CN115510679A - Modeling method for considering correlation between mechanical change and performance generated by fuel cell assembly - Google Patents

Modeling method for considering correlation between mechanical change and performance generated by fuel cell assembly Download PDF

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CN115510679A
CN115510679A CN202211279296.6A CN202211279296A CN115510679A CN 115510679 A CN115510679 A CN 115510679A CN 202211279296 A CN202211279296 A CN 202211279296A CN 115510679 A CN115510679 A CN 115510679A
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焦魁
霍文明
谢彪
杜青
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Tianjin University
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Abstract

The invention discloses a modeling method considering the correlation between mechanical change and performance generated by fuel cell assembly, which is used for establishing a fuel cell mechanical finite element model by setting the material properties of each component, setting the contact relation among the components, setting the boundary condition of the model and setting an applied load in order to construct a proton exchange membrane fuel cell three-dimensional model under real assembly. Obtaining the contact stress distribution of the contact surface of the gas diffusion layer and the bipolar plate and the volume of the gas diffusion layer after compression through a model; converting it into non-uniform contact resistance, porosity and permeability; inputting the data into a fuel cell performance model for calculation; finally, the polarization curve under the real assembly and pre-tightening and the distribution of key parameters are obtained. The model is helpful for intuitively, quickly and accurately obtaining the optimal pretightening force of the fuel cell and simultaneously obtaining the distribution in the cell so as to help the understanding of the relationship between the mechanical behavior and the output performance of the cell.

Description

Modeling method for considering correlation between mechanical change and performance generated by fuel cell assembly
Technical Field
The invention belongs to the fuel cell technology, and particularly relates to a modeling method for correlation between the change of mechanical behavior of a fuel cell and the performance of the fuel cell in the actual assembly process.
Background
A pem fuel cell is an energy conversion device that can convert chemical energy in hydrogen and oxygen into electric energy, has the advantages of high power density, rapid response and zero emission, and is considered to be one of the most potential power devices to replace internal combustion engines. The proton exchange membrane fuel cell can be widely applied to the fields of aviation, submarines, power stations, fuel cell automobiles and the like.
The proton exchange membrane fuel cell comprises an end plate, an insulating plate, a current collecting plate, a bipolar plate, a gas diffusion layer, a microporous layer, a catalyst layer, a proton exchange membrane, a sealing washer, a fastening bolt and the like. In order to obtain higher output power, the cell stack on the fuel cell automobile is mostly composed of 300-400 single cells, and a lot of mechanical behaviors are generated inside the cells during the assembly process. For example, the contact state or degree of contact between the bipolar plate and the gas diffusion layer will produce different mechanical behavior. Too low contact stress can result in higher contact resistance and greater ohmic loss of electrons; and the excessive contact stress can reduce the thickness, porosity and permeability of the gas diffusion layer, hinder gas transmission and increase mass transfer loss.
At present, the pre-tightening force for testing the assembly of the fuel cell is mainly to detect the performance of the cell under different pre-tightening forces in an experimental mode, but the experimental process is long in time consumption and high in cost. There are also simulation models to study the effect of fuel cell assembly on changes in gas diffusion layer parameters, but there are two main problems. The method is characterized in that a model is independently modeled for a bipolar plate and a gas diffusion layer, uniform pressure is applied to research the stress strain of the gas diffusion layer under different pressures, and the actual assembly condition of a battery is not considered. Secondly, the mechanical behavior and the performance change are separated by the established model at present, the influence of the mechanical behavior change on the performance caused by the assembling pretightening force is not comprehensively considered, and the optimal pretightening force with the highest performance cannot be given.
If a simulation model considering the mechanical behavior change of the assembly pretightening force and the correlation with the battery performance can be established, the parameter change, the stress distribution, the strain magnitude and the like of key components of the fuel cell can be obtained, and meanwhile, the changes can be considered in the full battery performance model to output the performance of the fuel cell under different pretightening forces and the distribution of the key parameters, which is inevitably required in the field of the fuel cell.
Disclosure of Invention
Aiming at the existing problems, the invention provides a modeling method considering the mechanical change and performance correlation generated by fuel cell assembly, which can simulate the mechanical behavior in the cell under the actual assembly condition of the fuel cell to obtain the change of parameters of a gas diffusion layer, including contact resistance, porosity and permeability, due to the cell assembly, further introduce the change caused by the mechanical behavior into a full cell model, simulate the performance of the cell under different pretightening forces, output a polarization curve, obtain the optimal pretightening force and realize the coupling of the mechanical behavior and the performance. The model is helpful for intuitively, quickly and accurately obtaining the optimal pretightening force of the fuel cell and simultaneously obtaining the distribution in the cell so as to help the understanding of the relationship between the mechanical behavior and the output performance of the cell.
The invention adopts the following technical scheme and steps:
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. The establishment of the model comprises the following steps:
(1) And 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 catalyst layer and the proton exchange membrane are integrated into a whole. The geometrical parameters of the parts involved in the determination required in this step include: end plate thickness, width, length; thickness, width, length of the insulating board; 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 and the outer diameter of the fastening bolt nut diameter, length.
(3) The mechanical parameters of the part involved in the input include: end plates, insulator plates, collector plates, bipolar plates, gas diffusion layers, membrane electrode assemblies, sealing gaskets, and fastening bolts.
(4) And (3) grid drawing and dividing: and drawing the grids of the related components by using grid drawing software, wherein the grid 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: the bipolar plate comprises an end plate, an insulating plate, a current collecting plate, a bipolar plate, a gas diffusion layer, a bipolar plate, a sealing gasket, a gas diffusion layer and a 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, and fixed support boundary conditions are required to be set on bottom surfaces of the membrane electrode assembly and the sealing washer.
(7) Setting load: a load is placed on the bolt hole, and the load is set to pressure.
The method for calculating the pressure on the bolt hole comprises the following steps:
relationship between torque and pretension: t = K × F × d, where T is torque, K is a bolt pretension coefficient, F is a pretension force, and d is a bolt diameter.
The relationship between the pretightening force and the pressure is as follows: p = F/S, where P is the pressure and 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.
Further, after a fuel cell mechanical finite element model is established, a pre-tightening torque is applied to obtain the contact stress distribution on the interface of the gas diffusion layer and the bipolar plate, and the volume of the compressed gas diffusion layer.
The contact stress and volume of the gas diffusion layer obtained by the fuel cell mechanics finite element model are converted into contact resistance, porosity and permeability.
The calculation formula of the contact resistance is as follows:
Figure BDA0003897418340000031
the contact stress of the gas diffusion layer obtained is not uniform, so the contact resistance calculated is also non-uniform contact resistance distribution.
The calculation formula of the porosity of the gas diffusion layer after compression is as follows:
Figure BDA0003897418340000032
the calculation formula of the permeability of the gas diffusion layer after compression is as follows:
Figure BDA0003897418340000033
the established full cell performance model of the fuel cell 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 and anode microporous layer, a cathode and anode catalytic layer and a proton exchange membrane. And setting calculation nodes on interfaces of all layers to form a one-dimensional model. The one-dimensional part is set in the extension layer for storage and calculation.
The conservation equations for the three-dimensional portion include:
(1) Conservation of mass equation
(2) Equation of conservation of momentum
(3) Conservation of composition equation
(4) Energy conservation equation
(5) Hydraulic conservation equation
(6) Conservation of electronic potential equation
In the one-dimensional part, the conservation equation is converted into a one-dimensional flux conservation equation, and each scalar is solved in the one-dimensional part. The calculation formula involved by each scalar includes:
(1) Components
(2) Temperature of
(3) Hydraulic pressure
(4) Water content in film form
(5) Electronic potential
(6) Ionic potential
Furthermore, the electrochemical reaction rate is calculated by considering the modification of the junction model in the one-dimensional model, the specific calculation formulas are (16) and (17), and the reversible voltage is calculated by the Nernst equation, such as the formula (18).
And adding the calculated uneven contact resistance, porosity and permeability into a full cell performance model of the fuel cell, simulating the performance of the full cell, and outputting a polarization curve and distribution of internal key parameters such as current density distribution, temperature distribution and the like.
The invention has the characteristics and beneficial effects that:
(1) The quantitative relation between the mechanical behavior change of the fuel cell and the performance of the fuel cell under the condition of real assembly is considered, the change of key parameters of the gas diffusion layer generated by the mechanical behavior of the fuel cell can be obtained under the condition of the real assembly of the fuel cell, and then the change is input into a performance simulation model to calculate the performance of the fuel cell. Compared with a continuously used experimental method, the method is beneficial to intuitively, quickly and accurately obtaining the optimal assembly pressure of the fuel cell, understanding the internal mechanical behavior of the fuel cell, understanding the relation between the mechanical behavior and the performance of the fuel cell and optimizing the assembly of the fuel cell.
(2) The established mechanical finite element model comprises all components of the fuel cell, is comprehensive and accurate, and can be calculated on a large-area flow field plate to obtain the mechanical relationship among all the components. In addition, the model can also extract the uneven contact stress distribution on the surface of the gas diffusion layer, which can be converted into uneven contact resistance later.
(3) The established three-dimensional and one-dimensional performance model can comprehensively consider the flow field form and structure of the fuel cell, is real and accurate, and can be calculated on a large-area flow field plate. In addition, the invention also considers non-uniform contact resistance distribution, porosity variation and permeability variation. Compared with the traditional three-dimensional performance model, the model has the advantages of rapid calculation and good convergence, and takes the nonuniform contact resistance inside the battery into consideration.
Drawings
FIG. 1 is a schematic block diagram of the steps of the modeling process of the present invention.
FIG. 2 is a schematic diagram of a finite element model of mechanics in an example calculation.
FIG. 3 is a schematic diagram of a performance model in an example calculation.
FIG. 4 is a schematic diagram of the processing of the non-uniform contact resistance in an example calculation.
Fig. 5 is a polarization curve output in an example calculation.
FIG. 6 is a cloud graph of the current density distribution output in an example calculation.
FIG. 7 is a cloud graph of the temperature distribution output from an example calculation.
Detailed Description
The technical solutions of the present invention are described in detail below by way of examples with reference to the accompanying drawings, and it should be noted that the examples are illustrative rather than limiting, and the scope of the present invention is not limited thereby.
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, insulating plate, current collector, bipolar plate, gas diffusion layer, membrane electrode assembly, seal ring and fastening bolt.
The fuel cell mechanical finite element model and the fuel cell full cell performance model in this example are non-limiting. As shown in figure 1. The overall step principle of the invention is to construct a proton exchange membrane fuel cell three-dimensional model under real assembly, set the material properties of each component, set the contact relation between each component, set the boundary condition of the model and set the applied load, thereby establishing a fuel cell mechanics finite element model. Obtaining the contact stress distribution of the contact surface of the gas diffusion layer and the bipolar plate and the volume of the gas diffusion layer after compression through a model; converting it into non-uniform contact resistance, porosity and permeability; inputting the data into a fuel cell performance model for calculation; finally, the polarization curve under the real assembly and pre-tightening and the distribution of key parameters are obtained. The establishment of the model for correlating the mechanical changes and the performance of the fuel cell assembly comprises the following steps:
(1) And 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 catalyst layer and the proton exchange membrane are integrated into a whole. The step of determining the geometric parameters of the involved parts includes: end plate thickness, width, length; thickness, width, length of the insulating board; 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 of the part involved in the input include: end plates, insulator plates, collector plates, bipolar plates, gas diffusion layers, membrane electrode assemblies, sealing gaskets, and fastening bolts.
(4) And (3) grid drawing and dividing: and drawing the grids of the related components by using grid drawing software, wherein the grid 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: the bipolar plate comprises an end plate, an insulating plate, a current collecting plate, a bipolar plate, a gas diffusion layer, a bipolar plate, a sealing gasket, a gas diffusion layer and a membrane electrode assembly.
(6) Setting a boundary condition: the fuel cell finite element mechanical model has symmetry in three directions, in order to reduce the calculation amount, a 1/8 model is selected for calculation, symmetrical boundary conditions are required to be arranged on two 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, and fixed support boundary conditions are required to be arranged on the bottom surfaces of the membrane electrode assembly and the sealing washer.
(7) Setting load: a load is placed on the bolt hole, and the load is set to pressure. In the calculation of the pressure on the bolt hole, the relationship between the torque and the pretension is: t = K × F × d. In the formula, T is torque, K is a bolt pre-tightening coefficient, F is pre-tightening force, and d is the diameter of the bolt. The relationship between pretightening force and pressure is as follows: p = F/S, where P is the pressure and 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.
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:
Figure BDA0003897418340000061
wherein R is contact For contact resistance, α and β are variable coefficients, P contact Is the contact stress.
Further, the obtained contact stress of the gas diffusion layer is not uniform, and the contact resistance calculated is also not uniform.
(2) The porosity of the gas diffusion layer after compression is calculated by the formula:
Figure BDA0003897418340000062
(3) The calculation formula of the permeability of the gas diffusion layer after compression is as follows:
Figure BDA0003897418340000063
further, a full cell performance model of the proton exchange membrane fuel cell considering a real flow field structure is established. Coupling the uneven contact resistance, the porosity and the permeability into a model, solving and calculating the distribution of an output polarization curve and key parameters, and specifically implementing the following steps:
(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, calculation nodes are arranged on the interfaces of all the layers to form a one-dimensional model, the one-dimensional part is arranged in the expansion layer to be stored and calculated,
(2) The three-dimensional partial conservation equation comprises:
(2.1) conservation of mass equation:
Figure BDA0003897418340000064
(2.2) conservation of momentum equation:
Figure BDA0003897418340000065
(2.3) component conservation equation:
Figure BDA0003897418340000066
(2.4) energy conservation equation:
Figure BDA0003897418340000067
(2.5) hydraulic conservation equation:
Figure BDA0003897418340000071
(2.6) conservation of electronic potential equation:
Figure BDA0003897418340000072
(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):
Figure BDA0003897418340000073
(3.2) temperature:
Figure BDA0003897418340000074
(3.3) hydraulic pressure:
Figure BDA0003897418340000075
(3.4) film Water content:
Figure BDA0003897418340000076
(3.5) electronic potential:
Figure BDA0003897418340000077
(3.6) ion potential:
Figure BDA0003897418340000078
correcting and calculating the electrochemical reaction rate by considering a block model in the one-dimensional model, wherein the calculation formula is as follows:
Figure BDA0003897418340000079
Figure BDA0003897418340000081
the reversible voltage is calculated by the nernst equation, and the calculation formula is as follows:
Figure BDA0003897418340000082
(4) And adding the non-uniform contact resistance, porosity and permeability obtained by the calculation into a full cell model of the proton exchange membrane fuel cell, solving and calculating, simulating the performance of the model, and outputting a polarization curve and the distribution of internal key parameters such as current density distribution and temperature distribution.
Examples
Firstly, establishing a mechanical finite element model considering the real assembly of the proton exchange membrane fuel cell to obtain the surface contact stress and the volume after compression of the gas diffusion layer. The contact stress and compressed volume are then converted to a non-uniform contact resistance, porosity and permeability. And establishing a full cell performance model of the proton exchange membrane fuel cell considering a real flow field structure, coupling the uneven contact resistance, the porosity and the permeability into the model, and solving and calculating the distribution of an output polarization curve and key parameters. The method specifically comprises the following steps:
1. and (3) establishing the three-dimensional geometry of the proton exchange membrane fuel cell mechanical finite element model, as shown in the attached figure 2. Material properties including density, young's modulus and poisson's ratio are set for each component involved. End plate density 2800kg m -3 Young modulus is 2.0e5 MPa, poisson ratio is 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 modulus of 1.2e5MPa, poisson's ratio of 0.33; bipolar plate density 2250kg m -3 Young modulus is 1.0e4MPa, poisson ratio is 0.25; gas diffusion layer density 440kg m -3 Young modulus is 10MPa, and Poisson ratio is 0.1; membrane electrode Assembly Density 2000kg m -3 Young modulus 320MPa, poisson's ratio 0.25; sealing washer density 1000kg m -3 Young's modulus 100MPa, poisson's ratio 0.4.
2. The contacting relationship of the components is set. Tangential and normal contacts are arranged among the end plate-insulating plate, the insulating plate-current collecting plate, the current collecting plate-bipolar plate, the bipolar plate-gas diffusion layer and the bipolar plate-sealing washer. A binding relationship is provided between the gas diffusion layer and the membrane electrode assembly.
3. Boundary conditions for the respective components are set. Symmetrical boundary conditions are set in two symmetrical directions of the end plate, the insulating plate, the current collecting plate, the bipolar plate, the gas diffusion layer, the membrane electrode assembly and the sealing gasket along the flow field, and fixed support boundary conditions are set on the bottom surfaces of the sealing gasket and the membrane electrode assembly.
4. A load is set. And setting load on the bolt hole contact surface of the end plate, wherein the pressure is selected as the pressure. The calculation method is as follows:
torque and pretension: t = K × F × d.
Relationship between pre-tightening force and pressure: p = F/S.
In this example, the torque T is selected to be 3Nm, the bolt diameter is 6.4mm, and the bolt hole area is 121.77mm 2 . From which the pressure exerted on each bolt hole can be calculated.
5. And based on the steps, finishing establishing the mechanical finite element model of the proton exchange membrane fuel cell in consideration of actual assembly. The contact stress distribution on the interface of the gas diffusion layer and the bipolar plate and the volume of the compressed gas diffusion layer can be obtained through solving.
6. Converting the obtained contact stress on the surface of the gas diffusion layer and the compressed volume into uneven contact resistance, porosity after compression and permeability after compression, wherein the calculation process is as follows:
contact resistance calculation formula:
Figure BDA0003897418340000091
in this calculation, α is 5.0, β is-0.719 contact (MPa) is the contact stress.
The contact stress of the gas diffusion layer obtained is not uniform, so the contact resistance calculated is also non-uniform contact resistance distribution.
Calculation formula of porosity:
Figure BDA0003897418340000092
530mm in this calculation 3 ，V c For compressing the volume of the gas diffusion layer i Which in this calculation is 0.7.
Calculation formula of permeability:
Figure BDA0003897418340000093
in this calculation, 8 μm.
7. And establishing a full cell performance model of the proton exchange membrane fuel cell. Fig. 3 shows a geometric schematic of the model. This model is a "three-dimensional + one-dimensional" model. The three-dimensional part comprises a cathode and anode distribution area, a cathode and anode flow field, a cathode and anode gas diffusion layer and a cathode and anode expansion layer. The one-dimensional model is stored and calculated in the anode-cathode extension layer. The one-dimensional model comprises a cathode-anode microporous layer, a cathode-anode catalytic layer and a proton exchange membrane. The calculation nodes of the one-dimensional part are selected on the interfaces between the layers.
The calculation formula of the performance model is as follows:
the three-dimensional partial conservation equation is:
(1) Conservation of mass equation:
Figure BDA0003897418340000094
where ρ is g (kg m -3 ) In order to be the density of the mixture,
Figure BDA0003897418340000101
(m s -1 ) Is the flow rate, S m (kg m -3 s -1 ) Is a source term of the conservation of mass equation.
(2) Conservation of momentum equation:
Figure BDA0003897418340000102
wherein, P g (Pa) is the pressure, μ mix (kg m -1 s -1 ) Is dynamic viscosity, S u (kg m -2 s -2 ) Is a source term of the momentum equation.
(3) Component conservation equation:
Figure BDA0003897418340000103
wherein, Y i (mol m -3 ) In terms of the concentrations of the components, D i,eff (m 2 s -1 ) Is the effective diffusion coefficient, S i (mol m -3 s -1 ) Is a source term of the component equation.
(4) Energy conservation equation:
Figure BDA0003897418340000104
wherein, C p,g (J mol -1 K -1 ) Is specific heat capacity, T (K) is temperature, K eff (W m -1 K -1 ) To be guideThermal coefficient, S T (W m -3 ) Is the source term of the energy equation.
(5) Hydraulic conservation equation:
Figure BDA0003897418340000105
wherein S is the liquid water saturation, S l (kg m -3 s -1 ) Is a source term of a hydraulic conservation equation.
(6) Electron potential conservation equation:
Figure BDA0003897418340000106
wherein,
Figure BDA0003897418340000107
(S m -1 ) Is effective conductivity, phi ele (V) is the electron potential, S ele (Am -3 ) Is the source term of the conservation equation of electron potential.
The one-dimensional partial flux conservation equation is:
(1) The components are as follows:
Figure BDA0003897418340000108
wherein n and n +1 represent two adjacent layers,
Figure BDA0003897418340000109
in order to have an effective diffusion coefficient of the component,
Figure BDA00038974183400001010
as component concentration, δ (m) is the layer thickness,
Figure BDA00038974183400001011
are in-layer source items.
(2) Temperature:
Figure BDA0003897418340000111
wherein,
Figure BDA0003897418340000112
to an effective thermal conductivity, T n (K) It is the temperature that is set for the purpose,
Figure BDA0003897418340000113
are in-layer source items.
(3) Hydraulic pressure:
Figure BDA0003897418340000114
wherein, K n (m 2 ) The permeability of the main body is taken as the permeability of the main body,
Figure BDA0003897418340000115
is the relative permeability coefficient.
(4) Film water content:
Figure BDA0003897418340000116
wherein ρ im (kg m -3 ) Film density in the dry state, D mw EW (kg mol) for diffusion coefficient -1 ) Is the equilibrium state mass of the membrane, λ n The content of water in a film state is,
Figure BDA0003897418340000117
are in-layer source items.
(5) Electron potential:
Figure BDA0003897418340000118
wherein,
Figure BDA0003897418340000119
in order to be of an effective electrical conductivity,
Figure BDA00038974183400001110
in order to be at the potential of the electrons,
Figure BDA00038974183400001111
is an in-layer source item.
(6) Ion potential:
Figure BDA00038974183400001112
wherein,
Figure BDA00038974183400001113
in order to be of an effective electrical conductivity,
Figure BDA00038974183400001114
in order to be at the ionic potential,
Figure BDA00038974183400001115
are in-layer source items. Correcting and calculating the electrochemical reaction rate by considering a block model in the one-dimensional model, wherein the calculation formula is as follows:
Figure BDA00038974183400001116
Figure BDA00038974183400001117
wherein j (A m) -3 ) For electrochemical reaction rate, i (A m) -2 ) For reference exchange current density, A (m) -1 ) For effective specific surface area, θ T For the temperature correction coefficient, R (J mol) -1 K -1 ) Is a general gas constant, H (Pa m) 3 mol -1 ) Is a Henry coefficient, F (C mol) -1 ) Is Faraday constant, alpha is transmission coefficient, eta (V) is overpotential, R local (s m -1 ) Is the local gas transmission resistance.
The reversible voltage is calculated by the nernst equation, and the calculation formula is as follows:
Figure BDA0003897418340000121
wherein, E rev (V) is the reversible voltage,. DELTA.S (J mol) -1 K -1 ) Is the change in entropy.
Based on the above steps, the full cell performance model of the pem fuel cell is established, and as shown in fig. 4, the non-uniform contact resistance matrix is added to the performance model. FIG. 4 is a 75X 180 matrix, where (1,1) represents row 1, column 1 data and (75,180) represents row 75, column 180 data. In addition, the calculated porosity and permeability of the gas diffusion layer after compression were also added to the performance model.
Based on the above steps, the performance model is solved to obtain an output polarization curve, as shown in fig. 5. The polarization curve may show the output voltage of the fuel cell at different current densities. The output voltage is mainly influenced by activation loss, ohmic loss and mass transfer loss, and the polarization curve of the simulated fuel cell is more real through the processing of the steps, and particularly the embodiment in the ohmic loss section is more practical.
In addition, a distribution of key parameters, such as catalytic layer current density distribution, can also be output, as shown in fig. 6. The current density distribution is an important factor affecting the performance of the fuel cell. It can be seen from fig. 6 that in the vicinity of the fastening bolt on the periphery, the contact resistance is small because the contact stress is large due to the influence of the bolt, and therefore the current density is high. In addition, the current density is also greater near the inlet on the left side due to the higher gas concentration.
Fig. 7 shows the catalytic layer temperature profile. The fastening action of the bolt affects the magnitude of the contact resistance, and the ohmic heat generated at a place where the contact resistance is large is high. The local temperature is higher and more unevenly distributed at the place with small contact stress and large contact resistance in the middle, and the generated heat is higher because the gas concentration is high and the reaction rate is faster near the left inlet. The distribution of the internal temperature of the fuel cell can be reflected more truly through the processing of the steps, and the heat management and the performance optimization of the fuel cell are facilitated.

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:
Figure FDA0003897418330000021
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:
Figure FDA0003897418330000022
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:
Figure FDA0003897418330000023
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:
Figure FDA0003897418330000024
where ρ is g In order to be the density of the mixture,
Figure FDA0003897418330000025
is the flow velocity, S m For the source term of the conservation of mass equation,
(2.2) conservation of momentum equation:
Figure FDA0003897418330000026
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:
Figure FDA0003897418330000031
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:
Figure FDA0003897418330000032
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:
Figure FDA0003897418330000033
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:
Figure FDA0003897418330000034
wherein,
Figure FDA0003897418330000035
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):
Figure FDA0003897418330000036
wherein n and n +1 represent two adjacent layers,
Figure FDA0003897418330000037
in order to have an effective diffusion coefficient of the component,
Figure FDA0003897418330000038
as component concentration, δ is layer thickness, S i n In the form of an in-layer source entry,
(3.2) temperature:
Figure FDA0003897418330000039
wherein,
Figure FDA00038974183300000310
to an effective thermal conductivity, T n It is the temperature that is set for the purpose,
Figure FDA00038974183300000311
is a source item in the layer, and is,
(3.3) hydraulic pressure:
Figure FDA0003897418330000041
wherein, K n The permeability of the main body is taken as the permeability of the main body,
Figure FDA0003897418330000042
in order to be a relative permeability coefficient,
(3.4) film-state water content:
Figure FDA0003897418330000043
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,
Figure FDA0003897418330000044
in the form of an in-layer source entry,
(3.5) electronic potential:
Figure FDA0003897418330000045
wherein,
Figure FDA0003897418330000046
in order to be of an effective electrical conductivity,
Figure FDA0003897418330000047
in order to be at the potential of the electrons,
Figure FDA0003897418330000048
in the form of an in-layer source entry,
(3.6) ion potential:
Figure FDA0003897418330000049
wherein,
Figure FDA00038974183300000410
in order to be of an effective electrical conductivity,
Figure FDA00038974183300000411
is a potential of an ion and is,
Figure FDA00038974183300000412
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:
Figure FDA00038974183300000413
Figure FDA00038974183300000414
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:
Figure FDA00038974183300000415
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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CN117292778A (en) * 2023-11-24 2023-12-26 中国石油大学(华东) Method for calculating mechanical properties of gradient hole anode of solid oxide fuel cell
CN117352782A (en) * 2023-10-31 2024-01-05 北京理工大学 Method for determining electrochemical performance of fuel cell
CN117352782B (en) * 2023-10-31 2024-10-29 北京理工大学 Method for determining electrochemical performance of fuel cell

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117352782A (en) * 2023-10-31 2024-01-05 北京理工大学 Method for determining electrochemical performance of fuel cell
CN117352782B (en) * 2023-10-31 2024-10-29 北京理工大学 Method for determining electrochemical performance of fuel cell
CN117292778A (en) * 2023-11-24 2023-12-26 中国石油大学(华东) Method for calculating mechanical properties of gradient hole anode of solid oxide fuel cell
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