CN115510679A - A modeling approach that considers the mechanical changes associated with fuel cell assembly and performance - Google Patents

Abstract

The invention discloses a modeling method that considers the mechanical changes and performance related to fuel cell assembly. In order to construct a three-dimensional model of a proton exchange membrane fuel cell under real assembly, the material properties of each component and the contact between each component are set. relationship, set the boundary conditions of the model and set the applied load, thus establishing the finite element model of fuel cell mechanics. The contact stress distribution of the gas diffusion layer and the bipolar plate interface and the compressed volume of the gas diffusion layer are obtained through the model; they are converted into non-uniform contact resistance, porosity and permeability; and then input into the fuel cell performance model, Perform calculations; finally obtain the polarization curve and the distribution of key parameters under real assembly and preload. This model helps to obtain the optimal preload of the fuel cell intuitively, quickly and accurately, and at the same time obtains the distribution inside the battery to help understand the relationship between the mechanical behavior of the battery and the output performance.

Description

A modeling approach that considers mechanical changes associated with fuel cell assembly and performance

technical field

The invention belongs to the fuel cell technology, and in particular relates to a modeling method for the correlation between the change of the mechanical behavior of the fuel cell and the performance of the cell in the actual assembly process.

Background technique

The proton exchange membrane fuel cell is an energy conversion device that can convert the chemical energy in hydrogen and oxygen into electrical energy. It has the advantages of high power density, rapid response and zero emissions. It is considered to be the most potential power device to replace the internal combustion engine. one. Proton exchange membrane fuel cells can be widely used in aviation, submarines, power stations and fuel cell vehicles and other fields.

The proton exchange membrane fuel cell consists of end plates, insulating plates, collector plates, bipolar plates, gas diffusion layers, microporous layers, catalytic layers, proton exchange membranes, sealing gaskets, and fastening bolts. In order to obtain higher output power, most of the battery stacks on fuel cell vehicles are composed of 300-400 single cells. During the assembly process, many mechanical behaviors will occur inside the battery. For example, the state or degree of contact between the bipolar plate and the gas diffusion layer will produce different mechanical behaviors. Too low contact stress will lead to higher contact resistance, resulting in greater electronic ohmic loss; while too large contact stress will reduce the thickness, porosity, and permeability of the gas diffusion layer, hinder gas transmission, and increase mass transfer loss.

At present, testing the preload force of fuel cell assembly is mainly through experiments to detect the battery performance under different preload forces, but the experimental process is time-consuming and expensive. At present, there are some simulation models to study the influence of fuel cell assembly on the change of gas diffusion layer parameters, but there are mainly two problems. One is that the model is modeled separately for the two components of the bipolar plate and the gas diffusion layer, and a uniform pressure is applied to study the stress and strain of the gas diffusion layer under different pressures, without taking into account the actual assembly of the battery. The second is that the currently established model separates the mechanical behavior from the change in performance, and does not comprehensively consider the impact of the change in mechanical behavior caused by the assembly preload on performance, and cannot give the optimal preload for the highest performance.

If it is possible to establish a simulation model that considers the changes in the mechanical behavior of the assembly preload force and the battery performance, and obtain the parameter changes, stress distribution, and strain of the key components of the fuel cell, and these changes can be taken into account in the full battery performance model, Outputting the performance of fuel cells under different preloads and the distribution of key parameters must become a demand in the field of fuel cells.

Contents of the invention

In view of the above existing problems, the present invention proposes a modeling method that considers the mechanical changes and performance related to fuel cell assembly, which can simulate the actual assembly of the fuel cell to the internal mechanical behavior of the battery, and obtain the gas due to battery assembly. Changes in the parameters of the diffusion layer, including contact resistance, porosity, and permeability, and then introduce the changes brought about by the mechanical behavior into the full battery model, simulate the performance of the battery under different preloads, and output the polarization curve to obtain the best prediction. The magnitude of the tightening force realizes the coupling of mechanical behavior and performance. This model helps to obtain the optimal preload of the fuel cell intuitively, quickly and accurately, and at the same time obtains the distribution inside the battery to help understand the relationship between the mechanical behavior of the battery and the output performance.

The present invention adopts following technical scheme and steps:

A modeling method that considers the mechanical changes and performance related to fuel cell assembly. The fuel cell components involved in the modeling include: end plates, insulating plates, collector plates, bipolar plates, gas diffusion layers, membrane electrode assemblies, and sealing gaskets and fastening bolts etc. The establishment of the model includes the following steps:

(1) Establish a mechanical finite element model of the fuel cell under real assembly. The finite element model includes three-dimensional geometric modeling, input of mechanical parameters of battery components, grid division, setting of contacts, setting of boundary conditions, and setting of loads.

(2) The components involved in three-dimensional geometric modeling are: end plate, insulating plate, current collector plate, bipolar plate, gas diffusion layer, membrane electrode assembly, sealing gasket and fastening bolts, among which the microporous layer, catalytic The layer and the proton exchange membrane are integrated into one. In this step, it is necessary to determine the geometric parameters of the components involved: end plate thickness, width, and length; insulating plate thickness, width, and length; collector plate 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, width; and fastening bolt inner diameter, outer diameter, nut diameter, and length.

(3) Input the mechanical parameters of the involved components including: density, Young's modulus and Poisson's ratio of end plates, insulating plates, current collector plates, bipolar plates, gas diffusion layers, membrane electrode assemblies, sealing gaskets and fastening bolts .

(4) Carry out grid division: Use grid division software to divide the grid of the parts involved. At the contact position between the gas diffusion layer and the bipolar plate, the grid density of the gas diffusion layer is equal to the grid density of the bipolar plate. double.

(5) Set the contact state: the contact pairs of the involved parts include: end plate-insulating plate, insulating plate-current collector plate, current collector plate-bipolar plate, bipolar plate-gas diffusion layer, bipolar plate-sealing gasket , Gas diffusion layer - membrane electrode assembly.

(6) Set the boundary conditions: the finite element mechanical model of the fuel cell has symmetry in three directions. In order to reduce the calculation amount, a 1/8 model is selected for calculation. Symmetrical boundary conditions are set on the symmetrical surfaces of the gas diffusion layer, membrane electrode assembly, and sealing gasket, and fixed support boundary conditions are set on the bottom surface of the membrane electrode assembly and sealing gasket.

(7) Set the load: set the load on the bolt hole, and set the load as pressure.

The calculation method of the pressure on the bolt hole:

The relationship between torque and pre-tightening force: T=K×F×d, where T is the torque, K is the bolt pre-tightening coefficient, F is the pre-tightening force, 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.

(8) After the model is established, the surface contact stress of the gas diffusion layer and the compressed volume of the gas diffusion layer are obtained by solving the solution.

Further, after the mechanical finite element model of the fuel cell is established, the preload torque is applied to obtain the contact stress distribution on the interface between the gas diffusion layer and the bipolar plate, and the volume of the gas diffusion layer after compression.

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

The formula for calculating contact resistance is:

The obtained contact stress of the gas diffusion layer is inhomogeneous, so the calculated contact resistance is also an inhomogeneous contact resistance distribution.

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

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

The fuel cell full cell performance model established is a "three-dimensional + one-dimensional" model, and the three-dimensional part includes cathode and anode flow channels, cathode and anode gas diffusion layers, and cathode and anode expansion layers. The one-dimensional part includes cathode and anode microporous layer, cathode and anode catalytic layer and proton exchange membrane. Set computing nodes on the interface of each layer to form a one-dimensional model. The 1D part is set to be stored and computed in the extension layer.

The conservation equations for the three-dimensional part include:

(1) Mass conservation equation

(2) Momentum conservation equation

(3) Component conservation equation

(4) Energy Conservation Equation

(5) Hydraulic conservation equation

(6) Electron potential conservation equation

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

(1) Components

(2) temperature

(3) hydraulic pressure

(4) Membrane water content

(5) Electron potential

(6) Ion potential

Furthermore, the electrochemical reaction rate is calculated by considering the caking model correction in the one-dimensional model, the specific calculation formulas are as (16) and (17), and the reversible voltage is calculated by the Nernst equation, as in (18).

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

Features and benefits of the present invention are:

(1) A quantitative relationship between the fuel cell mechanical behavior change and battery performance under real assembly is proposed, which can comprehensively consider the real assembly of the fuel cell, and obtain the key parameters of the gas diffusion layer due to its mechanical behavior Changes, and then input into the performance simulation model to calculate its performance. Compared with the experimental method that has been used all the time, it is helpful to obtain the optimal assembly pressure of fuel cells intuitively, quickly and accurately, understand its internal mechanical behavior, understand the relationship between its mechanical behavior and performance, and propose optimization for fuel cell assembly .

(2) The mechanical finite element model established 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 relationship between various components. In addition, this model can also extract the inhomogeneous contact stress distribution on the surface of the gas diffusion layer, which can later be converted into inhomogeneous contact resistance.

(3) The established "three-dimensional + one-dimensional" performance model can fully consider the form and structure of the fuel cell flow field, is true and accurate, and can be calculated on a large-area flow field plate. In addition, the present invention also takes into account non-uniform contact resistance distribution, porosity variation, and permeability variation. Compared with the traditional three-dimensional performance model, the calculation of this model is fast, the convergence is good, and the uneven contact resistance inside the battery is taken into account.

Description of drawings

Accompanying drawing 1 is the principle block diagram of the steps of the modeling process of the present invention.

Accompanying drawing 2 is the schematic diagram of the mechanical finite element model in the example calculation.

Accompanying drawing 3 is a schematic diagram of the performance model in the example calculation.

Accompanying drawing 4 is a schematic diagram of the processing method of uneven contact resistance in the example calculation.

Accompanying drawing 5 is the output polarization curve in the example calculation.

Accompanying drawing 6 is the cloud diagram of the current density distribution output in the example calculation.

Accompanying drawing 7 is the temperature distribution cloud map output in the example calculation.

detailed description

The technical solution of the present invention will be described in detail below in conjunction with the accompanying drawings and examples. It should be noted that this example is illustrative rather than limiting, and does not limit the protection scope of the present invention.

A modeling method that considers the mechanical changes and performance related to fuel cell assembly. The fuel cell components involved in the modeling include: end plates, insulating plates, collector plates, bipolar plates, gas diffusion layers, membrane electrode assemblies, and sealing gaskets and fastening bolts.

The mechanical finite element model of the fuel cell and the full cell performance model of the fuel cell in this example are non-limiting. As shown in Figure 1. The principle of the overall steps of the present invention is to construct a three-dimensional model of a proton exchange membrane fuel cell under real assembly, set the material properties of each component, set the contact relationship between each component, set the boundary conditions of the model and set the applied load, thereby establishing a fuel cell Finite element model of battery mechanics. Obtain the contact stress distribution of the gas diffusion layer and the bipolar plate interface and the compressed volume of the gas diffusion layer through the model; convert it into non-uniform contact resistance, porosity and permeability; then input it into the fuel cell performance model, Perform calculations; finally obtain the polarization curve and the distribution of key parameters under real assembly and preload. Considering the mechanical changes produced by fuel cell assembly and the establishment of performance-related models include the following steps:

(1) Establish a mechanical finite element model of the fuel cell under real assembly. The finite element model includes three-dimensional geometric modeling, input of mechanical parameters of battery components, grid division, setting of contacts, setting of boundary conditions, and setting of loads.

(2) The components involved in three-dimensional geometric modeling are: end plate, insulating plate, current collector plate, bipolar plate, gas diffusion layer, membrane electrode assembly, sealing gasket and fastening bolts, among which the microporous layer, catalytic The layer and the proton exchange membrane are integrated into one. In this step, it is necessary to determine the geometric parameters of the components involved: end plate thickness, width, and length; insulating plate thickness, width, and length; collector plate 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, width; and fastening bolt inner diameter, outer diameter, nut diameter, and length.

(3) Input the mechanical parameters of the involved components including: density, Young's modulus and Poisson's ratio of end plates, insulating plates, current collector plates, bipolar plates, gas diffusion layers, membrane electrode assemblies, sealing gaskets and fastening bolts .

(4) Carry out grid division: Use grid division software to divide the grid of the parts involved. At the contact position between the gas diffusion layer and the bipolar plate, the grid density of the gas diffusion layer is equal to the grid density of the bipolar plate. double.

(5) Set the contact state: the contact pairs of the involved parts include: end plate-insulating plate, insulating plate-current collector plate, current collector plate-bipolar plate, bipolar plate-gas diffusion layer, bipolar plate-sealing gasket , Gas diffusion layer - membrane electrode assembly.

(6) Set the boundary conditions: the finite element mechanical model of the fuel cell has symmetry in three directions. In order to reduce the calculation amount, a 1/8 model is selected for calculation. The symmetrical boundary conditions are set on the two symmetrical surfaces of the gas diffusion layer, the membrane electrode assembly and the sealing gasket, and the fixed support boundary conditions are set on the bottom surface of the membrane electrode assembly and the sealing gasket.

(7) Set the load: set the load on the bolt hole, and set the load as pressure. In the calculation of the pressure on the bolt hole, the relationship between the torque and the preload is: T=K×F×d. In the formula, T is the torque, K is the bolt pre-tightening coefficient, F is the pre-tightening force, 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.

(8) After the model is established, the surface contact stress of the gas diffusion layer and the compressed volume of the gas diffusion layer are obtained by solving the solution.

The specific implementation steps of converting contact stress and compressed volume into non-uniform contact resistance, porosity and permeability are as follows:

(1) The calculation formula of contact resistance is:

Among them, R _contact is the contact resistance, α and β are variable coefficients, and P _contact is the contact stress.

Furthermore, the obtained contact stress of the gas diffusion layer is inhomogeneous, and the calculated contact resistance is also inhomogeneous.

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

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

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

(1) Establish the performance model of the proton exchange membrane fuel cell full cell. This model is a "three-dimensional + one-dimensional" model. The three-dimensional part includes the cathode and anode flow channels, the cathode and anode gas diffusion layer, and the cathode and anode expansion layer; the one-dimensional part includes the cathode and anode. The ultra-microporous layer, cathode and anode catalytic layer and proton exchange membrane, set calculation nodes on the interface of each layer to form a one-dimensional model, set the one-dimensional part in the extension layer for storage and calculation,

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

(2.1) Mass conservation equation:

(2.2) Momentum conservation equation:

(2.3) Component conservation equation:

(2.4) Energy conservation equation:

(2.5) Hydraulic conservation equation:

(2.6) Electron potential conservation equation:

(3) In the one-dimensional part, the conservation equation is transformed into a one-dimensional flux conservation equation, and each scalar is solved in the one-dimensional part. The calculation formula of each scalar is:

(3.1) Components:

(3.2) Temperature:

(3.3) Hydraulic pressure:

(3.4) Membrane water content:

(3.5) Electron potential:

(3.6) Ion potential:

Considering the caking model correction in the one-dimensional model to calculate the electrochemical reaction rate, the calculation formula is:

The reversible voltage is calculated by the Nernst equation, and the calculation formula is:

(4) Add and couple the inhomogeneous contact resistance, porosity and permeability obtained from the above calculations into the full cell model of the proton exchange membrane fuel cell, solve the calculation, simulate its performance, and output the polarization curve and internal key parameters Distribution such as current density distribution, temperature distribution.

Example

First, a mechanical finite element model considering the actual assembly of the proton exchange membrane fuel cell was established to obtain the surface contact stress and the compressed volume of the gas diffusion layer. The contact stress and compressed volume are then converted to inhomogeneous contact resistance, porosity, and permeability. Based on this, a proton exchange membrane fuel cell full-cell performance model considering the real flow field structure is established, and the non-uniform contact resistance, porosity and permeability are coupled into the model, and the output polarization curve and the distribution of key parameters are solved and calculated. Specifically:

1. Establish the three-dimensional geometry of the mechanical finite element model of the proton exchange membrane fuel cell, as shown in Figure 2. Set material properties for each part involved, including density, Young's modulus, and Poisson's ratio. End plate density 2800kg m ^-3 , Young's modulus 2.0e5MPa, Poisson's ratio 0.33; insulation board density 1420kg m ^-3 , Young's modulus 1000MPa, Poisson's ratio 0.38; collector plate density 8940kg m ^-3 , Young's ratio Modulus 1.2e5MPa, Poisson's ratio 0.33; bipolar plate density 2250kg m ^-3 , Young's modulus 1.0e4MPa, Poisson's ratio 0.25; gas diffusion layer density 440kg m ^-3 , Young's modulus 10MPa, Poisson's ratio 0.1 ; MEA density 2000kg m ^-3 , Young's modulus 320MPa, Poisson's ratio 0.25; gasket density 1000kg m ^-3 , Young's modulus 100MPa, Poisson's ratio 0.4.

2. Set the contact relationship of each component. Tangential and normal contacts are set between the end plate-insulating plate, the insulating plate-collecting plate, the collecting plate-bipolar plate, the bipolar plate-gas diffusion layer, and the bipolar plate-sealing gasket. Set the binding relationship between the gas diffusion layer-membrane electrode assembly.

3. Set the boundary conditions of each component. Set symmetrical boundary conditions on the end plate, insulating plate, current collector plate, bipolar plate, gas diffusion layer, membrane electrode assembly, and sealing gasket along the two directions of flow field symmetry, and set fixed supports on the bottom surface of the sealing gasket and membrane electrode assembly Boundary conditions.

4. Set the payload. Set the load on the bolt hole contact face of the end plate, selected as pressure. Its calculation method is as follows:

Torque and preload: T=K×F×d.

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

In this example, the torque T is selected as 3Nm, the bolt diameter is 6.4mm, and the bolt hole area is 121.77mm ² . From this the pressure applied to each bolt hole can be calculated.

5. Based on the above steps, the mechanical finite element model of the proton exchange membrane fuel cell considering the actual assembly is established. After solving, the contact stress distribution on the interface between the gas diffusion layer and the bipolar plate and the volume of the compressed gas diffusion layer can be obtained.

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

Contact resistance calculation formula:

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

The obtained contact stress of the gas diffusion layer is inhomogeneous, so the calculated contact resistance is also an inhomogeneous contact resistance distribution.

The formula for calculating porosity is:

In this calculation, it is 530 mm ³ , V _c is the volume of the gas diffusion layer after compression, and ε _i is 0.7 in this calculation.

The formula for calculating permeability is:

8 μm in this calculation.

7. Establish the full cell performance model of proton exchange membrane fuel cell. The schematic diagram of the model geometry is shown in Figure 3. This model is a "3D + 1D" model. The three-dimensional part includes cathode and anode distribution areas, cathode and anode flow fields, cathode and anode gas diffusion layers, and cathode and anode expansion layers. Store and compute 1D models in the cathode and anode extension layers. The one-dimensional model includes the cathode and anode microporous layer, the cathode and anode catalytic layer and the proton exchange membrane. The computing nodes of the one-dimensional part are selected on the interface between layers.

The calculation formula for this performance model is as follows:

The three-dimensional partial conservation equation is:

(1) Mass conservation equation:

(m s^-1)为流速，S_m(kg m^-3s^-1)为质量守恒方程源项。Among them, ρ _g (kg m ^-3 ) is the density,

(ms ^-1 ) is the flow rate, and S _m (kg m ^-3 s ^-1 ) is the source term of the mass conservation equation.

(2) Momentum conservation equation:

Among them, P _g (Pa) is the pressure, μ _mix (kg m ^-1 s ^-1 ) is the dynamic viscosity, and S _u (kg m ^-2 s ^-2 ) is the source term of the momentum equation.

(3) Component conservation equation:

Among them, Y _i (mol m ^-3 ) is the concentration of each component, D _i,eff (m ² s ^-1 ) is the effective diffusion coefficient, and S _i (mol m ^-3 s ^-1 ) is the source term of the composition equation.

(4) Energy conservation equation:

Among them, C _p,g (J mol ^-1 K ^-1 ) is specific heat capacity, T(K) is temperature, k ^eff (W m ^-1 K ^-1 ) is thermal conductivity, S _T (W m ^-3 ) is energy Equation source term.

(5) Hydraulic conservation equation:

Among them, s is the liquid water saturation, and S _l (kg m ^-3 s ^-1 ) is the source term of the hydraulic conservation equation.

(6) Electron potential conservation equation:

(S m^-1)为有效电导率，φ_ele(V)为电子电势，S_ele(Am^-3)为电子电势守恒方程源项。in,

(S m ^-1 ) is the effective conductivity, φ _ele (V) is the electron potential, and S _ele (Am ^-3 ) is the source term of the electron potential conservation equation.

The one-dimensional partial flux conservation equation is:

(1) Components:

为组分有效扩散系数，

为组分浓度，δ(m)为层厚度，

为层内源项。Among them, n and n+1 represent two adjacent layers,

is the effective diffusion coefficient of the component,

is the component concentration, δ(m) is the layer thickness,

is the source item in the layer.

(2) Temperature:

为有效导热系数，Tⁿ(K)为温度，

为层内源项。in,

is the effective thermal conductivity, T ⁿ (K) is the temperature,

is the source item in the layer.

(3) Hydraulic pressure:

为相对渗透率系数。Among them, K ⁿ (m ² ) is bulk permeability,

is the relative permeability coefficient.

(4) Membrane water content:

为层内源项。Among them, ρ _im (kg m ^-3 ) is the dry film density, D _mw is the diffusion coefficient, EW (kg mol ^-1 ) is the equilibrium mass of the film, λ ⁿ is the film water content,

is the source item in the layer.

(5) Electron potential:

为有效电导率，

为电子电势，

为层内源项。in,

is the effective conductivity,

is the electron potential,

is the source item in the layer.

(6) Ion potential:

为有效电导率，

为离子电势，

为层内源项。在一维模型中考虑结块模型修正计算电化学反应速率，计算公式为:in,

is the effective conductivity,

is the ionic potential,

is the source item in the layer. Considering the caking model correction in the one-dimensional model to calculate the electrochemical reaction rate, the calculation formula is:

Among them, j(A m ^-3 ) is the electrochemical reaction rate, i(A m ^-2 ) is the reference exchange current density, A(m ^-1 ) is the effective specific surface area, θ _T is the temperature correction coefficient, R(J mol ^-1 K ^-1 ) is the universal gas constant, H (Pa m ³ mol ^-1 ) is the Henry coefficient, F (Cmol ^-1 ) is the Faraday constant, α is the transmission coefficient, η (V) is the overpotential, R _local ( sm ^-1 ) is the local gas transport resistance.

The reversible voltage is calculated by the Nernst equation, and the calculation formula is:

Wherein, E _rev (V) is the reversible voltage, and ΔS(J mol ^-1 K ^-1 ) is the entropy change.

Based on the above steps, the full cell performance model of the proton exchange membrane fuel cell is established, as shown in Figure 4, the non-uniform contact resistance matrix is added to the performance model. Figure 4 is a 75×180 matrix, where (1,1) represents the data in row 1 and column 1, and (75,180) represents the data in row 75 and column 180. In addition, the calculated porosity and permeability of the gas diffusion layer after compression are also added to the performance model.

Based on the above steps, the output polarization curve is obtained by solving the performance model, as shown in Fig. 5 . The polarization curve can show 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 section, which is more realistic.

In addition, the distribution of key parameters, such as the current density distribution of the catalytic layer, can also be output, as shown in Figure 6. Current density distribution is an important factor affecting the performance of fuel cells. It can be seen from Figure 6 that near the fastening bolts around, due to the influence of the bolts, the contact stress is relatively large and the contact resistance is small, so the current density will be relatively high. In addition, the current density is also higher on the left near the inlet due to the higher gas concentration.

Accompanying drawing 7 shows the temperature distribution of the catalytic layer. The fastening effect of the bolt will affect the size of the contact resistance, and the ohmic heat generated in the place where the contact resistance is large will be higher. In the place where the middle contact stress is small and the contact resistance is large, the local temperature is higher and the distribution is more uneven. Near the left inlet, due to the high gas concentration and fast reaction rate, the heat generated is also high. Through the processing of the above steps, the internal temperature distribution of the fuel cell can be reflected more truly, which is helpful for heat management and performance optimization of the fuel cell.

Claims (3)

1. A modeling method for taking into account performance-related mechanical changes resulting from fuel cell assembly, the modeling involving fuel cell components comprising: end plate, insulation board, current collector, bipolar plate, gas diffusion layer, membrane electrode assembly, seal ring and fastening bolt, characterized by: the establishment of the model comprises the following steps:

(1) Establishing a fuel cell mechanical finite element model under real assembly, wherein the finite element model comprises three-dimensional geometric modeling, cell component mechanical parameter input, grid drawing, contact setting, boundary condition setting and load setting,

(2) The components involved in three-dimensional geometric modeling are: the end plate, the insulating plate, the current collecting plate, the bipolar plate, the gas diffusion layer, the membrane electrode assembly, the sealing washer and the fastening bolt, wherein the microporous layer, the catalytic layer and the proton exchange membrane are integrated, and the geometric parameters of the related parts, including the thickness, the width and the length of the end plate, are required to be determined in the step; thickness, width and length of the insulating plate; the thickness, width and length of the current collecting plate; bipolar plate thickness, width, length; gas diffusion layer thickness, width, length; membrane electrode assembly thickness, width, length; thickness and width of the sealing gasket; and the inner diameter, the outer diameter, the nut diameter and the length of the fastening bolt,

(3) The mechanical parameters input to the involved components include: end plates, insulating plates, current collecting plates, bipolar plates, gas diffusion layers, membrane electrode assemblies, sealing gaskets, and fastening bolts,

(4) And (3) performing grid drawing and dividing: the meshes of the related components are drawn by using mesh drawing and dividing software, the mesh density of the gas diffusion layer is twice of that of the bipolar plate at the contact part of the gas diffusion layer and the bipolar plate,

(5) Setting a contact state: the contact pair of the parts involved comprises: end plate-insulating plate, insulating plate-current collecting plate, current collecting plate-double polar plate, double polar plate-gas diffusion layer, double polar plate-sealing washer, gas diffusion layer-membrane electrode assembly,

(6) Setting a boundary condition: the fuel cell finite element mechanical model has symmetry in three directions, in order to reduce calculated amount, 1/8 model is selected for calculation, symmetrical boundary conditions are required to be set on symmetrical surfaces of an end plate, an insulating plate, a current collecting plate, a bipolar plate, a gas diffusion layer, a membrane electrode assembly and a sealing washer, clamped boundary conditions are required to be set on the bottom surfaces of the membrane electrode assembly and the sealing washer,

(7) Setting load: loads are arranged on the bolt holes and are set to be pressure intensity,

the method for calculating the pressure on the bolt hole comprises the following steps:

relationship between torque and pretension: t = K x F x d, where T is torque, K is bolt pretension coefficient, F is pretension force, d is bolt diameter,

the relationship between pretightening force and pressure is as follows: p = F/S, where P is the pressure, S is the area of the bolt hole,

(8) And solving after establishing the model to obtain the surface contact stress of the gas diffusion layer and the volume of the gas diffusion layer after compression.

2. The modeling method for considering the mechanical change and performance correlation generated by the fuel cell assembly as set forth in claim 1, wherein: converting the contact stress and the compressed volume into non-uniform contact resistance, porosity and permeability, and the specific implementation steps are as follows:

(1) The calculation formula of the contact resistance is as follows:

wherein R is _contact For contact resistance, α and β are variable coefficients, P _contact In order to achieve the contact stress, it is preferable that,

further, the contact stress of the obtained gas diffusion layer is not uniform, the contact resistance calculated is also not uniform,

(2) The calculation formula of the porosity of the gas diffusion layer after compression is as follows:

wherein epsilon _c Porosity of the gas diffusion layer after compression, V _i For compressing the volume of the gas diffusion layer before, V _c For compressing the volume of the gas diffusion layer _i To be the gas diffusion layer porosity prior to compression,

(3) The calculation formula of the permeability of the gas diffusion layer after compression is as follows:

where K is the gas diffusion layer permeability,. Epsilon.is the porosity after compression, d _f Is the diameter of the fibers constituting the gas diffusion layer.

3. The modeling method for considering the mechanical change and performance correlation generated by the fuel cell assembly as set forth in claim 1, wherein: establishing a proton exchange membrane fuel cell full cell performance model considering a real flow field structure, coupling uneven contact resistance, porosity and permeability into the model, and solving and calculating the distribution of an output polarization curve and key parameters, wherein the specific implementation steps are as follows:

(1) Establishing a full cell performance model of the proton exchange membrane fuel cell, wherein the model is a three-dimensional and one-dimensional model, and the three-dimensional part comprises an anode and cathode runner, an anode and cathode gas diffusion layer and an anode and cathode expansion layer; the one-dimensional part comprises a cathode-anode microporous layer, a cathode-anode catalyst layer and a proton exchange membrane, computing nodes are arranged on interfaces of all the layers to form a one-dimensional model, the one-dimensional model is arranged in the expansion layer to be stored and computed,

(2) The three-dimensional partial conservation equation comprises:

(2.1) conservation of mass equation:

where ρ is _g In order to be the density of the mixture,

is the flow velocity, S _m For the source term of the conservation of mass equation,

(2.2) conservation of momentum equation:

wherein, P _g Is the pressure, mu _mix Is dynamic viscosity, S _u In order to be a source term of the momentum equation,

(2.3) component conservation equation:

wherein, Y _i In terms of the concentrations of the components, D _i,eff Is the effective diffusion coefficient, S _i In order to form the source terms of the component equations,

(2.4) energy conservation equation:

wherein, C _p,g Is the specific heat capacity, T is the temperature, k ^eff Is a coefficient of thermal conductivity, S _T In order to be the source term of the energy equation,

(2.5) hydraulic conservation equation:

wherein S is the liquid water saturation, S _l Is a source term of a hydraulic conservation equation,

(2.6) conservation of electronic potential equation:

wherein,

is effective conductivity, phi _ele To an electronic potential, S _ele As a source term of the conservation equation of the electron potential,

(3) In the one-dimensional part, the conservation equation is converted into a one-dimensional flux conservation equation, each scalar is solved in the one-dimensional part, and the calculation formula of each scalar is as follows:

(3.1) component (b):

wherein n and n +1 represent two adjacent layers,

in order to have an effective diffusion coefficient of the component,

as component concentration, δ is layer thickness, S _i ⁿ In the form of an in-layer source entry,

(3.2) temperature:

wherein,

to an effective thermal conductivity, T ⁿ It is the temperature that is set for the purpose,

is a source item in the layer, and is,

(3.3) hydraulic pressure:

wherein, K ⁿ The permeability of the main body is taken as the permeability of the main body,

in order to be a relative permeability coefficient,

(3.4) film-state water content:

where ρ is _im Film density in the dry state, D _mw For diffusion coefficient, EW is the membrane equilibrium mass, λ ⁿ The content of water in a film state is,

in the form of an in-layer source entry,

(3.5) electronic potential:

wherein,

in order to be of an effective electrical conductivity,

in order to be at the potential of the electrons,

in the form of an in-layer source entry,

(3.6) ion potential:

wherein,

in order to be of an effective electrical conductivity,

is a potential of an ion and is,

in the form of an in-layer source entry,

furthermore, a junction model is considered in the one-dimensional model for correction and calculation of the electrochemical reaction rate, and the calculation formula is as follows:

wherein j is the electrochemical reaction rate, i is the reference exchange current density, A is the effective specific surface area, and theta _T For temperature correction coefficient, R is the general gas constant, H is the Henry coefficient, F is the Faraday constant, α is the transmission coefficient, η is the overpotential, R _local In order to achieve a local gas transport resistance,

further, the reversible voltage is calculated by the nernst equation, and the calculation formula is as follows:

wherein E is _rev Is a reversible voltage, Δ S is a change in entropy,

(4) Adding coupling band to the proton exchange membrane fuel cell full cell model to solve and calculate the non-uniform contact resistance, porosity and permeability obtained in the previous claim 3, and simulating the performance of the proton exchange membrane fuel cell full cell model to output a polarization curve and distribution of internal key parameters such as current density distribution and temperature distribution.

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