CN117744438A - Fuel cell stack variable-scale modeling simulation method and system based on data driving - Google Patents
Fuel cell stack variable-scale modeling simulation method and system based on data driving Download PDFInfo
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Abstract
The invention discloses a fuel cell stack variable-scale modeling simulation method and system based on data driving, wherein the method comprises the following steps: s1: constructing an SOFC single cell multi-physical field coupling model; s2: constructing a cell proxy model based on the SOFC single cell multi-physical field coupling model; s3: establishing a SOFC electric pile geometric model; s4: defining a corresponding physical field and internally arranging a cell proxy model, and constructing an SOFC electric pile multi-physical field coupling model; s5: aiming at the SOFC cell stack multi-physical field coupling model, based on a finite element algorithm, carrying out SOFC cell-cell stack variable-scale simulation, and verifying the accuracy of the model by combining cell stack performance experimental data; s6: and (3) combining the electric pile numerical simulation model with an intelligent optimization algorithm to optimize electric pile operation parameters and electric pile structures. The invention effectively reduces the model solving memory and improves the model calculating speed while ensuring the model calculating precision and reliability, and can realize modeling simulation, performance analysis and optimization of a larger-scale electric pile under the condition of unchanged hardware calculation force.
Description
Technical Field
The invention belongs to the field of hydrogen energy and fuel cells, and particularly relates to a variable-scale modeling simulation method and system for a fuel cell stack based on data driving.
Background
The fuel cell is an energy conversion device for directly converting chemical energy in fuel into electric energy through electrochemical reaction, the process is not limited by Carnot cycle, the loss of secondary energy conversion is avoided, and the power generation process is clean and efficient.
The solid oxide fuel cell (Solid Oxide Fuel Cell, SOFC) is a type of fuel cell with rapid technical development and wide application prospect, the electrolyte of the fuel cell is of an all-solid structure, the working temperature is 600-1000 ℃, and the fuel cell is a typical high-temperature fuel cell. Because of the higher working temperature, the SOFC does not need noble metal as a catalyst, the cell cost is greatly reduced, meanwhile, the electrode reaction process is rapid, the fuel adaptability is wide, and hydrocarbon fuels such as natural gas, reformed gas, synthesis gas and the like can be used on the basis of pure hydrogen fuel. SOFCs generally consist of a porous anode, electrolyte, porous cathode, flow channels, and connectors.
The single cell power of the SOFC is smaller, and in order to meet the actual industrial production requirement, a plurality of unit cells are required to be stacked by series-parallel operation, so that larger power generation power is obtained. As a basic unit of the fuel cell power generation system, a solid oxide fuel cell stack (SOFC stack) is additionally provided with auxiliary elements including a heating device, a heat retaining structure, a gas pipe, and a gas distribution chamber, on the unit cell basis. The complex structural design of the electric pile and the stacking arrangement of the internal unit cells enhance the inconsistent distribution of the concentration field, the flow field, the thermal field and the electrochemical field of components in the pile, so that the fluctuation of the electric performance among the cell core groups in the pile is caused, and the long-term safe and stable operation of the electric pile is not facilitated. And as the number of chips increases, the non-uniformity of the spatial-temporal distribution of the state parameters in the stack and the performance differences among the cores are further enhanced.
At present, the solid oxide fuel cell stack still has the problems of unclear internal state parameter distribution characteristics, ambiguous operation and structural parameters, insufficient mastering of scale amplification rules, insufficient effective means for improving the performance of the stack, and the like. The method is limited by a measurement method and an experimental period, the measurement of flow distribution, concentration distribution and temperature distribution in a galvanic pile is difficult, and the mutual coupling among all physical fields is high in cost for acquiring the distribution information of the state parameters in the pile by the experimental method. The numerical simulation technology can perform simulation analysis on physical and chemical processes inside the pile, and provide detailed and visual information support, so that the experimental cost is reduced, and the research efficiency is greatly improved.
As an analysis object with complex structural characteristics and high coupling among different physical fields, the three-dimensional numerical simulation calculation amount for the SOFC pile is large, the calculation force requirement is high, the calculation time can be tens of hours or even longer, and the modeling simulation difficulty for developing the large-scale pile is extremely high. By omitting the simplification means of the partial structure information of the galvanic pile, the essence is based on a large number of ideal conditions and approximate assumptions, the simplified simulation result and the actual galvanic pile have an inherent error, and the structural optimization for auxiliary elements cannot be carried out later; the physical fields are directly reduced or the coupling relation between the physical fields is reduced, the influence of the coupling relation on the result is ignored, and the actual situation in the pile cannot be predicted.
Disclosure of Invention
The invention provides a variable-scale modeling simulation method and system for a fuel cell stack based on data driving, which are characterized in that a cell proxy model is built in each cell calculation domain in the stack, partial differential solution to part of processes in a primary cell calculation domain is replaced by an algebraic equation, the number of iterative convergence steps is reduced while the calculation precision and reliability of the model are ensured, the total number of degrees of freedom required for solution is reduced, so that the memory for solving the model is effectively reduced, the calculation rate of the model is improved, and modeling simulation, performance analysis and optimization of a larger-scale stack can be realized under the condition that the calculation force of hardware is unchanged.
A fuel cell stack variable-scale modeling simulation method based on data driving comprises the following steps:
s1: constructing an SOFC single cell multi-physical field coupling model;
s2: based on the SOFC single cell multi-physical field coupling model, carrying out multiple cell simulation under different operation conditions according to each sampling point of a sample set to obtain a corresponding simulation result, solving a function mapping relation representing input-output, and constructing a cell proxy model;
s3: establishing a SOFC electric pile geometric model;
s4: based on the SOFC electric pile geometric model, defining a corresponding physical field and internally arranging a cell proxy model, and constructing a SOFC electric pile multi-physical field coupling model;
s5: aiming at the SOFC cell stack multi-physical field coupling model, based on a finite element algorithm, carrying out SOFC cell-cell stack variable-scale simulation, and verifying the accuracy of the model by combining cell stack performance experimental data;
s6: and (3) combining the electric pile numerical simulation model with an intelligent optimization algorithm to optimize electric pile operation parameters and electric pile structures.
In step S1, constructing the SOFC single cell multi-physical field coupling model specifically includes:
the SOFC single cell multi-physical field coupling model is constructed according to the three-dimensional structure size of each part of an actual fuel cell and comprises a porous cathode, an electrolyte, a porous anode, a runner for conveying reaction gas and a connector for conducting and collecting current;
the physical parameters of materials related to the SOFC single cell multi-physical field coupling model are defined as temperature dependent functions according to the specific material composition of each component of the cell and the specific components of the cathode and anode side reaction gases; wherein, the physical parameters of the material comprise effective conductivity, exchange current density, heat conductivity coefficient, constant pressure heat capacity, specific heat rate, density, dynamic viscosity and gas diffusion coefficient of the electrode;
setting a corresponding physical field control equation and boundary conditions on each calculation domain by using the SOFC single cell multi-physical field coupling model, and coupling different processes by calling equation source items and common variables in consideration of actual heat exchange and heat radiation effects with the environment; wherein the control equation comprises a reaction equation, a charge conservation equation, a momentum conservation equation, a mass conservation equation and an energy conservation equation;
the SOFC single cell multi-physical field coupling model is solved based on a finite element algorithm, and the rationality and accuracy of the SOFC single cell multi-physical field coupling model are verified through grid independence analysis and experimental data.
In step S2, the battery agent model takes the average surface temperature of the anode reaction zone, the average surface temperature of the cathode reaction zone, the average surface hydrogen mole fraction of the anode reaction zone and the average surface oxygen mole fraction of the cathode reaction zone as agent model variables for input, and takes the battery reaction current and the heat generation power of the electrochemical reaction of the battery as agent model variables for output.
In step S3, the SOFC stack geometric model includes a cell core group, a stack heating element, insulation cotton, a gas supply and gas discharge pipeline and a gas distribution cavity, so as to avoid the simulation result and the congenital error of the actual stack caused by the ideal simplification of the stack geometric structure;
the cell core group is a group of SOFC unit cells which are arranged at equal intervals, and the geometric structure of each unit cell is consistent with that of the SOFC unit cell in the S1; the electric pile heating element provides heat required by the electric pile during operation, ensures that the inner core assembly of the pile is in a high-temperature working environment, and realizes simulation of the electric pile heating process and the space distribution of an actual temperature field by introducing the heating element, thereby avoiding the influence of setting isothermal or adiabatic boundary conditions on results; the heat preservation cotton wraps the battery core group, plays a role in heat preservation, and reduces heat dissipation of a hot zone and the environment due to convective heat transfer; the gas supply and gas discharge pipeline comprises a gas inlet pipeline, a gas outlet pipeline, an air inlet pipeline and an air outlet pipeline; the gas distribution chamber includes a gas distribution chamber and an air distribution chamber, which together with the gas supply lines determine the gas flow configuration within the stack.
In step S4, the specific steps of constructing the SOFC stack multi-physical field coupling model are as follows:
s41: defining corresponding physical parameters according to specific material compositions of all unit battery parts of the battery core group, specific components of reaction gases at the cathode side and the anode side, heating element materials, heat insulation cotton materials and gas pipeline materials; the physical parameters comprise effective conductivity, exchange current density, heat conductivity coefficient, constant pressure heat capacity, specific heat rate, density, dynamic viscosity, gas diffusion coefficient and emissivity of the electrode;
s42: setting a corresponding physical field control equation and a proxy model on each calculation domain of the SOFC stack geometric model; setting a corresponding momentum conservation equation, a mass conservation equation, an energy conservation equation and a proxy model function; the battery agent model is arranged on each battery domain in the pile, and the total number of independent variables to be solved is reduced by calling the output result of the battery agent model, so that the overall degree of freedom of the simulation model is reduced;
s43: setting boundary conditions, namely setting corresponding boundary conditions on different boundaries of the geometric model respectively; the boundary conditions include a flow inlet boundary condition, a pressure outlet boundary condition, a gas component inlet boundary condition, a temperature boundary condition;
s44: and performing grid division on the SOFC stack geometric model, and performing grid independence analysis.
The step S5 specifically comprises the following steps:
solving partial differential equations of control equations corresponding to all calculation domains of the pile model and algebraic equations corresponding to all battery calculation domains based on a finite element algorithm;
verifying the accuracy of the model based on the galvanic pile performance experimental data;
and (3) carrying out key parameter analysis based on simulation results under different operation conditions and feasible structural designs, and exploring key operation and structural parameters affecting the overall performance and the inconsistent distribution of internal state parameters of the electric pile.
In step S6, key operation and structural parameters which influence the overall performance and the internal state parameter inconsistency distribution of the pile are selected as decision variables, and optimization problems are built around the safety, economy and high efficiency targets of the pile in a feasible operation interval and an allowable design range;
the intelligent optimization algorithm gives specific values of related decision variables and inputs the specific values into a simulation model, the simulation model is solved to obtain corresponding calculation results, the calculation results are fed back to the optimization algorithm, iterative solution is carried out according to the searching direction of the objective function, and the optimal solution of the optimization problem is obtained through multiple simulation-optimization processes.
A data-driven fuel cell stack variable-scale modeling simulation system, comprising the following modules:
a first model building module: based on the SOFC single cell geometry, constructing a SOFC single cell multi-physical field coupling model according to preset material physical parameters, a physical field control equation and boundary conditions;
the first simulation solving module: based on a finite element algorithm, carrying out iterative solution on the SOFC single cell multi-physical field coupling model after grid division to obtain a model numerical solution, and providing a data sample for a cell proxy model;
the agent model building module: respectively constructing a cell reaction current and an electrochemical reaction heat source agent model based on the mapping relation between each sampling point of a sample set and the calculation result of the SOFC single cell multi-physical field coupling model;
and a second model building module: based on the SOFC pile geometry structure, according to preset material physical parameters, a physical field control equation and boundary conditions, the cell agent model is built in a cell calculation domain, so that a SOFC pile multi-physical field coupling model is constructed;
and a second simulation solving module: based on a finite element algorithm and an agent model function, carrying out iterative solution on the SOFC stack multi-physical field coupling model after grid division to obtain a model numerical solution, and obtaining key operation and structural parameters affecting the overall performance and internal state parameter inconsistency distribution of the stack through key parameter analysis;
and an optimization module: based on the improved SOFC pile multi-physical field coupling model, an intelligent optimization algorithm is called to optimize pile operation parameters and pile structures.
Compared with the prior art, the invention has the following beneficial effects:
1. according to the invention, the SOFC unit cell is accurately modeled, the actual structure of the cell is reduced, the concentration and temperature dependence of physical parameters are considered, the coupling effect between different physical fields is considered, the simulation result is verified by experiments, and the model predicts the fitting reality.
2. According to the invention, based on a test design and a proxy model technology, a data sample set is established by developing multiple SOFC unit cell numerical simulation, and an SOFC proxy model is established based on an input-output relationship, so that the electrical performance output and heat generation conditions of the cell under different operation conditions can be rapidly obtained, the calculation cost is reduced, and the response time is in the second level.
3. According to the invention, through carrying out accurate geometric modeling on the electric pile, the actual structure of the auxiliary element is included, the actual heating and heat preservation process is considered, the convective heat exchange with air rather than isothermal or adiabatic boundary conditions is set, meanwhile, the influence of radiation heat exchange on a temperature field in a high-temperature environment is considered, and the simulation model is closer to reality.
4. According to the invention, the battery agent model is built in each battery calculation domain in the galvanic pile model, the algebraic equation is used for replacing partial differential solution of processes such as conservation of charge, electrochemical reaction, secondary current and the like in the primary battery calculation domain, so that the number of iterative convergence steps is reduced and the total number of degrees of freedom required for solution is reduced while the calculation accuracy and reliability of the model are ensured, the model calculation memory is effectively reduced, the model calculation rate is improved, and modeling simulation, performance analysis and optimization of a larger-scale galvanic pile can be realized under the condition that the hardware calculation force is unchanged.
5. On the accurate and efficient three-dimensional cell stack model, the invention develops the joint simulation optimization based on the intelligent optimization algorithm through the program code, and solves the problem of optimizing the cell stack performance; the optimization algorithm and the simulation model are mutually called, so that the optimization of the operation condition and the structural design of the analyzed electric pile is realized.
Drawings
FIG. 1 is a flow chart of a method for modeling and simulating a variable scale of a fuel cell stack based on data driving according to an embodiment of the present invention;
FIG. 2 is a specific flowchart of step S1 in a modeling simulation method for variable scale of a fuel cell stack based on data driving according to an embodiment of the present invention;
FIG. 3 is a specific flowchart of step S2 in a modeling simulation method for variable scale of a fuel cell stack based on data driving according to an embodiment of the present invention;
FIG. 4 is a specific flowchart of step S4 in a modeling simulation method for variable scale of a fuel cell stack based on data driving according to an embodiment of the present invention;
fig. 5 is a schematic diagram of a variable-scale modeling simulation system of a fuel cell stack based on data driving according to an embodiment of the present invention.
Detailed Description
The invention will be described in further detail with reference to the drawings and examples, it being noted that the examples described below are intended to facilitate the understanding of the invention and are not intended to limit the invention in any way.
Example 1
As shown in fig. 1, the present embodiment provides a fuel cell stack variable-scale modeling simulation method based on data driving, which includes the following steps:
s1: constructing an SOFC single cell multi-physical field coupling model;
s2: based on the SOFC single cell multi-physical field coupling model, carrying out multiple cell simulation under different operation conditions according to each sampling point of a sample set to obtain a corresponding simulation result, solving a function mapping relation representing input-output, and constructing a cell proxy model;
s3: establishing a SOFC electric pile geometric model;
s4: based on the SOFC electric pile geometric model, defining a corresponding physical field and internally arranging a cell proxy model, and constructing a SOFC electric pile multi-physical field coupling model;
s5: aiming at the SOFC cell stack multi-physical field coupling model, based on a finite element algorithm, carrying out SOFC cell-cell stack variable-scale simulation, and verifying the accuracy of the model by combining cell stack performance experimental data;
s6: and (3) combining the electric pile numerical simulation model with an intelligent optimization algorithm to optimize electric pile operation parameters and electric pile structures.
Specifically, as shown in fig. 2, step S1 includes the steps of:
s11: and carrying out parametric modeling according to the three-dimensional structure size of each part of the actual fuel cell, and accurately constructing the SOFC three-dimensional geometric model. The SOFC geometry model includes a porous cathode, an electrolyte, a porous anode, flow channels for transporting reactant gases, and connectors for conducting and collecting electrical current.
The porous anode comprises an anode supporting layer and an anode functional layer, wherein the supporting layer plays a supporting role, and the functional layer catalyzes fuel and provides a reaction place; the porous cathode comprises a cathode supporting layer and a cathode functional layer; the flow channels comprise a fuel gas flow channel above the anode and an air flow channel above the cathode; the connector is made of high-conductivity metal or alloy material, is used for conducting and collecting reaction current, is connected with a wire and is used for conveying electrons to an external circuit.
S12: physical parameters of each material and physical parameters of the mixed gas are defined according to the specific material composition of each component of the fuel cell and the specific components of the reaction gas at the cathode and anode sides. The physical parameters comprise effective conductivity, exchange current density, heat conductivity coefficient, constant pressure heat capacity, specific heat rate, density, dynamic viscosity and gas diffusion coefficient of the electrode.
Wherein, the physical parameters consider the common influence of the physical parameters related to the porous electrode of the composite material solid phase and the gas in the pore; the influence of different gas components on the physical property parameters related to the mixed reaction gas is considered, the physical property parameters of the materials are not constant, and the temperature dependence function of the physical property parameters is determined through specific physical property experimental data.
S13: and setting a corresponding physical field control equation on each calculation domain of the geometric model. And setting a corresponding reaction equation, a charge conservation equation, a momentum conservation equation, a mass conservation equation and an energy conservation equation according to electrochemical reaction, charge transmission, momentum transmission, mass transmission and energy transmission processes which occur in the actual working process of the fuel cell.
The reaction equation is arranged on the two-pole reaction area of the battery, and takes electrochemical reaction and catalytic reforming reaction into consideration; the charge conservation equation is arranged on the two poles of the battery, the electrolyte and the connecting body, and takes the transmission of electrons and ions of the electrolyte and the electrode and the contact resistance effect on the contact surface of the connecting body and the electrode into consideration; the momentum conservation equation considers the flow process of the gas in the flow channel and the porous electrode; the mass conservation equation considers the molecular diffusion and the knudsen diffusion process inside the flow channel and the porous electrode, and the generation and consumption of substances on the cathode and anode reaction areas due to electrochemical reaction; the conservation of energy takes into account the coupling effects of heat conduction and heat convection processes across the computational domain of the cell, as well as the exothermic heat of the electrochemical reaction across the reaction zone of the cell.
The mutual coupling between the different processes is realized through calling source items and common variables in a control equation and a proxy model function.
S14: and setting boundary conditions. Corresponding boundary conditions are respectively set on different boundaries of the geometric model, wherein the boundary conditions comprise a flow inlet boundary condition, a pressure outlet boundary condition, a gas component inlet boundary condition, an electric potential boundary condition and a temperature boundary condition.
S15: and performing grid division on the geometric model, performing corresponding partial differential equation calculation on each subarea after grid division based on a finite element algorithm, and performing iterative solution until convergence to obtain a model numerical solution. And carrying out grid independence analysis, carrying out local grid encryption on the sensitive area, and determining the proper grid quantity according to the fluctuation condition of the calculation result under different grid quantities.
S16: and verifying the accuracy of the SOFC simulation model based on experiments. And carrying out an SOFC single cell performance experiment, and verifying the accuracy of a model calculation result based on the measured volt-ampere characteristic data of the cell under the standard working condition.
Specifically, as shown in fig. 3, step S2 includes the steps of:
s21: selecting the average surface temperature of the anode reaction zone, the average surface temperature of the cathode reaction zone, the average surface hydrogen mole fraction of the anode reaction zone and the average surface oxygen mole fraction of the cathode reaction zone of the battery as proxy model variables for input; and selecting the battery reaction current and the battery electrochemical reaction heat generation power as proxy model variables to output.
S22: and developing a test design to construct sampling points. And constructing a design space according to the value range allowed by each variable, and constructing a sample set and a test set sampling point based on the design space. The sample set and the test set sample space are randomly sampled in a design space based on a test design method, and the number of sampling points of the two sample spaces is 20N and 10N respectively, wherein N is the variable number.
Further, the test design method can be any one of Latin hypercube sampling, optimal Latin hypercube sampling or other random sampling methods.
S23: defining the average surface temperature of the electrode reaction zone and the average mole fraction of the reaction components of the electrode reaction zone as input parameters of an SOFC multi-physical field coupling model in S1, and setting the working voltage of the cell and the inlet flow of the reaction gas; and solving the current and electrochemical reaction thermal power output of the SOFC single cell model under the corresponding operation parameters. The simulation model input-output variables remain consistent with the proxy model.
S24: repeating S23 simulation work according to each sampling point of the sample set and the test set, carrying out multiple battery simulation under different operation conditions to obtain simulation results corresponding to each sampling point, and constructing a mapping relation representing input and output.
S25: according to the mapping relation between each sampling point of the sample set and the calculation result, respectively constructing a battery reaction current and an electrochemical reaction heat source proxy model, wherein the functional relation is shown in the following formula:
I cell ＝f Icell (V cell ,T av ,x av )
Q elec ＝f Qelec (V cell ,T av ,x av )
wherein I is cell For battery reaction current, Q elec Is the electrochemical reaction heat source of the battery, V cell For battery operating voltage, T av Is the average temperature of the surface of the electrode reaction zone, x av And f is a proxy model function relation and is used for mapping model input-output.
Further, verifying whether the accuracy of the proxy model meets the error requirement based on the test set, if not, increasing the number of the collection points of the sample set, and re-simulating to construct the functional relation of the proxy model again. The proxy model function form can be any one of polynomial form, radial basis function form, response surface form and kriging form.
Specifically, in step S3, parametric modeling is performed according to the three-dimensional characteristics of the structure of each component of the actual fuel cell stack, so as to accurately construct a three-dimensional geometric model of the SOFC stack. The SOFC electric pile geometric model comprises a cell core group, an electric pile heating element, heat preservation cotton, gas supply and gas discharge pipelines and a gas distribution cavity, and the natural errors of simulation results and actual electric piles caused by ideal simplification of electric pile geometric structures are avoided.
The cell stack is a group of SOFC unit cells which are arranged at equal intervals, and the geometric structure of each unit cell is consistent with that of the SOFC unit cell in S1.
The electric pile heating element provides heat required by the electric pile during operation, ensures that the inner core assembly of the electric pile is in a high-temperature working environment, and realizes simulation of the electric pile heating process and the actual temperature field spatial distribution by introducing the heating element, thereby avoiding the influence of setting isothermal or adiabatic boundary conditions on the result.
The heat preservation cotton wraps the battery core group, plays a role in heat preservation, and reduces heat dissipation of a hot zone and the environment due to convection heat exchange.
The gas supply and gas discharge pipeline comprises a gas inlet pipeline, a gas outlet pipeline, an air inlet pipeline and an air outlet pipeline.
The gas distribution chamber includes a gas distribution chamber and an air distribution chamber, which together with the gas supply lines determine the gas flow configuration within the stack.
Specifically, as shown in fig. 4, step S4 includes the steps of:
s41: defining corresponding physical parameters according to specific material compositions of all unit battery parts of the battery core group, specific components of reaction gases at the cathode side and the anode side, heating element materials, heat insulation cotton materials and gas pipeline materials; the physical parameters comprise effective conductivity, exchange current density, heat conductivity coefficient, constant pressure heat capacity, specific heat rate, density, dynamic viscosity, gas diffusion coefficient and emissivity of the electrode.
Further, the common influence of the physical parameters related to the porous electrode of the composite material solid phase and the gas in the pores is considered; the influence of different gas components on the physical property parameters related to the mixed reaction gas is considered, the physical property parameters of the materials are not constant, and the temperature dependence function of the physical property parameters is determined through specific physical property experimental data.
S42: setting a corresponding physical field control equation and a proxy model on each calculation domain of the SOFC stack geometric model; wherein, the corresponding momentum conservation equation, mass conservation equation, energy conservation equation and proxy model function are set.
The conservation of momentum equation takes into account the flow process of the gas within the gas supply lines, the gas distribution chamber, the flow channels within the cell stack, and the porous electrode.
The mass conservation equation takes into account the molecular diffusion and knudsen diffusion processes inside the gas supply lines, gas distribution chambers, flow channels inside the cell stack, and porous electrodes.
The existing numerical simulation research on the SOFC stack lacks sufficient consideration on the heat radiation effect. Since SOFCs operate at high temperatures, their surface temperature is high, and energy can be transferred out by means of thermal radiation. Radiation heat transfer significantly affects the temperature distribution in the stack and thus the current distribution, so that the effect of heat radiation is not negligible in calculating the heat transfer process. The conservation of energy takes into account the thermal conduction and convection processes across the stack computational domain, as well as the radiative heat transfer between the heating element surface and the cell surfaces and cavity wall surfaces.
The battery agent model is arranged on each battery domain in the pile and comprises battery reaction current and electrochemical reaction heat source agent models, so that the solution of an agent model algebraic equation is used for replacing partial differential equation solution of component generation and consumption (electrochemical reaction equation), charge transfer (secondary current equation) and electrochemical heat generation on each battery calculation domain, and the total number of independent variables to be solved is reduced by calling the output result of the battery agent model, so that the overall freedom degree of the simulation model is reduced. Furthermore, the built-in battery agent model takes the average temperature of the anode surface of each battery reaction zone, the average temperature of the cathode surface of the reaction zone, the average mole fraction of the anode surface of the reaction zone and the average mole fraction of the cathode surface of the reaction zone oxygen as input, and outputs the specific reaction current and electrochemical heat generation of each battery as source items which are reversely coupled to the mass transfer field and the temperature field.
Further, the consumption of the reaction gas on the two poles can be solved by the output current of the proxy model, and the gas can be obtainedThe bulk source term is coupled with a mass conservation equation, and the consumption source term of hydrogen at the anode side and the consumption source term S of oxygen at the cathode side mass Can be calculated by the following formula:
s43: setting boundary conditions, namely setting corresponding boundary conditions on different boundaries of the geometric model respectively; the boundary conditions include a flow inlet boundary condition, a pressure outlet boundary condition, a gas component inlet boundary condition, a temperature boundary condition.
Furthermore, the SOFC pile simulation model with the built-in cell proxy model does not need to set electrode potential boundary conditions, and the solution of the secondary current directly carries out algebraic solution through the proxy model function relation.
S44: and carrying out grid division on the geometric model and carrying out grid independence analysis.
Specifically, in step S5, partial differential equations of control equations corresponding to each calculation domain of the pile model and algebraic equations corresponding to each battery calculation domain are solved based on a finite element algorithm; verifying the accuracy of the model based on the galvanic pile performance experimental data; and (3) carrying out key parameter analysis based on simulation results under different operation conditions and feasible structural designs, and exploring key operation and structural parameters affecting the overall performance and the inconsistent distribution of internal state parameters of the electric pile.
Specifically, in step S6, key operation and structural parameters affecting the overall performance and the inconsistent distribution of internal state parameters of the pile are selected as decision variables, and optimization problems are built around the targets of safety, economy and high efficiency of long-term operation of the pile within a feasible operation interval and an allowable design range. Introducing an intelligent optimization algorithm, calling the variable-scale simulation model of the fuel cell stack based on data driving, and optimizing the operating parameters and the structure of the fuel cell stack.
Furthermore, the optimization algorithm gives specific values of related decision variables and inputs the specific values into a simulation model, the simulation model is solved to obtain corresponding calculation results, the calculation results are fed back to the optimization algorithm, iterative solution is carried out according to the searching direction of the objective function, and the optimal solution of the optimization problem is obtained through multiple simulation-optimization processes.
Example 2
As shown in fig. 5, the present embodiment provides a fuel cell stack variable-scale modeling simulation system based on data driving, which includes the following modules:
a first model building module: based on the SOFC single cell geometry structure, constructing a SOFC single cell multi-physical field coupling model according to preset material physical parameters, a physical field control equation and boundary conditions.
The first simulation solving module: and carrying out iterative solution on the SOFC single cell multi-physical field coupling model after grid division based on a finite element algorithm to obtain a model numerical solution, and providing a data sample for the cell proxy model.
The agent model building module: and respectively constructing a cell reaction current and electrochemical reaction heat source proxy model based on the mapping relation between each sampling point of the sample set and the calculation result of the SOFC single cell multi-physical field coupling model.
And a second model building module: based on the SOFC pile geometry structure, according to preset material physical parameters, a physical field control equation and boundary conditions, the cell agent model is built in a cell calculation domain, so that a SOFC pile multi-physical field coupling model is constructed.
And a second simulation solving module: based on a finite element algorithm and an agent model function, carrying out iterative solution on the SOFC stack multi-physical field coupling model after grid division to obtain a model numerical solution, and obtaining key operation and structural parameters affecting the overall performance and internal state parameter inconsistency distribution of the stack through key parameter analysis.
And an optimization module: based on the improved SOFC pile multi-physical field coupling model, an intelligent optimization algorithm is called to optimize pile operation parameters and pile structures.
The foregoing embodiments have described in detail the technical solution and the advantages of the present invention, it should be understood that the foregoing embodiments are merely illustrative of the present invention and are not intended to limit the invention, and any modifications, additions and equivalents made within the scope of the principles of the present invention should be included in the scope of the invention.
Claims (8)
1. The fuel cell stack variable-scale modeling simulation method based on data driving is characterized by comprising the following steps of:
s1: constructing an SOFC single cell multi-physical field coupling model;
s2: based on the SOFC single cell multi-physical field coupling model, carrying out multiple cell simulation under different operation conditions according to each sampling point of a sample set to obtain a corresponding simulation result, solving a function mapping relation representing input-output, and constructing a cell proxy model;
s3: establishing a SOFC electric pile geometric model;
s4: based on the SOFC electric pile geometric model, defining a corresponding physical field and internally arranging a cell proxy model, and constructing a SOFC electric pile multi-physical field coupling model;
s5: aiming at the SOFC cell stack multi-physical field coupling model, based on a finite element algorithm, carrying out SOFC cell-cell stack variable-scale simulation, and verifying the accuracy of the model by combining cell stack performance experimental data;
s6: and (3) combining the electric pile numerical simulation model with an intelligent optimization algorithm to optimize electric pile operation parameters and electric pile structures.
2. The method for modeling and simulating variable dimensions of a fuel cell stack based on data driving according to claim 1, wherein in step S1, constructing a SOFC single cell multi-physical field coupling model specifically includes:
the SOFC single cell multi-physical field coupling model is constructed according to the three-dimensional structure size of each part of an actual fuel cell and comprises a porous cathode, an electrolyte, a porous anode, a runner for conveying reaction gas and a connector for conducting and collecting current;
the physical parameters of materials related to the SOFC single cell multi-physical field coupling model are defined as temperature dependent functions according to the specific material composition of each component of the cell and the specific components of the cathode and anode side reaction gases; wherein, the physical parameters of the material comprise effective conductivity, exchange current density, heat conductivity coefficient, constant pressure heat capacity, specific heat rate, density, dynamic viscosity and gas diffusion coefficient of the electrode;
setting a corresponding physical field control equation and boundary conditions on each calculation domain by using the SOFC single cell multi-physical field coupling model, and coupling different processes by calling equation source items and common variables in consideration of actual heat exchange and heat radiation effects with the environment; wherein the control equation comprises a reaction equation, a charge conservation equation, a momentum conservation equation, a mass conservation equation and an energy conservation equation;
the SOFC single cell multi-physical field coupling model is solved based on a finite element algorithm, and the rationality and accuracy of the SOFC single cell multi-physical field coupling model are verified through grid independence analysis and experimental data.
3. The method for modeling and simulating variable dimensions of a fuel cell stack based on data driving according to claim 1, wherein in step S2, the cell proxy model uses the average surface temperature of the anode reaction zone, the average surface temperature of the cathode reaction zone, the average mole fraction of hydrogen on the surface of the anode reaction zone, and the average mole fraction of oxygen on the surface of the cathode reaction zone as proxy model variables for input, and uses the cell reaction current and the power generated by electrochemical reaction of the cell as proxy model variables for output.
4. The method for modeling and simulating a variable scale of a fuel cell stack based on data driving according to claim 1, wherein in step S3, the SOFC stack geometric model includes a cell core group, a stack heating element, insulation cotton, gas supply and gas exhaust pipelines and a gas distribution cavity, so as to avoid the natural errors of simulation results and actual stacks caused by the ideal simplification of the stack geometric structure;
the cell core group is a group of SOFC unit cells which are arranged at equal intervals, and the geometric structure of each unit cell is consistent with that of the SOFC unit cell in the S1; the electric pile heating element provides heat required by the electric pile during operation, ensures that the inner core assembly of the pile is in a high-temperature working environment, and realizes simulation of the electric pile heating process and the space distribution of an actual temperature field by introducing the heating element, thereby avoiding the influence of setting isothermal or adiabatic boundary conditions on results; the heat preservation cotton wraps the battery core group, plays a role in heat preservation, and reduces heat dissipation of a hot zone and the environment due to convective heat transfer; the gas supply and gas discharge pipeline comprises a gas inlet pipeline, a gas outlet pipeline, an air inlet pipeline and an air outlet pipeline; the gas distribution chamber includes a gas distribution chamber and an air distribution chamber, which together with the gas supply lines determine the gas flow configuration within the stack.
5. The method for modeling and simulating variable dimensions of a fuel cell stack based on data driving according to claim 1, wherein in step S4, the specific steps of constructing a multi-physical field coupling model of an SOFC stack are as follows:
s41: defining corresponding physical parameters according to specific material compositions of all unit battery parts of the battery core group, specific components of reaction gases at the cathode side and the anode side, heating element materials, heat insulation cotton materials and gas pipeline materials; the physical parameters comprise effective conductivity, exchange current density, heat conductivity coefficient, constant pressure heat capacity, specific heat rate, density, dynamic viscosity, gas diffusion coefficient and emissivity of the electrode;
s42: setting a corresponding physical field control equation and a proxy model on each calculation domain of the SOFC stack geometric model; setting a corresponding momentum conservation equation, a mass conservation equation, an energy conservation equation and a proxy model function; the battery agent model is arranged on each battery domain in the pile, and the total number of independent variables to be solved is reduced by calling the output result of the battery agent model, so that the overall degree of freedom of the simulation model is reduced;
s43: setting boundary conditions, namely setting corresponding boundary conditions on different boundaries of the geometric model respectively; the boundary conditions include a flow inlet boundary condition, a pressure outlet boundary condition, a gas component inlet boundary condition, a temperature boundary condition;
s44: and performing grid division on the SOFC stack geometric model, and performing grid independence analysis.
6. The method for modeling and simulating variable dimensions of a fuel cell stack based on data driving according to claim 1, wherein step S5 specifically comprises:
solving partial differential equations of control equations corresponding to all calculation domains of the pile model and algebraic equations corresponding to all battery calculation domains based on a finite element algorithm;
verifying the accuracy of the model based on the galvanic pile performance experimental data;
and (3) carrying out key parameter analysis based on simulation results under different operation conditions and feasible structural designs, and exploring key operation and structural parameters affecting the overall performance and the inconsistent distribution of internal state parameters of the electric pile.
7. The method for modeling and simulating variable dimensions of a fuel cell stack based on data driving according to claim 1, wherein in step S6, key operation and structural parameters affecting overall performance and internal state parameter inconsistency distribution of the stack are selected as decision variables, and optimization problems are built around targets of safety, economy and high efficiency of long-term operation of the stack within a feasible operation interval and an allowable design range;
the intelligent optimization algorithm gives specific values of related decision variables and inputs the specific values into a simulation model, the simulation model is solved to obtain corresponding calculation results, the calculation results are fed back to the optimization algorithm, iterative solution is carried out according to the searching direction of the objective function, and the optimal solution of the optimization problem is obtained through multiple simulation-optimization processes.
8. A data-driven fuel cell stack variable-scale modeling simulation system, which is characterized by comprising the following modules:
a first model building module: based on the SOFC single cell geometry, constructing a SOFC single cell multi-physical field coupling model according to preset material physical parameters, a physical field control equation and boundary conditions;
the first simulation solving module: based on a finite element algorithm, carrying out iterative solution on the SOFC single cell multi-physical field coupling model after grid division to obtain a model numerical solution, and providing a data sample for a cell proxy model;
the agent model building module: respectively constructing a cell reaction current and an electrochemical reaction heat source agent model based on the mapping relation between each sampling point of a sample set and the calculation result of the SOFC single cell multi-physical field coupling model;
and a second model building module: based on the SOFC pile geometry structure, according to preset material physical parameters, a physical field control equation and boundary conditions, the cell agent model is built in a cell calculation domain, so that a SOFC pile multi-physical field coupling model is constructed;
and a second simulation solving module: based on a finite element algorithm and an agent model function, carrying out iterative solution on the SOFC stack multi-physical field coupling model after grid division to obtain a model numerical solution, and obtaining key operation and structural parameters affecting the overall performance and internal state parameter inconsistency distribution of the stack through key parameter analysis;
and an optimization module: based on the improved SOFC pile multi-physical field coupling model, an intelligent optimization algorithm is called to optimize pile operation parameters and pile structures.
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