A method for multi-objective topology optimization and comprehensive evaluation of SOFC bipolar plate

Abstract

The application discloses a kind of SOFC bipolar plate multi-objective topology optimization and comprehensive evaluation method, belong to solid oxide fuel cell technical field.The method is first input initial design data, clear design domain and initial design variable, and establish the finite element discretization model of bipolar plate structure;Subsequently, according to the performance requirement of SOFC bipolar plate, the analysis of heat transfer performance and flow performance is carried out respectively, to ensure that bipolar plate has good thermal conductivity and gas flow characteristics;Based on the analysis result, multi-objective optimization function is constructed, and the optimization target of heat transfer and flow performance is reasonably weighted;Optimization algorithm is used to update design variable iteratively, to realize the optimization of bipolar plate geometry structure and material distribution.Judge whether to meet termination condition after each iteration, if not satisfied, continue optimization;If satisfied, output final optimization result.The method of the application can significantly improve the heat transfer and flow performance of SOFC bipolar plate, meet the multi-objective optimization requirement, and has high engineering practical value.

Description

Technical Field

[0001] This invention belongs to the field of solid oxide fuel cell technology, specifically relating to a multi-objective topology optimization and comprehensive evaluation method for SOFC bipolar plates. Background Technology

[0002] Solid oxide fuel cells (SOFCs), as a highly efficient and environmentally friendly energy conversion device, have attracted widespread attention in the energy field due to their high energy conversion efficiency and low pollution emissions. Bipolar plates (also known as connectors) are crucial components in SOFCs, responsible for connecting the various cells of the fuel cell in series and providing a current path, while also undertaking multiple functions such as gas distribution, thermal management, and electron conduction. Because SOFCs operate under complex conditions involving high temperature, high pressure, and high current density, the design of the bipolar plates is critical to the overall performance of the cell.

[0003] The optimized design of bipolar plates not only requires excellent heat transfer and gas flow performance, but also needs to meet multiple requirements such as lightweight structure, cost reduction, and manufacturing feasibility. Traditional bipolar plate design methods usually rely on experience and experimentation, which is not only time-consuming and costly, but also difficult to achieve globally optimal design under complex operating conditions. Therefore, how to improve the performance of SOFC bipolar plates through scientific design methods, especially through topology optimization to improve their heat transfer and flow performance, enhance their overall performance, and ultimately improve SOFC efficiency and extend their service life, has become a research hotspot.

[0004] Topology optimization is a technique that uses numerical methods to optimize the structure or material distribution, effectively improving structural performance. In SOFC bipolar plate design, topology optimization can not only optimize geometry but also adjust material distribution, thereby improving heat transfer efficiency and gas flow uniformity while minimizing material costs. However, traditional topology optimization methods often focus on optimizing single objectives, such as heat transfer or flow performance, failing to fully consider the synergistic effects and balance between multiple objectives. Therefore, in practical applications, designing a reasonable multi-objective optimization framework that comprehensively considers various performance requirements is crucial for solving bipolar plate design problems.

[0005] In recent years, multi-objective topology optimization methods based on numerical simulation have gradually become a research trend in bipolar plate design. Through methods such as finite element analysis (FEA) and computational fluid dynamics (CFD), the heat conduction and airflow distribution of bipolar plates can be accurately simulated. Then, optimization algorithms can be used to adjust the shape and material distribution to achieve optimal heat transfer and fluid flow performance. Furthermore, with the development of optimization algorithms, the application of advanced algorithms such as the Sparse Nonlinear OPTimizer (SNOPT) in multi-objective optimization problems has further improved design efficiency and the accuracy of optimization results.

[0006] In summary, optimizing heat transfer and flow performance comprehensively through numerical simulation and multi-objective optimization techniques has become an important research direction in SOFC bipolar plate design. To address this need, this invention proposes a multi-objective function topology optimization numerical simulation method for solid oxide fuel cell bipolar plate structures. The aim is to improve the overall performance of the bipolar plates through system optimization design, thereby achieving a more efficient, economical, and longer-lasting SOFC system. Summary of the Invention

[0007] To address the aforementioned technical problems in existing technologies, this invention proposes a multi-objective topology optimization and comprehensive evaluation method for SOFC bipolar plates. The method is rationally designed, overcomes the shortcomings of existing technologies, and has good results.

[0008] To achieve the above objectives, the present invention adopts the following technical solution: a multi-objective topology optimization and comprehensive evaluation method for SOFC bipolar plates, comprising the following steps: Step 1: Input initial design data and determine the design domain and initial design variables of the bipolar plate; Step 2: Establish a finite element model of the bipolar plate structure and mesh it; Step 3: Based on the finite element model, establish a heat transfer model and a flow model of the bipolar plate, analyze the heat transfer performance and flow performance of the bipolar plate, and obtain the temperature field, pressure drop, and flow distribution for evaluating its performance; Step 4: Based on the analysis results of Step 3, calculate the heat transfer performance index and flow performance index, and construct a comprehensive multi-objective optimization function accordingly; and weight the heat transfer performance and flow performance. Step 5: Using a swarm intelligence-based network optimization algorithm and a multi-objective optimization function, iteratively optimize the geometry and material distribution of the bipolar plate structure, updating the design variables after each iteration; Step 6: Filter and project the design variables after each iteration; Step 7: Determine if the iteration meets the termination conditions; termination conditions include achieving the expected performance target or reaching the maximum number of iterations; if the termination conditions are not met, return to step 5 to continue optimization; if the termination conditions are met, output the final topology-optimized structure; Step 8: Based on the topology-optimized structure, use the topology optimization index to characterize the comprehensive performance of the topology-optimized structure by weighted balancing of temperature gradient and material cost.

[0009] Preferably, in step 1, the initial design data includes parameters related to fluid and solid materials and flow heat transfer, as well as the geometric parameters of the bipolar plates.

[0010] Preferably, in step 2, the finite element model of the bipolar plate structure is simplified into a two-dimensional planar model, and then discretized using the finite element method. The continuous geometric model is decomposed into multiple finite elements by mesh generation.

[0011] Preferably, in step 3, the heat transfer performance and flow performance of the bipolar plate are analyzed, and the internal temperature distribution and gas flow are calculated respectively to ensure that the bipolar plate has good thermal conductivity and gas flow uniformity during operation, so as to optimize the overall performance of the bipolar plate.

[0012] Preferably, in step 4, the heat transfer performance index includes heat exchange and temperature gradient, and the flow performance index is fluid viscous dissipation work; the multi-objective optimization function is a weighted sum of the heat transfer performance index and the flow performance index; the multi-objective optimization function comprehensively considers the influence of heat exchange, temperature gradient and fluid viscous dissipation on the topology optimization shape of the flow channel.

[0013] Preferably, in step 5, the optimization algorithm used is a sparse nonlinear programming optimization method.

[0014] Preferably, in step 6, density filtering in the form of Holmz partial differential equations is used to improve the stability of the solution; and hyperbolic tangent projection is used to solve the grayscale problem in order to obtain a clear flow channel topology.

[0015] The beneficial technical effects of this invention are: (1) Traditional bipolar plate design usually relies on experience and experimentation, which has problems such as long cycle, high cost and difficulty in achieving global optimization. However, this invention achieves accurate optimization of bipolar plate structure by combining numerical simulation with multi-objective optimization, which significantly improves design efficiency and performance accuracy.

[0016] (2) The multi-objective optimization method of this invention comprehensively considers the heat transfer and flow performance of the bipolar plate, and reasonably weights different optimization objectives. It can optimize the geometry and material distribution while meeting different operational requirements, improving the uniformity of heat conduction and gas flow, and enhancing overall performance. Finally, by introducing the SNOPT optimization algorithm and density filtering technology, this invention effectively solves the problems of poor convergence and low stability commonly found in traditional optimization methods, ensuring the efficiency and stability of the optimization process. Therefore, this invention can significantly improve the overall performance of SOFC bipolar plates, providing a new technical path and solution for the optimized design of SOFC systems. Attached Figure Description

[0017] Figure 1 This is a flowchart of the method of the present invention; Figure 2 This is a schematic diagram of a fluid topology optimization model; Figure 3 A schematic diagram of the topological configuration for controlling the upper bound of different volumes; Figure 4 This is a schematic diagram of the topological shape; Figure 4 (a) shows the topology before and after density filtering; (b) shows the topology before and after projection. Figure 5 This is a schematic diagram of the iterative process of the flow channel topology. Figure 6 This is a schematic diagram of the flow channel structure; Figure 6 (a) is a schematic diagram of the flow channel structure after topology optimization; (b) is a schematic diagram of the flow channel structure before topology optimization. Figure 7 This is a diagram showing the velocity distribution within the flow channel. Figure 7 (a) shows the velocity distribution within the flow channel after topology optimization; (b) shows the velocity distribution within the flow channel before topology optimization. Figure 8 The temperature gradient distribution inside the material under different topology optimization conditions; Figure 8 In the diagram, (a) represents the maximum value γ of the fluid domain occupying the entire design domain. max Temperature gradient distribution at γ = 0.5; (b) is the temperature gradient distribution at γ = 0.5; max Temperature gradient distribution at γ = 0.6; (c) is γ max Temperature gradient distribution at γ = 0.7; (d) is the temperature gradient distribution at γ = 0.7. maxTemperature gradient distribution at 0.8. Detailed Implementation

[0018] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments: The present invention discloses a multi-objective function topology optimization modeling and comprehensive evaluation method for bipolar plate structures of solid oxide fuel cells, such as... Figure 1 As shown, the specific steps include: Step 1: Input initial design data and determine the design domain and initial design variables of the bipolar plate: When performing topology optimization design of a conjugate heat transfer system, it is necessary to determine the topology optimization design region and boundary conditions based on the heat source distribution and heat flow boundary conditions in complex actual heat transfer problems. This is done by establishing a geometry module in COMSOL as follows: Figure 2 The geometric model shown has a design domain that is symmetric about the midline, so a 1 / 2 model can be selected for calculation and solution. The optimized model control parameters are shown in Table 1. The initial boundary conditions are: inlet velocity of 0.45 m / s, outlet pressure of 0 Pa; fluid inlet temperature of 800°C, ambient temperature of 25°C; and initial value of control variables of 0.5.

[0019] Table 1: Control Parameters of the Optimized Model

[0020] .

[0021] Step 2: Establish a finite element model of the bipolar plate structure and mesh it: To achieve bipolar plate topology optimization design, a mathematical model of the flow and heat transfer topology optimization problem needs to be established. Therefore, flow and heat transfer fields are added in COMSOL software. Specific material physical property parameters are shown in Table 2. The governing equations are: 1. Flow equations; Assuming the flow within the bipolar plate is incompressible laminar flow, the governing equations are: (1); (2);

[0022] In the formula, u is velocity and p is pressure. For fluid density, Let F be the fluid viscosity and F be the volume force.

[0023] According to the Brinkman penalty model, the resistance to fluid flow through a porous medium is proportional to the fluid velocity. Therefore, the equation for the volume force is as follows: (3); where α is the reverse osmosis rate of the porous medium, which is related to the design variable γ. The equation using the Darcy interpolation model is as follows: (4); where q is the penalty factor of the Darcy interpolation model, It is the maximum value of the volume force and is related to the Reynolds number Re and the Darcy number Da, as shown in the following equation: (5); In this example, Da and q take values ​​of 0.0001 and 0.01, respectively.

[0024] For ease of calculation, the dimensionless forms of formulas (1) and (2) are as follows: (6); (7); The specific dimensionless method is as follows: (8); where L and U are the characteristic length and characteristic velocity, respectively, and p0 is the reference pressure, i.e., the outlet pressure.

[0025] 2. Energy Equations; Due to the different heat transfer mechanisms, the energy conservation equations for fluids and solids are also different. The convection equation for fluids and the heat conduction equation for solids are as follows: (9); (10); among which, It is the specific heat capacity of the fluid. It is the thermal conductivity of the fluid. It is the thermal conductivity of solids. The solid region is the heat source. According to the flow equation, the velocity in the solid region is 0. The thermal conductivity of the two regions is integrated through linear interpolation, and the combined energy equation is as follows: (11); Assuming heat generation is related to the reference temperature T r The heat generation equation is proportional to the temperature difference between the local temperatures and T. (12); where H is the heat generation coefficient. The dimensionless energy equation is as follows: (13); where dimensionless temperature Dimensionless heat generation coefficient And Prandtl The definition is as follows: (14); among which, It is the characteristic temperature. It is the heat generation coefficient.

[0026] Table 2: Material Physical Property Parameters

[0027] .

[0028] Step 3: Analyze the heat transfer and flow performance of the bipolar plate, and ensure that it has good heat conduction and gas flow characteristics during operation according to the working requirements of the bipolar plate.

[0029] In bipolar plate topology optimization design, the desired outcome is typically a design with superior heat transfer performance and lower flow resistance. This necessitates a trade-off between these two factors during the design process. Heat transfer performance metrics usually include requirements for temperature rise control and temperature uniformity of the heat-generating components, with optimization objectives typically focusing on minimizing heat dissipation weakness, average temperature, and temperature variance. Flow performance metrics typically focus on minimizing flow resistance, pressure drop, and fluid power dissipation. In this example, considering both heat transfer performance and fluid flow energy consumption, the optimization objectives are to maximize heat transfer, minimize temperature gradient, and minimize fluid power dissipation.

[0030] Step 4: Based on the analysis results, define a multi-objective optimization function, and weight the heat transfer performance and flow performance to determine the weights of the optimization objectives.

[0031] thermal performance target , and fluid flow target After normalization, the weights w1, w2, and w3 are combined to form the overall objective function J for topology optimization, which is expressed as: (15); among which, (16); (17); (18); (19); (20);

[0032] In the formula, For the design domain, The total volume of the design domain. To optimize the objective, For heat exchange terms, For temperature gradient term, This is the work dissipated by the fluid. For the import border, This represents the volume fraction occupied by the fluid channel. Figure 3 For the initial The topology optimization results for different values ​​are shown in the figure. , These are the weighting coefficients for heat exchange and fluid dissipation work, respectively. In this example, they are taken as 0.4, 0.2, and 0.4, respectively. Take 100.

[0033] Step 5: Using the SNOPT optimization algorithm, based on the multi-objective optimization function, iteratively optimize the geometry and material distribution of the bipolar plate structure, and update the design variables after each iteration.

[0034] This example requires solving a constrained nonlinear optimization problem. Compared with other optimization algorithms, the sequential quadratic programming method has good convergence, high computational efficiency, and strong boundary search capability, and is well-suited for small to medium-sized optimization problems.

[0035] Step 6: Process the optimization results through projection and filtering operations to improve the stability of the solution and eliminate the generation of grayscale cells.

[0036] In topology optimization problems, density filtering is necessary to avoid mesh dependency and improve robustness. Furthermore, in fluid-structure interaction (FSI) heat transfer topology optimization problems, density filtering can effectively avoid ill-posedness. Density filtering using Helmholtz-type partial differential equations is employed. Figure 4 (a) shows the topological configuration before and after filtering. The density filtering expression is as follows: (16); where r is the filtration radius, These are the design variables before filtering. For the filtered design variables, in this example, the filtering radius r is equal to the cell size.

[0037] While the density filtering described above can improve the numerical stability during the solution process, it also leads to the generation of a large number of grayscale cells, such as... Figure 4 As shown in (b), in order to solve the grayscale problem, hyperbolic sine projection is used to obtain a clear liquid cooling channel topology. The projection expression is as follows: (17); where, For the projected design variables, For the projection point, we take 0.5 in this paper. The slope is denoted as .

[0038] Step 7: Evaluate whether the optimization termination condition has been met. The termination condition includes achieving the performance target or the maximum number of iterations. If the termination condition has not been met, return to step 5 to continue optimization. If the termination condition has been met, output the optimized design result.

[0039] The optimization iteration termination condition is: / J k+1 -J k / <1×10 -6 Where k is the number of iterations, and the specific iteration process is as follows: Figure 5 As shown.

[0040] Establish the optimized flow channel structure as follows: Figure 6 The three-dimensional model shown in (a) is used for simulation calculations, and compared with that shown in (a). Figure 6 Compare the structural flow simulation results before topology optimization shown in (b) to those in the figure, such as... Figure 7 As shown in the image. It can be seen that before topology optimization, as... Figure 7As shown in (b), the range of velocities at the center of each gas channel is approximately 0.4 m / s, and the velocity in some gas channels is close to 0; after topology optimization, as shown in (b), the velocity range is approximately 0. Figure 7 As shown in (a), the range of the center velocities of each gas channel is approximately 0.2 m / s, which is a decrease of 50%, and it improves the problem that the flow velocity in some gas channels is close to 0, thereby improving the uniformity of fluid distribution within the bipolar plate.

[0041] Step 8: To quantitatively evaluate the merits of different topology optimization structures, a topology optimization index is proposed. The index characterizes the comprehensive performance of the topology optimization structure by weighted balancing of temperature gradient and material cost.

[0042] In the structural optimization design of SOFC bipolar plates, an increase in the proportion of the fluid domain to the total design domain means a larger space occupied by fluid passages and other fluid flow areas within the bipolar plate. Consequently, the amount of solid material used as the supporting structure of the bipolar plate decreases, reducing the procurement cost of precious metals. Simultaneously, less material translates to a lighter overall weight, which is particularly important for fuel cell systems in mobile applications. Therefore, while ensuring structural strength and performance, maximizing γ through methods such as topology optimization is crucial. max Value is an effective way to improve the economic efficiency of bipolar plate design.

[0043] To quantitatively evaluate the overall performance of different topology optimization structures, this example proposes a topology optimization index B, the expression of which is: (18); where grad.T is the maximum temperature gradient inside the material, K·cm -1 ;γ max is the maximum value of the fluid domain in the entire design domain; b is a coefficient, which is 0.5 in this example.

[0044] This index characterizes the overall performance of the topology-optimized structure by weighted balancing of temperature gradient and material cost; a smaller value indicates better overall performance. The temperature gradient distribution within the material under different topology optimization conditions is shown below. Figure 8 As shown, Figure 8 In the diagram, (a) represents the maximum value γ of the fluid domain occupying the entire design domain. max Temperature gradient distribution at 0.5; Figure 8 (b) in the text is γ max Temperature gradient distribution at 0.6; Figure 8 (c) in the text represents γ. max Temperature gradient distribution at 0.7; Figure 8 (d) in the text represents γ. max Temperature gradient distribution at 0.8.

[0045] The specific calculation results are shown in Table 3. It can be seen that as γmax As the value of B increases, its overall performance decreases, meaning it performs better overall.

[0046] Table 3: Calculation results of topology optimization index under different conditions

[0047] .

[0048] Of course, the above description is not intended to limit the present invention, and the present invention is not limited to the examples given above. Any changes, modifications, additions or substitutions made by those skilled in the art within the scope of the present invention should also fall within the protection scope of the present invention.

Claims

1. A method for multi-objective topology optimization and comprehensive evaluation of SOFC bipolar plates, characterized in that, Includes the following steps: Step 1: Input initial design data to determine the design domain and initial design variables of the bipolar plate; Step 2: Establish a finite element model of the bipolar plate structure and mesh it; Step 3: Based on the finite element model, establish the heat transfer model and flow model of the bipolar plate, and analyze the heat transfer performance and flow performance of the bipolar plate to obtain the temperature field, pressure drop and flow distribution for evaluating its performance. Step 4: Based on the analysis results of Step 3, calculate the heat transfer performance index and the flow performance index, and construct a comprehensive multi-objective optimization function accordingly; The heat transfer performance and flow performance are weighted to determine the weight of the optimization objective; Step 5: Using a swarm intelligence-based network optimization algorithm and a multi-objective optimization function, iteratively optimize the geometry and material distribution of the bipolar plate structure, and update the design variables after each iteration; Step 6: Perform filtering and projection operations on the design variables after each iteration; Step 7: Determine if the iteration meets the termination conditions; termination conditions include achieving the expected performance target or reaching the maximum number of iterations; If the termination condition is not met, return to step 5 to continue optimization; if the termination condition is met, output the final optimized topology structure. Step 8: Based on the topology optimization structure, the comprehensive performance of the topology optimization structure is characterized by using the topology optimization index and weighted balancing of temperature gradient and material cost. In step 4, the heat transfer performance index includes heat transfer and temperature gradient, and the flow performance index is fluid viscous dissipation work; the multi-objective optimization function is the weighted sum of the heat transfer performance index and the flow performance index; the multi-objective optimization function comprehensively considers the influence of heat transfer, temperature gradient and fluid viscous dissipation on the flow channel topology optimization shape. In step 5, the optimization algorithm used is the sparse nonlinear programming optimization method.

2. The method for multi-objective topology optimization and comprehensive evaluation of SOFC bipolar plates according to claim 1, characterized in that, In step 1, the initial design data includes parameters related to fluid and solid materials and flow heat transfer, as well as the geometric parameters of the bipolar plates.

3. The method for multi-objective topology optimization and comprehensive evaluation of SOFC bipolar plates according to claim 1, characterized in that, In step 2, the finite element model of the bipolar plate structure is simplified into a two-dimensional planar model, and then discretized using the finite element method. The continuous geometric model is decomposed into multiple finite elements by mesh generation.

4. The method for multi-objective topology optimization and comprehensive evaluation of SOFC bipolar plates according to claim 1, characterized in that, In step 3, the heat transfer and flow performance of the bipolar plate are analyzed, and the internal temperature distribution and gas flow are calculated to ensure that the bipolar plate has good thermal conductivity and gas flow uniformity during operation, so as to optimize the overall performance of the bipolar plate.

5. The method for multi-objective topology optimization and comprehensive evaluation of SOFC bipolar plates according to claim 1, characterized in that, In step 6, density filtering in the form of Holmtz partial differential equations is used to improve the stability of the solution; hyperbolic tangent projection is used to solve the grayscale problem in order to obtain a clear flow channel topology.

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