Modeling methods that consider mechanical changes in fuel cell assembly and their relation to performance

Abstract

The application discloses a modeling method considering mechanical changes and performance correlation generated by fuel cell assembly, and is used for constructing a three-dimensional model of a proton exchange membrane fuel cell under real assembly, setting material properties of each component, setting contact relations between the components, setting boundary conditions of the model and setting applied loads, thereby establishing a mechanical finite element model of the fuel cell. The model is used to obtain contact stress distribution of a contact surface between a gas diffusion layer and a bipolar plate and a volume of the gas diffusion layer after compression; the contact stress distribution and the volume are converted into uneven contact resistance, porosity and permeability; the contact resistance, the porosity and the permeability are input into a fuel cell performance model for calculation; and finally, a polarization curve under real assembly and pre-tightening and distribution of key parameters are obtained. The model is helpful for intuitively, rapidly and accurately obtaining an optimal pre-tightening force of the fuel cell and simultaneously obtaining the distribution in the fuel cell, so as to help understanding of the relationship between mechanical behaviors and output performances of the fuel cell.

Description

Technical Field

[0001] This invention pertains to fuel cell technology, specifically involving a modeling method for the correlation between changes in the mechanical behavior of a fuel cell and its performance during actual assembly. Background Technology

[0002] A proton exchange membrane fuel cell (PEMFC) is an energy conversion device that converts the chemical energy of hydrogen and oxygen into electrical energy. It boasts advantages such as high power density, rapid response, and zero emissions, and is considered one of the most promising power devices to replace internal combustion engines. PEMFCs can be widely used in aviation, submarines, power plants, and fuel cell vehicles.

[0003] A proton exchange membrane fuel cell (PEMFC) consists of end plates, insulating plates, current collectors, bipolar plates, a gas diffusion layer, a microporous layer, a catalyst layer, a proton exchange membrane, sealing gaskets, and fastening bolts. To achieve higher output power, the fuel cell stack in fuel cell vehicles typically consists of 300-400 individual cells. During assembly, various mechanical behaviors occur within the cell. For example, the contact state or degree of contact between the bipolar plates and the gas diffusion layer will produce different mechanical behaviors. Insufficient contact stress leads to higher contact resistance, resulting in greater electron ohmic losses; while excessive contact stress reduces the thickness, porosity, and permeability of the gas diffusion layer, hindering gas transport and increasing mass transfer losses.

[0004] Currently, testing the preload of fuel cell assembly is mainly done experimentally, examining battery performance under different preload forces. However, this experimental process is time-consuming and costly. Some simulation models exist to study the impact of fuel cell assembly on gas diffusion layer parameters, but these have two main problems. First, the models model the bipolar plates and gas diffusion layer separately, applying uniform pressure to study the stress and strain of the gas diffusion layer under different pressures, without considering the actual assembly conditions of the battery. Second, the current models separate mechanical behavior from performance changes, failing to comprehensively consider the impact of changes in mechanical behavior caused by assembly preload on performance, and thus cannot determine the optimal preload magnitude for maximum performance.

[0005] If a simulation model could be established that considers the relationship between the mechanical behavior of assembly preload and battery performance, and obtains the parameter changes, stress distribution, and strain magnitude of key components of the fuel cell, while also incorporating these changes into the full battery performance model to output the performance and key parameter distribution of the fuel cell under different preloads, it would undoubtedly become a sought-after technology in the fuel cell field. Summary of the Invention

[0006] To address the aforementioned problems, this invention proposes a modeling method that considers the mechanical changes and performance correlations resulting from fuel cell assembly. This method simulates the internal mechanical behavior of the fuel cell under actual assembly conditions, obtaining changes in gas diffusion layer parameters due to assembly, including contact resistance, porosity, and permeability. These mechanical changes are then incorporated into the full-cell model to simulate battery performance under different preload forces, outputting polarization curves and determining the optimal preload magnitude, thus achieving coupling between mechanical behavior and performance. This model helps to intuitively, quickly, and accurately obtain the optimal preload force for the fuel cell, while also revealing the internal distribution within the cell, aiding in the understanding of the relationship between battery mechanical behavior and output performance.

[0007] The present invention adopts the following technical solution and steps:

[0008] This paper considers a modeling method related to the mechanical changes and performance of fuel cell assembly. The fuel cell components involved in the modeling include: end plates, insulating plates, current collectors, bipolar plates, gas diffusion layers, membrane electrode assemblies, sealing gaskets, and fastening bolts. The model establishment includes the following steps:

[0009] (1) Establish a finite element model of fuel cell mechanics under actual assembly. The finite element model includes three-dimensional geometric modeling, input of mechanical parameters of battery components, mesh generation, setting of contact, setting of boundary conditions, and setting of loads.

[0010] (2) The components involved in the three-dimensional geometric modeling include: end plates, insulating plates, current collectors, bipolar plates, gas diffusion layers, membrane electrode assemblies, sealing gaskets, and fastening bolts. The microporous layer, catalytic layer, and proton exchange membrane are integrated into one unit. The geometric parameters of the components involved need to be determined in this step, including: end plate thickness, width, and length; insulating plate thickness, width, and length; current collector thickness, width, and length; bipolar plate thickness, width, and length; gas diffusion layer thickness, width, and length; membrane electrode assembly thickness, width, and length; sealing gasket thickness and width; and the inner diameter, outer diameter, nut diameter, and length of the fastening bolts.

[0011] (3) Input the mechanical parameters of the components involved, including the density, Young's modulus and Poisson's ratio of the end plate, insulating plate, current collector, bipolar plate, gas diffusion layer, membrane electrode assembly, sealing gasket and fastening bolt.

[0012] (4) Mesh division: Use mesh division software to divide the mesh of the components involved. At the contact area between the gas diffusion layer and the bipolar plate, the mesh density of the gas diffusion layer is twice that of the bipolar plate.

[0013] (5) Setting contact states: The contact pairs of the components involved include: end plate-insulating plate, insulating plate-current collector, current collector-bipolar plate, bipolar plate-gas diffusion layer, bipolar plate-sealing gasket, and gas diffusion layer-membrane electrode assembly.

[0014] (6) Setting boundary conditions: The finite element mechanical model of the fuel cell has symmetry in three directions. In order to reduce the amount of calculation, a 1 / 8 model is selected for calculation. Symmetrical boundary conditions need to be set on the symmetrical surfaces of the end plate, insulating plate, current collector, bipolar plate, gas diffusion layer, membrane electrode assembly, and sealing gasket. Fixed boundary conditions are set on the bottom surface of the membrane electrode assembly and sealing gasket.

[0015] (7) Set load: Set load on bolt hole, and set load to pressure.

[0016] Method for calculating pressure on bolt holes:

[0017] The relationship between torque and preload is: T = K × F × d, where T is the torque, K is the bolt preload coefficient, F is the preload, and d is the bolt diameter.

[0018] The relationship between preload and pressure is: P = F / S, where P is the pressure and S is the area of ​​the bolt hole.

[0019] (8) After establishing the model, solve for the surface contact stress of the gas diffusion layer and the volume of the gas diffusion layer after compression.

[0020] Furthermore, after establishing the finite element model of fuel cell mechanics, a preload torque is applied to obtain the contact stress distribution at the interface between the gas diffusion layer and the bipolar plate, as well as the volume of the compressed gas diffusion layer.

[0021] The gas diffusion layer contact stress and volume obtained from the finite element model of fuel cell mechanics are converted into contact resistance, porosity, and permeability.

[0022] The formula for calculating contact resistance is:

[0023]

[0024] The obtained gas diffusion layer contact stress is non-uniform, therefore the calculated contact resistance is also a non-uniform contact resistance distribution.

[0025] The formula for calculating the porosity of the gas diffusion layer after compression is:

[0026]

[0027] The formula for calculating the permeability of the gas diffusion layer after compression is:

[0028]

[0029] The established fuel cell full-cell performance model is a "three-dimensional + one-dimensional" model. The three-dimensional part includes the anode and cathode flow channels, anode and cathode gas diffusion layers, and anode and cathode extension layers. The one-dimensional part includes the anode and cathode microporous layers, anode and cathode catalyst layers, and proton exchange membranes. Computational nodes are set at the interfaces of each layer to form the one-dimensional model. The one-dimensional part is stored and calculated in the extension layer.

[0030] The conservation equations for the three-dimensional part include:

[0031] (1) Mass conservation equation

[0032] (2) Momentum conservation equation

[0033] (3) Component conservation equation

[0034] (4) Energy conservation equation

[0035] (5) Hydraulic conservation equation

[0036] (6) Electron potential conservation equation

[0037] In the one-dimensional part, the conservation equation is transformed into a one-dimensional flux conservation equation, and the scalars are solved in the one-dimensional part. The calculation formulas involved for each scalar include:

[0038] (1) Components

[0039] (2) Temperature

[0040] (3) Hydraulics

[0041] (4) Membrane water content

[0042] (5) Electron potential

[0043] (6) Ion potential

[0044] Furthermore, the electrochemical reaction rate is calculated by considering the agglomeration model in the one-dimensional model, and the specific calculation formulas are as follows (16) and (17). The reversible voltage is calculated by the Nernst equation, as shown in equation (18).

[0045] The calculated non-uniform contact resistance, porosity, and permeability are added to the full cell performance model of the fuel cell to simulate its performance and output polarization curves and the distribution of key internal parameters such as current density distribution and temperature distribution.

[0046] The features and advantages of this invention are as follows:

[0047] (1) A quantitative relationship between the changes in the mechanical behavior of fuel cells and their performance under actual assembly is proposed. This method can comprehensively consider the changes in key parameters of the gas diffusion layer caused by the mechanical behavior of fuel cells under actual assembly, and then input them into the performance simulation model to calculate its performance. Compared with the experimental methods that have been used, this method helps to intuitively, quickly and accurately obtain the optimal assembly pressure of fuel cells, understand their internal mechanical behavior, understand the relationship between their mechanical behavior and performance, and propose optimizations for fuel cell assembly.

[0048] (2) The established mechanical finite element model includes all components of the fuel cell. The model is comprehensive and accurate, and can be calculated on a large-area flow field plate to obtain the mechanical relationships between the components. In addition, this model can also extract the non-uniform contact stress distribution on the surface of the gas diffusion layer, which can be converted into non-uniform contact resistance later.

[0049] (3) The established "three-dimensional + one-dimensional" performance model can comprehensively consider the flow field form and structure of the fuel cell, is realistic and accurate, and can be calculated on a large-area flow field plate. In addition, this invention also considers the non-uniform contact resistance distribution, porosity variation, and permeability variation. Compared with the traditional three-dimensional performance model, this model is faster to calculate, has better convergence, and takes into account the non-uniform contact resistance inside the battery. Attached Figure Description

[0050] Appendix Figure 1 This is a block diagram illustrating the steps and principles of the modeling process of this invention.

[0051] Appendix Figure 2 This is a schematic diagram of the mechanical finite element model used in the example calculation.

[0052] Appendix Figure 3 This is a schematic diagram of the performance model in the example calculation.

[0053] Appendix Figure 4 This is a schematic diagram illustrating the handling of uneven contact resistance in the example calculation.

[0054] Appendix Figure 5 This is the polarization curve output in the example calculation.

[0055] Appendix Figure 6 This is a current density distribution cloud map output in the example calculation.

[0056] Appendix Figure 7 This is the temperature distribution cloud map output in the example calculation. Detailed Implementation

[0057] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and examples. It should be noted that the examples are descriptive rather than limiting and are not intended to limit the scope of protection of the present invention.

[0058] The modeling method considers the mechanical changes and performance-related factors resulting from fuel cell assembly. The fuel cell components involved in the modeling include: end plates, insulating plates, current collectors, bipolar plates, gas diffusion layers, membrane electrode assemblies, sealing gaskets, and fastening bolts.

[0059] The finite element model of fuel cell mechanics and the full cell performance model of fuel cell in this example are not restrictive. (See attached...) Figure 1 As shown. The overall principle of this invention is to construct a three-dimensional model of a proton exchange membrane fuel cell under actual assembly, set the material properties of each component, set the contact relationships between the components, set the boundary conditions of the model, and set the applied loads, thereby establishing a finite element mechanical model of the fuel cell. The model obtains the contact stress distribution of the gas diffusion layer and the bipolar plate contact surface, as well as the volume of the gas diffusion layer after compression; these are converted into non-uniform contact resistance, porosity, and permeability; then input into the fuel cell performance model for calculation; finally, the polarization curve and the distribution of key parameters under actual assembly and pre-tightening are obtained. The establishment of the model considering the mechanical changes and performance-related factors caused by fuel cell assembly includes the following steps:

[0060] (1) Establish a finite element model of fuel cell mechanics under actual assembly. The finite element model includes three-dimensional geometric modeling, input of mechanical parameters of battery components, mesh generation, setting of contact, setting of boundary conditions, and setting of loads.

[0061] (2) The components involved in the three-dimensional geometric modeling include: end plates, insulating plates, current collectors, bipolar plates, gas diffusion layers, membrane electrode assemblies, sealing gaskets, and fastening bolts. The microporous layer, catalytic layer, and proton exchange membrane are integrated into one unit. The geometric parameters of the components involved need to be determined in this step, including: end plate thickness, width, and length; insulating plate thickness, width, and length; current collector thickness, width, and length; bipolar plate thickness, width, and length; gas diffusion layer thickness, width, and length; membrane electrode assembly thickness, width, and length; sealing gasket thickness and width; and the inner diameter, outer diameter, nut diameter, and length of the fastening bolts.

[0062] (3) Input the mechanical parameters of the components involved, including the density, Young's modulus and Poisson's ratio of the end plate, insulating plate, current collector, bipolar plate, gas diffusion layer, membrane electrode assembly, sealing gasket and fastening bolt.

[0063] (4) Mesh division: Use mesh division software to divide the mesh of the components involved. At the contact area between the gas diffusion layer and the bipolar plate, the mesh density of the gas diffusion layer is twice that of the bipolar plate.

[0064] (5) Setting contact states: The contact pairs of the components involved include: end plate-insulating plate, insulating plate-current collector, current collector-bipolar plate, bipolar plate-gas diffusion layer, bipolar plate-sealing gasket, and gas diffusion layer-membrane electrode assembly.

[0065] (6) Setting boundary conditions: The finite element mechanical model of the fuel cell has symmetry in three directions. In order to reduce the amount of calculation, a 1 / 8 model is selected for calculation. Symmetrical boundary conditions need to be set on two symmetrical surfaces of the end plate, insulating plate, current collector, bipolar plate, gas diffusion layer, membrane electrode assembly, and sealing gasket. Fixed boundary conditions are set on the bottom surface of the membrane electrode assembly and sealing gasket.

[0066] (7) Applying a load: Apply a load to the bolt hole, setting the load as pressure. In calculating the pressure on the bolt hole, the relationship between torque and preload is: T = K × F × d. Where T is the torque, K is the bolt preload coefficient, F is the preload, and d is the bolt diameter. The relationship between preload and pressure is: P = F / S, where P is the pressure and S is the area of ​​the bolt hole.

[0067] (8) After establishing the model, solve for the surface contact stress of the gas diffusion layer and the volume of the gas diffusion layer after compression.

[0068] The specific steps for converting contact stress and compressed volume into non-uniform contact resistance, porosity, and permeability are as follows:

[0069] (1) The formula for calculating contact resistance is:

[0070]

[0071] Where R contact P is the contact resistance, α and β are variable coefficients, and P is the contact resistance. contact This refers to contact stress.

[0072] Furthermore, the obtained gas diffusion layer contact stress is non-uniform, and the calculated contact resistance is also non-uniform.

[0073] (2) The formula for calculating the porosity of the gas diffusion layer after compression is:

[0074]

[0075] (3) The formula for calculating the permeability of the gas diffusion layer after compression is:

[0076]

[0077] Furthermore, a full-cell performance model of a proton exchange membrane fuel cell considering the actual flow field structure is established. Non-uniform contact resistance, porosity, and permeability are coupled into the model, and the output polarization curve and the distribution of key parameters are calculated. The specific implementation steps are as follows:

[0078] (1) Establish a full-cell performance model for a proton exchange membrane fuel cell. This model is a "three-dimensional + one-dimensional" model. The three-dimensional part includes the anode and cathode channels, the anode and cathode gas diffusion layers, and the anode and cathode extension layers. The one-dimensional part includes the anode and cathode microporous layers, the anode and cathode catalyst layers, and the proton exchange membrane. Calculation nodes are set at the interfaces of each layer to form a one-dimensional model. The one-dimensional part is stored and calculated in the extension layer.

[0079] (2) The three-dimensional partial conservation equations include:

[0080] (2.1) Mass conservation equation:

[0081]

[0082] (2.2) Momentum conservation equation:

[0083]

[0084] (2.3) Component conservation equation:

[0085]

[0086] (2.4) Energy conservation equation:

[0087]

[0088] (2.5) Hydraulic conservation equation:

[0089]

[0090] (2.6) Electron potential conservation equation:

[0091]

[0092] (3) In the one-dimensional part, the conservation equation is transformed into a one-dimensional flux conservation equation. The scalars in the one-dimensional part are solved, and the formulas for calculating each scalar are as follows:

[0093] (3.1) Components:

[0094]

[0095] (3.2) Temperature:

[0096]

[0097] (3.3) Hydraulics:

[0098]

[0099] (3.4) Membrane water content:

[0100]

[0101] (3.5) Electron potential:

[0102]

[0103] (3.6) Ion potential:

[0104]

[0105] The electrochemical reaction rate is calculated by considering the agglomeration model correction in the one-dimensional model, and the calculation formula is as follows:

[0106]

[0107]

[0108] The reversible voltage can be calculated using the Nernst equation, and the formula is as follows:

[0109]

[0110] (4) The non-uniform contact resistance, porosity and permeability obtained from the above calculations are added to the proton exchange membrane fuel cell full cell model, and the calculation is performed to simulate its performance. The polarization curve and the distribution of key internal parameters such as current density distribution and temperature distribution are output.

[0111] Example

[0112] First, a mechanical finite element model considering the actual assembly of a proton exchange membrane fuel cell is established to obtain the surface contact stress and compressed volume of the gas diffusion layer. Then, the contact stress and compressed volume are converted into non-uniform contact resistance, porosity, and permeability. Based on this, a full-cell performance model of the proton exchange membrane fuel cell considering the actual flow field structure is established, coupling the non-uniform contact resistance, porosity, and permeability into the model to solve for the output polarization curve and the distribution of key parameters. Specifically:

[0113] 1. Establish the three-dimensional geometry of the finite element model of the proton exchange membrane fuel cell, as shown in the attached figure. Figure 2 As shown. Set the material properties of each component involved, including density, Young's modulus, and Poisson's ratio. The end plate density is 2800 kg / m³. -3 Young's modulus 2.0e5MPa, Poisson's ratio 0.33; insulation board density 1420kg m³ -3Young's modulus 1000 MPa, Poisson's ratio 0.38; manifold density 8940 kg m³ -3 Young's modulus 1.2e5 MPa, Poisson's ratio 0.33; bipolar plate density 2250 kg m³ -3 Young's modulus 1.0e4 MPa, Poisson's ratio 0.25; gas diffusion layer density 440 kg m³ -3 Young's modulus 10 MPa, Poisson's ratio 0.1; membrane electrode assembly density 2000 kg m³ -3 Young's modulus 320 MPa, Poisson's ratio 0.25; sealing gasket density 1000 kg m³ -3 Young's modulus is 100 MPa, and Poisson's ratio is 0.4.

[0114] 2. Establish the contact relationships between each component. Establish tangential and normal contacts between the end plate and the insulating plate, the insulating plate and the current collector, the current collector and the bipolar plate, the bipolar plate and the gas diffusion layer, and the bipolar plate and the sealing gasket. Establish a bonding relationship between the gas diffusion layer and the membrane electrode assembly.

[0115] 3. Set boundary conditions for each component. Set symmetrical boundary conditions for the end plate, insulating plate, current collector, bipolar plate, gas diffusion layer, membrane electrode assembly, and sealing gasket in two symmetrical directions along the flow field. Set fixed boundary conditions for the bottom surface of the sealing gasket and membrane electrode assembly.

[0116] 4. Apply load. Apply a load, selected as pressure, to the bolt hole contact surface of the end plate. The calculation method is as follows:

[0117] Torque and preload: T = K × F × d.

[0118] The relationship between preload and pressure: P = F / S.

[0119] In this example, the torque T is selected as 3 Nm, the bolt diameter is 6.4 mm, and the bolt hole area is 121.77 mm². 2 This allows us to calculate the pressure applied to each bolt hole.

[0120] 5. Based on the above steps, the mechanical finite element model of the proton exchange membrane fuel cell in actual assembly is now established. Solving this model yields the contact stress distribution at the interface between the gas diffusion layer and the bipolar plates, as well as the volume of the compressed gas diffusion layer.

[0121] 6. The obtained surface contact stress and compressed volume of the gas diffusion layer are converted into non-uniform contact resistance, compressed porosity, and compressed permeability. The calculation process is as follows:

[0122] Contact resistance calculation formula:

[0123]

[0124] In this calculation formula, α is 5.0, β is -0.719, and P... contact (MPa) represents the contact stress.

[0125] The obtained gas diffusion layer contact stress is non-uniform, therefore the calculated contact resistance is also a non-uniform contact resistance distribution.

[0126] The formula for calculating porosity is:

[0127]

[0128] In this calculation, it is 530mm. 3 V c ε is the volume of the gas diffusion layer after compression. i In this calculation, it is 0.7.

[0129] The formula for calculating penetration rate:

[0130]

[0131] In this calculation, it is 8 μm.

[0132] 7. Establish a full-cell performance model for a proton exchange membrane fuel cell. (See attached diagram) Figure 3 The diagram shows the geometric schematic of the model. This model is a "3D + 1D" model. The 3D part includes the anode and cathode distribution region, the anode and cathode flow field, the anode and cathode gas diffusion layer, and the anode and cathode extension layer. The 1D model is stored and computed in the anode and cathode extension layer. The 1D model includes the anode and cathode microporous layer, the anode and cathode catalytic layer, and the proton exchange membrane. The computational nodes for the 1D part are selected at the interfaces between the layers.

[0133] The calculation formula for this performance model is as follows:

[0134] The three-dimensional partial conservation equations are:

[0135] (1) Mass conservation equation:

[0136]

[0137] Where, ρ g (kg m -3 ) represents density. (ms -1 ) represents the flow velocity, S m (kg m -3 s -1 ) is the source term of the mass conservation equation.

[0138] (2) Momentum conservation equation:

[0139]

[0140] Among them, P g (Pa) represents pressure, μ mix (kg m -1 s -1 S represents the dynamic viscosity. u (kg m -2 s -2 ) is the source term of the momentum equation.

[0141] (3) Component conservation equation:

[0142]

[0143] Among them, Y i (mol m -3 ) represents the concentration of each component, D i,eff (m 2 s -1 S is the effective diffusion coefficient. i (mol m -3 s -1 ) is the source term of the component equation.

[0144] (4) Energy conservation equation:

[0145]

[0146] Among them, C p,g (J mol -1 K -1 K represents specific heat capacity, T(K) represents temperature, and k represents temperature. eff (W m -1 K -1 S is the thermal conductivity. T (W m -3 ) is the source term of the energy equation.

[0147] (5) Hydraulic conservation equation:

[0148]

[0149] Where s is the liquid water saturation, S l (kg m -3 s -1 ) is the source term of the hydraulic conservation equation.

[0150] (6) Electron potential conservation equation:

[0151]

[0152] in, (S m -1 φ is the effective conductivity. ele (V) is the electron potential, Sele (Am -3 ) is the source term of the electron potential conservation equation.

[0153] The one-dimensional partial flux conservation equation is:

[0154] (1) Components:

[0155]

[0156] Where n and n+1 represent two adjacent layers, The effective diffusion coefficient of the component is... Where δ(m) is the component concentration, and δ(m) is the layer thickness. This refers to the source term within the layer.

[0157] (2) Temperature:

[0158]

[0159] in, For effective thermal conductivity, T n (K) represents temperature. This refers to the source term within the layer.

[0160] (3) Hydraulics:

[0161]

[0162] Among them, K n (m 2 ) represents the bulk permeability. This represents the relative permeability coefficient.

[0163] (4) Membrane water content:

[0164]

[0165] Where, ρ im (kg m -3 ) represents the dry-state film density, D mw EW is the diffusion coefficient (kg mol). -1 ) represents the membrane equilibrium mass, λ n The content of membrane water, This refers to the source term within the layer.

[0166] (5) Electron potential:

[0167]

[0168] in, For effective conductivity, For electron potential, This refers to the source term within the layer.

[0169] (6) Ion potential:

[0170]

[0171] in, For effective conductivity, This is the ionic potential. This represents the intralayer source term. The electrochemical reaction rate is calculated by considering the clumping model correction in the one-dimensional model, and the calculation formula is:

[0172]

[0173]

[0174] Where, j(A m) -3 ) represents the electrochemical reaction rate, i(A m -2 ) is the reference exchange current density, A(m -1 θ represents the effective specific surface area. T R is the temperature correction factor, where R(J mol) -1 K -1 H is the universal gas constant (Pa·m). 3 mol -1 F(Cmol) is the Henry coefficient. -1 ) is Faraday constant, α is the transmission coefficient, η(V) is the overpotential, and R local (sm -1 ) represents the local gas transport resistance.

[0175] The reversible voltage can be calculated using the Nernst equation, and the formula is as follows:

[0176]

[0177] Among them, E rev (V) is the reversible voltage, ΔS(J mol) -1 K -1 ) represents entropy change.

[0178] Based on the above steps, the full-cell performance model of the proton exchange membrane fuel cell has been established, as follows: Figure 4 As shown, a non-uniform contact resistance matrix is ​​added to the performance model. Figure 4 It is a 75×180 matrix, where (1,1) represents the data in the 1st row and 1st column, and (75,180) represents the data in the 75th row and 180th column. In addition, the calculated porosity and permeability of the compressed gas diffusion layer are also added to the performance model.

[0179] Based on the above steps, the polarization curve of the output is obtained by solving this performance model, as shown in the attached figure. Figure 5As shown, the polarization curve can display the output voltage of the fuel cell at different current densities. The output voltage is mainly affected by activation loss, ohmic loss, and mass transfer loss. Through the above steps, the simulated fuel cell polarization curve is more realistic, especially in the ohmic loss segment, where it is more in line with reality.

[0180] In addition, it can output the distribution of key parameters, such as the catalyst layer current density distribution, as shown in the attached figure. Figure 6 As shown. Current density distribution is a crucial factor affecting fuel cell performance. From the attached... Figure 6 It can be seen that near the fastening bolts around the perimeter, the contact stress is greater and the contact resistance is lower due to the influence of the bolts, resulting in a higher current density. Furthermore, near the inlet on the left side, the current density is also higher due to the higher gas concentration.

[0181] Appendix Figure 7 The diagram shows the temperature distribution of the catalyst layer. The tightening of the bolts affects the contact resistance; areas with high contact resistance generate more ohmic heat. In the middle, where contact stress is low and contact resistance is high, the local temperature is higher and the distribution is more uneven. Near the left inlet, due to the high gas concentration and faster reaction rate, the heat generated is also higher. The above steps provide a more accurate representation of the internal temperature distribution of the fuel cell, which is beneficial for fuel cell thermal management and performance optimization.

Claims

1. A modeling method considering the mechanical changes and performance-related factors arising from fuel cell assembly. The fuel cell components involved in the modeling include: The model comprises end plates, insulating plates, current collectors, bipolar plates, gas diffusion layers, membrane electrode assemblies, sealing gaskets, and fastening bolts, characterized by the following steps in its establishment: (1) Establish a finite element model of the fuel cell under actual assembly. The finite element model includes three-dimensional geometric modeling, input of mechanical parameters of battery components, mesh generation, setting of contact, setting of boundary conditions, and setting of loads. (2) The components involved in the three-dimensional geometric modeling include: end plates, insulating plates, current collectors, bipolar plates, gas diffusion layers, membrane electrode assemblies, sealing gaskets, and fastening bolts. The microporous layer, catalytic layer, and proton exchange membrane are integrated into one unit. This step requires determining the geometric parameters of the components involved, including the thickness, width, and length of the end plates; the thickness, width, and length of the insulating plates; the thickness, width, and length of the current collectors; the thickness, width, and length of the bipolar plates; the thickness, width, and length of the gas diffusion layers; the thickness, width, and length of the membrane electrode assemblies; the thickness and width of the sealing gaskets; and the inner diameter, outer diameter, nut diameter, and length of the fastening bolts. (3) Input the mechanical parameters of the components involved, including: the density, Young's modulus, and Poisson's ratio of the end plate, insulating plate, current collector, bipolar plate, gas diffusion layer, membrane electrode assembly, sealing gasket, and fastening bolts. (4) Mesh generation: Use mesh generation software to generate the mesh of the components involved. At the contact area between the gas diffusion layer and the bipolar plate, the mesh density of the gas diffusion layer is twice that of the bipolar plate. (5) Setting contact states: The contact pairs of the components involved include: end plate-insulating plate, insulating plate-current collector, current collector-bipolar plate, bipolar plate-gas diffusion layer, bipolar plate-sealing gasket, and gas diffusion layer-membrane electrode assembly. (6) Setting boundary conditions: The finite element mechanical model of the fuel cell has symmetry in three directions. To reduce the amount of computation, a 1 / 8 model is selected for calculation. Symmetrical boundary conditions need to be set on the symmetrical surfaces of the end plate, insulating plate, current collector, bipolar plate, gas diffusion layer, membrane electrode assembly, and sealing gasket. Fixed boundary conditions are set on the bottom surfaces of the membrane electrode assembly and sealing gasket. (7) Set the load: Set the load on the bolt hole, and set the load to pressure. Method for calculating pressure on bolt holes: Relationship between torque and preload: In the formula, T is the torque, K is the bolt preload coefficient, F is the preload force, and d is the bolt diameter. The relationship between preload and pressure is as follows: Where P is the pressure and S is the area of ​​the bolt hole. (8) After establishing the model, solve for the surface contact stress of the gas diffusion layer and the volume of the gas diffusion layer after compression; It also includes: establishing an overall performance model of a proton exchange membrane fuel cell that considers the actual flow field structure, coupling non-uniform contact resistance, porosity and permeability into the model, and solving for the output polarization curve and the distribution of key parameters.

2. The modeling method for considering the mechanical changes and performance related to fuel cell assembly as described in claim 1, characterized in that: The specific steps for converting contact stress and compressed volume into non-uniform contact resistance, porosity, and permeability are as follows: (1) The formula for calculating contact resistance is: （1） Where R contact For contact resistance, and For variable coefficients, For contact stress, Furthermore, the obtained gas diffusion layer contact stress is non-uniform, and the calculated contact resistance is also non-uniform. (2) The formula for calculating the porosity of the gas diffusion layer after compression is: （2） in The porosity of the compressed gas diffusion layer. The volume of the gas diffusion layer before compression. This represents the volume of the gas diffusion layer after compression. The porosity of the gas diffusion layer before compression. (3) The formula for calculating the permeability of the gas diffusion layer after compression is: （3） in The permeability of the gas diffusion layer. Porosity after compression The diameter of the fibers that make up the gas diffusion layer.

3. The modeling method for considering the mechanical changes and performance related to fuel cell assembly as described in claim 1, characterized in that: The process involves establishing an overall performance model for a proton exchange membrane fuel cell that considers the actual flow field structure. This model couples non-uniform contact resistance, porosity, and permeability into the model, and then calculates the output polarization curve and the distribution of key parameters. The specific implementation steps are as follows: (1) Establish an overall performance model for the proton exchange membrane fuel cell. This model is a "three-dimensional + one-dimensional" model. The three-dimensional part includes the anode and cathode channels, the anode and cathode gas diffusion layers, and the anode and cathode extension layers. The one-dimensional part includes the anode and cathode microporous layers, the anode and cathode catalyst layers, and the proton exchange membrane. Calculation nodes are set at the interfaces of each layer to form a one-dimensional model. The one-dimensional model is stored and calculated in the extension layer. (2) The three-dimensional partial conservation equations include: (2.1) Mass conservation equation: （4） in, For density, For flow rate, For the source term of the mass conservation equation, (2.2) Momentum conservation equation: （5） in, For pressure, For dynamic viscosity, For the source term of the momentum equation, (2.3) Component conservation equation: （6） in, For the concentration of each component, For the effective diffusion coefficient, For the source terms of the component equation, (2.4) Energy conservation equation: （7） in, For specific heat capacity, For temperature, Thermal conductivity, For the source term of the energy equation, (2.5) Hydraulic conservation equation: （8） in, For liquid water saturation, For the source terms of the hydraulic conservation equation, (2.6) Electron potential conservation equation: （9） in, For effective conductivity, For electron potential, For the source term of the electron potential conservation equation, (3) In the one-dimensional part, the conservation equation is transformed into a one-dimensional flux conservation equation. Solving for each scalar in the one-dimensional part yields the following formulas: (3.1) Components: （10） Where n and n+1 represent two adjacent layers, The effective diffusion coefficient of the component is... For component concentration, For layer thickness, For in-layer source terms, (3.2) Temperature: （11） in, For effective thermal conductivity, For temperature, For in-layer source terms, (3.3) Hydraulics: （12） in, For bulk penetration rate, The relative permeability coefficient, (3.4) Membrane water content: （13） in, The dry film density, Where is the diffusion coefficient. For the membrane equilibrium mass, The content of membrane water, For in-layer source terms, (3.5) Electron potential: （14） in, For effective conductivity, For electron potential, For in-layer source terms, (3.6) Ion potential: （15） in, For effective conductivity, This is the ionic potential. For in-layer source terms, Furthermore, the electrochemical reaction rate is calculated by considering the agglomeration model in the one-dimensional model, and the calculation formula is as follows: (16) (17) in, For electrochemical reaction rate, For reference exchange current density, For effective specific surface area, This is a temperature correction factor. The universal gas constant, Henry's coefficient, It is Faraday's constant. For transmission coefficient, For overpotential, For local gas transport resistance, Furthermore, the reversible voltage is calculated using the Nernst equation, with the following formula: （18） in, It is a reversible voltage. For entropy change, (4) The non-uniform contact resistance, porosity and permeability obtained above are added to the overall model of the proton exchange membrane fuel cell, and the solution is calculated to simulate its performance. The polarization curve and the distribution of key internal parameters such as current density distribution and temperature distribution are output.

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