Optimal design method for high-temperature air preheater for solid oxide fuel cells based on three-periodic minimal surfaces

Abstract

The present invention discloses a method for optimizing the design of a high-temperature air preheater for a solid oxide fuel cell based on a three-periodic minimal surface. First, a sample database between the three-periodic minimal surface single cell structure and hydraulic characteristic parameters, and between the head structure and the local resistance coefficient is established. Based on the sample database, an artificial neural network model of the single cell structure and hydraulic characteristics, and between the head and the local resistance is constructed. According to the model, a cell-by-cell adaptive thermal balance calculation process of a cross-flow heat exchanger is designed in combination with a nonlinear optimization algorithm on the basis of design requirements. With the pressure drop on both the hot and cold sides as the optimization target, an optimization design method for an air preheater with a minimal surface structure is developed based on a multi-objective genetic optimization algorithm. Finally, the geometric structure of the single cell, the overall size of the air preheater and its corresponding thermal performance are obtained. The method can automatically obtain the optimal matching scheme between the single cell and the overall size, thereby improving the design optimization efficiency and being more conducive to engineering applications.

Description

Technical Field

[0001] The present invention relates to the technical field of high-temperature heat exchangers for solid oxide fuel cells, and in particular to an optimization design method for a high-temperature air preheater for a solid oxide fuel cell based on a three-periodic minimal surface. Background Art

[0002] Solid oxide fuel cells (SOFCs) are widely used in hydrogen energy applications due to their diverse fuel sources, high electrothermal efficiency, and high exhaust gas temperatures. They are widely used in industrial parks and distributed energy systems. Because their operating temperatures typically range from 600-800°C, they require appropriate heat balance components, such as steam generators, air preheaters, reformers, and burners, to maintain proper operation. The air preheater heats ambient air to or near the stack's operating temperature, reducing internal temperature gradients and extending its service life. Currently, these heat balance components suffer from low compactness and high flow resistance, hindering the miniaturization of SOFCs and limiting their application scenarios. Tri-periodic minimal surface structures, composed of non-self-intersecting periodic surfaces in three directions with zero average curvature, possess a large specific surface area, an interconnected internal structure, and excellent heat transfer capacity due to their smooth surface. These properties make tri-periodic minimal surface structures highly promising for high-temperature air preheater design. The flow and heat transfer capacity of the three-period minimal surface is affected by both its own structural parameters and operating parameters. Compared with the traditional straight channel structure, its improved heat transfer capacity also brings an increase in flow resistance. Reasonable design of the unit structure and overall structure according to the working state of the air preheater can improve the compactness of the thermal balance components and provide support for expanding the application scenarios of solid oxide fuel cells. The current design process for high-temperature air preheaters usually adopts the method of designing the single cell structure first and then designing the overall size, without considering the mutual influence between the single cell and the whole. In order to further improve the development efficiency of air preheaters for solid oxide fuel cells, it is of great significance to develop a comprehensive optimization design method. Summary of the Invention

[0003] In view of the shortcomings or defects of the above-mentioned prior art, the purpose of the present invention is to provide a high-temperature air preheater optimization design method for solid oxide fuel cells based on three-periodic minimal surfaces, so as to achieve rapid, efficient and comprehensive optimization design of highly compact thermal balance components, thereby expanding the application scenarios of solid oxide fuel cells.

[0004] The purpose of the present invention is achieved through the following technical solutions.

[0005] A method for optimizing the design of a high-temperature air preheater for a solid oxide fuel cell based on a three-periodic minimal surface comprises the following steps:

[0006] S1: Build a sample database of single cell geometric parameters and hydraulic characteristic parameters, head structure and local resistance coefficient, and construct the corresponding artificial neural network model based on the sample database;

[0007] S2: Based on the consideration of the head structure, a three-period minimal surface structure is selected according to the cross-flow heat transfer structure. The flow and heat transfer performance are calculated cell by cell, and the overall thermal performance is finally obtained.

[0008] S3: Based on the nonlinear optimization algorithm fmincon, adaptive heat balance calculation is realized on a cell-by-cell basis, and the operating parameters of the dual-fluid heat exchanger under a given structure are obtained by solving the problem cell by cell;

[0009] S4: Using unit cell size, wall thickness, heat exchange core size, and head height as decision variables, minimizing the pressure drop on both the hot and cold sides as the optimization goal, and overall size limit and hot side temperature outlet as constraints, a multi-objective genetic algorithm was used to optimize the design of a high-temperature air preheater.

[0010] S5: Calculate the optimal solution set and select the design scheme that meets the requirements to obtain the overall design parameters of the optimized three-period minimal surface structure heat exchanger and complete the design of the high-temperature air preheater.

[0011] The single cell geometric parameters include the single cell size uc and wall thickness δ uc , the hydraulic characteristic parameters of the single cell include hydraulic diameter D h , flow cross-sectional area A cross , single-side heat exchange area HSA uc ; The head structure includes the diameter of the head bundle tube d bt , height δ along the fluid flow direction end , the length of the head l core and width w core , the local resistance coefficient of the head is ξ, which represents the pressure drop generated by the heads at both ends;

[0012] The sample database is a one-to-one correspondence library constructed after the corresponding parameters are calculated by modeling software and numerical simulation software. The modeling software is used to construct single cell models under different unit size-wall thickness combinations, and the hydraulic characteristic parameters of the single cell under each combination are calculated to form the sample database. The local resistance coefficient of the head is calculated by modeling software and numerical simulation software, and together with the head structure, it constitutes the sample database.

[0013] The artificial neural network model includes two models: a single cell structure-hydraulic characteristic parameter prediction model and a head height-local resistance coefficient prediction model, which are constructed based on a double-layer feedforward network fitting model.

[0014] The model is used to calculate the flow and heat transfer performance of the heat exchanger under a given structure, which can be expressed as:

[0015] [D h ,A cross ,HSA uc ]=f(size uc ,δ uc )

[0016] ξ=f(l core ,w core ,d bt ,δ end )

[0017] Where: D h represents the hydraulic diameter of the unit cell, A cross Represents the cross-sectional area of ​​a single cell, HSA uc Indicates the heat transfer area on one side of a single cell, size uc represents the unit cell size, δ uc represents the thickness of the single cell wall, l core Indicates the length of the head, w core Indicates the width of the head, d bt Indicates the diameter of the bundled tube at the head, δ end It represents the height of the head along the fluid flow direction, and ξ represents the local resistance coefficient of the head.

[0018] The cross-flow heat exchange structure is the heat exchange core and the heat calculation area. The head is mainly used to calculate the total pressure drop, and the heat exchange at the head is ignored. The heat exchange is calculated by a cell layer method. The heat exchange in the normal direction of the intersection surface in the flow direction of the hot and cold fluids is considered to be uniform. The single cell is used as the basic heat exchange unit. The heat exchange state of each unit is solved layer by layer, and the heat exchange inlet and outlet parameters of the unit are passed to the other two adjacent units as input parameters. After the cycle solution is completed, the total heat exchange and the temperature distribution at the hot and cold side outlets are obtained. The area average is taken as the final temperature result, and the pressure drop is calculated according to the parallel pipeline.

[0019] The process of temperature parameter transfer between adjacent unit cells:

[0020]

[0021] The relationship between the total heat transfer and the heat transfer of a single unit cell:

[0022]

[0023] The relationship between the total pressure drop of the heat exchanger and the pressure drop of the single cell and the head:

[0024]

[0025] Calculation of average temperature at heat exchanger outlet:

[0026]

[0027] Where, represents the temperature at the entrance of the i+1th row of cells, represents the temperature at the outlet of the i-th row cell, represents the temperature at the entrance of the j+1th column unit cell, represents the temperature at the outlet of the j-th column unit cell; Q represents the total heat exchange, Q ij is the heat transfer of the unit cell in the i-th row and j-th column, m and n represent the total number of units along the hot and cold fluid directions, i and j represent the single unit cell in the i-th row and j-th column, ΔP represents the total pressure drop, ΔP 1,j represents the voltage drop of the unit cell in row 1 and column j, Represent the total pressure drop of the first and second row of unit cells respectively, Represents the total pressure drop of the i-th row and the m-th row of cells, ΔP end Indicates the head pressure drop; t ave,out Indicates the average temperature at the outlet, A i A represents the cross-sectional area of ​​the single cell in row i and column n, total It represents the total flow cross-sectional area at the outlet, t i,out represents the outlet temperature of the single unit cell in the i-th row and n-th column. The subscripts in, out, and ave represent the unit inlet, outlet, and total average temperature of the heat exchanger, respectively.

[0028] When calculating the flow and heat transfer performance of each single cell layer, that is, the heat transfer performance, the thermal balance is automatically calculated based on the fmincon algorithm to achieve adaptive thermal balance calculation for each cell. At this time, the objective function is the thermal balance error ERROR:

[0029]

[0030] Where Q kAt is the heat transfer calculated based on the total heat transfer coefficient, Q hot is the heat transfer calculated based on the thermal fluid flow rate, Q cold The heat transfer rate is calculated based on the cold fluid flow rate. The subscript hot represents the hot fluid, cold represents the cold fluid, and kAt represents the total heat transfer coefficient method. By calculating the heat balance state of each unit cell, the total heat transfer rate of the heat exchanger is finally obtained.

[0031] Based on the above heat exchanger design calculation process, the single cell unit size, wall thickness, length, width, height, and head height of the heat exchange core are used as decision variables. The constraints include the outlet temperature requirements of the fluids on the hot and cold sides and the overall size requirements of the heat exchanger. The optimization target is set as the pressure drop on the hot and cold sides. Combined with the multi-objective genetic optimization algorithm, a heat exchanger optimization design method is constructed based on this. Finally, the optimal solution set for the pressure drop on the hot and cold sides of the heat exchanger is obtained. From this solution set, the final design scheme is selected according to the heat exchange and pressure drop requirements to complete the design of the high-temperature air preheater.

[0032] Compared with the prior art, the present invention has the following beneficial effects:

[0033] The purpose of this invention is to develop an optimization design method for solid oxide fuel cell air preheaters. Generally speaking, the hydraulic properties corresponding to three-periodic minimal surface structures are difficult to directly calculate using geometric parameters. Therefore, this invention constructs a sample database and further develops an artificial neural network model to rapidly predict and calculate the hydraulic properties of single-cell structures, providing input parameters for heat transfer calculations. Furthermore, the head is incorporated into the flow resistance calculation process, and a sample library and artificial neural network model corresponding to the head structure and local resistance coefficient are established to rapidly calculate the flow characteristics at the head under different overall dimensions. Given the significant influence of temperature on physical properties, a cell-by-cell approach is used to calculate the total heat transfer and flow performance of the heat exchange core, and the thermal equilibrium conditions are automatically calculated at each single cell, which is closer to the actual heat transfer process. Finally, considering the interaction between the single cell and the entire system, a multi-objective genetic optimization algorithm is used to optimize the design of the high-temperature air preheater, using the single cell parameters and overall dimensions as decision variables and the pressure drop between the hot and cold sides as the optimization objective. This algorithm can output the optimal solution set for the final design according to the design requirements, improving design efficiency and providing a solution for the rapid and efficient development of highly compact solid oxide fuel cell thermal balance components. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Various other advantages and benefits of the present invention will become apparent to those skilled in the art upon reading the detailed description of the preferred embodiments below. The accompanying drawings are intended only to illustrate preferred embodiments and are not to be construed as limiting the present invention. It should be understood that the drawings described below are merely examples of the present invention, and that those skilled in the art will be able to derive other drawings from these drawings without inventive effort. Throughout the drawings, identical reference numerals are used to denote identical components.

[0035] In the attached figure:

[0036] Figure 1 It is a schematic flow chart of a method for optimizing the design of a high-temperature air preheater for a solid oxide fuel cell based on a three-periodic minimal surface according to the present invention.

[0037] Figure 2 It is the optimal solution set distribution diagram calculated by the present invention. DETAILED DESCRIPTION

[0038] Specific embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. Although specific embodiments of the present invention are shown in the accompanying drawings, it should be understood that the present invention can be implemented in various forms and should not be limited by the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the present invention and to fully convey the scope of the present invention to those skilled in the art.

[0039] It should be noted that certain words are used in the specification and claims to refer to specific components. Those skilled in the art should understand that technicians may use different nouns to refer to the same component. This specification and claims do not use the difference in nouns as a way to distinguish components, but use the difference in the functions of the components as the criterion for distinction. As mentioned throughout the specification and claims, "including" or "comprising" is an open term, so it should be interpreted as "including but not limited to". The subsequent description of the specification is a preferred embodiment of the present invention, but the description is based on the general principles of the specification and is not intended to limit the scope of the invention. The scope of protection of the present invention shall be as defined in the attached claims.

[0040] To facilitate understanding of the embodiments of the present invention, several specific embodiments will be further explained below with reference to the accompanying drawings. However, the accompanying drawings do not limit the embodiments of the present invention.

[0041] For better understanding, Figure 1 and Figure 2 As shown, a method for optimizing the design of a high-temperature air preheater for a solid oxide fuel cell based on a three-periodic minimal surface includes:

[0042] S1: Build a sample database of single cell geometric parameters and hydraulic characteristic parameters, head structure and local resistance coefficient, and construct the corresponding artificial neural network model based on the sample database;

[0043] S2: Based on the consideration of the head structure, a three-period minimal surface structure is selected according to the cross-flow heat transfer structure. The flow and heat transfer performance are calculated cell by cell, and the overall thermal performance is finally obtained.

[0044] S3: Based on the nonlinear optimization algorithm fmincon, adaptive heat balance calculation is realized on a cell-by-cell basis, and the operating parameters of the dual-fluid heat exchanger under a given structure are obtained by solving the problem cell by cell;

[0045] S4: Using unit cell size, wall thickness, heat exchange core size, and head height as decision variables, minimizing the pressure drop on both the hot and cold sides as the optimization goal, and overall size limit and hot side temperature outlet as constraints, a multi-objective genetic algorithm was used to optimize the design of a high-temperature air preheater.

[0046] S5: Calculate the optimal solution set and select the design scheme that meets the requirements to obtain the overall design parameters of the optimized three-period minimal surface structure heat exchanger and complete the design of the high-temperature air preheater.

[0047] The calculation method in the specific embodiment includes:

[0048] The single cell geometric parameters include the single cell size uc and wall thickness δ uc , the hydraulic characteristic parameters of the single cell include hydraulic diameter D h , flow cross-sectional area A cross , single-side heat transfer area HSA uc According to the size of the single unit cell and the wall thickness, a three-periodic minimal surface unit structure with corresponding parameters can be designed. The flow cross-sectional area A can be obtained by viewing the cross-sectional area of ​​the single unit cell solid wall through the modeling software. cross , single-side heat exchange area HSA uc , the hydraulic diameter is calculated according to the following formula:

[0049]

[0050] Where V f,s Indicates the fluid volume corresponding to the fluid on one side.

[0051] According to this method, modeling software was used to construct minimal surface single cell models of different structures, and their hydraulic characteristics were checked and calculated to form a sample database. The following artificial neural network model was constructed by combining the double-layer feedforward network fitting model:

[0052] [D h ,A cross ,HSA uc ]=f(size uc ,δ uc )

[0053] The model quickly calculates the corresponding hydraulic characteristic parameters based on the size and wall thickness of the single cell, solving the problem of difficulty in directly calculating the hydraulic characteristics of the three-periodic minimal surface structure, and facilitating the subsequent optimization of the single cell structure.

[0054] The head structure includes the head bundle tube diameter d bt , height δ along the fluid flow direction end , the length of the head l core and width w coreThe local resistance coefficient of the head is ξ, which represents the pressure drop generated by the heads at both ends; the length and width of the heads on the hot and cold sides are equal to the corresponding side dimensions of the heat exchanger core. First, the modeling software is used to establish the head model with different bundle tube diameters, lengths, widths and heights, and the corresponding pressure drop ΔP is calculated using numerical simulation software. end , calculate the local resistance coefficient ξ according to the following formula:

[0055]

[0056] Where ρ represents the average density of the fluid at the head, v ave Indicates the average flow rate at the inlet and outlet.

[0057] Based on this, different l core ,w core ,d bt ,δ end The ξ sample database corresponding to the parameter combination is combined with the double-layer feedforward network fitting model to construct the following artificial neural network model:

[0058] ξ=f(l core ,w core ,d bt ,δ end )

[0059] The cross-flow heat exchange structure is the heat exchange core and the heat calculation area. The head is mainly used to calculate the total pressure drop, and the heat exchange at the head is ignored. The heat exchange is calculated using a unit cell calculation method. The heat exchange in the normal direction of the intersection of the cold and hot fluid flow directions is considered uniform. The single unit cell is used as the basic heat exchange unit. The heat exchange state of each unit is solved one by one, and the heat exchange inlet and outlet parameters of the unit are passed to the other two adjacent units as input parameters. After the cycle is solved, the total heat exchange and the temperature distribution at the hot and cold side outlets are obtained. The area average is taken as the final temperature result. The pressure drop is calculated according to the parallel pipeline.

[0060] The single cell heat transfer correlation formula adopts the existing correlation formula in the literature.

[0061] Nu=0.471·Re 0.627 Pr 1 / 3

[0062] f=2.577·Re -0.095

[0063]

[0064] Where h is the convection heat transfer coefficient on the corresponding side, λ is the average thermal conductivity of the fluid, L is the length of the fluid flow direction in the single cell, and v ucis the average flow velocity in the unit cell, Nu is the Nusselt number, Re is the Reynolds number, Pr is the Prandtl number of the corresponding fluid, f is the friction factor of the corresponding fluid channel, ρ is the density of the corresponding fluid, ΔP uc Represents the pressure drop on the fluid side of the single cell. According to the above formula, the heat transfer of the single cell is further calculated, including the heat exchange of the fluids on both the cold and hot sides (Q hot and Q cold ) and the heat transfer through the wall (Q kAt ), these three heat transfer rates follow the energy conservation law, and the calculation formula is as follows:

[0065] Q kAt =k·HSA·ΔT m

[0066] Q hot =m hot c p,hot ·(t in,hot -t out,hot )

[0067] Q cold =m cold c p,cold ·(t out,cold -t in,cold )

[0068] Where k represents the total heat transfer coefficient of the unit cell, HSA represents the total heat transfer area of ​​the unit cell, and ΔT m is the logarithmic mean temperature difference, m hot represents the mass flow rate of thermal fluid, c p,hot is the specific heat capacity of the thermal fluid at constant pressure, t in,hot represents the hot fluid inlet temperature, t out,hot Indicates the outlet temperature of the hot fluid, m cold is the mass flow rate of the cold fluid, c p,cold is the specific heat capacity of the cold fluid at constant pressure, t out,cold is the outlet temperature of the cold fluid, t in,cold is the cold fluid inlet temperature.

[0069] The above formula is the basic formula for calculating unit cell flow and heat transfer. However, the input and output parameters of each unit cell are interrelated. The unit cells in the same row or column are connected in series, so the mass flow rate remains unchanged. The inlet temperature is the outlet temperature of the previous unit cell. Therefore, the temperature parameter transfer process between adjacent unit cells is:

[0070]

[0071] The relationship between the total heat transfer and the heat transfer of a single unit cell:

[0072]

[0073] The relationship between the total pressure drop of the heat exchanger and the pressure drop of the single cell and the head:

[0074]

[0075] Calculation of average temperature at heat exchanger outlet:

[0076]

[0077] Where, represents the temperature at the entrance of the i+1th row of cells, represents the temperature at the outlet of the i-th row cell, represents the temperature at the entrance of the j+1th column unit cell, represents the temperature at the outlet of the j-th column unit cell; Q represents the total heat exchange, Q ij is the heat transfer of the unit cell in the i-th row and j-th column, m and n represent the total number of units along the hot and cold fluid directions, i and j represent the single unit cell in the i-th row and j-th column, ΔP represents the total pressure drop, ΔP 1,j represents the voltage drop of the unit cell in row 1 and column j, Represent the total pressure drop of the first and second row of unit cells respectively, Represents the total pressure drop of the i-th row and the m-th row of cells, ΔP end Indicates the head pressure drop; t ave,out Indicates the average temperature at the outlet, A i A represents the cross-sectional area of ​​the single cell in row i and column n, total It represents the total flow cross-sectional area at the outlet, t i,out represents the outlet temperature of the single unit cell in the i-th row and n-th column. The subscripts in, out, and ave represent the unit inlet, outlet, and total average temperature of the heat exchanger, respectively.

[0078] When calculating the heat transfer performance of each single cell layer, the thermal balance is automatically calculated based on the fmincon algorithm to achieve adaptive thermal balance calculation for each cell. At this time, the objective function is the thermal balance error ERROR:

[0079]

[0080] Where Q kAt is the heat transfer calculated based on the total heat transfer coefficient, Q hot is the heat transfer calculated based on the thermal fluid flow rate, Q cold It represents the heat transfer calculated based on the flow rate of the cold fluid. The subscript hot represents the hot fluid, cold represents the cold fluid, and kAt represents the total heat transfer coefficient method. By calculating the heat balance state of each unit cell, the total heat transfer of the heat exchanger is finally obtained.

[0081] Based on the above heat exchanger design calculation process, the unit size is uc , wall thickness δuc , length of heat exchange core l core 、Width w core 、height core , Head height δ end is the decision variable, the constraints include the outlet temperature requirements of the hot and cold fluids, the overall size requirements of the heat exchanger, and the optimization target is the pressure drop (ΔP cold , ΔP hot ), combined with the multi-objective genetic optimization algorithm, a heat exchanger optimization design method is constructed based on this, and finally the optimal solution set of the pressure drop on both sides of the heat exchanger is obtained (such as Figure 2 In this solution set, the final design scheme is selected according to the heat exchange and pressure drop requirements to complete the design of the high-temperature air preheater.

[0082] The basic principles of the present application have been described above in conjunction with specific embodiments. However, it should be noted that the advantages, strengths, and effects mentioned in this application are merely illustrative and not restrictive, and it should not be assumed that these advantages, strengths, and effects are required of each embodiment of this application. In addition, the specific details disclosed above are merely illustrative and facilitating understanding, and are not restrictive. The above details do not limit this application to necessarily being implemented using the above specific details.

[0083] The above description has been provided for the purpose of illustration and description. Furthermore, this description is not intended to limit the embodiments of the present application to the forms disclosed herein. Although a number of example aspects and embodiments have been discussed above, those skilled in the art will recognize certain variations, modifications, alterations, additions, and sub-combinations thereof.

Claims

1. A method for optimizing the design of a high-temperature air preheater for a solid oxide fuel cell based on a three-periodic minimal surface, characterized in that: The steps include: S1: Build a sample database of single cell geometric parameters and hydraulic characteristic parameters, head structure and local resistance coefficient, and construct the corresponding artificial neural network model based on the sample database; S2: Based on the consideration of the head structure, a three-period minimal surface structure is selected according to the cross-flow heat transfer structure. The flow and heat transfer performance are calculated cell by cell, and the overall thermal performance is finally obtained. S3: Based on the nonlinear optimization algorithm fmincon, adaptive heat balance calculation is realized on a cell-by-cell basis, and the operating parameters of the dual-fluid heat exchanger under a given structure are obtained by solving the problem cell by cell; S4: A high-temperature air preheater is optimized based on a multi-objective genetic algorithm, with unit cell size, wall thickness, heat exchange core size, and head height as decision variables, minimum pressure drop on both the hot and cold sides as the optimization goal, and total size limit and hot side temperature outlet as constraints. S5: Calculate the optimal solution set and select the design scheme that meets the requirements to obtain the overall design parameters of the optimized three-period minimal surface structure heat exchanger, completing the design of the high-temperature air preheater; The cross-flow heat exchange structure is the heat exchange core and the heat calculation area. The head is mainly used to calculate the total pressure drop, and the heat exchange at the head is ignored. The heat exchange is calculated using a cell-by-cell layer method. The heat exchange in the normal direction of the intersection of the cold and hot fluid flow directions is considered uniform. The single cell is used as the basic heat exchange unit. The heat exchange state of each unit is solved layer by layer, and the heat exchange inlet and outlet parameters of the unit are passed to the other two adjacent units as input parameters. After the cycle is solved, the total heat exchange and the temperature distribution at the hot and cold side outlets are obtained. The average area value is taken as the final temperature result, and the pressure drop is calculated according to the parallel pipeline. The temperature parameter transfer process between adjacent cells is as follows: The relationship between the total heat transfer and the heat transfer of a single unit cell: The relationship between the total pressure drop of the heat exchanger and the pressure drop of the single cell and the head: Calculation of average temperature at heat exchanger outlet: Where, represents the temperature at the entrance of the i+1th row of cells, represents the temperature at the outlet of the i-th row of cells, represents the temperature at the entrance of the j+1th column unit cell, represents the temperature at the outlet of the j-th column unit cell; Q represents the total heat exchange, Q ij Then is the heat transfer of the unit cell in the i-th row and j-th column, m and n represent the total number of unit cells along the hot and cold fluid directions, respectively, and i and j represent the single unit cell in the i-th row and j-th column, respectively; ΔP represents the total pressure drop, ΔP 1,j represents the voltage drop of the unit cell in row 1 and column j, Represent the total pressure drop of the first and second row of unit cells respectively, Represents the total pressure drop of the i-th row and the m-th row of cells, ΔP end Indicates the head pressure drop; t ave,out Indicates the average temperature at the outlet, A i A represents the cross-sectional area of ​​the single cell in row i and column n, total It represents the total flow cross-sectional area at the outlet, t i,out represents the outlet temperature of the single unit cell in the i-th row and n-th column. The subscripts in, out, and ave represent the unit inlet, outlet, and total average temperature of the heat exchanger, respectively.

2. The method for optimizing the design of a high-temperature air preheater for a solid oxide fuel cell based on a three-periodic minimal surface according to claim 1, wherein: The single cell geometric parameters include the single cell size uc and wall thickness δ uc , the hydraulic characteristic parameters of the single cell include hydraulic diameter D h , flow cross-sectional area A cross and single-side heat exchange area HSA uc ; The head structure includes the diameter of the head bundle tube d bt , height δ along the fluid flow direction end , the length of the head l core and width w core , the local resistance coefficient of the head is ξ, which represents the pressure drop generated by the heads at both ends.

3. The method for optimizing the design of a high-temperature air preheater for a solid oxide fuel cell based on a three-periodic minimal surface according to claim 1, wherein: The sample database is a one-to-one correspondence library constructed after the corresponding parameters are calculated by modeling software and numerical simulation software. The modeling software is used to construct single cell models under different unit size-wall thickness combinations, and the hydraulic characteristic parameters of the single cell under each combination are calculated to form a sample database. The local resistance coefficient of the head is calculated by modeling software and numerical simulation software, and together with the head structure, it constitutes a sample database.

4. The method for optimizing the design of a high-temperature air preheater for a solid oxide fuel cell based on a three-periodic minimal surface according to claim 1, wherein: The artificial neural network model includes two models: a single cell structure-hydraulic characteristic parameter prediction model and a head height-local resistance coefficient prediction model. It is constructed based on a double-layer feedforward network fitting model. The model is used to calculate the flow and heat transfer performance of the heat exchanger under a given structure. It is expressed as follows: [D h ,A cross ,HSA uc ]=f(size uc ,δ uc ) ξ=f(l core ,w core ,d bt ,d end ) Where: D h represents the hydraulic diameter of the unit cell, A cross Represents the cross-sectional area of ​​a single cell, HSA uc Indicates the heat transfer area on one side of a single cell, size uc represents the unit cell size, δ uc represents the thickness of the single cell wall, l core Indicates the length of the head, w core Indicates the width of the head, d bt Indicates the diameter of the bundled tube at the head, δ end It represents the height of the head along the fluid flow direction, and ξ represents the local resistance coefficient of the head.

5. The method for optimizing the design of a high-temperature air preheater for a solid oxide fuel cell based on a three-periodic minimal surface according to claim 1, wherein: When calculating the flow and heat transfer performance of each single cell layer, that is, the heat transfer performance, the thermal balance is automatically calculated based on the fmincon algorithm to achieve adaptive thermal balance calculation for each cell. At this time, the objective function is the thermal balance error ERROR: Where Q kAt is the heat transfer calculated based on the total heat transfer coefficient, Q hot is the heat transfer calculated based on the thermal fluid flow rate, Q cold It represents the heat transfer calculated based on the flow rate of the cold fluid. The subscript hot represents the hot fluid, cold represents the cold fluid, and kAt represents the total heat transfer coefficient method. By calculating the heat balance state of each unit cell, the total heat transfer of the heat exchanger is finally obtained.

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