Quasi-two-dimensional multi-physical field modeling method of reversible solid oxide fuel cell

Abstract

The invention belongs to the field of fuel cells in the field of chemical engineering, and particularly relates to a quasi-two-dimensional multi-physical field modeling method of a reversible solid oxide fuel cell. The method is a universal quasi-two-dimensional multi-physical field modeling method which considers dynamic processes such as electrochemical reaction, heat transfer, gas diffusion and conversion in the reversible solid oxide fuel cell, explores an electricity-hydrogen-heat coupling relation in a single cell and can describe the distribution condition of physical variables in the airflow direction. According to the invention, a general battery electrochemical model formula is adopted, and the mode switching can be easily carried out by changing the symbol of the current density (the fuel battery mode is' + ', and the electrolytic cell mode is'-'); a finite volume method thought is adopted, a single battery model is simplified into a channel model, and five temperature layers are considered; three dynamic processes of heat transfer, gas diffusion and conversion are calculated according to the law of conservation, and thermoelectric data and other model parameters are obtained.

Description

Technical Field

[0001] The present invention belongs to the field of fuel cells in the chemical industry, and in particular relates to a quasi-two-dimensional multi-physical field modeling method for a reversible solid oxide fuel cell. Background Art

[0002] Reversible solid oxide fuel cells (SOFCs) are considered one of the most promising candidates for energy storage technology. Capable of generating electricity and heat in fuel cell mode and valuable fuels in electrolysis mode, SOFCs are considered a promising technology for hydrogen-based energy storage systems.

[0003] Reversible solid oxide fuel cell systems are the only technology available to date that can operate in fuel cell and electrolysis modes in a single system. Any other technology requires at least two independent systems. The key advantages of reversible solid oxide fuel cells include high scalability, attractive cost-effectiveness, excellent high efficiency and flexibility in fuel use. The literature [Y.Qi, B.Huang, J.Luo.Dynamic modeling of a finite volume of solid oxide fuel cell:The effect of transport dynamics[J].Chemical Engineering Science.2006,61(18):6057-6076.] studied the influence of airflow direction in solid oxide fuel cells on system performance based on 2D model comparison and gave the optimal stack airflow direction selection. However, 2D modeling has problems such as large workload and high computational cost. A large number of studies [Depature C, Boulon L, Sicard P, et al. Simulation model of a multi-stack fuel cell system[C]. 2013 15th European Conference on Power Electronics and Applications(EPE). IEEE, 2013: 1–10.] have shown that the air excess ratio is a trade-off between the efficiency of the reversible solid oxide fuel cell system and the stack temperature uniformity, and the stack temperature gradient and round-trip efficiency decrease with the increase of the air excess ratio.

[0004] The above-mentioned technology has been used to study the simulation modeling and thermal management strategies of reversible solid oxide fuel cells and has achieved remarkable results. However, previous studies have not given sufficient comprehensive consideration to the modeling accuracy and computational efficiency of reversible solid oxide fuel cells. It is necessary to find a modeling method that can accurately simulate the "electricity-hydrogen-heat" coupling relationship inside reversible solid oxide fuel cells and has high computational efficiency. Summary of the Invention

[0005] To solve the above problems, the purpose of the present invention is to provide a quasi-two-dimensional multi-physics modeling method for a reversible solid oxide fuel cell. The method is a general quasi-two-dimensional multi-physics modeling method that considers the dynamic processes such as electrochemical reactions, heat transfer, gas diffusion, and conversion within a reversible solid oxide fuel cell, explores the "electricity-hydrogen-heat" coupling relationship within a single cell, and can describe the distribution of physical variables in the direction of airflow. The present invention adopts a general battery electrochemical model formula, which can easily switch modes by changing the sign of the current density j (the fuel cell mode is "+" and the electrolyzer mode is "-"); the finite volume method is used to simplify the single cell model into a channel model, considering five temperature layers; the three dynamic processes of heat transfer, gas diffusion, and conversion are calculated according to the conservation law to obtain thermoelectric data and other model parameters.

[0006] The present invention is achieved through the following technical solutions:

[0007] A quasi-2D multiphysics modeling method for reversible solid oxide fuel cells (SOFCs) can simulate the dynamic response of the temperature layer and the mole fraction of each gas within the cell, solve for voltage loss, and meet the requirements of high computational efficiency. The details are as follows:

[0008] The reversible solid oxide fuel cell is considered as a model composed of multiple single cells connected in series. The single cell model is simplified to a channel model. Using the finite volume method, the planar single cell channel is discretized into n nodes. Each node consists of five temperature layers: fuel channel, air channel, positive electrode-electrolyte-negative electrode (PEN), fuel side connector, and air side connector. It is divided into a fluid control unit and a solid control unit. The fluid control unit includes the fuel channel and the air channel, and the solid control unit includes the PEN, the fuel side connector, and the air side connector. Thermoelectric data and other model parameters are calculated in each control unit according to the conservation law, and the output parameter of the node is equal to the input of the next node. Therefore, the construction method adopts the process from node model to channel model, and then to battery model.

[0009] The following assumptions are made for the quasi-two-dimensional multi-physics model of the reversible solid oxide fuel cell in the present invention:

[0010] (a) All gases are ideal gases and satisfy the ideal gas equation;

[0011] (b) each control unit satisfies continuous stirred tank reactor (CSTR) conditions, i.e., the temperature and mole fraction of the fluid in the control unit are equal to the corresponding outflow values ​​of the control unit;

[0012] (c) The battery’s gas inlet and outlet are both adiabatic boundaries, and there is no heat exchange between the battery stack and the external environment;

[0013] (d) The temperature of PEN is lumped, without considering the temperature difference between different layers inside the electrode;

[0014] (e) The direction of the one-dimensional model of the battery cell is along the gas channel. The distribution of temperature and current in the three-dimensional direction of the battery space is uniform and consistent, and the gas flow rate allocated to different gas channels is the same;

[0015] (f) Due to the high conductivity of the connector, the outer side of the connector at both ends of the battery stack unit is an equipotential surface;

[0016] (g) The electrochemical reaction occurs at the triple-phase line (TPB) at the interface between the anode and the electrolyte, where the reaction rate is controlled by the local PEN temperature.

[0017] (h) The PEN region corresponding to the connector rib is the active region for chemical and electrochemical reactions, and participates in the chemical and electrochemical reactions inside the solid battery.

[0018] Each node undergoes three dynamic processes: electrochemical reactions, heat transfer, and gas diffusion and conversion. Therefore, the node model consists of three submodels: an electrical properties submodel, a gas conservation submodel, and an energy conservation submodel. The electrical properties submodel allows the reversible solid oxide fuel cell's operating voltage to be determined at different current densities. The gas conservation submodel allows the mole fraction of each gas in the fuel and air channels to be determined. The energy conservation submodel allows the temperature changes of the five temperature layers to be determined, thus enabling quasi-two-dimensional multiphysics modeling of the reversible solid oxide fuel cell.

[0019] The detailed descriptions of the electrical property submodel, gas conservation submodel, and energy conservation submodel are as follows:

[0020] (1) Electrical characteristic quantum model

[0021] The Gibbs free energy of the reactants determines the highest voltage achievable in a chemical reaction—the Nernst voltage. When a battery outputs voltage, it also needs to overcome polarization losses such as gas transport, electrochemical activation, and impedance during the conduction process. Therefore, it is necessary to establish a battery electrochemical model to characterize the electrical characteristics of the corresponding battery.

[0022] (1.1) Equilibrium potential

[0023] The relationship between the operating voltage, Nernst voltage and the three polarization losses is:

[0024] V SOFC =E Nernst -(η act +η ohm +η con ) (1)

[0025] V SOEC =E Nernst +(η act +η ohm +η con ) (2)

[0026] Among them, the battery voltage V in fuel cell mode SOFC Using formula (1), the cell voltage V in electrolysis mode is calculated. SOEC Calculate using formula (2). E nernst is the Nernst voltage, η act ,η ohm ,η con They represent the voltage losses caused by activation polarization, ohmic polarization and concentration polarization respectively.

[0027]

[0028] Where E0 is the standard equilibrium potential, which varies only with temperature. R and F are the ideal gas constant and Faraday constant, respectively. are the partial pressures of hydrogen, water vapor, and oxygen at the three-phase reaction interface. PEN is the temperature of PEN at the node.

[0029] (1.2) Activation polarization

[0030] Activation polarization η act Represents the voltage lost to overcome the activation energy barrier associated with the electrochemical reaction. act The relationship between the current density j can be expressed using the Butler-Volmer equation:

[0031]

[0032] Among them, j ref is the exchange current density, α f , β f are the transfer coefficients for the forward and reverse reactions, respectively, and n is the number of moles of electrons transferred per mole of reaction.

[0033] Assuming the forward transmission coefficient α f and the reverse transmission coefficient β f If the values ​​are the same, equation (5) can be transformed into the display form of activation polarization:

[0034]

[0035] Among them, η act,fuel ,η act,air represent the activation polarization overpotentials of the fuel electrode and oxygen electrode, respectively. represents the transmission coefficient of the fuel electrode, represents the transmission coefficient of the oxygen electrode. ref,fuel 、j ref,air Represent the exchange current density of the fuel electrode and oxygen electrode respectively. ref,fuel and j ref,air According to the Arrhenius formula, it can be expressed as a semi-empirical formula related to the reaction gas composition and temperature:

[0036]

[0037] Among them, E act,fuel is the fuel electrode activation energy, E act,air is the activation energy of the oxygen electrode. fuel is the pre-exponential kinetic parameter of the fuel electrode, γ air is the pre-exponential kinetic parameter of oxygen electrode. ref is atmospheric pressure. a, b, and c are electrochemical parameters.

[0038] (1.3) Ohmic polarization

[0039] Ohmic polarization η ohm It is the voltage loss caused by the internal resistance of ion transmission in the electrolyte and the internal resistance of electron transmission in the electrode. Its resistance value R ohm Basically fixed. Ohm's law is used to calculate the ohmic polarization overpotential:

[0040] η ohm =R ohm ·j (10)

[0041]

[0042] Among them, δ i , σ i represent thickness and conductivity respectively, and i represents fuel electrode, oxygen electrode, electrolyte or interconnect.

[0043] (1.4) Concentration polarization

[0044] Concentration polarization is a voltage loss caused by the fuel diffusion rate in porous media being slower than the electrochemical reaction rate. At this time, the fuel diffusion rate cannot keep up with the demand, the battery performance is greatly affected, and it is easy to cause fuel deficit.

[0045]

[0046] Among them, η con,fuel ,η con,air represent the concentration polarization overpotentials of the fuel electrode and oxygen electrode, respectively. represent the mole fractions of H2, H2O and O2 at TPB, respectively. The Dusty Gas model is applied to calculate and the pressure change inside the electrode is ignored.

[0047]

[0048] in, For calculating intermediate variables, it has no actual physical meaning. fuel , δ air Represent the thickness of the fuel electrode and the thickness of the oxygen electrode respectively. fuel Indicates the pressure of the fuel gas in the fuel channel, p air Indicates the pressure of the air in the air channel. are the effective diffusion coefficients of H2, H2O, and O2, respectively. The effective diffusion coefficient needs to be calculated based on the kinetic theory of gases, combined with the effective Knudsen diffusion coefficient and the effective molecular diffusion coefficient.

[0049]

[0050] in, are the effective Knudsen diffusion coefficients of H2, H2O and O2, respectively. is the effective molecular diffusion coefficient of the H2 and H2O gas mixture. is the effective molecular diffusion coefficient of the mixed gas of O2 and N2.

[0051] The effective Knudsen diffusion coefficient was calculated based on the Knudsen diffusion coefficient.

[0052]

[0053]

[0054] in, are the Knudsen diffusion coefficients of H2, H2O, and O2, respectively. ζ represents the electrode porosity, and τ represents the tortuosity. pore is the average pore diameter. Represent the molecular weights of H2, H2O and O2 respectively.

[0055] The effective molecular diffusion coefficient of the mixed gas is calculated based on the molecular diffusion coefficient of the mixed gas.

[0056]

[0057] in, is the diffusion coefficient of H2 and H2O mixed gas molecules. is the diffusion coefficient of O2 and N2 mixed gas molecules. Calculated using the Fuller equation.

[0058]

[0059] in, is the molecular weight of N2. represent the Fuller binary diffusion volumes of H2, H2O, O2, and N2, respectively.

[0060] (2) Gas conservation submodel

[0061] The gas conservation submodule can be used to obtain the mole fraction of gas in the fluid control unit, that is, the fuel channel and the air channel. The mole fraction x of gas k in the fluid control unit k and electrochemical reaction rate R k related.

[0062]

[0063]

[0064] N out =N in -R k (35)

[0065]

[0066] Among them, N in is the molar flow rate of gas entering the node, N out is the molar flow rate of gas flowing out of the node. k,in is the mole fraction of gas k in the molar flow of gas entering the node. k,out The mole fraction of gas K in the molar flow of gas out of the node. I is the current. A area is the area of ​​the active region where the reaction occurs; N is the total number of gas moles in the node unit channel; P, V, and T are the pressure, volume, and temperature of the gas in the node channel, respectively.

[0067] (3) Energy conservation submodel

[0068] The temperature changes of the fuel channel and air channel in the fluid control unit, and the PEN, fuel-side connector, and air-side connector in the solid control unit can be obtained through the energy conservation sub-model.

[0069] (3.1) Fluid control unit

[0070] The fluid control unit includes fuel and air channels. The energy conservation equation for the fluid control unit is constructed as follows: the change in heat within the control unit is the chemical energy introduced by the fuel minus the chemical energy removed by the fuel, the energy transferred to the fluid by the PEN, the energy transferred to the fluid by the metal connector, and the energy change caused by the electrochemical reaction.

[0071]

[0072]

[0073] Q PEN,fuel =S PEN-fuel ×k PEN-fuel ×(T PEN -T fuel ) (44)

[0074] Q PEN,air =S PEN-air ×k PEN-air ×(T PEN -T air ) (45)

[0075] Q IC-fuel,fuel =S IC-fuel ×k IC-fuel ×(T IC-fuel -T fuel ) (46)

[0076] Q IC-air,air =S IC-air ×k IC-air ×(T IC-air -T air ) (47)

[0077] Among them, N fuel 、N air are the flow rates of fuel gas and air, respectively, h k is the specific enthalpy of gas k, is the average constant volume molar heat capacity of the mixed gas in the node fuel channel and air channel. PEN 、T fuel 、T air are the temperatures of the node PEN layer, fuel channel and air channel respectively. IC-fuel 、T IC-air are the temperatures of the fuel side connector and the air side connector, respectively. fuel(air),in , Q fuel(air),out are the chemical energy brought in and taken out by the fuel fluid and the air fluid, respectively, Q PEN,fuel , Q PEN,air The energy transferred from the PEN layer to the fuel gas layer and the air layer respectively. IC-fuel,fuelThe energy of the fuel gas in the fuel channel transferred from the fuel side connector. IC-air,air It is the energy transferred from the air side connector to the gas in the air channel. IC-air S is the heat convection heat exchange area between the air side connector and the air. IC-fuel S is the heat convection transfer area between the fuel side connector and the fuel. PEN-fuel S is the heat convection transfer area between PEN and fuel gas. PEN-air k is the heat convection transfer area between PEN and air. IC-fuel is the convective heat transfer coefficient between the fuel side connector and the fuel gas, k IC-air k is the convection heat transfer coefficient between the air side connector and the air gas. PEN-air k is the convective heat transfer coefficient between PEN and air. PEN-fuel is the convective heat transfer coefficient between PEN and fuel gas.

[0078] (3.2) Solid state control unit

[0079] The solid control unit includes a PEN, a fuel side connector, and an air side connector.

[0080] The nodal heat increment of PEN is the air side convective heat transfer Q air,PEN , fuel side convective heat transfer Q fuel,PEN , heat radiation transfer Q of the connector rad,PEN , heat conduction heat transfer Q of adjacent nodes cond 、The total heat released by the chemical reaction is Q r .

[0081]

[0082] Q fuel,PEN =S PEN-fuel ×k PEN-fuel ×(T fuel -T PEN ) (49)

[0083] Q air,PEN =S PEN-air ×k PEN-air ×(T air -T PEN ) (50)

[0084]

[0085] Among them, ρ PEN 、V PEN 、C P,PEN are the density, nodal volume and specific heat capacity of the PEN layer respectively. σ is the Stefan-Boltzmann constant, which is 5.67×10 -8 Wgm -2gK -4 ; ε PEN is the surface emissivity of PEN, ε IC is the surface emissivity of the connector, which are 0.82 and 0.64 respectively; F IC-PEN A represents the angular coefficient between the connector and PEN, which is taken as 1 in this paper; PEN 、A IC is the heat radiation area. S cond-PEN is the heat conduction area, k cond-PEN is the thermal conductivity between PEN, T j-1 、T j+1 The solid temperature of the previous node and the next node respectively. Δx represents the distance between the previous and next nodes. The heat released by the electrochemical reaction Q r It is closely related to the rate of electrochemical reaction and is equal to the total energy of the chemical reaction minus the electrical energy released P. cel .

[0086]

[0087] P cel =I×V (54)

[0088] Where I is the node current and V is the node voltage.

[0089] The energy conservation equations for the fuel side connector and the air side connector are constructed in the same way. The heat increment of the fuel side connector or the air side connector node is the fuel / air side convective heat transfer Q fuel,IC-fuel / Q air,IC-air 、PEN thermal radiation heat transfer Q rad,PEN , heat conduction heat transfer Q of adjacent nodes cond .

[0090]

[0091]

[0092] Q fuel,IC-fuel =S IC-fuel ×k IC-fuel ×(T fuel -T IC-fuel ) (57)

[0093] Q air,IC-air =S IC-air ×k IC-air ×(T air -T IC-air ) (58)

[0094]

[0095] Among them, ρ IC 、VIC 、C P,IC are the density, node volume and specific heat capacity of the connector respectively. cond-IC is the heat conduction area, k cond-IC is the thermal conductivity between the connectors.

[0096] Compared with the prior art, the present invention has the following beneficial effects:

[0097] (1) The process of the present invention is simple and easy to operate, and the internal mechanism relationship of the reversible solid oxide fuel cell is successfully simulated using a quasi-two-dimensional multi-physics field modeling method.

[0098] (2) Compared with the zero-dimensional modeling method, the quasi-two-dimensional multi-physics field modeling method used in the present invention can more accurately analyze the "electricity-hydrogen-heat" coupling relationship inside the battery; compared with the two-dimensional modeling method, the use of the quasi-two-dimensional modeling method can reduce the amount of calculation, reduce the time cost, and improve the calculation rate. BRIEF DESCRIPTION OF THE DRAWINGS

[0099] Figure 1 Node heat transfer analysis diagram of the quasi-two-dimensional multi-physics field model of the reversible solid oxide fuel cell of the present invention.

[0100] Figure 2 The voltage-current density relationship diagram is obtained by simulating the existing zero-dimensional model in Example 1 and compared with the experimental data.

[0101] Figure 3 The polarization curves obtained by simulating the existing zero-dimensional model in Example 1 include a fuel electrode activation polarization curve, an oxygen electrode activation polarization curve, a concentration polarization curve, and an ohmic polarization curve.

[0102] Figure 4 The voltage-current density relationship diagram obtained by simulating the quasi-two-dimensional model of the reversible solid oxide fuel cell in Example 2 is compared with the experimental data.

[0103] Figure 5 The polarization curves obtained by simulating the quasi-two-dimensional model of the reversible solid oxide fuel cell in Example 2 include the fuel electrode activation polarization curve, the oxygen electrode activation polarization curve, the concentration polarization curve and the ohmic polarization curve.

[0104] Figure 6 The figure shows the PEN temperature variation diagrams in the five nodes obtained by simulating the quasi-two-dimensional model of the reversible solid oxide fuel cell in Example 2.

[0105] Figure 7 The simulation of the quasi-two-dimensional model of the reversible solid oxide fuel cell in Example 2 shows the changes in the mole fraction of H2 in the fuel channel at the five nodes obtained by running.

[0106] Figure 8 The simulation of the quasi-two-dimensional model of the reversible solid oxide fuel cell in Example 2 shows the changes in the mole fraction of O2 in the air channel at the five nodes obtained by running. DETAILED DESCRIPTION

[0107] The specific implementation of the present invention is further described below in conjunction with the accompanying drawings and technical solutions.

[0108] The present invention provides a quasi-two-dimensional multi-physics modeling method for the reversible solid oxide fuel cell mechanism that can explore the "electricity-hydrogen-heat" coupling relationship within a single cell, wherein the heat transfer analysis of the battery node is as follows: Figure 1 As shown, two specific examples are used to explain the process and effects of the present invention.

[0109] Example 1 (Comparative Example)

[0110] A reversible solid oxide fuel cell model was constructed based on the existing zero-dimensional model. The electrolyte material is YSZ, the fuel electrode material is Ni-YSZ, and the oxygen electrode material is LSM-YSZ. The structural parameters and operating parameters of the reversible solid oxide fuel cell are as follows:

[0111] Table 1 Battery electrochemical model parameters of Example 1

[0112]

[0113]

[0114] Table 2 Battery structure parameters of Example 1

[0115]

[0116] Table 3 Operating parameters of Example 1

[0117]

[0118] P cell 、T cell are the operating pressure and temperature, respectively. are the mole fractions of H2, H2O and O2 in the feed gas, respectively. air 、N fuel are the feed rates of air gas and fuel gas, respectively.

[0119] First, the zero-dimensional model is simulated and verified. The relationship between battery voltage and current density and the polarization curve are obtained by running the zero-dimensional model. Figure 2 and Figure 3 shown.

[0120] from Figure 2 It can be seen that the results obtained by running the zero-dimensional model do not fit the experimental data well, so the simulation of reversible solid oxide fuel cells using the existing zero-dimensional model is not accurate.

[0121] Example 2:

[0122] According to the method of the present invention, a model was built and a reversible solid oxide fuel cell was verified. The same battery materials and structures as in Example 1 were used, as shown in Tables 1 and 2. The single cell was divided into five nodes, and processes such as heat transfer, heat conduction, and gas transfer within the cell were considered. The fuel utilization rate was set to 68%, the air excess ratio was set to 8, and other operating parameters were shown in Table 4. The reversible solid oxide fuel cell was operated in fuel cell mode, with the operating time set to 3000 seconds, and the changes in the internal cell temperature and gas mole fraction during operation were observed.

[0123] Table 4 Operating parameters of Example 2

[0124]

[0125] Depend on Figure 4 It can be seen that the quasi-two-dimensional model taking into account the electrochemical reaction, heat transfer, heat conduction and other processes inside the battery fits the experimental data well, which illustrates the accuracy of the model of the present invention.

[0126] Depend on Figure 5 It can be seen that the voltage polarization loss of the reversible solid oxide fuel cell in the fuel cell mode and the electrolyzer mode is not symmetrical. Figure 6 It can be seen that the reversible solid oxide fuel cell reaches stability at 500 seconds, and the temperature of the battery PEN layer continues to rise along the channel direction. This is because the fuel cell reaction is an exothermic reaction, so the temperature of the PEN continues to rise along the gas flow direction, and the temperature rises by about 110K. Figure 7 The mole fraction of H2 in the fuel channel at the five nodes changes with time. The mole fraction of H2 decreases continuously along the gas flow direction. Figure 8 The mole fraction of O2 in the air channel at the five nodes changes with time. The mole fraction of O2 decreases continuously along the direction of gas flow.

[0127] This shows that the zero-dimensional model's assumption that the reversible solid oxide fuel cell temperature and the mole fraction of each gas are uniform is inaccurate. Using the quasi-two-dimensional multiphysics modeling method of the present invention to simulate the cell's interior, it is possible to accurately simulate the temperature distribution of the reversible solid oxide fuel cell's fuel channel, air channel, cathode-electrolyte-anode (PEN), fuel-side connector, and air-side connector, examine the dynamic response of the mole fraction of each gas, and solve for voltage loss, while also offering the advantage of high computational efficiency.

Claims

1. A quasi-two-dimensional multi-physics modeling method for a reversible solid oxide fuel cell, characterized in that: The details are as follows: The reversible solid oxide fuel cell is considered as a model composed of multiple single cells connected in series. The single cell model is simplified to a channel model. The planar single cell channel is discretized into n nodes. Each node consists of five temperature layers: the fuel channel, the air channel, the cathode-electrolyte-cathode PEN, the fuel-side connector, and the air-side connector. It is divided into a fluid control unit and a solid control unit. The fluid control unit includes the fuel channel and the air channel, and the solid control unit includes the PEN, the fuel-side connector, and the air-side connector. The thermoelectric data and other model parameters are calculated in each control unit according to the conservation law. The output parameter of the node is equal to the input of the next node. For each node, the node model consists of three sub-models: an electrical properties sub-model, a gas conservation sub-model, and an energy conservation sub-model. The electrical properties sub-model is used to obtain the operating voltage of the reversible solid oxide fuel cell at different current densities. The gas conservation sub-model is used to obtain the mole fraction of each gas in the fuel channel and the air channel. The energy conservation sub-model is used to obtain the temperature changes of the five temperature layers, thus realizing quasi-two-dimensional multi-physics field modeling of the reversible solid oxide fuel cell. The detailed descriptions of the electrical property submodel, gas conservation submodel, and energy conservation submodel are as follows: (1) Electrical characteristic quantum model (1.1) Equilibrium potential The relationship between the operating voltage, Nernst voltage and the three polarization losses is: V SOFC =E Nernst -(or act +n ohm +n con ) (1) V SOEC =E Nernst +(the act +n ohm +n con ) (2) Among them, the battery voltage V in fuel cell mode SOFC Using formula (1), the cell voltage V in electrolysis mode is calculated. SOEC Calculate using formula (2); E nernst is the Nernst voltage, η act ,η ohm ,η con They represent the voltage loss caused by activation polarization, ohmic polarization and concentration polarization respectively; Where E0 is the standard equilibrium potential, which changes only with temperature; R and F are the ideal gas constant and Faraday constant, respectively; are the gas partial pressures of hydrogen, water vapor and oxygen at the three-phase reaction interface respectively; T PEN is the temperature of PEN at the node; (1.2) Activation polarization Activation polarization η act The relationship between θ and current density j is expressed using the Butler-Volmer equation: Among them, j ref is the exchange current density, α f , β f are the transfer coefficients for the forward and reverse reactions, respectively, and n is the number of moles of transferred electrons per mole of reaction; Assume the forward transmission coefficient α f and the reverse transmission coefficient β f If the values ​​are the same, equation (5) can be transformed into the display form of activation polarization: Among them, η act,fuel ,η act,air represent the activation polarization overpotentials of the fuel electrode and oxygen electrode, respectively; represents the transmission coefficient of the fuel electrode, represents the transmission coefficient of the oxygen electrode; j ref,fuel 、j ref,air represent the exchange current density of the fuel electrode and oxygen electrode respectively; j ref,fuel and j ref,air According to the Arrhenius formula, it is expressed as a semi-empirical formula related to the reaction gas composition and temperature: Among them, E act,fuel is the fuel electrode activation energy, E act,air is the activation energy of the oxygen electrode; γ fuel is the pre-exponential kinetic parameter of the fuel electrode, γ air is the oxygen electrode pre-exponential kinetic parameter; p ref is atmospheric pressure; a, b, c are electrochemical parameters respectively; (1.3) Ohmic polarization or ohm =R ohm ·j (10) Among them, η ohm Represents ohmic polarization, R ohm Indicates resistance, δ i , σ i represent thickness and conductivity, respectively, i represents the fuel electrode, oxygen electrode, electrolyte or interconnect; (1.4) Concentration polarization Among them, η con,fuel ,η con,air represent the concentration polarization overpotentials of the fuel electrode and oxygen electrode respectively; represent the mole fractions of H2, H2O, and O2 at TPB, respectively, and are calculated using the Dusty Gas model, ignoring the pressure changes inside the electrode; in, To calculate the intermediate variable; δ fuel , δ air represent the thickness of the fuel electrode and the thickness of the oxygen electrode respectively; p fuel Indicates the pressure of the fuel gas in the fuel channel, p air Indicates the pressure of the air in the air passage; are the effective diffusion coefficients of H2, H2O, and O2, respectively. The effective diffusion coefficient needs to be calculated based on the kinetic theory of gases, combined with the effective Knudsen diffusion coefficient and the effective molecular diffusion coefficient. in, are the effective Knudsen diffusion coefficients of H2, H2O and O2, respectively; is the effective molecular diffusion coefficient of the H2 and H2O mixed gas; is the effective molecular diffusion coefficient of the mixed gas of O2 and N2; The effective Knudsen diffusion coefficient was calculated based on the Knudsen diffusion coefficient; in, are the Knudsen diffusion coefficients of H2, H2O, and O2, respectively; ζ represents the electrode porosity, τ represents the tortuosity; d pore is the average pore diameter; represent the molecular weights of H2, H2O, and O2, respectively; The effective molecular diffusion coefficient of the mixed gas is calculated based on the molecular diffusion coefficient of the mixed gas; in, is the diffusion coefficient of H2 and H2O mixed gas molecules; is the diffusion coefficient of O2 and N2 mixed gas molecules; Calculated using the Fuller equation; in, is the molecular weight of N2; represent the Fuller binary diffusion volumes of H2, H2O, O2, and N2, respectively; (2) Gas conservation submodel The mole fraction of gas in the fluid control unit, that is, the fuel channel and the air channel, is obtained through the gas conservation submodule; the mole fraction of gas k in the fluid control unit x k and electrochemical reaction rate R k related; Among them, N in is the molar flow rate of gas entering the node, N out is the molar flow rate of gas flowing out of the node; x k,in is the mole fraction of gas k in the molar flow of gas entering the node; x k,out The mole fraction of gas K in the molar flow of gas out of the node; I is the current; A area is the area of ​​the active region where the reaction occurs; N is the total number of gas moles in the node unit channel, P, V, and T are the pressure, volume, and temperature of the gas in the node channel, respectively; (3) Energy conservation submodel The temperature changes of the fuel channel and air channel in the fluid control unit, and the PEN, fuel-side connector, and air-side connector in the solid control unit are obtained through the energy conservation submodel. (3.1) Fluid control unit Q PEN,fuel =S PEN-fuel ×k PEN-fuel ×(T PEN -T fuel ) (44) Q PEN,air =S PEN-air ×k PEN-air ×(T PEN -T air ) (45) Q IC-fuel,fuel =S IC-fuel ×k IC-fuel ×(T IC-fuel -T fuel ) (46) Q IC-air,air =S IC-air ×k IC-air ×(T IC-air -T air ) (47) Among them, N fuel 、N air are the flow rates of fuel gas and air, respectively, h k is the specific enthalpy of gas k, is the average constant-volume molar heat capacity of the mixed gas in the node fuel channel and air channel; T PEN 、T fuel 、T air are the temperatures of the node PEN layer, fuel channel and air channel respectively; T IC-fuel 、T IC-air are the temperatures of the fuel side connector and the air side connector, respectively; Q fuel(air),in , Q fuel(air),out are the chemical energy brought in and taken out by the fuel fluid and the air fluid, respectively, Q PEN,fuel , Q PEN,air are the energy transferred from the PEN layer to the fuel gas layer and the air layer respectively; Q IC-fuel,fuel The energy of the fuel gas in the fuel channel transferred from the fuel side connector; Q IC-air,air The energy transferred from the air side connector to the gas in the air channel; S IC-air is the heat convection heat exchange area between the air side connector and the air; S IC-fuel is the heat convection heat transfer area between the fuel side connector and the fuel; S PEN-fuel is the heat convection heat transfer area between PEN and fuel gas; S PEN-air k is the heat convection heat transfer area between PEN and air; IC-fuel is the convective heat transfer coefficient between the fuel side connector and the fuel gas, k IC-air k is the convection heat transfer coefficient between the air side connector and the air gas; PEN-air k is the convective heat transfer coefficient between PEN and air; PEN-fuel is the convective heat transfer coefficient between PEN and fuel gas; (3.2) Solid state control unit The nodal heat increment of PEN is the air side convective heat transfer Q air,PEN , fuel side convective heat transfer Q fuel,PEN , heat radiation transfer Q of the connector rad,PEN , heat conduction heat transfer Q of adjacent nodes cond 、The total heat released by the chemical reaction is Q r ; Q fuel,PEN =S PEN-fuel ×k PEN-fuel ×(T fuel -T PEN ) (49) Q air,PEN =S PEN-air ×k PEN-air ×(T air -T PEN ) (50) Among them, ρ PEN 、V PEN 、C P,PEN are the density, nodal volume and specific heat capacity of the PEN layer respectively; σ is the Stefan-Boltzmann constant, which is 5.67×10 -8 Wgm -2 gK -4 ; ε PEN is the surface emissivity of PEN, ε IC is the surface emissivity of the connector, which are 0.82 and 0.64 respectively; F IC-PEN A represents the angular coefficient between the connector and PEN, which is taken as 1 in this paper; PEN 、A IC is the heat radiation area; S cond-PEN is the heat conduction area, k cond-PEN is the thermal conductivity between PEN, T j-1 、T j+1 are the solid temperatures of the previous and next nodes respectively; Δx represents the distance between the previous and next nodes; the heat released by the electrochemical reaction Q r It is closely related to the rate of electrochemical reaction and is equal to the total energy of the chemical reaction minus the electrical energy released P. cel ; P cel =I×V (54) Where I is the node current and V is the node voltage; The heat increment of the fuel side connector or air side connector node is the fuel / air side convective heat transfer Q fuel,IC-fuel / Q air,IC-air 、PEN thermal radiation heat transfer Q rad,PEN , heat conduction heat transfer Q of adjacent nodes cond ; Q fuel,IC-fuel =S IC-fuel ×k IC-fuel ×(T fuel -T IC-fuel ) (57) Q air,IC-air =S IC-air ×k IC-air ×(T air -T IC-air ) (58) Among them, ρ IC 、V IC 、C P,IC are the density, node volume and specific heat capacity of the connector respectively; S cond-IC is the heat conduction area, k cond-IC is the thermal conductivity between the connectors.

2. The quasi-two-dimensional multi-physics field modeling method for a reversible solid oxide fuel cell according to claim 1, characterized in that: The quasi-2D multiphysics model of a reversible solid oxide fuel cell uses the following assumptions: (a) All gases are ideal gases and satisfy the ideal gas equation; (b) each control unit satisfies continuous stirred tank reactor (CSTR) conditions, i.e., the temperature and mole fraction of the fluid in the control unit are equal to the corresponding outflow values ​​of the control unit; (c) The battery’s gas inlet and outlet are both adiabatic boundaries, and there is no heat exchange between the battery stack and the external environment; (d) The temperature of PEN is lumped, without considering the temperature difference between different layers inside the electrode; (e) The direction of the one-dimensional model of the battery cell is along the gas channel. The distribution of temperature and current in the three-dimensional direction of the battery space is uniform and consistent, and the gas flow rate allocated to different gas channels is the same; (f) Due to the high conductivity of the connector, the outer side of the connector at both ends of the battery stack unit is an equipotential surface; (g) The electrochemical reaction occurs at the three-phase line TPB at the junction of the anode and electrolyte, and its reaction rate is controlled by the local PEN temperature; (h) The PEN region corresponding to the connector rib is the active region for chemical and electrochemical reactions, and participates in the chemical and electrochemical reactions inside the solid battery.

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