Dimension reduction modeling method suitable for proton exchange membrane fuel cell short stack

Abstract

The invention discloses a dimension reduction modeling method suitable for a proton exchange membrane fuel cell short stack, which is characterized in that a membrane electrode assembly is solved by adopting a one-dimensional flux equation, and a PEMFC short stack polar plate, a flow channel and a gas diffusion layer assembly are solved by adopting a three-dimensional computational domain. Comprising a mass conservation equation, a momentum conservation equation, a component conservation equation, an energy conservation equation, a liquid water equation and an electron potential conservation equation; the one-dimensional domain comprises electrochemical reaction, membrane state water, electroosmosis dragging and a flux conservation equation related to a catalytic layer and a proton exchange membrane. A three-dimensional domain calculation result is used as a one-dimensional domain boundary condition, and the one-dimensional domain calculation result is converted into a three-dimensional domain source phase and is connected with the three-dimensional domain through an expansion layer. According to the method, modeling is carried out on the PEMFC short pile, the number of grids can be reduced to one tenth of that of a traditional three-dimensional model, mass and heat transfer, electrochemical reaction, membrane water balance and other processes occurring in the PEMFC are considered, and accurate simulation can be carried out on the PEMFC pile with the activation area exceeding 300 cm < 2 > and the number of battery blocks larger than 10.

Description

Technical Field

[0001] This invention belongs to the field of fuel cell technology, specifically relating to the simulation of design to improve the efficiency of proton exchange membrane fuel cells. Background Technology

[0002] Against the backdrop of the urgent need to reduce global carbon emissions, hydrogen energy has garnered widespread attention from researchers and industry. Hydrogen is a versatile, distributed energy carrier and an ideal decarbonization fuel. In the application of hydrogen energy, fuel cells are widely regarded as the ideal power generation technology and have been a hot research topic for decades. Proton exchange membranes (PEMs), with their advantages of high power density and low operating temperature, are currently the closest to large-scale commercialization of fuel cells and have received extensive attention in their technological development.

[0003] For a single proton exchange membrane fuel cell (PEMFC), the maximum reversible voltage produced by the hydrogen-oxygen reaction under standard operating conditions is 1.229V. Considering its operating conditions and various losses, the power output of a single cell is relatively small. Therefore, in industrial applications, multiple PEMFCs are usually connected in series to form a stack to achieve higher power output. The reactant gases in each fuel cell within the stack need to be distributed through manifolds, with the inlet and outlet manifolds being the main channels for gas flow within the PEMFC stack. When multiple single cells are connected in series, due to issues such as manufacturing processes, packaging processes, and gas distribution, the operating conditions of different cells within the same stack often differ, resulting in inconsistent performance. The inconsistency problem between cells within the stack is also constantly intensifying. PEMFC inconsistency leads to poor catalyst utilization and accelerated degradation, which are currently the main reasons for the poor durability and high cost of PEMFCs. Due to limitations in experimental costs, simulation methods are crucial for analyzing PEMFC stacks, revealing and improving stack inconsistency phenomena. However, the cross-scale and complex multi-field coupling issues between the MEA (membrane electrode), BP (plate), and manifold in PEMFC stacks necessitate the use of high-resolution meshes in simulations to accurately capture both microscopic electrochemical reactions and macroscopic fluid dynamics processes. This results in extremely high computational costs, making industrial-scale simulations difficult. Furthermore, fuel cell stacks typically contain multiple individual cells, further complicating the process of conducting industrial-scale multi-field coupling simulations of PEMFC stacks. Summary of the Invention

[0004] To address the above problems, the purpose of this invention is to propose a dimensionality reduction modeling method suitable for short-stack proton exchange membrane fuel cells. This method reduces the dimensionality of the MEA and BP components of the proton exchange membrane fuel cell, solves the cross-scale problem between the MEA, BP and manifold of the stack, significantly reduces the number of meshes, and lowers the simulation cost of proton exchange membrane fuel cells, thereby achieving low-cost and high-efficiency simulation of proton exchange membrane fuel cell stacks.

[0005] The technical solution of the present invention is as follows:

[0006] A dimensionality reduction modeling method applicable to short-stack proton exchange membrane fuel cells (PEMFCs) is proposed. While the membrane electrode assembly (MEA) is solved using a one-dimensional flux equation, the electrode plates, flow channels, and gas diffusion layer components of the short-stack PEMFC are solved using a three-dimensional computational domain. The flow field portion of the three-dimensional domain undergoes equivalent dimensionality reduction and pseudo-three-dimensional modeling. Equivalent dimensionality reduction treats the ridge flow field as a porous medium, adjusting the permeability and porosity of the porous medium region based on the ridge-to-groove ratio and pressure distribution. The porous medium region is divided into a distribution zone and an activation zone, with different physical properties selected for each region to achieve similar pressure distribution. Pseudo-three-dimensional modeling involves dividing the three-dimensional domain components into only a single-layer mesh. After these simplifications, the number of meshes in the PEMFC stack is significantly reduced, thereby improving the efficiency of cross-scale simulation calculations between the MEA, electrode plates, and manifold components.

[0007] The three-dimensional domain solution includes equations for mass conservation, momentum conservation, composition conservation, energy conservation, liquid water conservation, and electron potential conservation. The one-dimensional domain solution includes flux conservation equations related to electrochemical reactions, membrane water, electroosmotic drag, and catalyst layers and proton exchange membranes. The three-dimensional domain calculation results serve as the one-dimensional domain boundary conditions, and the one-dimensional domain calculation results are transformed into the three-dimensional domain source phase. This process is performed once in each iteration step.

[0008] The specific modeling method implementation steps are as follows:

[0009] (1) The governing equations of the three-dimensional sub-model include: mass equation, momentum equation, composition equation, energy equation, liquid pressure equation, liquid water saturation equation and electron potential, etc.

[0010] (2) The flux equations in the one-dimensional model include six equations: component equation, temperature equation, liquid pressure equation, membrane water content equation, electronic potential equation, and ion potential equation.

[0011] (3) The electrochemical reaction rate was calculated using the Butler-Volmer equation modified by the agglomeration model.

[0012] Furthermore, the reversible voltage is obtained from the Nernst equation and is expressed as:

[0013]

[0014] Furthermore, based on the PEMFC three-dimensional model, dimensionality reduction modeling was performed on the membrane electrode assembly (MEA) and the bipolar plate (BP) assembly through dimensionality reduction equivalent and pseudo-three-dimensional modeling, establishing a PEMFC short-reactor dimensionality reduction model. The PEMFC short-reactor dimensionality reduction model consists of a three-dimensional computational domain and a one-dimensional computational domain. The three-dimensional computational domain includes the bipolar plate (dimensionality reduction equivalent and pseudo-three-dimensional modeling), gas channels (dimensionality reduction equivalent and pseudo-three-dimensional modeling), gas diffusion layer (pseudo-three-dimensional modeling), and anode and cathode extension layers. The extension layers include all components of the MEA (microporous layer, catalyst layer, proton exchange membrane).

[0015] The features and significance of this invention are as follows:

[0016] (1) The dimension reduction calculation model for PEMFC short stack proposed in this invention solves the cross-scale problem between manifold, plate and membrane electrode components in the PEMFC stack simulation by reducing the dimension of MEA, BP and other components. It reduces the number of grids in PEMFC short stack to one-tenth of the traditional model, greatly improving the simulation efficiency of the model. In addition, the model fully considers the mass transfer and heat transfer, electrochemical reaction and membrane water balance processes that occur in the proton exchange membrane fuel cell.

[0017] (2) The accuracy of the model is ensured by adjusting the physical properties of the porous medium region and the gas diffusion coefficient, enabling it to be applied to activated areas exceeding 300 cm². 2 This invention enables accurate simulation of PEMFC stacks with more than 10 battery cells. The model allows for detailed investigation of the short-stack manifold structure, flow characteristics, and thermal management strategies. This method significantly reduces the economic and time costs of PEMFC short-stack simulation, making it possible. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of the dimensionality reduction process of MEA components.

[0019] Figure 2 This is a schematic diagram of the dimensionality reduction equivalence and pseudo-3D modeling process.

[0020] Figure 3a In this embodiment, the activated area is 300 cm². 2 A schematic diagram of the computational domain size of a single cell in a short stack of 10 cells.

[0021] Figure 3b This is a schematic diagram of the geometric dimensions of the short stack simulation model.

[0022] Figure 4a This is a comparison chart of the simulation results of the short stack dimensionality reduction model and the polarization curves obtained from experiments in the embodiment.

[0023] Figure 4b This is a comparison chart of the short stack dimensionality reduction model and experimental results under two different electrical densities.

[0024] Figure 5a This is a comparison chart of the simulation results obtained by using the short stack dimensionality reduction model and the simulation results of a single cell in the embodiment.

[0025] Figure 5b This describes the relationship between various losses within the short stack and the cell location.

[0026] Figure 6 This is the cathode manifold streamline diagram obtained from the simulation of the short stack dimensionality reduction model in this embodiment. Detailed Implementation

[0027] The method steps of the present invention will be further described below with reference to the accompanying drawings and specific calculation examples. It should be noted that this embodiment is descriptive and not limiting, and is not intended to limit the scope of protection of the present invention.

[0028] A dimensionality reduction modeling method applicable to short-stack proton exchange membrane fuel cells (PEMFCs) is proposed. The specific implementation process is as follows: While the membrane electrode assembly (MEA) of the PEMFC is solved using a one-dimensional flux equation, the electrode plates, flow channels, and gas diffusion layer components of the short-stack PEMFC are all solved using a three-dimensional computational domain. The three-dimensional flow field is subjected to equivalent dimensionality reduction and pseudo-three-dimensional modeling. Equivalent dimensionality reduction involves treating the groove-ridge flow field as a porous medium, and adjusting the permeability and porosity of the porous medium region based on the groove-ridge ratio and pressure distribution. The porous medium region is divided into a distribution zone and an activation zone, with different physical property parameters selected for each zone to achieve similar pressure distribution. Pseudo-three-dimensional modeling involves dividing the three-dimensional domain components into only a single-layer mesh. After these simplifications, the number of meshes in the PEMFC stack is significantly reduced, thereby improving the efficiency of cross-scale simulation calculations between the MEA, electrode plates, and manifold components.

[0029] The three-dimensional domain solution includes equations for mass conservation, momentum conservation, composition conservation, energy conservation, liquid water conservation, and electron potential conservation. The one-dimensional domain solution includes flux conservation equations related to electrochemical reactions, membrane water, electroosmotic drag, and catalyst layers and proton exchange membranes. The three-dimensional domain calculation results serve as the one-dimensional domain boundary conditions, and the one-dimensional domain calculation results are transformed into the three-dimensional domain source phase. This process is performed once in each iteration step.

[0030] The specific modeling method implementation steps are as follows:

[0031] (1) Governing equations for the three-dimensional sub-model:

[0032] (1.1) Mass equation:

[0033]

[0034] (1.2) Momentum equation:

[0035]

[0036] (1.3) Component equation:

[0037]

[0038] (1.4) Energy Equation:

[0039]

[0040] (1.5) Liquid pressure equation:

[0041]

[0042] (1.6) Equation for the saturation of liquid water:

[0043]

[0044] (1.7) Electron potential equation:

[0045]

[0046] Where: ε - porosity, ρ - density (kg / m³) -3 , - Velocity vector (ms) -1 s - liquid water saturation, P - pressure (Pa), μ - viscosity (kg m³) -1 s -1 Y - component mass fraction, D eff -Effective gas diffusion coefficient m 2 s -1 C p -Specific heat capacity (J / mol) -1 K -1 T - temperature (K), k eff -Effective thermal conductivity (W / m) -1 K -1 K - Intrinsic Permeability m 2 ,k lw -Liquid phase relative permeability, -Effective electronic conductivity Sm -1 and -Electron potential V.

[0047] S m -Source phase in the mass equation (kg m) -3 s -1 ,S u -Source phase N m in the momentum equation -3 ,S i -Source phase kg m in the composition equation-3 s -1 ,S T -Source phase W m in the energy equation -3 ,S lw -The common source phase for both the liquid pressure equation and the liquid water saturation equation is kg m⁻³ s. -1 S ele -Source phase A m in the electronic potential equation -3 The subscript g represents a gas mixture, lw represents liquid water, and i represents a mixture of hydrogen, oxygen, and water vapor.

[0048] (2) The flux equations in the one-dimensional model include:

[0049] (2.1) Component equation:

[0050]

[0051] (2.2) Temperature equation:

[0052]

[0053] (2.3) Liquid pressure equation:

[0054]

[0055] (2.4) Equation for membrane water content:

[0056]

[0057] (2.5) Electron potential equation:

[0058]

[0059] (2.6) Ion potential equation:

[0060]

[0061] In each equation, the values ​​of n, 0 and 1, represent the two adjacent layers of components for each computation node. D eff -Effective gas diffusion coefficient m 2 s -1 k eff -Effective thermal conductivity W m - 1 K -1 T - temperature (K), ρ - density (kg / m³) -3 P - pressure (Pa), δ - thickness (m), C i -Gas molar concentration (mol / m) -3 EW-dry ionomer equivalent (kg mol) -1λ - membrane water content, φ - electrical potential. Subscripts im - ionomer, ion - ion, lw - liquid water, ele - electron, mw - membrane water. S i -Source phase kg m in the composition equation -3 s -1 ,S T -Source phase W m in the temperature equation -3 ,S l -Source phase in the liquid pressure equation (kg m) -3 s -1 ,S mw -Source phase m in the film water content equation -3 s -1 ,S ele -Source phase A m in the electronic potential equation -3 S ion -Source phase Am in the ionic potential equation -3 .

[0062] (3) The electrochemical reaction rate was calculated using the Butler-Volmer equation modified by the agglomeration model:

[0063]

[0064]

[0065] Where: j represents the electrochemical reaction rate, i represents the exchange current density, A represents the specific area, and θ T R represents the temperature correction factor, H represents the universal gas constant, F represents the Henry's law constant, α represents the transfer factor, and η represents the overpotential gas transport resistance. local This represents the local gas transport resistance. The superscript ref indicates the reference value, eff indicates the effective value, and the subscript a indicates the anode, c indicates the cathode, pt indicates the platinum loading, H2 indicates hydrogen, and O2 indicates oxygen.

[0066] Furthermore, the reversible voltage is obtained from the Nernst equation and is expressed as:

[0067]

[0068] Where: ΔS represents the entropy change of the electrochemical reaction, P H2,a P represents the inlet hydrogen pressure. O2,c T represents oxygen pressure. ref P represents the reference temperature. ref The reference pressure is represented by the subscript 'a', which indicates the anode and 'c', which indicates the cathode.

[0069] The proton exchange membrane fuel cell is subjected to dimensionality reduction equivalence and pseudo-3D modeling in the three-dimensional domain. In the dimensionality reduction equivalence step, the specific structure of the real flow field is ignored, and the flow fields of the anode and cathode are equivalent to porous media. The pressure distribution is changed by adjusting the permeability of the porous media region, so as to ensure the similarity of flow characteristics.

[0070] In the pseudo-3D modeling step, only a single-layer mesh is divided for the anode and cathode channels and the anode and cathode gas diffusion layers (GDL) in the fuel cell. The current density distribution is modified by changing the diffusion coefficient of liquid water to ensure the similarity of electrochemical characteristics.

[0071] Figure 1 This is a schematic diagram of the MEA dimensionality reduction model. The MEA dimensionality reduction model consists of a three-dimensional domain and a one-dimensional domain. The three-dimensional domain includes the bipolar plate, gas channel, gas diffusion layer, and extended layers in the anode and cathode, while the one-dimensional domain is solved in the extended layers.

[0072] Figure 2 This diagram illustrates the dimensionality reduction and equivalence process of the short-reactor model. The short-reactor model simplifies the fuel cell stack structure twice based on the MEA dimensionality reduction model. The first simplification ignores the specific structure of the actual flow field, treating the anode and cathode flow fields as equivalent to a porous medium. The second simplification divides the anode and cathode channels and the anode and cathode GDL into only a single-layer mesh. Through these simplifications, the number of meshes in the short-reactor model is significantly reduced, enabling high-efficiency simulation of the proton exchange membrane fuel cell short-reactor.

[0073] Figure 3a The activated area is 300cm². 2 A schematic diagram of the computational domain size of a single cell in a short stack of 10 batteries. The single cells are divided into activation and distribution regions due to differences in flow and reaction characteristics, and are outlined with dashed lines in the diagram. Figure 3b This is a schematic diagram of the short stack dimensions. The cells in the short stack are numbered 1-10 from bottom to top. The reaction gases and coolant are supplied and discharged centrally through the manifold structure shown in the diagram.

[0074] The equations for mass conservation, momentum conservation, component conservation, energy conservation, liquid water conservation, and electronic potential conservation within the fuel cell are solved in a three-dimensional sub-model; the flux conservation equations related to electrochemical reactions, membrane water, and the catalyst layer and proton exchange membrane are solved in a one-dimensional sub-model.

[0075] The conservation equations are partial differential equations, solved using the finite volume method. First, the conservation equations are discretized using the finite volume method, dividing the entire computational domain into several control volumes (grid cells). The corresponding conservation equations are then solved within each control volume. During the solution process, the partial differential equations within the grid cells need to be transformed into linear algebraic equations. Then, an iterative method is used to solve the equations step by step, updating the variables such as flow velocity, pressure, temperature, and concentration in the conservation equations at each iteration until the convergence criteria are met.

[0076] (2) The governing equations for the one-dimensional sub-model are as follows:

[0077] (2.1) Component equation:

[0078]

[0079] (2.2) Temperature equation:

[0080]

[0081] (2.3) Hydraulic equation:

[0082]

[0083] (2.4) Equation for membrane water content:

[0084]

[0085] (2.5) Electron potential equation:

[0086]

[0087] (2.6) Ion potential equation:

[0088]

[0089] In the one-dimensional computational domain, the conservation equations for gas component concentration, temperature, hydraulic pressure, etc., which are solved in the three-dimensional computational domain, are transformed into flux equations for one-dimensional nodes. In addition, equations related to the catalytic layer and proton exchange membrane, such as electrochemical reactions and membrane water, are also described as flux equations.

[0090] In the flux equation, only the diffusion effect along the thickness direction is considered. The flux equation in the one-dimensional computational domain is also solved step by step in each iteration using an iterative method. During computation, the scalar values ​​solved in the three-dimensional computational domain provide boundary conditions for the one-dimensional computational domain. At the same time, the solution results in the one-dimensional computational domain provide the necessary physical parameters and source terms for the three-dimensional computational domain. Each iteration process realizes the data exchange between the two computational domains.

[0091] (3) Electrochemical reactions were calculated using the Butler-Volmer equation modified by the agglomeration model:

[0092]

[0093] In this embodiment, R = 8.314 J mol -1 K -1 F = 96487.0 C mol -1 α a =0.5, αc =0.5, A im =4.0×10 7 m -1 ,

[0094] 2. Dimensionality reduction and pseudo-3D modeling are performed on the 3D domain. The specific process is as follows:

[0095] (1) Dimensionality reduction and simplified modeling transforms the traditional groove and ridge flow field structure into a porous medium, thereby significantly reducing the number of grids. The values ​​of the physical properties (porosity and permeability) of the porous medium region are based on the following:

[0096] For porosity, in order to ensure that the equivalent flow field is the same as the actual structural fluid flow space, the ribs and channel widths of the reactants are used for calculation, and the calculation formula is shown in Equation (17):

[0097]

[0098] Where ε eq W represents the porosity of the equivalent porous medium region. ch and W rib These represent the channel width and the ridge width, respectively. For the actual flow field selected in this example, the channel-to-ridge ratio of both the distribution zone and the activation zone is 1.0, therefore the porosity of the equivalent porous medium region is 0.5.

[0099] For permeability, the pressure distribution of the actual flow field under the same working conditions was used as a basis, and the values ​​of the distribution zone and the activation zone (the locations of the distribution zone and the activation zone are shown in Figure 3) were adjusted to make the pressure distribution approximate the actual flow field. Table 1 shows the porosity and permeability values ​​of the equivalent porous medium in this example.

[0100] Table 1. Porosity and permeability values ​​of the equivalent porous media region.

[0101]

[0102]

[0103] (2) In pseudo-3D modeling, only a single-layer mesh is used for the anode and cathode channels and the anode and cathode GDL, further reducing the number of meshes. At the same time, the gas diffusion coefficient correction is adjusted to offset the calculation error caused by mesh simplification. For this example, the Bruggman coefficient of water vapor in the single-layer mesh is corrected to 3.0, which is the same as the simulation result of the multi-layer mesh.

[0104] 3. Simulation model verification and application, the specific process is as follows:

[0105] This embodiment uses experimental data from the Toyota MIRAI Gen 2 short-reactor reactor to validate the model. (Appendix) Figure 4aThe figure shows a comparison between the simulation results of the short-reactor model and the polarization curves obtained from the experiment. It can be seen from the figure that the error of each point in the polarization curve of the short-reactor model and the experimental results is controlled within 5%, which proves that the simulation accuracy of the model is high and can accurately reflect the working characteristics of the proton exchange membrane fuel cell.

[0106] Appendix Figure 4b This is a comparison chart of the short-stack dimensionality reduction model and experimental results under two different energy densities. The comparison reveals that the fuel cell performance obtained from simulation and experiment exhibits a parabolic distribution with "lower performance in the middle and higher performance at both ends" as the position changes. This indicates that the model can accurately reflect the influence of heat and mass transfer on the cells at different locations within the stack.

[0107] Appendix Figure 5a The results are compared between simulations using a short-reactor model and a single-cell model. The comparison reveals that the single-cell simulation model fails to account for the "restrictive" effect of the manifold on water vapor diffusion. Therefore, the single-cell model's simulation results are lower at low charge density and higher at high charge density, demonstrating that the short-reactor simulation is more accurate than the single-cell simulation.

[0108] Appendix Figure 5b This demonstrates the relationship between various losses within the short stack and the cell location. The results prove that the short stack dimensionality reduction model can reflect the impact of manifold distribution, fluid flow, and stack heat distribution on stack performance and consistency. This modeling and simulation improves the simulation efficiency of proton exchange membrane fuel cell short stacks by more than 10 times.

[0109] Appendix Figure 6 This demonstrates the velocity streamline distribution in the cross-section of the cathode manifold obtained by simulating different cathode manifold diameters using this model. The results show that as the cathode manifold diameter decreases, the flow dead zone within the manifold (the area highlighted by the dashed line in the figure) is reduced, altering the streamline distribution within the manifold and thus affecting the flow distribution.

Claims

1. A dimensionality reduction modeling method applicable to short stacks of proton exchange membrane fuel cells, characterized in that: In addition to solving the membrane electrode assembly (MEA) of a proton exchange membrane fuel cell (PEMFC) using a one-dimensional flux equation, the short stack plates, flow channels, and gas diffusion layer components are all solved using a three-dimensional computational domain. The three-dimensional flow field is subjected to equivalent dimensionality reduction and pseudo-three-dimensional modeling. Equivalent dimensionality reduction involves treating the groove-ridge flow field as a porous medium and adjusting the permeability and porosity of the porous medium region based on the groove-ridge ratio and pressure distribution. The porous medium region is divided into a distribution zone and an activation zone, with different physical property parameters selected for each zone to achieve similar pressure distribution. Pseudo-three-dimensional modeling involves dividing the three-dimensional domain components into only a single-layer mesh. After these simplifications, the number of meshes in the PEMFC stack is significantly reduced, thereby improving the efficiency of cross-scale simulation calculations between the MEA, plates, and manifold components. The three-dimensional domain solution includes equations for mass conservation, momentum conservation, composition conservation, energy conservation, liquid water conservation, and electron potential conservation. The one-dimensional domain solution includes flux conservation equations related to electrochemical reactions, membrane water, electroosmotic drag, and the catalyst layer and proton exchange membrane. The three-dimensional domain calculation results serve as the boundary conditions for the one-dimensional domain, and the one-dimensional domain calculation results are transformed into the three-dimensional domain source phase. This process is performed once in each iteration step. The specific modeling method implementation steps are as follows: (1) Governing equations for the three-dimensional sub-model: (1.1) Mass equation: (1.2) Momentum equation: (1.3) Component equation: (1.4) Energy Equation: (1.5) Liquid pressure equation: (1.6) Equation for the saturation of liquid water: (1.7) Electron potential equation: Where: ε represents porosity, and ρ represents density. The vector represents velocity, s represents liquid water saturation, P represents pressure, μ represents viscosity, Y represents component mass fraction, and D represents the velocity vector. eff C represents the effective gas diffusion coefficient. p Specific heat capacity is represented by T, temperature is represented by kJ / kJ. eff K represents the effective thermal conductivity, and K represents the intrinsic permeability. lw Indicates the relative permeability of the liquid phase. Indicates effective electronic conductivity and Represents electron potential, S m S represents the source phase in the mass equation. u S represents the source phase in the momentum equation. i S represents the source phase in the composition equation. T S represents the source phase in the energy equation. lw S represents the common source phase in both the liquid pressure equation and the liquid water saturation equation. ele The symbol represents the source phase in the electron potential equation; the subscript g represents a gas mixture; lw represents liquid water; and i represents the hydrogen, oxygen, and water vapor components. (2) The flux equations in the one-dimensional model include: (2.1) Component equation: (2.2) Temperature equation: (2.3) Liquid pressure equation: (2.4) Equation for membrane water content: (2.5) Electron potential equation: (2.6) Ion potential equation: In each equation, the values ​​of n, 0 and 1, represent the two adjacent layers of components for each computation node, D. eff k represents the effective gas diffusion coefficient. eff The effective thermal conductivity is represented by T, temperature by ρ, density by P, pressure by δ, and thickness by C. i The expression represents the gas molar concentration, EW represents the dry ionomer equivalent, λ represents the membrane water content, φ represents the potential, and the subscripts im represent ionomer, ion represent ions, lw represent liquid water, ele represent electrons, mw represent membrane water, and S i S represents the source phase in the composition equation. T S represents the source phase in the temperature equation. l S represents the source phase in the liquid pressure equation. mw S represents the source phase in the membrane water content equation. ele S represents the source phase in the electron potential equation. ion This represents the source phase in the ionic potential equation. (3) The electrochemical reaction rate was calculated using the Butler-Volmer equation modified by the agglomeration model: Where: j represents the electrochemical reaction rate, i represents the exchange current density, A represents the specific area, and θ T R represents the temperature correction factor, H represents the universal gas constant, F represents the Henry's law constant, α represents the transfer factor, and η represents the overpotential gas transport resistance. local This represents the local gas transport resistance. The superscript ref indicates the reference value, eff indicates the effective value, and the subscripts a, c, pt, pt, H2, and O2 represent oxygen. Furthermore, the reversible voltage is obtained from the Nernst equation and is expressed as: Where: ΔS represents the entropy change of the electrochemical reaction, Represents the inlet hydrogen pressure. T represents oxygen pressure. ref P represents the reference temperature. ref The reference pressure is represented by the subscript 'a', which indicates the anode and 'c', which indicates the cathode.

2. The dimensionality reduction modeling method for short proton exchange membrane fuel cell stacks according to claim 1, characterized in that: The proton exchange membrane fuel cell undergoes dimensionality reduction and pseudo-3D modeling in its three-dimensional domain. In the dimensionality reduction step, the specific structure of the actual flow field is ignored, and the flow fields of the anode and cathode are equivalent to porous media. The pressure distribution is changed by adjusting the permeability of the porous media region, thereby ensuring the similarity of flow characteristics.

3. The dimensionality reduction modeling method for short stacks of proton exchange membrane fuel cells according to claim 1 or 2, characterized in that: The pseudo-3D modeling step involves dividing the anode and cathode channels and anode and cathode gas diffusion layers in the fuel cell into a single-layer mesh. The current density distribution is modified by changing the liquid water diffusion coefficient, thereby ensuring the similarity of electrochemical characteristics.

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