results obtained through coupling are used for the physical field parameter setting; and the entire model adopts structured meshes, boundary layer meshes are added to the anode and cathode flow channels, and finer meshes are used in a part near the electrolyte; wherein in step 4, stationary solving is performed on the multiphysics model that does not involve a cell anode creep, to obtain the time-independent cell polarization curve, the temperature field distribution, and the stress field distribution, and corresponding distribution diagrams are drawn; wherein in step 5, after the anode creep effect is applied, the stationary solving result obtained in step 4 is used as an initial value for transient state solving in this step, to obtain the stress field distribution of the SOFC after long-term operation with the anode creep considered.

FIG. 1 －1/5－

DRAWINGS

FIG. 2 －2/5－

FIG. 3 －3/5－

－4/5－

FIG. 4

－5/5－

FIG. 5