A method for bipolar plate topology optimization and comprehensive evaluation based on variable density method

Abstract

The application discloses a kind of bipolar plate topology optimization and comprehensive evaluation method based on variable density method, it is related to fuel cell bipolar plate structure optimization technical field, including: based on the velocity field inside bipolar plate, pressure drop and oxygen molar concentration distribution calculates the mass transfer performance index and flow performance index of bipolar plate, and with average reaction rate maximization as optimization goal, with volume fraction as constraint condition, constructs bipolar plate flow field optimization objective function;Based on bipolar plate flow field optimization objective function and constraint condition, the geometry of bipolar plate structure and material distribution are iteratively optimized using moving asymptote method, and the design variables are updated in each iteration process to obtain updated design variables;The application improves the overall reaction performance of bipolar plate by maximizing the average reaction rate as the optimization goal.

Description

Technical Field

[0001] This invention relates to the field of bipolar plate structure optimization technology for fuel cells, and in particular to a bipolar plate topology optimization and comprehensive evaluation method based on the variable density method. Background Technology

[0002] As a key functional component in fuel cell stacks, bipolar plates play multiple roles, including reactant gas distribution, electron conduction, heat transfer, and product water discharge. Their flow field structure directly affects the uniformity of reactant gas transport within the electrode region, pressure loss levels, and overall battery output performance. With the development of fuel cells towards higher power density, lower energy consumption, and longer lifespan, traditional regular flow field structures such as parallel channels, serpentine channels, and interdigitated channels are increasingly unable to meet the demands for synergistic optimization of mass transfer efficiency and flow resistance under complex operating conditions. Therefore, topology optimization of bipolar plate flow field structures using finite element analysis, variable density methods, and numerical optimization algorithms has become an important research direction for improving the design freedom and overall performance of bipolar plate structures.

[0003] Existing bipolar plate flow field optimization techniques largely rely on empirical channel configurations or parametric adjustments to existing channel dimensions. They typically focus on reducing pressure drop or improving local gas distribution, making it difficult to simultaneously characterize the combined effects of velocity field, pressure drop, and oxygen molar concentration distribution on reaction performance during the same optimization process. While some topology optimization methods can alter material distribution or channel morphology, their computational complexity for the three-dimensional bipolar plate structure is high, and they lack an iterative optimization mechanism that unifies and couples mass transfer performance indicators, flow performance indicators, average reaction rate optimization objectives, and volume fraction constraints. This leads to optimization results that either reduce flow resistance but result in insufficient oxygen supply in the reaction region, or improve mass transfer but result in excessive pressure drop, thus limiting the engineering applicability of bipolar plate flow field topologies. Summary of the Invention

[0004] In view of the aforementioned existing problems, the present invention is proposed.

[0005] Therefore, this invention provides a bipolar plate topology optimization and comprehensive evaluation method based on the variable density method to solve the problem of difficulty in co-optimizing flow performance and structural material distribution in bipolar plate flow field structure optimization.

[0006] To solve the above-mentioned technical problems, the present invention provides the following technical solution: This invention provides a bipolar plate topology optimization and comprehensive evaluation method based on the variable density method, comprising: defining the bipolar plate design domain based on initial design data, configuring bipolar plate boundary conditions and initial design variables; performing depth averaging on the bipolar plate structure based on the bipolar plate design domain, bipolar plate boundary conditions, and bipolar plate geometric parameters to simplify the bipolar plate structure into a two-dimensional planar model, and discretizing and meshing the two-dimensional planar model using the finite element method to obtain a two-dimensional discretized finite element model of the bipolar plate; establishing a flow model and a mass transfer model of the bipolar plate based on the two-dimensional discretized finite element model and initial design variables, and calculating the velocity field, pressure drop, and oxygen molar concentration distribution inside the bipolar plate using the flow model and mass transfer model; and calculating the velocity field, pressure drop, and oxygen molar concentration distribution inside the bipolar plate based on the velocity field, pressure drop, and oxygen molar concentration distribution inside the bipolar plate. The mass transfer performance and flow performance of the bipolar plate are calculated based on the pressure drop and oxygen molar concentration distribution. An objective function for bipolar plate flow field optimization is constructed, with maximizing the average reaction rate as the optimization objective and volume fraction as the constraint. Based on the objective function and constraints, the geometry and material distribution of the bipolar plate structure are iteratively optimized using the moving asymptote method, updating the design variables in each iteration. Density filtering and Heaviside projection are then applied to the updated design variables to obtain the projected design variables. Based on the projected design variables, the velocity field, pressure drop, and oxygen molar concentration distribution inside the bipolar plate are recalculated, and the termination condition of the iterative optimization is determined, outputting the final optimized topology structure.

[0007] As a preferred embodiment of the bipolar plate topology optimization and comprehensive evaluation method based on the variable density method described in this invention, the initial design data includes the activation area, bipolar plate thickness, gas diffusion layer thickness, catalyst layer thickness, membrane electrode thickness, flow field channel height, and membrane electrode length and width. The bipolar plate boundary conditions include inlet flow velocity and outlet pressure.

[0008] As a preferred embodiment of the bipolar plate topology optimization and comprehensive evaluation method based on the variable density method described in this invention, the specific steps for obtaining the two-dimensional discretized finite element model of the bipolar plate are as follows: Based on the bipolar plate design domain and bipolar plate geometric parameters, a three-dimensional geometric model of the bipolar plate structure is established; depth averaging is performed on the three-dimensional geometric model of the bipolar plate structure to obtain a two-dimensional planar model of the bipolar plate. The two-dimensional planar model of the bipolar plate is discretized using the finite element method. The continuous geometric model is decomposed into multiple finite elements by mesh generation, resulting in a two-dimensional discretized finite element model of the bipolar plate.

[0009] As a preferred embodiment of the bipolar plate topology optimization and comprehensive evaluation method based on the variable density method described in this invention, the depth averaging process includes averaging the physical properties of the gas channel, ribs and gas diffusion layer along the through plane direction, and using the thickness of the gas channel, ribs and gas diffusion layer as the thickness parameters of the averaging process to obtain the local porosity of the region corresponding to the gas channel and the local porosity of the region corresponding to the rib in the two-dimensional planar model of the bipolar plate.

[0010] As a preferred embodiment of the bipolar plate topology optimization and comprehensive evaluation method based on the variable density method described in this invention, the flow model of the bipolar plate includes incompressible laminar flow control equations, local porosity interpolation relationships, local permeability interpolation relationships, and porous media resistance terms. The local porosity interpolation relationship is established based on design variables, and the porous media resistance term includes Brinkman sink and Poisson sink; The flow model also includes a momentum penalty term constructed based on the volume force term, which includes Brinkman constant, local porosity, fluid velocity, and fluid density.

[0011] As a preferred embodiment of the bipolar plate topology optimization and comprehensive evaluation method based on the variable density method described in this invention, the mass transfer model of the bipolar plate includes a two-dimensional transport equation, a reaction mass flux calculation relationship, a current density calculation relationship, a cathode overpotential calculation relationship, and a local reaction rate calculation relationship. The two-dimensional transport equation is used to calculate the oxygen molar concentration distribution, and the local reaction rate calculation relationship is established based on the reaction rate constant and the oxygen concentration.

[0012] As a preferred embodiment of the bipolar plate topology optimization and comprehensive evaluation method based on the variable density method described in this invention, the objective function for optimizing the bipolar plate flow field is constructed with maximizing the average reaction rate of the bipolar plate flow field as the optimization objective and with volume fraction as the constraint condition. The average reaction rate is obtained based on the local reaction rate, which is calculated based on the reaction rate constant and the oxygen concentration.

[0013] As a preferred embodiment of the bipolar plate topology optimization and comprehensive evaluation method based on the variable density method described in this invention, the specific steps for obtaining the updated design variables are as follows: Input the current design variables into the bipolar flow model and the bipolar mass transfer model, and calculate the velocity field, pressure drop and oxygen molar concentration distribution inside the bipolar plate under the current iteration state. Based on the velocity field, pressure drop, and oxygen molar concentration distribution inside the bipolar plate under the current iteration state, calculate the mass transfer performance index and flow performance index under the current iteration state. Based on the mass transfer performance index, flow performance index, optimization objective of maximizing average reaction rate, and volume fraction constraint under the current iteration state, construct the current iteration optimization problem; The moving asymptote method is used to solve the current iteration optimization problem, obtain the candidate design variables corresponding to the current iteration, and update the current design variables based on the candidate design variables to obtain the updated design variables.

[0014] As a preferred embodiment of the bipolar plate topology optimization and comprehensive evaluation method based on the variable density method described in this invention, the density filtering and Heaviside projection processing involve inputting the updated design variables as the original density field into the Helmholtz type partial differential equation, solving the Helmholtz type partial differential equation, smoothing the original density field, and obtaining the filtered density field. A hyperbolic tangent projection operator is constructed based on the projection threshold parameter and the projection sharpness parameter. The filtered density field is then subjected to Heaviside projection processing using the hyperbolic tangent projection operator to obtain the projected design variables.

[0015] As a preferred embodiment of the bipolar plate topology optimization and comprehensive evaluation method based on the variable density method described in this invention, the output final topology optimization structure is based on the projected design variables to recalculate the velocity field, pressure drop and oxygen molar concentration distribution inside the bipolar plate, and to determine whether the iterative optimization meets the termination condition. The termination conditions include achieving the expected performance target or reaching the maximum number of iterations; if the termination condition is not met, the iteration optimization continues; if the termination condition is met, the final optimized topology structure is output.

[0016] The beneficial effects of this invention are as follows: by defining the bipolar plate design domain based on the initial design data and configuring the bipolar plate boundary conditions and initial design variables, by taking the maximization of the average reaction rate as the optimization objective and the volume fraction as the constraint, and by using the moving asymptote method to iteratively update the design variables, the invention improves oxygen transport efficiency, reduces unreasonable flow losses, and enhances the overall reaction performance of the bipolar plate. Attached Figure Description

[0017] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a flowchart of a bipolar plate topology optimization and comprehensive evaluation method based on the variable density method.

[0019] Figure 2 The flowchart for generating a two-dimensional discretized finite element model of a bipolar plate.

[0020] Figure 3 A flowchart for constructing the objective function for bipolar plate flow field optimization.

[0021] Figure 4 This is a flowchart of density filtering, Heaviside projection processing, and the final topology-optimized structure output. Detailed Implementation

[0022] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0023] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0024] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.

[0025] Reference Figures 1-4 This is one embodiment of the present invention, which provides a bipolar plate topology optimization and comprehensive evaluation method based on the variable density method, including the following steps: S1. Define the bipolar plate design domain based on the initial design data, and configure the bipolar plate boundary conditions and initial design variables.

[0026] The initial design data includes the activation area, bipolar plate thickness, gas diffusion layer thickness, catalyst layer thickness, membrane electrode thickness, flow channel height, and membrane electrode length and width; the bipolar plate boundary conditions include the inlet velocity and outlet pressure.

[0027] Furthermore, based on the initial design data, the design domain and initial design variables of the bipolar plate are determined: when performing topology optimization design, the topology optimization design region and boundary conditions are determined according to the oxygen distribution and mass exchange boundary conditions in complex actual mass transfer problems.

[0028] S2. Based on the bipolar plate design domain, bipolar plate boundary conditions, and bipolar plate geometric parameters, the bipolar plate structure is subjected to depth averaging to simplify it into a two-dimensional planar model. The two-dimensional planar model is then discretized and meshed using the finite element method to obtain a two-dimensional discretized finite element model of the bipolar plate.

[0029] Based on the bipolar plate design domain and bipolar plate geometric parameters, a three-dimensional geometric model of the bipolar plate structure is established; depth averaging is performed on the three-dimensional geometric model of the bipolar plate structure to obtain a two-dimensional planar model of the bipolar plate.

[0030] Specifically, the depth averaging process includes averaging the physical properties of the gas channel, ribs, and gas diffusion layer along the through-plane direction, and using the thickness of the gas channel, ribs, and gas diffusion layer as the thickness parameters for averaging to obtain the local porosity of the region corresponding to the gas channel and the region corresponding to the rib in the two-dimensional planar model of the bipolar plate.

[0031] Furthermore, the three-dimensional geometric model of the bipolar plate structure includes gas channels, ribs, and a gas diffusion layer. Before performing topology optimization calculations, the thickness of the gas channels and gas diffusion layers, as well as the ribs and gas diffusion layers, is averaged along the through-plane direction. This converts the physical properties of the thickness direction in the three-dimensional geometric model into the two-dimensional planar model, thereby reducing the number of meshes and computational complexity of the three-dimensional full-size model.

[0032] For any physical property of the gas channel or rib and the gas diffusion layer in the thickness direction, the equivalent physical property expression after depth averaging is: ; in, This represents a certain equivalent physical property after depth averaging. This represents the physical property value of the corresponding region on the bipolar plate side. This indicates the thickness parameter of the corresponding region on the bipolar plate side. Indicates the thickness of the gas diffusion layer. This represents the physical property value of the gas diffusion layer.

[0033] When the physical property is porosity, the expression for the local porosity of the region corresponding to the gas channel is: ; in, This indicates the local porosity of the region corresponding to the gas channel. This indicates the porosity of the gas diffusion layer.

[0034] Rib region porosity The expression is: ; in, This indicates the local porosity of the region corresponding to the rib.

[0035] Through depth averaging, the physical properties of the gas channel and gas diffusion layer in the thickness direction are equivalent to the local equivalent parameters in the two-dimensional plane model, thus obtaining the two-dimensional plane model of the bipolar plate.

[0036] The two-dimensional planar model of the bipolar plate is discretized using the finite element method. The continuous geometric model is decomposed into multiple finite elements by mesh generation, resulting in a two-dimensional discretized finite element model of the bipolar plate.

[0037] Specifically, the two-dimensional planar model of the bipolar plate is discretized using the finite element method. The computational domain corresponding to the two-dimensional planar model of the bipolar plate is divided into several finite elements. The finite elements are interconnected through nodes to form a mesh structure for numerical solution. The finite elements located at the inlet boundary are used to apply inlet velocity boundary conditions, the finite elements located at the outlet boundary are used to apply outlet pressure boundary conditions, and the finite elements located inside the bipolar plate design domain are used to participate in flow mass transfer calculation and topology optimization iteration.

[0038] S3. Based on the two-dimensional discretized finite element model of the bipolar plate and the initial design variables, establish the flow model and mass transfer model of the bipolar plate, and calculate the velocity field, pressure drop and oxygen molar concentration distribution inside the bipolar plate through the flow model and mass transfer model.

[0039] It should be noted that, based on the two-dimensional discretized finite element model of the bipolar plate and the initial design variables, a flow model is established to describe the gas flow state inside the bipolar plate, and a mass transfer model is established to describe the oxygen transport and reaction consumption processes. The flow model is used to calculate the velocity field, pressure field, and pressure drop inside the bipolar plate, while the mass transfer model is used to calculate the oxygen molar concentration distribution, reaction mass flux, current density, and cathode overpotential inside the bipolar plate.

[0040] The flow model of bipolar plates includes the incompressible laminar flow control equation, local porosity interpolation relationship, local permeability interpolation relationship, and porous media resistance term.

[0041] The local porosity interpolation relationship is established based on design variables, and the porous media resistance term includes Brinkman sink and Poisson sink.

[0042] The flow model also includes a momentum penalty term constructed based on the volume force term, which includes the Brinkman constant, local porosity, fluid velocity, and fluid density.

[0043] Specifically, the gas flow within the bipolar plate is an incompressible laminar flow. A continuity equation and a momentum equation are established. The incompressible laminar flow continuity equation is expressed as: ; in, Indicates the fluid velocity at the th velocity components in each direction Indicates direction index, Indicates the first Spatial coordinates in each direction.

[0044] The expression for the incompressible layer flow equation is: ; in, This indicates the actual porosity of the porous ribs or porous channels. Indicates design variables, Indicates pressure, Indicates the fluid velocity at the th velocity components in each direction Indicates the first Spatial coordinates in each direction, where ρ represents the gas density. This refers to the force generated due to the presence of porous media.

[0045] Using the continuity and momentum equations, the velocity and pressure fields at different locations inside the bipolar plate are calculated. The pressure drop is obtained based on the inlet and outlet pressures. Within the topology optimization framework, the local porosity is calculated using design variables. The expression for the local porosity interpolation relationship is as follows: ; By using local porosity interpolation, the design variables are correlated with the porosity of each finite element in the two-dimensional discretized finite element model of the bipolar plate. When the design variables take different values, the finite elements change between the fluid region and the solid material region, thereby realizing the variable density description of the bipolar plate structure.

[0046] The force term in the momentum equation represents the resistance caused by the porous medium. The porous medium resistance term is: ; in, It is the Brinkman sink. It is called Poiseuille sink.

[0047] The expression for Brinkman's convergence is: ; in, This represents the Brinkman drag coefficient. Indicates the dynamic viscosity of a fluid. This indicates the permeability of the gas diffusion layer.

[0048] The expression for Bosuyehui is: ; in, The total thickness of the model is expressed as follows: , This indicates the thickness parameter of the corresponding region on the bipolar plate side. This indicates the thickness of the gas diffusion layer.

[0049] Regarding permeability, the actual permeability of the rib is zero. The permeability of the gas channel is calculated based on the Poisson flow assumption, and the expression is: ; in, This represents the equivalent permeability of the region corresponding to the gas channel on the bipolar plate side.

[0050] The mass transfer model of bipolar plates includes two-dimensional transport equations, calculation relationships for reaction mass flux, calculation relationships for current density, calculation relationships for cathode overpotential, and calculation relationships for local reaction rate.

[0051] Two-dimensional transport equations are used to calculate the oxygen molar concentration distribution, and the local reaction rate calculation relationship is established based on the reaction rate constant and the oxygen concentration.

[0052] Specifically, based on the above premises, the transportation equations of the two-dimensional model are simplified to: ; in, Components molar concentration, Components The effective diffusion coefficient, Components The mass flux is calculated using the following relationship: ; in, Components molar mass, The local current density at the cathode. It is Faraday's constant. The cathode reaction rate is represented by .

[0053] Current density and cathode overpotential Based on the half-cell modeling rules, the expression is: ; in, This is a cathode overpotential. Open circuit voltage, This is the battery operating voltage. For ohmic resistance, This represents the local current density.

[0054] S4. Based on the velocity field, pressure drop and oxygen molar concentration distribution inside the bipolar plate, calculate the mass transfer performance index and flow performance index of the bipolar plate, and construct the objective function for optimizing the bipolar plate flow field with the maximization of average reaction rate as the optimization objective and the volume fraction as the constraint.

[0055] The objective function for bipolar plate flow field optimization is constructed with the goal of maximizing the average reaction rate of the bipolar plate flow field and with volume fraction as the constraint condition.

[0056] The average reaction rate is obtained based on the local reaction rate, which is calculated based on the reaction rate constant and oxygen concentration.

[0057] It should be noted that the mathematical expression of the objective function is: ; in, This represents the objective function to be optimized. Represents the computational region volume, This represents the computational or design domain for bipolar plate flow field topology optimization. Indicates the local reaction rate. This represents a micro-element within the computational region.

[0058] S5. Based on the objective function and constraints of bipolar plate flow field optimization, the geometry and material distribution of the bipolar plate structure are iteratively optimized using the moving asymptote method, and the design variables are updated in each iteration to obtain the updated design variables.

[0059] Input the current design variables into the bipolar flow model and the bipolar mass transfer model to calculate the velocity field, pressure drop, and oxygen molar concentration distribution inside the bipolar plate under the current iteration state.

[0060] Specifically, in each iteration, the current design variables are substituted into the local porosity interpolation relationship, local permeability interpolation relationship, and momentum penalty term in the bipolar plate flow model, and the current design variables are substituted into the two-dimensional transport equation, reaction mass flux calculation relationship, and local reaction rate calculation relationship in the bipolar plate mass transfer model to obtain the velocity field, pressure drop, and oxygen molar concentration distribution inside the bipolar plate under the current iteration state.

[0061] Based on the velocity field, pressure drop, and oxygen molar concentration distribution inside the bipolar plate under the current iteration state, calculate the mass transfer performance index and flow performance index under the current iteration state.

[0062] Specifically, the local reaction rate is calculated based on the oxygen molar concentration distribution under the current iteration state, and the mass transfer performance index is obtained based on the local reaction rate; the flow performance index is obtained based on the velocity field and pressure drop under the current iteration state; the mass transfer performance index is used to characterize the ability of the bipolar flow field structure to promote reactant transport and reaction consumption, and the flow performance index is used to characterize the gas flow uniformity and flow resistance of the bipolar flow field structure.

[0063] Based on the mass transfer performance index, flow performance index, optimization objective of maximizing average reaction rate, and volume fraction constraint under the current iteration state, construct the current iteration optimization problem.

[0064] Specifically, maximizing the average reaction rate is taken as the optimization objective of the current iterative optimization problem, and the volume fraction is taken as the constraint condition of the current iterative optimization problem. Combined with the mass transfer performance index and flow performance index under the current iterative state, the performance of the bipolar plate structure corresponding to the current design variables is evaluated to form the current iterative optimization problem.

[0065] The moving asymptote method is used to solve the current iteration optimization problem, obtain the candidate design variables corresponding to the current iteration, and update the current design variables based on the candidate design variables to obtain the updated design variables.

[0066] Specifically, the moving asymptote method is used to solve the current iterative optimization problem. Based on the mass transfer performance index, flow performance index, optimization objective, and constraints corresponding to the current design variables, the geometry and material distribution of the bipolar plate structure are adjusted to obtain candidate design variables for the current iteration. These candidate design variables are then used as the update result to obtain the updated design variables. The updated design variables are used for subsequent density filtering and Heaviside projection processing.

[0067] S6. Perform density filtering and Heaviside projection on the updated design variables to obtain the projected design variables.

[0068] Density filtering and Heaviside projection processing involve inputting the updated design variables as the original density field into a Helmholtz-type partial differential equation, solving the Helmholtz-type partial differential equation, and smoothing the original density field to obtain the filtered density field.

[0069] Specifically, density filtering eliminates abrupt changes in the original design variables by applying Helmholtz-type partial differential equations to the original design variables, thereby obtaining a smooth density field.

[0070] It should be noted that the filtering formula is: ; in, For design variables, For the filtered field variables, The filter radius parameter directly controls the filtration space and smoothness; a smaller radius... More details are retained, but numerical instability may not be completely eliminated; larger values... Filtering is more thorough but blurs boundary features and may lose important geometric information, so... Set to twice the grid size.

[0071] A hyperbolic tangent projection operator is constructed based on the projection threshold parameter and the projection sharpness parameter. The filtered density field is then subjected to Heaviside projection processing using the hyperbolic tangent projection operator to obtain the projected design variables.

[0072] Specifically, the Heaviside projection will obtain the intermediate density after density filtering. Further approaching 0 or 1, thereby eliminating grayscale units, i.e., using the hyperbolic tangent function (tanh) to construct the projection operator, and taking advantage of the characteristic of the tanh function to saturate quickly when the independent variable is large, to achieve effective binarization of the intermediate density.

[0073] It should be noted that the projection formula is: ; in, For the filtered field variables, γ β =0.5 is the projection threshold parameter, which determines the boundary position of the projection; β is the projection sharpness parameter, which controls the steepness of the transition from the intermediate density to 0 or 1.

[0074] S7. Based on the projected design variables, recalculate the velocity field, pressure drop, and oxygen molar concentration distribution inside the bipolar plate, determine whether the iterative optimization meets the termination condition, and output the final topology optimization structure.

[0075] The velocity field, pressure drop, and oxygen molar concentration distribution inside the bipolar plate are recalculated based on the projected design variables, and it is determined whether the iterative optimization meets the termination condition.

[0076] Specifically, the projected design variables are re-input into the bipolar plate flow model and the bipolar plate mass transfer model. The velocity field and pressure drop inside the bipolar plate are recalculated using the bipolar plate flow model, and the oxygen molar concentration distribution inside the bipolar plate is recalculated using the bipolar plate mass transfer model. Based on the recalculated velocity field, pressure drop, and oxygen molar concentration distribution, the performance of the bipolar plate flow field structure corresponding to the current projected design variables is evaluated, and the mass transfer performance index and flow performance index under the current iteration state are obtained.

[0077] Furthermore, the mass transfer performance and flow performance indicators in the current iteration state are compared with the expected performance targets, and the current iteration count is recorded. If the mass transfer performance and flow performance indicators in the current iteration state do not meet the expected performance targets, and the current iteration count has not reached the maximum iteration count, the iteration optimization is determined to not meet the termination condition. The projected design variables are used as the input for the next iteration optimization, and the iteration optimization of the bipolar plate structure's geometry and material distribution is continued.

[0078] It should be noted that the termination conditions include reaching the expected performance target or reaching the maximum number of iterations; if the termination condition is not met, the iteration optimization continues; if the termination condition is met, the final optimized topology structure is output.

[0079] In summary, this invention achieves the beneficial effects of improving oxygen transport efficiency, reducing unreasonable flow losses, and enhancing the overall reaction performance of the bipolar plate by: defining the bipolar plate design domain based on initial design data and configuring bipolar plate boundary conditions and initial design variables; optimizing the average reaction rate as the optimization objective and using volume fraction as the constraint; and iteratively updating the design variables using the moving asymptote method.

[0080] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A bipolar plate topology optimization and comprehensive evaluation method based on the variable density method, characterized in that, include: Delineate the bipolar plate design domain based on the initial design data, and configure the bipolar plate boundary conditions and initial design variables; Based on the bipolar plate design domain, bipolar plate boundary conditions, and bipolar plate geometric parameters, the bipolar plate structure is subjected to depth averaging to simplify it into a two-dimensional planar model. The two-dimensional planar model is then discretized and meshed using the finite element method to obtain a two-dimensional discretized finite element model of the bipolar plate. Based on the two-dimensional discretized finite element model of the bipolar plate and the initial design variables, the flow model and mass transfer model of the bipolar plate are established. The velocity field, pressure drop and oxygen molar concentration distribution inside the bipolar plate are calculated through the flow model and mass transfer model. Based on the velocity field, pressure drop and oxygen molar concentration distribution inside the bipolar plate, the mass transfer performance index and flow performance index of the bipolar plate are calculated. The objective function for optimizing the bipolar plate flow field is constructed with the maximization of average reaction rate as the optimization objective and the volume fraction as the constraint. Based on the objective function and constraints of bipolar plate flow field optimization, the moving asymptote method is used to iteratively optimize the geometry and material distribution of the bipolar plate structure, and the design variables are updated in each iteration to obtain the updated design variables. The updated design variables are subjected to density filtering and Heaviside projection to obtain the projected design variables. Based on the projected design variables, the velocity field, pressure drop, and oxygen molar concentration distribution inside the bipolar plate are recalculated, and it is determined whether the iterative optimization meets the termination condition, and the final topology optimization structure is output.

2. The bipolar plate topology optimization and comprehensive evaluation method based on the variable density method as described in claim 1, characterized in that, The initial design data includes activation area, bipolar plate thickness, gas diffusion layer thickness, catalyst layer thickness, membrane electrode thickness, flow field channel height, and membrane electrode length and width; The bipolar plate boundary conditions include inlet flow velocity and outlet pressure.

3. The bipolar plate topology optimization and comprehensive evaluation method based on the variable density method as described in claim 2, characterized in that, The specific steps for obtaining the two-dimensional discretized finite element model of the bipolar plate are as follows: A three-dimensional geometric model of the bipolar plate structure is established based on the bipolar plate design domain and bipolar plate geometric parameters. The three-dimensional geometric model of the bipolar plate structure is subjected to depth averaging to obtain a two-dimensional planar model of the bipolar plate. The two-dimensional planar model of the bipolar plate is discretized using the finite element method. The continuous geometric model is decomposed into multiple finite elements by mesh generation, resulting in a two-dimensional discretized finite element model of the bipolar plate.

4. The bipolar plate topology optimization and comprehensive evaluation method based on the variable density method as described in claim 3, characterized in that, The depth averaging process includes averaging the physical properties of the gas channel, ribs, and gas diffusion layer along the through-plane direction, and using the thickness of the gas channel, ribs, and gas diffusion layer as the thickness parameters for averaging to obtain the local porosity of the region corresponding to the gas channel and the region corresponding to the rib in the two-dimensional planar model of the bipolar plate.

5. The bipolar plate topology optimization and comprehensive evaluation method based on the variable density method as described in claim 4, characterized in that, The flow model of the bipolar plate includes the incompressible laminar flow control equation, local porosity interpolation relationship, local permeability interpolation relationship, and porous media resistance term; The local porosity interpolation relationship is established based on design variables, and the porous media resistance term includes Brinkman sink and Poisson sink; The flow model also includes a momentum penalty term constructed based on the volume force term, which includes Brinkman constant, local porosity, fluid velocity, and fluid density.

6. The bipolar plate topology optimization and comprehensive evaluation method based on the variable density method as described in claim 5, characterized in that, The mass transfer model of the bipolar plate includes two-dimensional transport equations, calculation relationships for reaction mass flux, calculation relationships for current density, calculation relationships for cathode overpotential, and calculation relationships for local reaction rate. The two-dimensional transport equation is used to calculate the oxygen molar concentration distribution, and the local reaction rate calculation relationship is established based on the reaction rate constant and the oxygen concentration.

7. The bipolar plate topology optimization and comprehensive evaluation method based on the variable density method as described in claim 6, characterized in that, The objective function for optimizing the bipolar plate flow field is constructed with the goal of maximizing the average reaction rate of the bipolar plate flow field and with volume fraction as the constraint condition. The average reaction rate is obtained based on the local reaction rate, which is calculated based on the reaction rate constant and the oxygen concentration.

8. The bipolar plate topology optimization and comprehensive evaluation method based on the variable density method as described in claim 7, characterized in that, The specific steps to obtain the updated design variables are as follows: Input the current design variables into the bipolar flow model and the bipolar mass transfer model, and calculate the velocity field, pressure drop and oxygen molar concentration distribution inside the bipolar plate under the current iteration state. Based on the velocity field, pressure drop, and oxygen molar concentration distribution inside the bipolar plate under the current iteration state, calculate the mass transfer performance index and flow performance index under the current iteration state. Based on the mass transfer performance index, flow performance index, optimization objective of maximizing average reaction rate, and volume fraction constraint under the current iteration state, construct the current iteration optimization problem; The moving asymptote method is used to solve the current iteration optimization problem, obtain the candidate design variables corresponding to the current iteration, and update the current design variables based on the candidate design variables to obtain the updated design variables.

9. The bipolar plate topology optimization and comprehensive evaluation method based on the variable density method as described in claim 1, characterized in that, The density filtering and Heaviside projection processing involve taking the updated design variables as the original density field input to the Helmholtz type partial differential equation, solving the Helmholtz type partial differential equation, smoothing the original density field, and obtaining the filtered density field. A hyperbolic tangent projection operator is constructed based on the projection threshold parameter and the projection sharpness parameter. The filtered density field is then subjected to Heaviside projection processing using the hyperbolic tangent projection operator to obtain the projected design variables.

10. The bipolar plate topology optimization and comprehensive evaluation method based on the variable density method as described in claim 9, characterized in that, The final topology optimization structure output is based on the projected design variables to recalculate the velocity field, pressure drop and oxygen molar concentration distribution inside the bipolar plate, and to determine whether the iterative optimization meets the termination condition. The termination conditions include achieving the expected performance target or reaching the maximum number of iterations; If the termination condition is not met, continue iterative optimization; if the termination condition is met, output the final optimized topology structure.

Images