CN115642269B - Solid oxide fuel cell structure and optimal design method thereof - Google Patents
Solid oxide fuel cell structure and optimal design method thereof Download PDFInfo
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Abstract
The invention discloses a solid oxide fuel cell structure, which comprises an anode matrix, wherein the upper surface and the lower surface of the anode matrix are respectively provided with an anode current collecting strip, electrolyte, a cathode and a cathode connector in sequence; the inside of the anode matrix is provided with two layers of gas passages with a cross-shaped structure, and the inside of each layer of gas passage is communicated with each other; the anode current collecting strips are arranged along the central line of the width direction of the anode matrix; the cathode connector is provided with a plurality of ribs which are arranged at intervals on one side facing the cathode, and the width of the ribs is gradually enlarged along the gas flow direction, so that the width of an air passage in the gas flow direction is gradually reduced. The battery structure of the invention enhances the strength of the battery to a certain extent, reduces the ohmic loss of current transmission on the anode matrix, effectively increases the air back-flow velocity and the oxygen molar concentration, and improves the output performance and durability of the battery. Meanwhile, the invention also discloses a battery structure optimization design method, and the battery output performance is further improved by optimizing key structure parameters of the battery.
Description
Technical Field
The invention belongs to the field of fuel cells, and particularly relates to a solid oxide fuel cell structure and an optimal design method thereof.
Background
The solid oxide fuel cell (Solid oxide fuel cell, SOFC) is a ceramic electrochemical conversion device for directly converting fuel chemical energy into electric energy, has the advantages of all-solid-state cell structure, high energy utilization rate, no need of noble metal catalyst, strong fuel adaptability and the like, and has wider development prospect.
The basic composition of a solid oxide fuel cell includes at least one layer of dense solid electrolyte, at least one anode, at least one cathode, an electrode connection, and a number of gas channels. When the battery works, fuel gas is introduced into the anode, oxidant gas represented by air is introduced into the cathode, oxygen undergoes a reduction reaction on the cathode side to generate oxygen ions, the oxygen ions pass through the electrolyte to enter the anode side under the action of electrochemical potential energy, the oxygen ions undergo an oxidation reaction with the fuel gas to generate water, and electrons migrate to the cathode from the anode to form a loop through the outer circuit.
The traditional electrolyte supporting plate type solid oxide fuel cell is of an asymmetric structure in the thickness direction, and because of uneven internal temperature distribution and unmatched thermal expansion coefficients among components of the cell in the working process of the cell, thermal stress is generated, thermal deformation occurs, and the service life of the cell is influenced. The cathode and anode sides of the battery are respectively provided with a connector with higher cost, so that the current collection is realized while the distribution of the reaction gas is completed. The inside of the connector is provided with an air passage groove with a fixed section size for the reaction gas to flow through the whole electrode; the outer convex ribs of the connector are attached to the electrodes, so that the collection and transmission of the reaction current on the high-conductivity connector are realized. In the aspect of connector structural design, the competing relationship between the airway size and the rib size in the connector needs to be processed: the wider rib design increases the contact area of the connector and the electrode, and shortens the flow path of current from the three-phase region to the connector, thereby reducing ohmic loss caused by current transmission on the electrode (the electrode conductance is lower than that of the current collector); on the other hand, the wider rib design reduces the direct contact area of the reaction gas and the electrode, the diffusion of the reaction gas in the electrode area under the rib is limited, the concentration of the reaction gas in the three-phase area under the rib is lower, even a gas-free area can appear, the effective reaction area of the battery is obviously influenced, and the output performance of the battery is reduced.
The solid oxide fuel cell structure is optimally designed, so that the overall output performance of the cell can be improved. The prior research researches structural factors influencing the performance output of the battery based on experimental design and three-dimensional numerical simulation, but the variable size selected in the research process is discrete in numerical value, and by setting a certain parameter change range and change interval, each parameter combination is processed by an enumeration method or modeled and simulated, so that the economic cost in the processing experiment and the time cost in the modeling and simulation process are very high, the battery structure cannot be optimized rapidly and economically, and the aim of further improving the performance of the solid oxide fuel battery is fulfilled.
Disclosure of Invention
The invention provides a solid oxide fuel cell structure, which can realize secondary distribution of fuel gas in the cell and enhance the strength of the cell to a certain extent; simultaneously, ohmic loss of current transmission on the anode matrix is reduced; the air back-flow speed and the oxygen molar concentration are effectively increased, so that the output performance of the battery is improved, and the durability of the battery is improved to a certain extent.
The solid oxide fuel cell structure comprises an anode matrix, wherein the upper surface and the lower surface of the anode matrix are respectively provided with an anode current collecting strip, electrolyte, a cathode and a cathode connector in sequence, and the whole structure is a symmetrical structure;
the inside of the anode matrix is provided with two layers of gas passages with a cross-shaped structure, and the inside of each layer of gas passage is communicated with each other; the electrolyte is coated on the upper surface and the lower surface of the anode matrix, and the anode current collecting strip is clamped between the electrolyte and the anode matrix; the anode current collecting strips are arranged along the central line of the width direction of the anode matrix; the cathode is coated on the outer surface of the electrolyte;
the cathode connector is provided with a plurality of ribs which are arranged at intervals on one side facing the cathode, and the width of the ribs is gradually enlarged along the gas flow direction, so that the air passage of the gas flow direction is gradually reduced.
According to the invention, by improving the structure of the solid oxide fuel cell, the built-in air passage of the anode is provided with two layers of intercommunicated gas passages which are distributed in a cross shape, and the independent longitudinal penetrating air passages are communicated through the design of the transverse air passages which are distributed at intervals, so that the secondary distribution of gas in the cell is realized. Compared with the existing anode built-in air passage, the cross section of the built-in air passage arranged in a cross shape is round, the size is smaller, and the built-in air passage is arranged inside the anode in a double-layer symmetrical mode. The built-in air flue of the anode enhances the strength of the battery to a certain extent, effectively increases the air flow speed in the air flue, increases the mole fraction of the reaction gas, thereby improving the output performance of the battery, and meanwhile, the cross-shaped air flue configuration can realize more uniform gas flow configuration, so that the anode reaction is more sufficient, and more uniform anode current distribution is realized, thereby improving the uneven distribution of electrochemical reaction heat in a reaction area of the battery, reducing the internal temperature gradient of the battery, reducing the internal thermal stress of the battery, and improving the durability of the battery to a certain extent.
The invention sets up the positive electrode current collecting strip to be clamped between the positive electrode base body and the electrolyte at two sides by improving the structure of the solid oxide fuel cell. The anode current collecting strips are arranged along the center line of the width direction of the battery and are attached to the outer surface of the anode, so that the transmission path of current on the anode matrix can be reduced, and the ohmic loss of current transmission on the anode matrix can be reduced.
The invention improves the structure of the solid oxide fuel cell, and arranges the ribs of the cathode connector into a gradual change structure with the width gradually expanding along the gas flow direction, correspondingly, the width of the air passage gradually decreases along the gas flow direction, thereby realizing the design of the widened air passage. The cathode connector structure effectively increases the air back-flow speed and the oxygen molar concentration while ensuring a certain contact area with the cathode, enhances the capacity of Cheng Kuosan after air, thereby improving the output performance of the battery, and simultaneously, the cathode air channel structure with wide front and narrow back can realize more uniform cathode current distribution, thereby improving the uneven distribution of electrochemical reaction heat in a reaction area of the battery, reducing the internal temperature gradient of the battery, reducing the internal thermal stress of the battery and improving the durability of the battery to a certain extent.
Further, the anode matrix and the cathode are porous media and are simultaneously electron and ion conductors. The electrolyte is shown as a solid gas-impermeable medium, as an ionic conductor.
Further, the anode matrix and the cathode are made of porous metal ceramic composite materials, the electrolyte is made of ceramic materials, and the cathode connector and the anode current collector are made of high-conductivity metal or alloy materials. The conductivity of the cathode connector is higher than that of the cathode, so that the cathode connector can resist high temperature; the rib cross section shape is set to be rectangular, and the corresponding air passage cross section shape is also rectangular, so that air uniformly flows in the air passage. The anode matrix is further subdivided into an intermediate supporting layer for supporting and internally arranging a gas flue, and two side active layers which are in contact with electrolyte for electrochemical reaction, wherein the materials of different functional layers are consistent in composition, and the proportions of the components are different.
Further, the inner part of each layer of gas air passage is communicated with the original independent longitudinal air passage by arranging the transverse air passages which are distributed at intervals, so that the gas air passages with mutually communicated cross structures are formed. The two layers of gas channels which are arranged in a cross shape are respectively arranged close to the surfaces of two sides of the anode, so that the diffusion path of the gas in the anode porous medium to the three-phase reaction area is shortened. Because the material strength of the anode porous material is lower than that of the metal connector, the section shape of the gas flue is circular, and the phenomenon of stress concentration of the hollow structure inside the anode is avoided. The interval between the longitudinal air passage and the transverse air passage is an independent structural design parameter.
Further, the anode current collector bar is an elongated narrow bar, one end of the anode current collector bar is flush with the end face of the anode matrix in the length direction, and the other end of the anode current collector bar extends to a cell reaction zone between the anode matrix and electrolyte, and the conductivity of the anode current collector bar is higher than that of the anode. This arrangement can reduce the transmission path of the current on the anode substrate and reduce the ohmic loss of the current transmitted on the anode substrate.
Further, the cathode connector comprises a body and a plurality of ribs arranged in the body at intervals; the outer end surfaces of the ribs are closely attached to the surface of the cathode, and a plurality of air passages are formed between the interval areas among the ribs and the surface of the cathode;
the two ends of the body in the length direction are respectively provided with an air distribution groove and an air collection groove; one end of the air distribution groove is provided with an air inlet hole penetrating through the body, and one end of the air collection groove far away from the air inlet hole is provided with an air outlet hole penetrating through the body.
Preferably, the width of the rib at the air inlet side is 1-2 mm, the width of the rib at the air outlet side is 2-3 mm, each air passage and the adjacent rib thereof are a connector internal unit, and the sum of the section widths of the two is certain, namely the interval between the two adjacent air passages. The length, width and height dimensions of the anode current collector bar are 5-90 mm multiplied by 2-10 mm multiplied by 0.015mm. In the anode base body, the radius of the section of the gas air passage is 0.2-0.6 mm, the interval between the longitudinal air passages is 1.5-2.5 mm, and the interval between the transverse air passages is 5-15 mm.
The invention also provides an optimization design method of the solid oxide fuel cell structure, which aims at physical parameters and electrochemical characteristics of the cell, optimizes the solid oxide fuel cell structure and further improves the output performance of the cell, and comprises the following steps:
s1: based on three-dimensional size parameters of each component of the solid oxide fuel cell structure, parametric modeling is carried out to obtain a cell geometric model;
s2: constructing an optimization problem, determining an objective function, determining an optimization variable and a design space, and determining constraint conditions;
s3: based on a test design method, a sample set and a test set sampling point are constructed in a design space of S2;
s4: setting corresponding physical and electrochemical control equations and boundary conditions based on the battery geometric model established in the step S1, constructing a simulation model, and verifying the rationality of a simulation result based on the performance curve data measured by experiments; calling a simulation model to respectively calculate response values of sampling points of a sample set and a test set;
s5: based on a Kriging proxy model approximation method, invoking a sample set input-output relation in S4 to construct a proxy model; invoking the input-output relation of the test set in S4 to evaluate the accuracy of the proxy model, judging whether the response value and the simulation result of the proxy model on each sampling point of the test set meet the error requirement, if not, carrying out S3 test design again, and increasing the sampling point number of the sample set;
s6: based on a gray wolf intelligent optimization algorithm, invoking the agent model constructed in the step S5 to solve the optimization problem of the step S2, updating the battery geometric structure according to the obtained optimal parameter combination, performing three-dimensional simulation calculation, checking whether the error between the agent model prediction result and the simulation result meets the requirement, and if the error meets the error requirement, finishing optimization, and outputting the optimal structure parameter combination of the battery; if the error requirement is not met, adding the simulation data of the group into the sample set, reconstructing the proxy model, and continuing to optimize until the error requirement is met.
Further, in step S1, the parameterized modeling object is a solid oxide fuel cell structure, and the parameters include three-dimensional parameters of each component of the cell, and the cell structure is adjusted by changing the variables of each parameter.
Further, in step S2, the output power is determined as an objective function; respectively selecting the width of the rib at the air inlet side of the cathode connector, the width of the rib at the air outlet side of the cathode connector, the width of the anode current collecting strip, the length of the anode current collecting strip, the inner diameter of the gas channel in the anode matrix, the arrangement interval of the longitudinal gas channel in the anode matrix and the arrangement interval of the transverse gas channel as optimization variables; based on the overall structure requirement of the battery, the value range of each optimized variable is designed, and corresponding constraint conditions are determined.
Further, in step S3, the optimal latin hypercube design method is used to generate sampling points of the sample set and the test set respectively, and the optimal latin hypercube design method obtains sampling points distributed more uniformly in the design space by adding a criterion. And the sample set and the test set sampling points are obtained through two independent optimal Latin hypercube experiments, and the two sampling points are full of the whole design space and are not overlapped with each other. The specific steps of the step S3 are as follows:
s31: normalizing the value range of each optimized variable, and mapping each variable range into a [0,1] interval;
s32: equally dividing each dimension into m intervals in a 7-dimensional sample space consisting of 7 optimization variables, so that the probability of each interval is the same;
s33: randomly sampling in each interval of each optimization variable;
s34: the values are randomly paired, each level of a factor is guaranteed to be researched only once, an orthogonality criterion is applied to achieve better space filling characteristics, and a sample set containing m sampling points is generated;
s35: inversely normalizing the extracted points according to the value range of each variable, and mapping the extracted points into a real design space;
s36: repeating the steps to generate test set sampling points.
Further, in step S4, the simulation model is a multi-physical field coupling model, and the specific steps of constructing the simulation model are as follows:
s41: defining physical parameters corresponding to materials of each part of the fuel gas, the air and the battery;
s42: setting corresponding control equations and boundary conditions on different domains and boundaries of a parameterized model of the solid oxide fuel cell structure;
s43: performing grid division on the model geometric structure, and calculating partial differential equation problem numerical solutions for all subareas after grid division based on a finite element method; performing grid independence analysis, and determining the grid number according to simulation result errors under different grid numbers;
s44: performing a battery performance experiment, obtaining a current-voltage polarization curve of the battery at the working temperature, and checking the accuracy of a simulation model based on the experimental curve;
s45: and (3) updating a model structure and adaptively adjusting grids according to the structural parameter combination of each sampling point in the sample set and the test set in the S3, solving the response value of each sampling point based on multi-physical field coupling simulation, and constructing the mapping relation between each sampling point and power in the sample set and the test set.
Compared with the prior art, the invention has the following beneficial effects:
1. the invention improves the structure of the solid oxide fuel cell and sets the built-in air flue of the anode to be two layers of intercommunicating gas air flue structures which are distributed in a cross shape. The built-in air passage structure of the anode is circular in cross section shape by reducing the size of the air passage, so that the strength of the battery is enhanced to a certain extent, the flow speed of the internal combustion air in the air passage is effectively increased, the mole fraction of the reaction gas is increased, and the output performance of the battery is improved. Meanwhile, the well-shaped air passage structure can realize more uniform gas flow configuration, so that the anode reaction is more complete, and more uniform anode current distribution is realized, thereby improving uneven electrochemical reaction heat distribution in a battery reaction area, reducing the internal temperature gradient of the battery, reducing the internal thermal stress of the battery and improving the durability of the battery to a certain extent.
2. The present invention provides an anode collector bar sandwiched between an anode substrate and electrolytes on both sides by improving the structure of a solid oxide fuel cell. The anode current collecting strip structure can reduce the transmission path of current on the anode substrate and reduce the ohmic loss of current transmission on the anode substrate.
3. The invention realizes the design of the widened air passage by improving the structure of the solid oxide fuel cell and arranging the air passage of the cathode connector to be a gradual change structure with the width gradually reduced along the gas flowing direction. The cathode connector structure effectively increases the air rear-end flow speed and the oxygen molar concentration, enhances the capacity of Cheng Kuosan after air, thereby improving the output performance of the battery, and simultaneously, the cathode air passage structure with wide front and narrow rear can realize more uniform cathode current distribution, thereby improving the uneven distribution of electrochemical reaction heat in a battery reaction area, reducing the temperature gradient in the battery, reducing the thermal stress in the battery and improving the durability of the battery to a certain extent.
4. The invention keeps the formula of each component material of the battery in the prior art unchanged, and achieves the aim of improving the output performance and durability of the battery by improving the battery structure; on the basis, the battery performance is further improved by optimizing key structural parameters influencing the battery output performance based on the agent model and the intelligent optimization algorithm, and the optimal design method has the advantages of low time cost, high reliability, no need of expensive and repeated processing tests and wider engineering application prospect on the premise of ensuring the accuracy.
Drawings
FIG. 1 is a schematic diagram of a solid oxide fuel cell according to an embodiment of the present invention;
FIG. 2 is a schematic view of an anode collector bar structure and an anode internal air channel structure according to an embodiment of the present invention;
FIG. 3 is a schematic view of a cathode connector according to an embodiment of the present invention;
fig. 4 is a flow chart of an optimization design method of a solid oxide fuel cell structure according to an embodiment of the 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.
It should be noted that the same reference numerals appearing in different figures are denoted by the same items, and that the terms "upper", "lower", "upper surface", "lower surface", "side" and other positional relationship descriptions appearing therein are based on the positional relationship in the figures, and that the term "spacing" refers to the distance at the center point of the two parts, and the length is expressed in millimeters (mm).
As shown in fig. 1, a solid oxide fuel cell structure comprises an anode matrix 5, wherein anode collector bars 4, electrolyte 3, a cathode 2 and a cathode connector 1 are sequentially arranged on the upper surface and the lower surface of the anode matrix 5, and the whole structure is distributed in a symmetrical double-electrolyte-double-cathode structure. The anode substrate 5 is thicker than the electrolyte and cathode and serves as a battery support layer. The main body of the battery adopts an anode supporting plate type structure, and the rest parts are processed and formed on the upper surface and the lower surface of the anode according to the assembly sequence, wherein an anode current collecting strip 4 is parallel clamped between an anode matrix 5 and an electrolyte 3 and is used as a current collecting component of anode reaction current.
The anode matrix and the cathode are made of porous metal ceramic composite materials, the electrolyte 3 is made of ceramic materials, and the cathode connector 1 and the anode current collector 4 are made of high-conductivity metal or alloy materials, so that the high-temperature-resistant composite material can resist high temperature. The anode matrix 5 can be further subdivided into an intermediate support layer for supporting and incorporating gas channels, and two side active layers for electrochemical reactions in contact with the electrolyte; the anode has the advantages that the material compositions of different functional layers of the anode are consistent, the proportion of each component is different, and the electrochemical reaction is better carried out while the strength of the battery is ensured.
As shown in fig. 2, the anode base 5 is internally provided with two layers of gas passages 10 in a cross-shaped structure, the interiors of the gas passages 10 in each layer are communicated with each other, and the structure cut along the central section of the gas passage is illustrated in fig. 2. Compared with the existing anode built-in air passage, the cross-sectional size of the built-in air passage arranged in a cross shape is smaller, and the built-in air passage is symmetrically arranged inside the anode and is close to the outer surface of the anode. The anode built-in air passage comprises a plurality of longitudinal air passages 10-1 distributed along the flowing direction of the fuel gas and a plurality of transverse air passages 10-2 distributed at intervals. The gas channels of each layer are communicated internally, the section of the gas channel is circular, wherein the longitudinal gas channel 10-1 is a through hole penetrating through the anode, the transverse gas channel 10-2 is an anode internal gas channel, and the interval between the longitudinal gas channel 10-1 and the transverse gas channel 10-2 is an independent structural design parameter. The upper and lower surfaces of the anode substrate 5 are coated with long and narrow anode collector bars 4, which are arranged at the center line in the width direction, one end of each collector bar is flush with the end face of the anode, and the other end of each collector bar is introduced into a cell reaction zone, so that the transmission path of current on the anode substrate is reduced.
As shown in fig. 3, the body 11 of the cathode connector 1 is a plate-shaped cover plate. The air distribution groove 6 and the air collection groove 7 are respectively arranged at two ends of the body 11 in the length direction; one end of the air distribution groove 6 is provided with an air inlet hole 12 penetrating through the body 11, and the air collection groove 7 is provided with an air outlet hole 13 penetrating through the body 11 at one end far away from the air inlet hole 12. The inside many ribs 8 that are equipped with the downward arch of body 11, rib 8 are the gradual change type structure of quadrilateral, and the cross-section is the rectangle, and the width of rib 8 increases gradually along the flow direction, and each rib 8 interval arrangement forms air flue 9, realizes the width-widening runner design that the air flue reduces gradually along the flow direction.
In this embodiment, the air duct 9 relates only to the lateral duct in the air flow direction shown in fig. 2, and does not include the longitudinal flow passages of the air distribution grooves 6 and the air collection grooves 7. The lower end surfaces of all the ribs 8 are flush with the lower end surface of the body 11, namely the height of the ribs and the height of the air passages are the same as the depths of the air distribution grooves and the air collection grooves on the two sides; the lower end face of the cathode connector 1 is assembled with the upper surface of the cathode 2 in a fitting way, and the lower end face of the connector rib and the surface of the cathode form an air passage 9.
As shown in fig. 4, the method for optimizing the structure of the solid oxide fuel cell further optimizes structural parameters affecting the performance of the cell based on the existing structure of the solid oxide fuel cell, thereby outputting the performance of the cell, and comprises the following steps:
s1: based on three-dimensional size parameters of each component of the solid oxide fuel cell structure, parametric modeling is carried out to obtain a cell geometric model;
s2: constructing an optimization problem, determining an objective function, determining an optimization variable and a design space, and determining constraint conditions;
s3: based on a test design method, a sample set and a test set sampling point are constructed in an S2 design space;
s4: setting corresponding physical and chemical control equations and boundary conditions based on the S1 battery geometric model, constructing a simulation model, and verifying the rationality of a simulation result based on the experimentally measured performance curve data; calling a simulation model to respectively calculate response values of sampling points of a sample set and a test set;
s5: based on the proxy model approximation method, invoking the input-output relation of the sample set in S4 to construct a proxy model; selecting the maximum relative error as a model precision evaluation index, and calling the precision of the agent model established by evaluating the input-output relation of the test set in S4;
s6: based on an intelligent optimization algorithm, the agent model in S5 is called to solve the optimization problem of S2, and the optimal structural parameter combination of the solid oxide fuel cell is obtained through calculation, so that the output performance of the cell is further improved on the basis of the structure of the solid oxide fuel cell.
In step S1, the parameterized modeling object is a solid oxide fuel cell structure, and the overall three-dimensional size (length, width, and height) is 90×43×11.6mm. The main dimensions include the three-dimensional dimensions of the anode substrate 90X 43X 4.5mm, the three-dimensional dimensions of the electrolyte 90X 38X 0.03mm, the three-dimensional dimensions of the cathode 80X 38X 0.02mm, and the three-dimensional dimensions of the cathode connector 90X 43X 3.55mm. Wherein, the width of the rib at the air inlet side is 1.4mm, the width of the rib at the air outlet side is 2.6mm, the height of the rib is 1.5mm, the length of the rib is 80mm, the radius of the gas passage in the anode matrix is 0.4mm, the interval between the longitudinal gas passages is 2mm, the interval between the transverse gas passages is 5mm, and the three-dimensional size of the anode current collecting strip is 45 multiplied by 4 multiplied by 0.015mm.
Step S2, constructing an optimization problem by determining an objective function, the number of optimization variables and a value range and constraint conditions, wherein the specific form is as follows:
maxP cell (x)
x＝(d 1 ,d 2 ,d 3 ,d 4 ,d 5 ,d 6 )
s.t.d 1 ∈[1,2)；d 2 ∈[2,3]；
d 3 ∈[2,10]；d 4 ∈[5,90]；
d 5 ∈[0.2,0.6]；d 6 ＝[1.5,2.5]；d 7 ＝[5,15]；
d 1 +d 2 ＝4
the optimization problem is established by taking the battery output power at the working temperature and the working voltage as an objective function to determine the rib width d of the air inlet side of the cathode connector as the structural parameter 1 Rib width of air outlet side of cathode connectorDegree d 2 Width d of anode collector bar 3 Length d of anode collector bar 4 Internal diameter d of gas passage in anode matrix 5 Longitudinal air passage arrangement interval d in anode matrix 6 Interval d for transverse air passage arrangement 7 To optimize the variables, the value ranges of all the structural parameters are respectively determined in the feasible design range, and the total section size of the rib is controlled to be consistent through equality constraint. The number of the built-in longitudinal air passages and the number of the built-in transverse air passages of the anode are used as intermediate variables and are determined through the aperture and the interval.
Step S3, respectively generating sampling points of a sample set and a test set by using an optimal Latin hypercube test design method, wherein the specific steps are as follows:
s31: normalizing the value range of each optimized variable, and mapping each variable range into a [0,1] interval;
s32: in a 7-dimensional sample space formed by 7 optimization variables, equally dividing each dimension into m intervals, so that the probability of each interval is the same;
s33: randomly sampling in each interval of each optimization variable;
s34: the values are randomly paired, each level of a factor is guaranteed to be researched only once, an orthogonality criterion is applied to achieve better space filling characteristics, and a sample set containing m sampling points is generated;
s35: inversely normalizing the extracted points according to the value range of each variable, and mapping the extracted points into a real design space;
s36: repeating the steps to generate test set sampling points.
In step S4, the simulation model is a multi-physical field coupling model, and the specific steps of constructing the simulation model are as follows:
s41: defining physical parameters corresponding to materials of each part of the fuel gas, the air and the battery;
s42: setting corresponding control equations and boundary conditions on different domains and boundaries of a parameterized model of the solid oxide fuel cell structure;
wherein the control equation comprehensively considers the coupling relation among electrochemical reaction, charge transfer, mass transfer, momentum transfer and energy transfer processes; further, the electrochemical reaction process considers the influence of contact resistance between the cathode connector and the cathode; the mass transfer process is based on considering inter-diffusion between molecules, and also considers Knudsen diffusion of gas molecules and pore walls of a porous medium (electrode); the energy transfer process is based on heat conduction and heat convection, and simultaneously considers the surface-to-surface heat radiation effect between the battery and the connector. The gas flow selects flow inlet boundary conditions and pressure outlet boundary conditions, corresponding gas component mole fractions are set at the gas inlet and the gas outlet, corresponding potential boundary conditions are set at the cathode and anode boundaries, and corresponding temperature boundary conditions are set at each boundary of the battery;
s43: performing grid division on the model geometric structure, and calculating partial differential equation problem numerical solutions for all subareas after grid division based on a finite element method; developing grid independence analysis, and determining proper grid quantity according to simulation result errors under different grid quantities;
s44: performing a battery performance experiment, obtaining a current-voltage polarization curve of the battery at the working temperature, and checking the accuracy of a simulation model based on the experimental curve;
s45: and (3) updating a model structure and adaptively adjusting grids according to the structural parameter combination of each sampling point in the sample set and the test set in the S3, solving the response value of each sampling point based on multi-physical field coupling simulation, and constructing the mapping relation between each sampling point and power in the sample set and the test set.
In step S5, the proxy model approximation method is a Kriging approximation method, the constructed Kriging approximation model is a semi-parameterized difference model, the overall idea of Kriging is to predict the response value of an unknown point based on the weighted summation of information of other points around the unknown point, and the method has the characteristic of local estimation through the action of a correlation function, and specifically comprises the following steps:
s51: by each sampling point x= { X in the sample set 1 ,x 2 ,…,x m } T And its corresponding response value y= { y 1 ,y 2 ,…,y m } T Constructing a proxy model to realize the realization of unknown point x new And predicting the response value of the (c). Determination ofKriging model form y (x) =f (x) T beta+Z (x), where y (x) is the response function, is determined by a deterministic regression function f (x) T Beta and a random process function Z (x); z (x) is subjected to normal distribution, the mean value is 0, and the variance is sigma 2 ；
S52: definition of covariance function Cov [ z (x) i ),z(x j )]＝σ 2 R(θ,x i ,x j ) Providing an approximation of some local deviation of the design space, where R (θ, x i ,x j ) Is a correlation function of any two data points. The present embodiment provides Gauss basis functions
For a correlation function between data points, the fixed basis function index value is 2, n=7 represents the number of optimization variables, +.>
Representing the distance, θ, between the kth component in any two points in the sample set data points k The correlation parameters to be estimated for fitting the model are obtained;
s53: determining θ based on the maximum likelihood estimate;
s54: and calling the constructed Kriging approximate model, predicting the response value of each sampling point on the test set based on the spatial correlation between the to-be-predicted point and each sample point, judging whether the predicted result and the simulation result of each point meet the error requirement, and if not, carrying out S3 test design again to increase the sampling point number of the sample set.
In step S6, the intelligent optimization algorithm is a wolf intelligent optimization algorithm, which is a group intelligent optimization algorithm simulating a wolf cooperative hunting object (optimal solution), the algorithm takes the optimal solution with the best current adaptability as α, the suboptimal solution and the suboptimal solution as β and δ, the rest candidate solutions are all categorized as ω, the hunting (searching) process is performed by α leader, β and δ cooperation, ω follows, and the main steps in the optimization process are as follows:
s61: randomly initializing wolf group X;
s62: calculating the fitness of the gray wolf individuals, and setting the first three wolf individuals with the best fitness in the current step as alpha, beta and delta;
s63: updating the current position of the wolf group, and closing the wolf group towards the head wolf;
s64: calculating the adaptability of all the gray wolves;
s65: updating alpha, beta and delta;
s66: and (5) meeting a tolerance criterion or maximum iteration times and outputting an optimization result.
In step S6, the battery geometry is updated according to the optimal parameter combination obtained by solving the optimization algorithm, three-dimensional simulation calculation is carried out, whether the errors of the agent model prediction result and the simulation result meet the requirements or not is checked, if the errors meet the error requirements, the optimization is finished, and the optimal structural parameters of the battery and the corresponding output performance of the battery are output; if the error requirement is not met, adding the simulation data of the group into the sample set, reconstructing the proxy model, and continuing to optimize until the error requirement is met.
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 (9)
1. The solid oxide fuel cell structure is characterized by comprising an anode matrix (5), wherein the upper surface and the lower surface of the anode matrix (5) are respectively provided with an anode current collecting strip (4), an electrolyte (3), a cathode (2) and a cathode connector (1) in sequence, and the whole structure is symmetrical;
the inside of the anode matrix (5) is provided with two layers of gas passages (10) with a well-shaped structure, and the inside of each layer of gas passage (10) is communicated with each other; the electrolyte (3) is coated on the upper surface and the lower surface of the anode matrix (5), and the anode current collecting strip (4) is clamped between the electrolyte (3) and the anode matrix (5); the anode current collecting strips (4) are arranged along the central line of the width direction of the anode matrix (5); the cathode (2) is coated on the outer surface of the electrolyte (3);
the cathode connector (1) is provided with a plurality of ribs (8) which are arranged at intervals on one side facing the cathode (2), and the width of the ribs (8) is gradually enlarged along the gas flow direction, so that the width of an air passage (9) in the gas flow direction is gradually reduced.
2. The solid oxide fuel cell structure according to claim 1, wherein the anode substrate (5) and the cathode (2) are made of porous metal ceramic composite materials, the electrolyte (3) is made of ceramic materials, and the cathode connector (1) and the anode current collector (4) are made of high-conductivity metal or alloy materials and are resistant to high temperature; the anode substrate (5) is further subdivided into a middle supporting layer for supporting and internally arranging a gas flue (10), and two side active layers which are in contact with the electrolyte (3) for electrochemical reaction, wherein the material compositions of different functional layers are consistent, and the component proportions of the materials in the different functional layers are different.
3. The solid oxide fuel cell structure according to claim 1, wherein the inside of each layer of gas passages (10) is communicated with the originally independent longitudinal gas passages (10-1) by arranging transverse gas passages (10-2) which are arranged at intervals, thereby forming the gas passages (10) of the mutually communicated cross-shaped structure;
the radius of the section of the gas air passage (10) is 0.2-0.6 mm, the interval of the longitudinal air passages (10-1) is 1.5-2.5 mm, and the interval of the transverse air passages (10-2) is 5-15 mm.
4. The solid oxide fuel cell structure according to claim 1, characterized in that the anode collector bar (4) is an elongated narrow bar, one end of which is flush with the end face in the length direction of the anode base body (5), and the other end of which extends to the cell reaction zone between the anode base body (5) and the electrolyte (3), and the electrical conductivity of which is higher than that of the anode.
5. The solid oxide fuel cell structure according to claim 1, characterized in that the cathode connector (1) comprises a body (11) and a plurality of ribs (8) arranged at intervals inside the body (11); the outer end surfaces of the ribs (8) are closely attached to the surface of the cathode (2), and a plurality of air passages (9) are formed between the spacing areas among the ribs (8) and the surface of the cathode (2); the cross sections of the ribs (8) and the air passages (9) are rectangular;
an air distribution groove (6) and an air collection groove (7) are respectively arranged at two ends of the inside of the body (11) in the length direction; one end of the air distribution groove (6) is provided with an air inlet hole (12) penetrating through the body (11), and one end of the air collection groove (7) far away from the air inlet hole (12) is provided with an air outlet hole (13) penetrating through the body (11).
6. A solid oxide fuel cell structure according to claim 1, characterized in that the rib width on the air inlet side is 1-2 mm and the rib width on the air outlet side is 2-3 mm, and the sum of the sectional widths of each air passage (9) and its adjacent ribs (8) is fixed.
7. A method for optimizing the design of a solid oxide fuel cell structure according to any one of claims 1 to 6, comprising the steps of:
s1: based on three-dimensional size parameters of each component of the solid oxide fuel cell structure, parametric modeling is carried out to obtain a cell geometric model;
s2: constructing an optimization problem, determining an objective function, determining an optimization variable and a design space, and determining constraint conditions;
specifically, determining output power as an objective function; respectively selecting the width of the rib at the air inlet side of the cathode connector, the width of the rib at the air outlet side of the cathode connector, the width of the anode current collecting strip, the length of the anode current collecting strip, the inner diameter of the gas channel in the anode matrix, the arrangement interval of the longitudinal gas channel in the anode matrix and the arrangement interval of the transverse gas channel as optimization variables; based on the overall structure requirement of the battery, designing the value range of each optimized variable, and determining corresponding constraint conditions;
s3: based on a test design method, a sample set and a test set sampling point are constructed in a design space of S2;
s4: setting corresponding physical and electrochemical control equations and boundary conditions based on the battery geometric model established in the step S1, constructing a simulation model, and verifying the rationality of a simulation result based on the performance curve data measured by experiments; calling a simulation model to respectively calculate response values of sampling points of a sample set and a test set;
s5: based on a Kriging proxy model approximation method, invoking a sample set input-output relation in S4 to construct a proxy model; invoking the input-output relation of the test set in S4 to evaluate the accuracy of the proxy model, judging whether the response value and the simulation result of the proxy model on each sampling point of the test set meet the error requirement, if not, carrying out S3 test design again, and increasing the sampling point number of the sample set;
s6: based on a gray wolf intelligent optimization algorithm, invoking the agent model constructed in the step S5 to solve the optimization problem of the step S2, updating the battery geometric structure according to the obtained optimal parameter combination, performing three-dimensional simulation calculation, checking whether the error between the agent model prediction result and the simulation result meets the requirement, and if the error meets the error requirement, finishing optimization, and outputting the optimal structure parameter combination of the battery; if the error requirement is not met, adding the simulation data of the group into the sample set, reconstructing the proxy model, and continuing to optimize until the error requirement is met.
8. The optimization design method according to claim 7, wherein in step S3, the sample points of the sample set and the test set are generated by using the optimal latin hypercube design method, respectively, and the specific steps are as follows:
s31: normalizing the value range of each optimized variable, and mapping each variable range into a [0,1] interval;
s32: equally dividing each dimension into m intervals in a 7-dimensional sample space consisting of 7 optimization variables, so that the probability of each interval is the same;
s33: randomly sampling in each interval of each optimization variable;
s34: the values are randomly paired, each level of a factor is guaranteed to be researched only once, an orthogonality criterion is applied to achieve better space filling characteristics, and a sample set containing m sampling points is generated;
s35: inversely normalizing the extracted points according to the value range of each variable, and mapping the extracted points into a real design space;
s36: repeating the steps to generate test set sampling points.
9. The optimization design method according to claim 7, wherein in step S4, the simulation model is a multi-physical field coupling model, and the specific steps of constructing the simulation model are as follows:
s41: defining physical parameters corresponding to materials of each part of the fuel gas, the air and the battery;
s42: setting corresponding control equations and boundary conditions on different domains and boundaries of a parameterized model of the solid oxide fuel cell structure;
s43: performing grid division on the model geometric structure, and calculating partial differential equation problem numerical solutions for all subareas after grid division based on a finite element method; performing grid independence analysis, and determining the grid number according to simulation result errors under different grid numbers;
s44: performing a battery performance experiment, obtaining a current-voltage polarization curve of the battery at the working temperature, and checking the accuracy of a simulation model based on the experimental curve;
s45: and (3) updating the simulation model structure and adaptively adjusting grids according to the structural parameter combination of each sampling point in the sample set and the test set in the S3, solving the response value of each sampling point based on multi-physical field coupling simulation, and constructing the mapping relation between each sampling point and power in the sample set and the test set.
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