Modelica-based two-dimensional dynamic characteristic modeling and evaluation method for cross-flow SOFC (Solid Oxide Fuel Cell)

Abstract

The invention discloses a Modelica-based two-dimensional dynamic characteristic modeling and evaluation method for a cross-flow SOFC (Solid Oxide Fuel Cell). The method comprises the following steps: determining the physical field involved in a two-dimensional cross-flow SOFC dynamic simulation model; the two-dimensional cross flow SOFC is divided into four parts including an interconnection body, an anode flow channel, a PEN layer and a cathode flow channel in the height direction; aiming at a plurality of infinitesimal modules in the two-dimensional cross flow SOFC, respectively establishing corresponding dynamic mathematical models according to different physical and chemical processes of the infinitesimal modules; an overall two-dimensional cross flow SOFC dynamic model is constructed; establishing a two-dimensional cross flow SOFC performance comprehensive evaluation method; and carrying out two-dimensional cross flow SOFC dynamic simulation research. According to the method, the strong coupling system can be more effectively described and simulated, the maintainability and simulation efficiency of the model are improved, the progress of the engineering design and optimization process is promoted, and the method is suitable for the strong coupling solid oxide fuel cell system containing multiple physical domains.

Description

Technical Field

[0001] The invention belongs to the field of energy technology, and in particular relates to a two-dimensional dynamic characteristic modeling and evaluation method of a cross-flow SOFC based on Modelica. Background Art

[0002] The excessive use of fossil fuels has led to excessive emissions of greenhouse gases, which has profoundly affected the global climate and threatened the long-term development of mankind. Therefore, the necessity of researching efficient, sustainable, low-emission and environmentally friendly power generation systems is self-evident.

[0003] Fuel cell technology can directly convert chemical energy in fuel into electrical energy. Compared with solar power generation and wind power generation, it has the advantages of high reliability, continuous power generation, and no environmental impact. Among various types of fuel cells, solid oxide fuel cells (SOFCs) have attracted much attention due to their high power generation efficiency, all-solid structure, wide fuel compatibility, and low catalyst material cost. Crossflow is a SOFC flow arrangement in which the flow directions of air and fuel are perpendicular to each other. This method allows the intake and exhaust manifolds to be easily arranged around the cell, which has unique advantages for the production and manufacturing of SOFC and the integration of SOFC units. However, the crossflow arrangement is prone to uneven distribution of SOFC temperature and current density, which can easily lead to higher local hot spots and larger temperature gradients, threatening the safe operation of SOFC. It is difficult to obtain the dynamic distribution characteristics of SOFC internal variables through experimental methods. Therefore, it is necessary to establish a SOFC distribution parameter mechanism model.

[0004] For SOFC, a device with strong thermal and electrical coupling, traditional modeling methods have problems such as high model complexity, difficulty in accurately capturing coupling effects, difficulty in cross-disciplinary integration, low simulation efficiency, and poor model reusability and scalability. These problems make traditional methods inflexible and inefficient when facing complex dynamic systems. Summary of the invention

[0005] Purpose of the invention: The purpose of the present invention is to provide a two-dimensional dynamic characteristics modeling and evaluation method of cross-flow SOFC based on Modelica, by discretizing the battery into a large number of micro-element modules in terms of thickness, length and width. In each micro-element, a corresponding mathematical model is defined according to the actual physical and chemical processes inside it, and then the micro-element modules are sequentially connected using defined and customized connectors to finally form an overall two-dimensional cross-flow SOFC dynamic model. The model is used to obtain accurate and complete dynamic characteristics of SOFC. And the performance evaluation index of SOFC is designed to evaluate the comprehensive performance of the battery under different working conditions.

[0006] Technical solution: A two-dimensional dynamic characteristic modeling and evaluation method of a cross-flow SOFC based on Modelica of the present invention comprises the following steps: Step 1, determine the physical fields involved in the two-dimensional cross-flow SOFC dynamic simulation model, and design the connector model under each physical field; Step 2, dividing the two-dimensional cross-flow SOFC into four parts in the height direction: an interconnector, an anode flow channel, a PEN layer and a cathode flow channel; the flow directions of the anode fuel gas and the cathode air of the two-dimensional cross-flow SOFC are perpendicular to each other, and the four parts of the two-dimensional cross-flow SOFC are divided into multiple micro-modules along the flow directions of the anode and the cathode; Step 3: For multiple micro-element modules in the two-dimensional cross-flow SOFC, corresponding dynamic mathematical models are established according to their different physical and chemical processes; Step 4: Connect the heat flow, material flow and current of each micro-module in sequence using the defined connectors to form an overall two-dimensional cross-flow SOFC dynamic model; Step 5, establishing a comprehensive evaluation method for the performance of a two-dimensional cross-flow SOFC, including its dynamic characteristics, temperature distribution characteristics, and current distribution characteristics; Step 6: Conduct a dynamic simulation study on the two-dimensional cross-flow SOFC. By performing step change experiments on current and air flow, the dynamic response characteristics of the two-dimensional cross-flow SOFC are obtained, and the reasons for the formation of the dynamic characteristics are analyzed.

[0007] Furthermore, step 1 is specifically as follows: design connectors of different physical domains in the two-dimensional cross flow, and define the type, flow variable, potential variable and flow variable in each connector; wherein the connector type includes material flow interface, electrical interface and thermal interface; the material flow interface, its corresponding flow variable is material flow rate, and the potential variable includes pressure, enthalpy value and component; the electrical interface, its corresponding flow variable is current, and the potential variable is voltage; the thermal interface, its corresponding flow variable is heat flow rate, and the potential variable is temperature.

[0008] Furthermore, step 2 is specifically as follows: the actual physical structure of the two-dimensional cross-flow SOFC includes: an interconnect, an anode flow channel, an anode diffusion layer, an anode catalyst layer, an electrolyte, a cathode catalyst layer, a cathode diffusion layer and a cathode flow channel; the anode diffusion layer, the anode catalyst layer, the electrolyte, the cathode catalyst layer and the cathode diffusion layer can be processed as one module due to their overall thin thickness, becoming an anode-electrolyte-cathode layer, i.e., a PEN layer; the anode flow direction of the SOFC is set to the x-axis, and the cathode flow direction is set to the y-axis; the four parts of the SOFC are divided into n*n nodes along the x-axis and the y-axis directions, and the two-dimensional cross-flow SOFC has a total of 4*n*n micro-element modules.

[0009] Furthermore, step 3 specifically includes the following steps: S31: SOFC mass conservation equation: The electrochemical reactions in SOFC include the oxidation of hydrogen and the reduction of oxygen: At the anode electrode: ; At the cathode electrode: ; The mass conservation equation is as follows: In the anode channel: ; In the cathode flow channel: ; in, C is the concentration of each reactant gas, u is the gas flow rate, the subscripts an and ca represent the anode and cathode respectively, x and y Represent the anode and cathode gas flow directions, respectively. t It's time. i is the current density, F is Faraday's constant, h is the height of the channel, is the partial differential symbol, and the material flow is connected through the fluid interface of each flow channel element; S32: SOFC energy conservation equation: The electrochemical reaction of SOFC generates a large amount of heat, part of which is transferred to the anode and cathode channels through thermal convection, and the other part is transferred to the interconnection through thermal radiation. At the same time, the anode and cathode channels and the interconnection also transfer heat through thermal convection. The above heat transfer is connected using a thermal interface. The energy conservation equation of each layer of SOFC is as follows: Anode channel: ; Cathode channel: ; PEN layer: ; Interconnects: ; In the formula T is the temperature, ρ is the density, c p is the specific heat capacity, λ is the thermal conductivity, σ is the Stephen Boltzmann constant, ε PEN and ε I is the emissivity of the PEN layer and interconnects,k is the heat transfer coefficient between the fluid and the solid structure, the subscript I represents the interconnect component, τ Indicates the thickness of each component; S33: SOFC electrochemical equation: ; In the formula, R is the universal gas constant, are the partial pressures of hydrogen, oxygen and steam, E 0 Represents the reversible voltage, the battery voltage is affected by the activation loss η act , Ohm loss η ohm , and concentration loss η conc The impact can be calculated as: Activation loss η act is the energy barrier that the reactants need to overcome and is calculated as follows: ; in i 0 is the exchange current density, whose value depends on the material and microscopic properties of the electrode, the type of gas, the operating temperature and pressure; ; p ref is the reference pressure, E act,an and E act,ca are the activation energies of the anode and cathode, respectively; Ohmic loss η ohm It can be calculated by the following formula: ; in σ an , and σ ca are the anode and cathode conductivities, σ ele is the electrolyte ionic conductivity; ; Concentration loss η conc Caused by resistance to gas transport near the reaction interface and to product departure from the reaction interface; ; The gas in the channel iThe partial pressure, p i is the gas at the reaction interface i The partial pressure can be calculated by the following formula: ; in p ca is the working pressure in the cathode channel, D eff is the effective diffusion coefficient.

[0010] Furthermore, step 4 specifically includes the following steps: S41: Anode flow channel micro-element module: There are n rows and n columns of flow channel micro-elements in total, each micro-element has a fluid interface at the front and back for fluid inlet and outlet, and is sequentially connected with other anode flow channel micro-elements in the same column to form n connected anode flow channels; at the same time, each flow channel micro-element also has two thermal interfaces, one of which is connected to the thermal interface of the PEN layer micro-element at the same position in the height direction, and the other is connected to the thermal interface of the interconnector micro-element at the same position in the height direction for heat convection; S42: Cathode flow channel micro-element module: There are n rows and n columns of flow channel micro-elements; each micro-element has a fluid interface at the front and back for fluid inlet and outlet, which is sequentially connected with other cathode flow channel micro-elements in the same column to form n connected cathode flow channels; at the same time, each flow channel micro-element also has two thermal interfaces, one of which is connected to the thermal interface of the PEN layer micro-element at the same position in the height direction, and the other is connected to the thermal interface of the interconnector micro-element at the same position in the height direction for thermal convection; S43: PEN layer microelement module: There are n rows and n columns of PEN layer microelement; each microelement space contains a thermal interface in front, back, left and right respectively, and along the x-axis and y-axis, each PEN layer microelement is connected in sequence for heat conduction; in addition, each microelement has three thermal interfaces, two of which are connected to the thermal interfaces of the anode flow channel microelement and the cathode flow channel microelement at the same position in the height direction for heat convection; the other is connected to the thermal interface of the interconnector for radiation heat transfer; the PEN layer microelement module also has two electrical interfaces, namely the positive electrode and the negative electrode, and the positive and negative electrical interfaces of all PEN layer microelements are connected in parallel; S44: Interconnector micro-element module: There are n rows and n columns of interconnector micro-elements, each of which contains a thermal interface in the front, back, left and right directions. Along the x-axis and y-axis, each interconnector micro-element is connected in sequence for heat conduction. In addition, each micro-element has three thermal interfaces, two of which are connected to the thermal interfaces of the anode flow channel micro-element and the cathode flow channel micro-element at the same position in the height direction for heat convection; the other is connected to the thermal interface of the PEN layer module for radiation heat transfer. S45: After the connections of the interfaces inside the microelement are completed, the microelement and the external interfaces of the SOFC model are connected, including the anode and cathode fluid inlet and outlet interfaces, and the SOFC electrical interface; the connection method is as follows: The inlet fluid interface of the SOFC model is connected in parallel with the n rows of flow channel inlets. When the external fluid enters the SOFC, it is evenly divided into n streams. When the fluid in each flow channel leaves the SOFC model, it converges to the SOFC outlet fluid interface and leaves the battery. The positive and negative electrical interfaces of the SOFC model are connected in parallel with the positive and negative electrical interfaces of the PEN layer, respectively.

[0011] Furthermore, step 5 specifically includes the following steps: SOFC comprehensive performance evaluation indicators include: S51: SOFC PEN layer temperature distribution standard deviation: ; in, For the i Row, No. j The PEN layer temperature of the column, is the average temperature of the PEN layer; S52: SOFC inlet and outlet exergy: SOFC inlet and outlet exergy includes physical exergy and chemical exergy, and the calculation formula is as follows: ; in, h is the enthalpy value, s is the entropy value, is the mass flow rate, x is the mole fraction of each component, T 0 is the ambient temperature; S53: SOFC exergy loss: The exergy loss of SOFC can be calculated by the exergy balance formula: ; In the formula, W is the power generated by SOFC.

[0012] Furthermore, step 6 specifically includes the following steps: S61: Connect the positive and negative electrode electrical interfaces of the established two-dimensional cross-flow SOFC dynamic model to the negative and positive electrode electrical interfaces of the external current source respectively; connect the inlet fluid interfaces of the anode and cathode to the fuel gas and air mass flow sources; connect the outlet fluid interfaces of the anode and cathode to the fuel gas and air pressure boundaries; set the fuel gas hydrogen to be mixed with a small amount of water vapor, set its mass fraction, mass flow rate, and temperature; set the cathode gas to be air, set its mass fraction and temperature; set the anode and cathode outlet boundary pressures, the length and width of the SOFC, and the initial current; S62: setting the initial current, and after the SOFC reaches a steady state, when the time changes, the current changes stepwise, and other parameters remain unchanged; As the current increases in steps, the voltage of SOFC responds quickly, and under the influence of the polarization characteristics of SOFC itself, it decreases in steps. Then, as the temperature of SOFC gradually increases, the ohmic loss of SOFC decreases, and the voltage gradually increases. Under the influence of the changes in voltage and current, the power of SOFC increases rapidly and significantly at first, then decreases slightly, and finally increases gradually. The average temperature of the PEN layer of SOFC gradually increases and then stabilizes. As the current density of SOFC increases, the electrochemical reaction of SOFC intensifies, the heat generation increases, and the temperature increases. S63: The dynamic response characteristics of temperature, current, hydrogen and oxygen mass fractions at different nodes inside the SOFC are different; nodes inside the SOFC are selected to analyze the dynamic characteristics inside the SOFC; S64: The standard deviation of the temperature distribution of the PEN layer of SOFC reflects the uniformity of the temperature distribution in the SOFC. The lower the value, the more uniform the temperature distribution. When the current density increases stepwise, the standard deviation of the temperature distribution of the PEN layer gradually increases, and the uniformity of the temperature distribution of SOFC decreases. The exergy loss of SOFC reflects the change in the working capacity of SOFC during variable operating conditions. When the current increases, the exergy loss of SOFC first decreases rapidly and then increases rapidly, and finally decreases gradually, but is still higher than the initial value. Due to the increase in current, according to the polarization characteristics of SOFC, the voltage decreases, the irreversible loss of SOFC increases, and the working efficiency decreases, which is consistent with the power generation characteristics of SOFC.

[0013] The present invention also discloses a computer device, comprising a memory, a processor and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method of the present invention.

[0014] The present invention also discloses a computer-readable storage medium on which a computer program / instruction is stored. When the computer program / instruction is executed by a processor, the steps of the method of the present invention are implemented.

[0015] The present invention also discloses a computer program product, comprising a computer program / instruction, which implements the steps of the method of the present invention when executed by a processor.

[0016] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: The present invention discloses a two-dimensional dynamic modeling and evaluation method of cross-flow SOFC based on Modelica, and proposes a micro-element model including anode flow channel, cathode flow channel, PEN layer, and interconnect, a connection method of each micro-element model, and a combination method of a two-dimensional cross-flow SOFC model; an evaluation index of the standard deviation of the temperature distribution of the PEN layer and the exergy loss of SOFC is proposed to comprehensively evaluate the comprehensive performance of SOFC. Then, through the current step response experiment, the open-loop dynamic response of each variable of the two-dimensional cross-flow SOFC is obtained. The modern modeling language Modelica can more effectively describe and simulate strongly coupled systems through its declarative and multi-physical domain integration capabilities, improve the maintainability and simulation efficiency of the model, promote the progress of engineering design and optimization processes, and is suitable for strongly coupled solid oxide fuel cell systems including multi-physical domains. The solid oxide fuel cell designed by the optimization design method of the present invention can be widely used in new energy equipment, including new energy distributed microgrids, new energy power stations, etc. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is a schematic diagram of the structure of the SOFC of the present invention in the height direction.

[0018] Figure 2 It is a node division diagram of the SOFC of the present invention along the anode and cathode gas flow directions.

[0019] Figure 3 This is a schematic diagram of the connection of the SOFC micro-element module of the present invention.

[0020] Figure 4 It is a dynamic response diagram of SOFC voltage when current undergoes a step change in a specific embodiment of the present invention.

[0021] Figure 5 It is a dynamic response diagram of SOFC power when the current undergoes a step change in a specific embodiment of the present invention.

[0022] Figure 6 It is a dynamic response diagram of the average temperature of the SOFC PEN layer when the current undergoes a step change in a specific embodiment of the present invention.

[0023] Figure 7 It is a dynamic response diagram of different node temperatures of the SOFC PEN layer when the current undergoes a step change in a specific embodiment of the present invention.

[0024] Figure 8 It is a dynamic response diagram of current density at different nodes of the SOFC PEN layer when the current undergoes a step change in a specific embodiment of the present invention.

[0025] Fig. 9It is a dynamic response diagram of the hydrogen mass fraction at different nodes of the SOFC anode flow channel when the current undergoes a step change in a specific embodiment of the present invention.

[0026] Fig.10 It is a dynamic response diagram of oxygen mass fraction at different nodes of the SOFC cathode flow channel when the current undergoes a step change in a specific embodiment of the present invention.

[0027] Fig.11 It is a dynamic response diagram of the standard deviation of the temperature distribution of the SOFC PEN layer when the current undergoes a step change in a specific embodiment of the present invention.

[0028] Fig.12 It is a dynamic response diagram of SOFC exergy loss when the current changes stepwise in a specific embodiment of the present invention. DETAILED DESCRIPTION

[0029] The technical solution of the present invention is further described below in conjunction with the accompanying drawings.

[0030] The present invention provides a two-dimensional dynamic characteristic modeling and evaluation method of cross-flow SOFC based on Modelica, which discretizes the battery into a plurality of micro-element modules in terms of thickness, length and width. In each micro-element, a corresponding mathematical model is defined according to the actual physical and chemical process inside it, and then the micro-element modules are sequentially connected using defined and customized connectors to finally form an overall two-dimensional cross-flow SOFC dynamic model. The model is used to obtain accurate and complete dynamic characteristics of SOFC. The performance evaluation index of SOFC is designed to evaluate the comprehensive performance of the battery under different working conditions.

[0031] Technical solution: A two-dimensional dynamic characteristic modeling and evaluation method of a cross-flow SOFC based on Modelica of the present invention comprises the following steps: S1: Determine the physical domains involved in the two-dimensional cross-flow SOFC dynamic simulation model and design the connector model under each physical domain; S2: Divide the SOFC into four parts in the height direction: interconnect, anode flow channel, PEN layer and cathode flow channel. The anode fuel gas and cathode air flow directions of the two-dimensional cross-flow SOFC are perpendicular to each other. Divide the four parts of the SOFC into multiple micro-modules along the anode and cathode flow directions.

[0032] S3: Different dynamic mathematical models are established for each micromodule in the two-dimensional cross-flow SOFC according to its different physical and chemical processes.

[0033] S4: Connect the heat flow, material flow and current of each micromodule in sequence using the defined connectors to form an overall two-dimensional cross-flow SOFC dynamic model.

[0034] S5: Establish a comprehensive evaluation method for SOFC performance, including its dynamic characteristics, temperature distribution characteristics, and current distribution characteristics.

[0035] S6: Conduct dynamic simulation research on two-dimensional cross-flow SOFC. By performing step change experiments on current and air flow, the dynamic response characteristics of two-dimensional cross-flow SOFC are obtained, and the reasons for the formation of dynamic characteristics are analyzed.

[0036] Furthermore, step 1 is specifically as follows: design connectors of different physical domains in the two-dimensional cross flow, and define the type, flow variable, potential variable and flow variable in each connector. Among them, the connector types include material flow interface, whose corresponding flow variable is material flow rate, and potential variables include pressure, enthalpy value, and component; electrical interface, whose corresponding flow variable is current, and potential variable is voltage; thermal interface, whose corresponding flow variable is heat flow, and potential variable is temperature.

[0037] Furthermore, step 2 is specifically as follows: the actual physical structure of SOFC includes: interconnect, anode flow channel, anode diffusion layer, anode catalyst layer, electrolyte, cathode catalyst layer, cathode diffusion layer and cathode flow channel. The anode diffusion layer, anode catalyst layer, electrolyte, cathode catalyst layer and cathode diffusion layer can be processed into one module to become an anode-electrolyte-cathode layer (PEN layer) due to their overall thin thickness. Therefore, the present invention divides SOFC into four parts in the height direction, namely, interconnect, anode flow channel, PEN layer and cathode flow channel, as shown in FIG. Figure 1 As shown. Set the SOFC anode flow direction to x axis, the cathode flow direction is set to y Axis. Along x Axis and y The axial direction divides the four parts of SOFC into n*n nodes, such as Figure 2 As shown. So far, the two-dimensional cross-flow SOFC has a total of 4*n*n micro-modules.

[0038] Furthermore, step 3 specifically includes the following steps: S31: SOFC mass conservation equation: The electrochemical reactions in SOFC include the oxidation of hydrogen and the reduction of oxygen: At the anode electrode: At the cathode electrode: The mass conservation equation is as follows: In the anode channel: In the cathode flow channel: in, C is the concentration of each reactant gas, u is the gas flow rate, the subscripts an and ca represent the anode and cathode respectively, x and y Represent the anode and cathode gas flow directions, respectively. t It's time. i is the current density, F is Faraday's constant, h is the height of the channel. The above material flows are connected through the fluid interfaces of each flow channel element.

[0039] S32: SOFC energy conservation equation: The electrochemical reaction of SOFC generates a large amount of heat, part of which is transferred to the anode and cathode channels through thermal convection, and the other part is transferred to the interconnection through thermal radiation. At the same time, the anode and cathode channels and the interconnection also transfer heat through thermal convection. The above heat transfer is connected using a thermal interface. The energy conservation equations of each layer of SOFC are as follows: Anode channel: Cathode channel: PEN layer: Interconnects: In the formula T is the temperature, ρ is the density, c p is the specific heat capacity, λ is the thermal conductivity, σ is the Stephen Boltzmann constant, ε PEN and ε I is the emissivity of the PEN layer and interconnects, k is the heat transfer coefficient between the fluid and the solid structure.

[0040] S33: SOFC electrochemical equation:

[0041] In the formula, R is the universal gas constant, is the partial pressure of hydrogen, oxygen and vapor. E 0 It can represent the reversible voltage. The battery voltage is affected by the activation loss. η act , Ohmic loss η ohm , and concentration loss η conc The impact of Activation loss η act is the energy barrier that the reactants must overcome and is calculated as:

[0042] in i 0 is the exchange current density, and its value depends largely on the material and microscopic properties of the electrodes, the type of gas, and the operating temperature and pressure.

[0043] p ref is the reference pressure, E act,an and E act,ca are the activation energies of the anode and cathode, respectively.

[0044] Ohmic loss η ohm It can be calculated by the following formula: in σ an , and σ ca are the anode and cathode conductivities, σ ele is the electrolyte ionic conductivity.

[0045] Concentration loss η conc It is caused by the resistance to gas transport near the reaction interface and the resistance to products leaving the reaction interface.

[0046] Flow variables are used to represent energy; differences in potential variables are used to represent temperature and pressure; and flow variables are used to describe enthalpy or composition. The gas in the channel i The partial pressure, p i is the gas at the reaction interface i The partial pressure can be calculated by the following formula: in p ca is the working pressure in the cathode channel, Deff is the effective diffusion coefficient.

[0047] Furthermore, step 4 specifically connects the above defined micro-element modules to each other according to their own types of interfaces, such as Figure 3 The specific steps include: S41: Anode channel micromodule: Total n Row n Each microelement has a fluid interface at the front and back for fluid in and out, which is connected to other anode microelements in the same column in sequence. n At the same time, each channel element has two thermal interfaces, one of which is connected to the thermal interface of the PEN layer element at the same position in the height direction, and the other is connected to the thermal interface of the interconnector element at the same position in the height direction for heat convection.

[0048] S42: Cathode channel micromodule: Total n Row n Each microelement has a fluid interface at the front and back for fluid in and out, which is connected to other cathode microelements in the same column in sequence. n At the same time, each channel element has two thermal interfaces, one of which is connected to the thermal interface of the PEN layer element at the same position in the height direction, and the other is connected to the thermal interface of the interconnector element at the same position in the height direction for heat convection.

[0049] S43: PEN layer micromodule: total n Row n Each microelement has a thermal interface on the front, back, left, and right sides. x Axis and y Axis, each PEN layer microelement is connected in sequence for heat conduction. In addition, each microelement has three thermal interfaces, two of which are connected to the thermal interfaces of the anode flow channel microelement and the cathode flow channel microelement at the same position in the height direction for heat convection. The other is connected to the thermal interface of the interconnector for radiation heat transfer. The PEN layer microelement module also has two electrical interfaces, namely the positive electrode and the negative electrode. The positive and negative electrical interfaces of all PEN layer microelements are connected in parallel.

[0050] S44: Interconnect micromodule: Total n Row n The interconnected micro-element is arranged in a row, and each micro-element space contains a thermal interface on the front, back, left and right sides respectively. x Axis and yAxis, each interconnector microelement is connected in sequence for heat conduction. In addition, each microelement has three thermal interfaces, two of which are connected to the thermal interfaces of the anode flow channel microelement and the cathode flow channel microelement at the same position in the height direction for heat convection. The other is connected to the thermal interface of the PEN layer module for radiation heat transfer.

[0051] S45: After the connections of the interfaces inside the microelement are completed, the microelement and the external interfaces of the SOFC model are connected, including the anode and cathode fluid inlet and outlet interfaces, and the SOFC electrical interface. The connection method is as follows: SOFC model inlet fluid interface and n The inlet of the drainage channel is connected in parallel, and when the external fluid enters the SOFC, it is evenly divided into n When the fluids in each flow channel leave the SOFC model, they converge to the SOFC outlet fluid interface and leave the battery. The positive and negative electrode electrical interfaces of the SOFC model are connected in parallel with the positive and negative electrode electrical interfaces of the PEN layer, respectively.

[0052] Furthermore, step 5 specifically includes: SOFC comprehensive performance evaluation indicators include: S51: SOFC PEN layer temperature distribution standard deviation: in, For the i Row, No. j The PEN layer temperature of the column, is the average temperature of the PEN layer.

[0053] S52: SOFC inlet and outlet exergy: SOFC inlet and outlet exergy includes physical exergy and chemical exergy. The calculation formula is as follows:

[0054] here h is the enthalpy value, s is the entropy value, is the mass flow rate, x is the mole fraction of each component, T 0 is the ambient temperature.

[0055] S53: SOFC exergy loss: The exergy loss of SOFC can be calculated by the exergy balance formula: In the formula, W is the power generated by SOFC.

[0056] Furthermore, step 6 specifically includes: The positive and negative electrode electrical interfaces of the established two-dimensional cross-flow SOFC dynamic model are connected to the negative and positive electrode electrical interfaces of the external current source respectively; the inlet fluid interfaces of the anode and cathode are connected to the fuel gas and air mass flow sources; the outlet fluid interfaces of the anode and cathode are connected to the fuel gas and air pressure boundaries. The fuel gas hydrogen is set to be mixed with a small amount of water vapor, with mass fractions of 90% and 10% respectively. The mass flow rate is 1.44×10 -6 kg / s, the temperature is 700℃; the cathode gas is air, and the mass flow rate is 1.05×10 -4 kg / s, the temperature is 700℃. The boundary pressure of the anode and cathode outlets is 1 bar. The length and width of SOFC are both 0.1 m, and the current is 100A.

[0057] The initial current is 100 A. After SOFC reaches steady state, t = 5000 s, the current is stepped to 110 A, and the other parameters remain unchanged. Figure 4 The figure is the dynamic response diagram of SOFC voltage when the current changes step by step. As the current increases step by step, the voltage of SOFC responds quickly, and due to the influence of the polarization characteristics of SOFC itself, it decreases step by step. Then, as the temperature of SOFC gradually increases, the ohmic loss of SOFC decreases, and the voltage gradually increases. The SOFC power changes with time as shown in Figure 5 As shown in Figure 1, under the influence of voltage and current changes, the power of SOFC shows a rapid and substantial increase at first, then a slight decrease, and finally a gradual increase. The dynamic response of the average temperature of the SOFC PEN layer is shown in Figure 1. Figure 6 As shown in Figure 1, the average temperature of the SOFCPEN layer gradually increases and then stabilizes. This is because the increase in SOFC current density intensifies the SOFC electrochemical reaction, increases heat generation, and increases the temperature.

[0058] The dynamic response characteristics of temperature, current, hydrogen and oxygen mass fractions at different nodes inside SOFC are different. Nodes [2, 2], [3, 4], [4,5] and [5, 3] inside SOFC are selected to analyze the dynamic characteristics inside SOFC. Figure 7 The figure is the dynamic response diagram of different node temperatures of the SOFC PEN layer. It can be seen that with the step increase of current, the temperature of each node gradually increases, but the increase amplitude of each node is different. The temperature increase amplitude of nodes [2,2] and [3,4] is greater than that of nodes [4,5] and [5,3]. This is because nodes [2,2] and [3,4] are closer to the fuel gas inlet, the hydrogen supply is more sufficient, the polarization loss is smaller, and the electrochemical reaction is more intense. Figure 8The figure is a dynamic response diagram of the current density at different nodes of the SOFC PEN layer. As the current increases step by step, the current density at each node increases step by step. Afterwards, due to differences in position and hydrogen concentration, the current density at each node changes with time in different trends. The hydrogen concentration at node [2,2] is relatively high, and the current density gradually increases; the current density at node [3,4] gradually decreases slightly, but is still higher than the current density value before 5000 s; the current density at node [4, 5] also gradually decreases, slightly lower than the previous steady-state value; the current at node [5, 3] gradually decreases, and the decrease is greater. The change of hydrogen mass fraction at different nodes in the SOFC anode flow channel with time is shown in the figure. Fig. 9 As shown. When the current step increases, the hydrogen mass fraction of each node first decreases rapidly and then gradually decreases. It can be seen that although the closer to the anode gas outlet, the smaller the amount of hydrogen consumed, the greater the decrease in mass fraction. This is because as the amount of water vapor generated by the electrochemical reaction increases, the mixed gas flow rate is increased, further reducing the proportion of hydrogen in the mixed gas. Fig.10 The dynamic response diagram of oxygen mass fraction at different nodes of the SOFC cathode flow channel shows that the oxygen mass fraction at each node drops rapidly when the current increases stepwise. Afterwards, the mass fractions of nodes [2, 2] and [3, 4] continue to drop due to the high electrochemical reaction rates. Nodes [4, 5] and [5, 3] then show a gradual increase trend, and the oxygen mass fraction at node [5, 3] is slightly higher than the initial state.

[0059] The standard deviation of the temperature distribution in the SOFC PEN layer reflects the uniformity of the temperature distribution in the SOFC. The lower the value, the more uniform the temperature distribution. Fig.11 The dynamic response diagram of the standard deviation of the temperature distribution of the SOFC PEN layer is shown in Figure 2. It can be seen that when the current density increases stepwise, the standard deviation of the temperature distribution of the PEN layer gradually increases, and the uniformity of the SOFC temperature distribution decreases. The SOFC exergy loss reflects the change in the working capacity of the SOFC during the variable operating conditions. The dynamic response diagram of the SOFC exergy loss is shown in Figure 2. Fig.12 As shown in the figure. When the current increases, the exergy loss of SOFC first decreases rapidly and then increases rapidly, and finally decreases gradually, but is still higher than the initial value. This is because as the current increases, according to the polarization characteristics of SOFC, the voltage decreases, the irreversible loss of SOFC increases, and the work efficiency decreases, which is consistent with the power generation characteristics of SOFC.

Claims

1. A two-dimensional dynamic characteristics modeling and evaluation method of cross-flow SOFC based on Modelica, characterized in that: The steps include: Step 1, determine the physical fields involved in the two-dimensional cross-flow SOFC dynamic simulation model, and design the connector model under each physical field; Step 2, dividing the two-dimensional cross-flow SOFC into four parts in the height direction: an interconnector, an anode flow channel, a PEN layer and a cathode flow channel; the flow directions of the anode fuel gas and the cathode air of the two-dimensional cross-flow SOFC are perpendicular to each other, and the four parts of the two-dimensional cross-flow SOFC are divided into multiple micro-modules along the flow directions of the anode and the cathode; Step 3: For multiple micro-element modules in the two-dimensional cross-flow SOFC, corresponding dynamic mathematical models are established according to their different physical and chemical processes; Step 4: Connect the heat flow, material flow and current of each micro-module in sequence using the defined connectors to form an overall two-dimensional cross-flow SOFC dynamic model; Step 5, establishing a comprehensive evaluation method for the performance of a two-dimensional cross-flow SOFC, including its dynamic characteristics, temperature distribution characteristics, and current distribution characteristics; Step 6: Conduct a dynamic simulation study on the two-dimensional cross-flow SOFC. By performing step change experiments on current and air flow, the dynamic response characteristics of the two-dimensional cross-flow SOFC are obtained, and the reasons for the formation of the dynamic characteristics are analyzed.

2. The two-dimensional dynamic characteristics modeling and evaluation method of cross-flow SOFC based on Modelica according to claim 1, characterized in that: Step 1 is specifically as follows: design connectors of different physical domains in the two-dimensional cross flow, and define the type, flow variable, potential variable and flow variable in each connector; wherein the connector type includes material flow interface, electrical interface and thermal interface; the material flow interface, its corresponding flow variable is material flow rate, and the potential variable includes pressure, enthalpy value and component; the electrical interface, its corresponding flow variable is current, and the potential variable is voltage; the thermal interface, its corresponding flow variable is heat flow rate, and the potential variable is temperature.

3. The two-dimensional dynamic characteristics modeling and evaluation method of cross-flow SOFC based on Modelica according to claim 1, characterized in that: Step 2 is specifically as follows: the actual physical structure of the two-dimensional cross-flow SOFC includes: an interconnect, an anode flow channel, an anode diffusion layer, an anode catalyst layer, an electrolyte, a cathode catalyst layer, a cathode diffusion layer and a cathode flow channel; the anode diffusion layer, the anode catalyst layer, the electrolyte, the cathode catalyst layer and the cathode diffusion layer can be processed as one module due to their overall thin thickness, becoming an anode-electrolyte-cathode layer, i.e., a PEN layer; the anode flow direction of the SOFC is set to the x-axis, and the cathode flow direction is set to the y-axis; the four parts of the SOFC are divided into n*n nodes along the x-axis and the y-axis directions, and the two-dimensional cross-flow SOFC has a total of 4*n*n micro-element modules.

4. The two-dimensional dynamic characteristics modeling and evaluation method of cross-flow SOFC based on Modelica according to claim 1, characterized in that: Step 3 specifically includes the following steps: S31: SOFC mass conservation equation: The electrochemical reactions in SOFC include the oxidation of hydrogen and the reduction of oxygen: At the anode electrode: ； At the cathode electrode: ； The mass conservation equation is as follows: In the anode flow channel: ； In the cathode flow channel: ； in, C is the concentration of each reactant gas, u is the gas flow rate, the subscripts an and ca represent the anode and cathode respectively, x and y Represent the anode and cathode gas flow directions, respectively. t It's time. i is the current density, F is Faraday's constant, h is the height of the channel, is the partial differential symbol, and the material flow is connected through the fluid interface of each flow channel element; S32: SOFC energy conservation equation: The electrochemical reaction of SOFC generates a large amount of heat, part of which is transferred to the anode and cathode channels through thermal convection, and the other part is transferred to the interconnection through thermal radiation. At the same time, the anode and cathode channels and the interconnection also transfer heat through thermal convection. The above heat transfer is connected using a thermal interface. The energy conservation equation of each layer of SOFC is as follows: Anode channel: ； Cathode channel: ； PEN layer: ； Interconnects: ； In the formula T is the temperature, ρ is the density, c p is the specific heat capacity, λ is the thermal conductivity, σ is the Stephen Boltzmann constant, ε PEN and ε I is the emissivity of the PEN layer and interconnects, k is the heat transfer coefficient between the fluid and the solid structure, the subscript I represents the interconnect component, τ Indicates the thickness of each component; S33: SOFC electrochemical equation: ； In the formula, R is the universal gas constant, are the partial pressures of hydrogen, oxygen and steam, E 0 Represents the reversible voltage, the battery voltage is affected by the activation loss η act , Ohm loss η ohm , and concentration loss η conc The impact can be calculated as: Activation loss η act is the energy barrier that the reactants need to overcome and is calculated as follows: ； in i 0 is the exchange current density, whose value depends on the material and microscopic properties of the electrode, the type of gas, the operating temperature and pressure; ； p ref is the reference pressure, E act,an and E act,ca are the activation energies of the anode and cathode, respectively; Ohmic loss η ohm It can be calculated by the following formula: ； in σ an , and σ ca are the anode and cathode conductivities, σ ele is the electrolyte ionic conductivity; ； Concentration loss η conc Caused by resistance to gas transport near the reaction interface and to product departure from the reaction interface; ； The gas in the channel i The partial pressure, p i is the gas at the reaction interface i The partial pressure can be calculated by the following formula: ； in p ca is the working pressure in the cathode channel, D eff is the effective diffusion coefficient.

5. The two-dimensional dynamic characteristics modeling and evaluation method of cross-flow SOFC based on Modelica according to claim 1, characterized in that: Step 4 specifically includes the following steps: S41: Anode flow channel micro-element module: There are n rows and n columns of flow channel micro-elements in total, each micro-element has a fluid interface at the front and back for fluid inlet and outlet, and is sequentially connected with other anode flow channel micro-elements in the same column to form n connected anode flow channels; at the same time, each flow channel micro-element also has two thermal interfaces, one of which is connected to the thermal interface of the PEN layer micro-element at the same position in the height direction, and the other is connected to the thermal interface of the interconnector micro-element at the same position in the height direction for heat convection; S42: cathode flow channel micro-element module: there are n rows and n columns of flow channel micro-elements; Each microelement has a fluid interface at the front and back for fluid inflow and outflow, which is connected with other cathode flow channel microelements in the same column in sequence to form n connected cathode flow channels; at the same time, each flow channel microelement also has two thermal interfaces, one of which is connected with the thermal interface of the PEN layer microelement at the same position in the height direction, and the other is connected with the thermal interface of the interconnector microelement at the same position in the height direction for thermal convection; S43: PEN layer micro-element module: there are n rows and n columns of PEN layer micro-elements; Each microelement space contains a thermal interface on the front, back, left and right sides respectively. Along the x-axis and y-axis, each PEN layer microelement is connected in sequence for heat conduction. In addition, each microelement has three thermal interfaces, two of which are connected to the thermal interfaces of the anode flow channel microelement and the cathode flow channel microelement at the same position in the height direction for heat convection; the other is connected to the thermal interface of the interconnector for radiation heat transfer. The PEN layer microelement module also has two electrical interfaces, namely the positive electrode and the negative electrode. The positive and negative electrical interfaces of all PEN layer microelements are connected in parallel. S44: Interconnector micro-element module: There are n rows and n columns of interconnector micro-elements, each of which contains a thermal interface in the front, back, left and right directions. Along the x-axis and y-axis, each interconnector micro-element is connected in sequence for heat conduction. In addition, each micro-element has three thermal interfaces, two of which are connected to the thermal interfaces of the anode flow channel micro-element and the cathode flow channel micro-element at the same position in the height direction for heat convection; the other is connected to the thermal interface of the PEN layer module for radiation heat transfer. S45: After the connections of the interfaces inside the microelement are completed, the microelement and the external interfaces of the SOFC model are connected, including the anode and cathode fluid inlet and outlet interfaces, and the SOFC electrical interface; the connection method is as follows: The inlet fluid interface of the SOFC model is connected in parallel with the n rows of flow channel inlets. When the external fluid enters the SOFC, it is evenly divided into n streams. When the fluid in each flow channel leaves the SOFC model, it converges to the SOFC outlet fluid interface and leaves the battery. The positive and negative electrical interfaces of the SOFC model are connected in parallel with the positive and negative electrical interfaces of the PEN layer, respectively.

6. The two-dimensional dynamic characteristics modeling and evaluation method of cross-flow SOFC based on Modelica according to claim 1, characterized in that: Step 5 specifically includes the following steps: SOFC comprehensive performance evaluation indicators include: S51: SOFC PEN layer temperature distribution standard deviation: ； in, For the i Row, No. j The PEN layer temperature of the column, is the average temperature of the PEN layer; S52: SOFC inlet and outlet exergy: SOFC inlet and outlet exergy includes physical exergy and chemical exergy, and the calculation formula is as follows: ； in, h is the enthalpy value, s is the entropy value, is the mass flow rate, x is the mole fraction of each component, T 0 is the ambient temperature; S53: SOFC exergy loss: The exergy loss of SOFC can be calculated by the exergy balance formula: ； In the formula, W is the power generated by SOFC.

7. The two-dimensional dynamic characteristics modeling and evaluation method of cross-flow SOFC based on Modelica according to claim 1, characterized in that: Step 6 specifically includes the following steps: S61: Connect the positive and negative electrode electrical interfaces of the established two-dimensional cross-flow SOFC dynamic model to the negative and positive electrode electrical interfaces of the external current source respectively; connect the inlet fluid interfaces of the anode and cathode to the fuel gas and air mass flow sources; connect the outlet fluid interfaces of the anode and cathode to the fuel gas and air pressure boundaries; set the fuel gas hydrogen to be mixed with a small amount of water vapor, set its mass fraction, mass flow rate, and temperature; set the cathode gas to be air, set its mass fraction and temperature; set the anode and cathode outlet boundary pressures, the length and width of the SOFC, and the initial current; S62: setting the initial current, and after the SOFC reaches a steady state, when the time changes, the current changes stepwise, and other parameters remain unchanged; As the current increases in steps, the voltage of SOFC responds quickly, and under the influence of the polarization characteristics of SOFC itself, it decreases in steps. Then, as the temperature of SOFC gradually increases, the ohmic loss of SOFC decreases, and the voltage gradually increases. Under the influence of the changes in voltage and current, the power of SOFC increases rapidly and significantly at first, then decreases slightly, and finally increases gradually. The average temperature of the PEN layer of SOFC gradually increases and then stabilizes. As the current density of SOFC increases, the electrochemical reaction of SOFC intensifies, the heat generation increases, and the temperature increases. S63: The dynamic response characteristics of temperature, current, hydrogen and oxygen mass fractions at different nodes inside the SOFC are different; nodes inside the SOFC are selected to analyze the dynamic characteristics inside the SOFC; S64: The standard deviation of the temperature distribution of the PEN layer of SOFC reflects the uniformity of the temperature distribution in the SOFC. The lower the value, the more uniform the temperature distribution. When the current density increases stepwise, the standard deviation of the temperature distribution of the PEN layer gradually increases, and the uniformity of the temperature distribution of SOFC decreases. The exergy loss of SOFC reflects the change in the working capacity of SOFC during variable operating conditions. When the current increases, the exergy loss of SOFC first decreases rapidly and then increases rapidly, and finally decreases gradually, but is still higher than the initial value. Due to the increase in current, according to the polarization characteristics of SOFC, the voltage decreases, the irreversible loss of SOFC increases, and the working efficiency decreases, which is consistent with the power generation characteristics of SOFC.

8. A computer device comprising a memory, a processor and a computer program stored in the memory, characterized in that: The processor executes the computer program to implement the steps of the method of claim 1.

9. A computer-readable storage medium having a computer program / instruction stored thereon, characterized in that: When the computer program / instructions are executed by a processor, the steps of the method according to claim 1 are implemented.

10. A computer program product comprising a computer program / instructions, characterized in that When the computer program / instructions are executed by a processor, the steps of the method according to claim 1 are implemented.

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