CN106848351B - Method for establishing proton exchange membrane fuel cell performance prediction model - Google Patents

Method for establishing proton exchange membrane fuel cell performance prediction model Download PDF

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CN106848351B
CN106848351B CN201611221206.2A CN201611221206A CN106848351B CN 106848351 B CN106848351 B CN 106848351B CN 201611221206 A CN201611221206 A CN 201611221206A CN 106848351 B CN106848351 B CN 106848351B
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焦魁
王博文
蒋杨
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Tianjin University
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Abstract

The invention discloses a method for establishing a proton exchange membrane fuel cell performance prediction model, wherein the established model comprises a one-dimensional model vertical to a polar plate direction and a 1+1+ 1-dimensional quasi-three-dimensional model, and the establishment of the one-dimensional model vertical to the polar plate direction specifically comprises the following four steps: determining battery output voltage, determining ohmic loss, determining activation loss, and water management; the 1+1+1 dimensional quasi-three-dimensional model is based on a one-dimensional model vertical to the polar plate direction, and the directions of rib plates along the battery flow channel and vertical to the flow channel are increased. Solving the mass conservation equation of the reactant and the water to obtain the average liquid water volume fraction in each layer of the cell and the reactant concentration in the catalytic layer, thereby solving the ohmic loss and the activation loss, adjusting the working conditions such as current density, temperature, relative humidity of air inlet and the like, and predicting the output voltage of the proton exchange membrane fuel cell under different working conditions. The establishment of the proton exchange membrane fuel cell performance prediction model can effectively save development cost and shorten development period.

Description

Method for establishing proton exchange membrane fuel cell performance prediction model
Technical Field
The invention belongs to the field of electrochemical fuel cells, and particularly relates to a method for establishing a proton exchange membrane fuel cell performance prediction model.
Background
Proton Exchange Membrane Fuel Cells (PEMFCs) have the advantages of high power density, zero emission, etc., and are regarded as the most promising power source for automobile power, and the technical development thereof is deeply valued by researchers at home and abroad. In order to ensure that the PEMFC has stable and reliable performance (including high proton conductivity of the exchange membrane, transport of reactants, and discharge of products), the water, hydrogen, and oxygen transport processes of each layer inside the PEMFC are studied, so that it is very important to provide good water management in the cell, and guidance is provided for improving the performance of the PEMFC.
The fuel cell simulation modeling is used as an important means for fuel cell research, and not only is the primary screening performed on the suitable working condition of the cell and the cell material; and the reason of the battery performance difference can be analyzed from the aspects of material transportation and electrochemical reaction mechanism in the battery, so that the guarantee is provided for optimizing the battery design and improving the battery performance.
The anode of the proton exchange membrane fuel cell supplies hydrogen, the cathode supplies oxygen, the high concentration of reactants in the catalytic layer is maintained, and the key for ensuring the performance of the cell is to ensure the efficient transportation of reaction gas to the catalytic layer. Proper water distribution in the cell is also important in addition to hydrogen and oxygen, so that the proton exchange membrane has a certain humidity to ensure high proton conductivity, and cathode flooding is avoided. Most of the current prediction methods predict the output voltage of the fuel cell from the perspective of system control, and neglect the influence of the distribution of substances in the cell and the electrochemical reaction mechanism on the cell performance. Because the model is lack of a substance transportation mechanism, the operation working condition parameters and actually possessed material parameters of a plurality of batteries can not be reflected in the model, and the influence of the working condition and the battery design parameters on the battery performance can not be researched.
The fuel cell model which is accurate and effective and has a short operation period is established, so that development cost is effectively saved and the development period is shortened. The three-dimensional numerical model capable of comprehensively researching the battery performance has the problems of high requirement on computing capacity, long computing period and the like, a workstation with high computing performance is required to be used for computing, only a single working condition is computed, the time of one day is required, the application of the model in engineering practice is not facilitated, and the model capable of rapidly predicting the influence of battery design parameters on the performance of the battery design parameters is required at the initial stage of the battery design. The invention provides a model method capable of rapidly and accurately testing the performance of a proton exchange membrane fuel cell according to an electrochemical reaction mechanism, mass transfer analysis in the cell and a water management method. The method can be used for establishing a one-dimensional analytical model perpendicular to the polar plate direction and can also be used for establishing 3 one-dimensional superposed quasi-three-dimensional analytical models. Compared with a three-dimensional numerical model, the calculation period of the quasi three-dimensional model is greatly shortened, and the research content is widened without increasing excessive calculation amount.
Disclosure of Invention
The invention aims to provide a method for establishing a model for rapidly and accurately predicting the performance of a proton exchange membrane fuel cell according to an electrochemical mechanism and an analysis theory of mass transfer in the cell, which can be used for testing the influence of various working conditions and design parameters on the performance of the cell.
The constructed model comprises a one-dimensional model vertical to the polar plate direction and a quasi three-dimensional model of 1+1+1 dimension. The method for constructing the one-dimensional model vertical to the polar plate direction specifically comprises the following four steps: determination of cell output voltage, determination of ohmic losses, determination of activation losses, and water management are described below.
(1) Determining battery output voltage
Eout＝Erev-ηohm-ηact1-1
Wherein EoutRepresents the battery output voltage; erevIndicating a reversible voltage ηohmRepresenting ohmic losses of voltage ηactThe voltage activation loss is expressed, and the ohmic loss and the activation loss include voltage loss due to the reactant concentration and the water loss.
The reversible voltage is obtained by the nernst equation:
Figure BDA0001191443490000021
the output voltage of the battery can be determined from 1-1 by determining both the ohmic loss and the activation loss.
(2) Determination of ohmic losses
(2.1) the ohmic loss comprises the sum of ohmic losses caused by the polar plate, the porous medium layer and the proton exchange membrane, namely:
Figure BDA0001191443490000022
η thereinohm，P、ηohm，porAnd ηohm，mOhmic overpotential caused by the polar plate, the porous medium layer and the proton exchange membrane respectively; i is the current density;
Figure BDA0001191443490000023
the surface resistances are respectively used for transmitting electrons for the flow channel polar plate and each layer of the porous medium;
Figure BDA0001191443490000024
Figure BDA0001191443490000025
respectively the area resistance of the catalytic layer and the proton exchange membrane for transferring the protons. Solving general formula of resistance:
Ω＝L/σeff2-2
wherein L is the transmission distance, also denoted thickness; sigmaeffIs provided withEffective conductivity.
The next step is to find the effective conductivity of electrons in each layer and the proton conductivity in the catalyst layer and the proton exchange membrane.
(2.2) effective conductivity of electrons in porous dielectric layer
The effective value of the variables in the porous medium is usually corrected by Bruggemann, and the correction coefficient is 1.5:
for a diffusion layer or microporous layer or catalytic layer:
Figure BDA0001191443490000026
in the formula
Figure BDA0001191443490000027
Represents the effective conductivity of the electrons; sigmasIs the electron intrinsic conductivity; ε is the porosity.
(2.3) effective conductivity of protons in the proton exchange Membrane and in the catalytic layer
Figure BDA0001191443490000028
In the formula
Figure BDA0001191443490000029
Effective conductivity for protons in the catalytic layer; xmThe volume fraction of electrolyte Nafion in the catalytic layer; sigmamIs the proton conductivity of the proton exchange membrane Nafion.
σmDepending on the water content in Nafion:
Figure BDA0001191443490000031
wherein λ is the Nafion water content.
Figure BDA0001191443490000032
Wherein a is the water activity of the water,
for the catalytic layer:
ac1＝RH+2s 2-7
wherein RH is the relative humidity of gas in the catalytic layer, and s is the volume fraction of liquid water in pores of the catalytic layer;
for proton exchange membranes, water activity aaverApproximately equal to the average water activity in the anode catalytic layer and in the cathode catalytic layer:
Figure BDA0001191443490000033
(3) determination of activation loss
(3.1) analytical solution of activation loss:
Figure BDA0001191443490000034
Figure BDA0001191443490000035
η thereinact，ano，ηact，catRespectively representing the activation overpotential of anode and cathode, R is ideal gas constant, T is working condition temperature, α is charge transfer coefficient, n is electron number transferred in unit reaction, j is0，refIs a reference current density;
Figure BDA0001191443490000036
the hydrogen concentration in the anode catalytic layer and the oxygen concentration in the cathode catalytic layer are respectively under the actual condition;
Figure BDA0001191443490000037
reference hydrogen concentration and reference oxygen concentration, respectively.
(3.2) gas concentration in the catalytic layer:
the diffusion and transmission mode of hydrogen and oxygen in the porous medium structure in the battery follows Fick's law:
Figure BDA0001191443490000041
the anode and the cathode respectively comprise four solution domains, namely a flow channel, a diffusion layer, a microporous layer and a catalytic layer.
Anode catalyst layer hydrogen concentration:
Figure BDA0001191443490000042
wherein
Figure BDA0001191443490000043
Hydrogen concentration at the interface of the microporous layer and the catalytic layer;
Figure BDA0001191443490000044
hydrogen concentration at the interface of the catalyst layer and the proton exchange membrane;
Figure BDA0001191443490000045
is the effective diffusion coefficient of hydrogen in the anode catalytic layer, and is obtained by correction of Bruggemann
Figure BDA0001191443490000046
Unit is m2/s；δCLIs the thickness of the catalyst layer and has the unit of m.
Average hydrogen concentration of anode catalyst layer:
Figure BDA0001191443490000047
cathode catalyst layer oxygen concentration:
Figure BDA0001191443490000048
wherein
Figure BDA0001191443490000049
Is the oxygen concentration at the interface of the microporous layer and the catalytic layer;
Figure BDA00011914434900000410
is the oxygen concentration at the interface of the catalyst layer and the proton exchange membrane;
Figure BDA00011914434900000411
is the effective diffusion coefficient of oxygen in the cathode catalytic layer.
Average oxygen concentration of cathode catalyst layer:
Figure BDA00011914434900000412
the control equations of the reaction gases in the flow channel, the diffusion layer and the microporous layer region can be similarly listed, and then the real concentration of the reaction gases in the catalytic layer can be obtained by combining the boundary conditions of the hydrogen concentration in the anode flow channel and the oxygen concentration in the cathode flow channel.
(4) Water management
The water transmembrane transport mode comprises three modes of electroosmosis dragging, membrane water diffusion and differential pressure diffusion.
The electroosmotic drag effect is represented by proton transport across the membrane, and at the same time, will drag a certain amount of water from the anode to the cathode, and the electroosmotic drag coefficient ndFor the number of water molecules accompanying each proton transmembrane from anode to cathode:
Figure BDA00011914434900000413
film state water diffusion coefficient DmThe calculation method of (2) is as follows:
Figure BDA0001191443490000051
for anode catalyst layer water conservation equation:
Figure BDA0001191443490000052
Figure BDA0001191443490000053
wherein JvapWater vapor transport flux; c. Cvap，MPL-CLThe water vapor concentration of the interface of the anode microporous layer and the catalytic layer; c. Cvap，CL-PEMIs the water vapor concentration of the interface of the catalyst layer and the proton exchange membrane;
Figure BDA0001191443490000054
effective diffusion rate of water vapor in the catalyst layer; rhodryDry film density; EW is equivalent mass of the proton exchange membrane; lambda [ alpha ]aclλcclAnode and cathode catalytic layer modal water content, respectively; kmIs the permeability of the membrane;
Figure BDA0001191443490000055
anode and cathode catalytic layers respectively.
Equation for conservation of water for the cathode catalyst layer:
Figure BDA0001191443490000056
Figure BDA0001191443490000057
where ρ islThe density of the liquid water is;
Figure BDA0001191443490000058
is the molar mass of water; scclIs liquid water volume fraction of the cathode catalyst layer; epsiloncclPorosity of the cathode catalytic layer; kl，clIs the permeability of water in the catalyst layer; mu.slIs the kinetic viscosity of water;
Figure BDA0001191443490000059
is the hydraulic pressure of the interface of the cathode catalyst layer and the proton exchange membrane;
Figure BDA00011914434900000510
is the hydraulic pressure of the interface of the cathode microporous layer and the catalytic layer; j. the design is a squarelIs a liquid water flux.
The water control equations of the diffusion layer and the microporous layer region can be similarly listed, and the water vapor concentration of each anode layer and the interface hydraulic pressure of each cathode layer are obtained by assuming that no liquid water exists in the middle flow channel and combining the boundary condition that the water vapor concentration in the anode flow channel and the hydraulic pressure at the interface of the cathode flow channel and the diffusion layer are equal to one atmosphere.
Obtaining capillary pressure p in the porous medium by Leverett equationcAnd liquid water volume fraction s:
Pc＝Pg-Pl4-7
Figure BDA0001191443490000065
Figure BDA0001191443490000061
wherein
Figure BDA0001191443490000062
A surface tension coefficient; theta is the hydraulic pressure P obtained by the contact angle of the porous mediumlThen, the volume fraction s of liquid water in each part of the battery is obtained.
Substituting the water distribution condition in the battery obtained in the step (4) into the step (2) and the step (3), calculating the ohmic loss and the activation loss according to the formulas 2-1, 3-1 and 3-2, substituting the ohmic loss and the activation loss into the formula 1-1, and finally calculating the battery predicted output voltage of the one-dimensional model.
The 1+1+1 quasi-three-dimensional model comprises the superposition of the x direction perpendicular to the polar plate direction, the y direction along the flow passage direction, and the z direction perpendicular to the flow passage and the ribbed plate.
The one-dimensional model in the X direction is to determine the voltage by setting the current, and after determining the voltage of the first group of cells, determine the current density of the second group of cells by using the voltage.
The method for constructing the 1+1+ 1-dimensional quasi-three-dimensional model comprises the following specific steps:
(1) the establishment of the x-direction vertical plate direction one-dimensional model is the same as the 4 steps described in claim 1.
(2) The method for establishing the one-dimensional model along the flow direction in the y direction comprises the following specific steps:
two groups of battery segments are connected in parallel, the output voltage is the same, the output current density is different, and the battery is divided into two parts along the flow direction.
Given a first set of cell segment current densities IaThe output voltage E of the first group of battery segments is determined by the 4 steps of claim 1a，out。
Eb，out＝Ea，out5-1
Current density I of second group of battery segmentsbThe method comprises the following steps:
Figure BDA0001191443490000063
ηact，cat＝Erev-Eout-ηohm-ηact，ano5-3
Figure BDA0001191443490000064
wherein
Figure BDA0001191443490000071
The hydrogen concentration in the anode catalytic layer and the oxygen concentration in the cathode catalytic layer of the second cell segment are respectively shown.
Assuming a current density of Iassume，
Anode catalyst layer hydrogen concentration:
Figure BDA0001191443490000072
Figure BDA0001191443490000073
cathode catalyst layer oxygen concentration:
Figure BDA0001191443490000074
Figure BDA0001191443490000075
on the boundary condition, the outlet hydrogen concentration of the anode of the first group of cell segments is the inlet hydrogen concentration of the second group of cell segments, and the outlet oxygen concentration of the cathode of the first group of cell segments is the inlet oxygen concentration of the second group of cell segments.
Will be provided with
Figure BDA0001191443490000076
Carry over 5-2 to obtain ηact，anoη will beact，anoCarry over 5-3 to obtain ηact，catThe current density I can be determined from 5 to 4solve。
When in use
Figure BDA0001191443490000077
When, IsolveI.e. the solved current density of the second set of cell segments.
(3) The method comprises the following steps of establishing a one-dimensional model in a direction perpendicular to a flow channel and a ribbed plate along a z direction:
the battery is divided into a first group of battery sections below the runner and a third group of battery sections below the rib plate along the z direction, the first group of battery sections and the third group of battery sections are connected in parallel, and output voltages are the same.
Current density I of the first group of cell segmentsaThe output voltage E can be determined by the 4 steps of claim 1a，out，
Ec，out＝Ea，out6-1
Current density I of the third group of cell segmentscThe method comprises the following steps:
Figure BDA0001191443490000078
ηact，cat＝Erev-Eout-ηohm-ηact，ano6-3
Figure BDA0001191443490000079
wherein
Figure BDA00011914434900000710
The hydrogen concentration in the anode catalytic layer and the oxygen concentration in the cathode catalytic layer of the third cell segment are respectively shown.
Assuming a current density of Iassume，
The reaction gas in the third group of cell section catalytic layers comprises a reaction gas diffused by the third group of cell section microporous layers and the first group of cell section catalytic layers.
Hydrogen concentration of anode catalyst layer of third group of cell segments:
Figure BDA0001191443490000081
Figure BDA0001191443490000082
oxygen concentration of cathode catalyst layer of third group of cell segments:
Figure BDA0001191443490000083
Figure BDA0001191443490000084
wherein
Figure BDA0001191443490000085
Respectively representing the hydrogen and oxygen concentrations of the interface of the microporous layer and the catalytic layer of the third group of cell sections and the interface of the catalytic layer and the proton exchange membrane;
Figure BDA0001191443490000086
respectively representing the average concentration of hydrogen and oxygen in the catalytic layer of the third group of cell segments;
Figure BDA0001191443490000087
respectively, represent the average hydrogen and oxygen concentrations in the catalytic layer of the first cell segment.
The concentration of the reaction gas in the catalyst layer of the first group of cell segments is determined from the above step (3.2) and is a known amount.
Will be provided with
Figure BDA0001191443490000088
Carry over 6-2 to obtain ηact，anoη will beact，anoCarry over 6-3 to obtain ηact，catThe current density I can be determined from 6-4solve。
When in use
Figure BDA0001191443490000089
When, IsolveThe solved current density of the third group of battery segments.
In order to obtain the average liquid water volume fraction s in each layer of the cell and the reactant concentration in the catalytic layer, a calculation domain is established according to the physical structure of the proton exchange membrane fuel cell, as shown in fig. 1, and each layer of interface is used as a solving node.
The invention uses hydraulic pressure plAs the solving parameter of the liquid water control equation, the hydraulic pressure p at the interface is solved firstlAnd then the liquid water volume fraction s on both sides of the interface is obtained by a Leverett equation.
And solving a mass conservation equation of the reactant and the water to obtain an average liquid water volume fraction s in each layer of the battery and the concentration of the reactant in the catalytic layer, thereby solving ohmic loss and activation loss and solving the predicted output voltage. The output voltage of the proton exchange membrane fuel cell under different working conditions can be predicted by adjusting the working conditions such as current density, temperature, relative humidity of inlet air and the like. The influence of the battery structure and design parameters on the battery performance can also be researched by adjusting the battery design parameters, such as the porosity and hydrophobicity of each layer of porous medium.
The invention has the characteristics and beneficial effects that:
(1) the prediction method has high efficiency and accuracy, can predict the output voltage of the proton exchange membrane fuel cell under different working conditions, and can be used for researching the influence of cell design parameters on the performance. The actual applicability of the fuel cell control model is higher than that of the fuel cell control model because the voltage prediction is performed on the actual reactant gas concentration and water management under various working conditions. Due to the analytical model method, the calculation time can be greatly saved by the numerical model.
(2) The method can be used for developing a one-dimensional analytical model perpendicular to the polar plate direction and a quasi three-dimensional analytical model with 1+1+1 dimension. The quasi-three-dimensional analytical model can ensure the calculation efficiency and obtain the research results of some three-dimensional models.
(3) In the water management solution, the control equation of water takes hydraulic pressure as the solution quantity, the concept of 'liquid water step change at the interface' is introduced, the condition that the volume fractions of liquid water at two sides of the interface of the adjacent layers are discontinuous due to the fact that the adjacent two layers are made of porous medium materials with different structural parameters and hydrophobicity is considered, and the influence on the water management caused by the difference of the material parameters of the layers can be obtained.
Drawings
FIG. 1 is a physical structure diagram of a one-dimensional model perpendicular to the polar plate direction and a quasi-three-dimensional model with 1+1+1 dimensions.
FIG. 2 is a block diagram of an iterative method of solving the water control equation in the present invention.
FIG. 3 compares the predicted voltage using the model of the present invention with the experimental results.
Fig. 4 illustrates the effect of battery operating temperature on battery performance using the inventive model quantification.
Fig. 5 uses the present model to quantify the effect of catalytic and microporous layer hydrophobicity (contact angle) combinations on cell performance.
Detailed Description
The design of the present invention is further illustrated by the following examples in conjunction with the drawings, and it should be noted that the examples are illustrative for clearly explaining the modeling steps, and not to limit the scope of the present invention.
The proton exchange membrane fuel cell performance prediction model establishing method includes one-dimensional model perpendicular to polar plate direction and 1+1+1 dimensional quasi-three-dimensional model.
The specific steps of the method for constructing the one-dimensional model vertical to the polar plate direction comprise:
(1) determining the battery output voltage Eout
Eout＝Erev-ηohm-ηact1-1
The output voltage of the battery is equal to the reversible voltage ErevOhmic loss η of reduced voltageohmAnd activation loss of voltage ηactOhmic losses and activation losses include voltage losses due to reactant concentrations and water losses.
ErevThe method is obtained by the Nernst equation:
Figure BDA0001191443490000091
in the formula: Δ G-Gibbs free energy change; F-Faraday constant 96487C/mol; Δ S is entropy change; r-ideal gas constant 8.314J/mol K; t-working condition temperature K; t isref-a reference temperature K;
Figure BDA0001191443490000101
the anode catalytic layer hydrogen pressure and the cathode catalytic layer oxygen pressure are respectively.
Ohmic loss and activation loss were determined, and the cell output voltage was determined from 1-1.
(2) Determining ohmic losses ηohm
(2.1) ohmic losses including plate ηohm，PLayer η of porous mediaohm，porAnd ohmic losses η caused by the proton exchange membraneohm，mAnd (c) the sum, i.e.:
Figure BDA0001191443490000102
ηohmalso known as ohmic overpotential, where I is the current density A/m2；
Figure BDA0001191443490000103
The surface resistances are respectively used for transmitting electrons for the flow channel polar plate and each layer of the porous medium;
Figure BDA0001191443490000104
the surface resistance of the catalytic layer and the proton exchange membrane for transferring protons is respectively represented by the following solving general formula:
Ω＝L/σeff2-2
wherein L is the transmission distance, also denoted thickness; sigmaeffIs the effective conductivity.
And the effective electric conductivity of electrons in each layer and the electric conductivity of protons in the catalytic layer and the proton exchange membrane are obtained in the next step.
(2.2) effective conductivity of electrons in porous dielectric layer
The porous medium layer includes a diffusion layer, a microporous layer, and a catalytic layer. The effective value of the variables in the porous medium is usually corrected by Bruggemann, and the correction coefficient is 1.5:
for a diffusion layer or microporous layer or catalytic layer:
Figure BDA0001191443490000105
in the formula
Figure BDA0001191443490000106
Represents the effective conductivity of the electrons; sigmasIs the electron intrinsic conductivity; ε is the porosity.
(2.3) effective conductivity of protons in the proton exchange Membrane and in the catalytic layer
Figure BDA0001191443490000107
Figure BDA0001191443490000108
σmDepending on the water content in Nafion:
Figure BDA0001191443490000109
wherein λ is the Nafion water content.
Figure BDA00011914434900001010
For the catalytic layer, the water activity is: a isc1RH is the relative humidity of the gas in the catalyst layer, and s is the gas in the pores of the catalyst layerLiquid water volume fraction. For proton exchange membranes, the water activity is approximately equal to the average of the water activities in the anode catalytic layer and the cathode catalytic layer:
Figure BDA0001191443490000111
the proton conductivity is related to the water management in the battery, and the water distribution condition in the battery is obtained, so that the proton conductivity can be obtained.
(3) Determination of activation loss
(3.1) analytical solution of activation loss:
Figure BDA0001191443490000112
Figure BDA0001191443490000113
since the porous medium contains gas and liquid water in the gaps thereof at the same time
Figure BDA0001191443490000114
And
Figure BDA0001191443490000115
respectively the apparent concentration of hydrogen in the anode catalytic layer and the apparent concentration of oxygen in the cathode catalytic layer,
Figure BDA0001191443490000116
wherein
Figure BDA0001191443490000117
The actual concentration of hydrogen in the anode catalytic layer and the actual concentration of oxygen in the cathode catalytic layer are respectively; epsilonacl，εcclPorosity of the anode catalyst layer and the cathode catalyst layer respectively; saclAnd scclLiquid water volume fractions of the anode catalytic layer and the cathode catalytic layer, respectively.
And (5) obtaining the activation overpotential, and obtaining the real concentration of the reaction gas in the catalytic layer and the water distribution in the cell.
(3.2) gas concentration in the catalytic layer:
and (4) obtaining the hydrogen concentration in the anode catalytic layer and the oxygen concentration in the cathode catalytic layer under various working conditions through gas transmission analysis in the battery. The diffusion transmission mode of hydrogen and oxygen in the porous medium structure in the battery follows Fick's law:
Figure BDA0001191443490000118
anode catalyst layer hydrogen concentration:
Figure BDA0001191443490000119
average hydrogen concentration of anode catalyst layer:
Figure BDA00011914434900001110
cathode catalyst layer oxygen concentration:
Figure BDA0001191443490000121
average oxygen concentration of cathode catalyst layer:
Figure BDA0001191443490000122
the transmission process of the gas in the battery is influenced by the water distribution in the battery, and the water distribution needs to be solved first when the solution is carried out, and then the solution is carried out on a gas transport equation.
(4) Water management
And (4) as described in the step (2) and the step (3), the proton conductivity and the gas transmission in the porous medium layer are both related to the water distribution in the cell, and the gas-liquid-water conservation equation with the hydraulic pressure as a variable is solved to further obtain the water distribution in the cell.
The water in the cell exists in three forms of gaseous water, liquid water and membrane water, and the water content of Nafion mentioned in the above formula (1.3) is membrane water.
The water transmembrane transport mode comprises three modes of electroosmosis dragging, membrane water diffusion and differential pressure diffusion.
The electroosmotic drag effect is represented by proton transmembrane transport and electroosmotic drag coefficient ndFor the number of water molecules accompanying each proton transmembrane from anode to cathode:
Figure BDA0001191443490000123
according to the steady-state lower phase equilibrium principle, liquid water is formed after water vapor is saturated, water is generated by electrochemical reaction and cathode reaction, water is brought from an anode to a cathode by the electroosmosis dragging effect, the cathode water vapor is always in a saturated state and exists in the liquid water, the anode water vapor is difficult to saturate, and therefore the anode does not have the liquid water.
Film state water diffusion coefficient DmThe calculation method of (2) is as follows:
Figure BDA0001191443490000124
for anode catalyst layer water conservation equation:
Figure BDA0001191443490000125
Figure BDA0001191443490000131
equation for conservation of water for the cathode catalyst layer:
Figure BDA0001191443490000132
Figure BDA0001191443490000133
obtaining capillary pressure p in the porous medium by Leverett equationcAnd liquid water volume fraction sThe relationship is as follows:
Pc＝Pg-Pl4-7
Figure BDA0001191443490000134
Figure BDA0001191443490000135
substituting the water distribution condition in the battery obtained in the step (4) into the step (2) and the step (3), calculating the ohmic loss and the activation loss according to the formulas 2-1, 3-1 and 3-2, substituting the ohmic loss and the activation loss into the formula 1-1, and finally calculating the battery predicted output voltage of the one-dimensional model.
The 1+1+1 quasi-three-dimensional model comprises a flow channel and a rib plate, wherein the x direction is vertical to the polar plate direction, the y direction is vertical to the flow channel direction, the z direction is vertical to the flow channel and the rib plate, the 1+1+1 quasi-three-dimensional model is constructed by the superposition of the three directions, and the specific steps comprise:
(1) the establishment of the one-dimensional model in the direction perpendicular to the polar plate in the x direction is the same as the 4 steps.
(2) The method for establishing the one-dimensional model along the flow direction in the y direction comprises the following specific steps:
as shown in fig. 1, two groups of battery segments are connected in parallel, the output voltages are the same, but the output current densities are different, and the battery is divided into two parts along the flow direction.
Given a current density I of a first group of battery segments aaObtaining the output voltage E of the first group of battery segments by the 4 stepsa，out：
Eb，out＝Ea，out5-1
Second group of battery segments b current density IbThe method comprises the following steps:
Figure BDA0001191443490000136
ηact，cat＝Erev-Eout-ηohm-ηact，ano5-3
Figure BDA0001191443490000141
finally obtaining the solution quantity from the current density, and solving
Figure BDA00011914434900001410
The process requires the use of a current density, thus the current density is assumed to be Iassume，
Anode catalyst layer hydrogen concentration:
Figure BDA0001191443490000142
Figure BDA0001191443490000143
cathode catalyst layer oxygen concentration:
Figure BDA0001191443490000144
Figure BDA0001191443490000145
will be provided with
Figure BDA0001191443490000146
Carry over 5-2 to obtain ηact，anoη will beact，anoCarry over 5-3 to obtain ηact，catThe current density I can be determined from 5 to 4solve，
When in use
Figure BDA0001191443490000147
When, IsolveI.e. the solved current density of the second set of cell segments.
(3) The method comprises the following steps of establishing a one-dimensional model in a direction perpendicular to a flow channel and a ribbed plate along a z direction:
the first group of battery segments a and the third group of battery segments c are connected in parallel, and the output voltage E can be obtained by the 4 stepsa，out：
Ec，out＝Ea，out6-1
Current density I of third group of battery segments ccThe method comprises the following steps:
Figure BDA0001191443490000148
ηact，cat＝Erev-Eout-ηohm-ηact，ano6-3
Figure BDA0001191443490000149
the reaction gas in the third group of cell section catalytic layers comprises a reaction gas diffused by the third group of cell section microporous layers and the first group of cell section catalytic layers.
Hydrogen concentration of anode catalyst layer of third group of cell segments:
Figure BDA0001191443490000151
Figure BDA0001191443490000152
oxygen concentration of cathode catalyst layer of third group of cell segments:
Figure BDA0001191443490000153
Figure BDA0001191443490000154
will be provided with
Figure BDA0001191443490000155
Carry over 6-2 to obtain ηact，anoη will beact，anoCarry over 6-3 to obtain ηact，catThe current density I can be determined from 6-4solve，
When in use
Figure BDA0001191443490000156
When, IsolveThe solved current density of the third group of battery segments.
Detailed description of the preferred embodiments
Establishing a physical model according to the physical structure of the proton exchange membrane fuel cell, wherein the physical model comprises the following assumptions:
(a) the gas flow channel in the flow channel is regarded as one-dimensional steady laminar flow;
(b) the flow channel is set to be a straight flow channel, namely, liquid water in the flow channel can be quickly blown away by the intake air;
(c) the temperature and the air pressure of each part in the battery are regarded as the same, the temperature is a given working temperature, and the air pressure is one atmosphere;
(d) because of the lower working temperature, the water generated by the electrochemical reaction is liquid water, and the membrane water content in the proton exchange membrane is an equilibrium value;
(e) the materials of the cell layers are considered to be isotropic.
The present example relates to the following main parameters:
the battery works at constant current, the temperature T is 343.15K, and the current density I is 10000A/m2Or 1A/cm2The inlet of the cathode and anode is 1atm, the anode hydrogen and the cathode air are supplied with ST-2 in a given stoichiometric ratio, the inlet air of the cathode and anode is fully humidified RH-100%, the flow channel is 0.1m long, and the area of the electrode plate is 2 multiplied by 10-4m2。
The design parameters of the cell comprise that Nafion212 is adopted as a proton exchange membrane, and the thickness is 5 multiplied by 10-5m, equivalent mass EW of 2.1 kg/mol.
The porosity of the diffusion layer, the micropore layer and the catalytic layer is 0.6, 0.4 and 0.3 in sequence, the contact angle reflects the hydrophobicity, and the integral number of the electrolyte bodies of the anode catalytic layer and the cathode catalytic layer is 0.2 at 100 degrees, 110 degrees and 100 degrees in sequence.
(1) Output voltage of battery
Eout＝Erev-ηohm-ηact
Figure BDA0001191443490000161
(2) Ohmic loss
Figure RE-GDA0001271400410000162
The water content in the cell is obtained first, then the proton conductivity is obtained, and further the ohmic loss is obtained.
(3) Loss of activation
Hydrogen and oxygen with certain humidity are respectively introduced into the anode and cathode flow channels, and the concentration of water vapor in the inlet air
Figure BDA0001191443490000163
In anode inlet gas H2At a concentration of
Figure BDA0001191443490000164
The cathode intake air is air, and the oxygen accounts for the volume fraction of the air
Figure BDA0001191443490000165
0.21, O in cathode intake gas2At a concentration of
Figure BDA0001191443490000166
The actual supply of the fuel cell is always given a stoichiometric ratio ST of the reactants, from which the cathode and anode inlet flow rates V are determinedinGas concentration at the outlet coutAnd the average gas concentration c in the flow channelch：
Anode hydrogen gas:
Figure BDA0001191443490000167
Figure BDA0001191443490000168
cathode oxygen:
Figure BDA0001191443490000169
Figure BDA00011914434900001610
law of fick
Figure BDA00011914434900001611
Can find out
Figure BDA00011914434900001612
Activation overpotential solving equation:
Figure BDA0001191443490000171
Figure BDA0001191443490000172
the proton conductivity in the catalyst layer is included, and the activation overpotential can be obtained by obtaining the water content in the battery.
(4) Water management
Conservation equation of water in the anode catalyst layer:
Figure BDA0001191443490000173
cathode catalyst layer water conservation equation:
Figure BDA0001191443490000174
an iterative method is adopted to solve the control equation of water, the iterative flow is shown in figure 2, and the specific iterative process is as follows:
the iteration variable is the average liquid water volume fraction s in each layer of the cell structure, the s value is between 0 and 1, 0.5 is taken as the initial value of s in each layer, the selection of the initial value has no influence on the final true value result,
Figure BDA0001191443490000175
wherein s iskAssigning a value of s to the k-th iterationSubstituting the initial value as the initial value calculated in the step (k + 1) to obtain an old value;
Figure BDA0001191443490000176
for the k +1 step, the value of s is calculatedk+1Giving the value of s after the (k + 1) th iteration, namely a new value; urf is a relaxation factor, and in the present example, urf is 0.1; first term on right of equation
Figure BDA0001191443490000177
I.e. the increment per iteration.
After each iteration, if the difference between the new value and the old value is less than a certain condition, the equation is considered to be converged, and the residual error is used in the embodiment
Figure BDA0001191443490000178
As a convergence criterion, the value of s is now the true value that satisfies the equation. Obtaining by solution:
water vapor concentration at each layer interface of the anode:
Figure BDA0001191443490000179
hydraulic pressure at each interface of the cathode:
Figure BDA00011914434900001710
the air pressure of each part in the cell is 101325Pa, and the capillary pressure at the interface of each layer of the cathode:
Figure BDA0001191443490000181
by
Figure BDA0001191443490000182
Obtaining the liquid water volume fraction at the interface of each layer of the cathode:
{sGDL-mpl，sgdl-MPL，sMPL-cl，smpl-CL，scl-pem}＝{0.299，0.145，0.213，0.413，0.416}
wherein s isGDL-mplThe volume fraction of liquid water on the diffusion layer side of the interface of the diffusion layer and the microporous layer, sgdl-MPLThe liquid water volume fraction on the microporous layer side of the interface of the diffusion layer and the microporous layer.
The average water vapor concentration or liquid water volume fraction in each layer is the average value at both ends of the layer:
average water vapor concentration in each layer of the anode:
Figure BDA0001191443490000183
relative humidity in each layer of the anode:
Figure BDA0001191443490000184
average liquid water volume fraction in each layer of the cathode:
Figure BDA0001191443490000185
and (3) substituting the water distribution in the battery into (2) and (3) respectively calculating ohmic loss and activation loss:
water activity of anode catalyst layer: a isac1＝RHacl+2sacl＝0.7754
Water activity of the cathode catalyst layer: a iscc1＝RHccl+2sccl＝1.810
Water activity in the proton exchange membrane:
Figure BDA0001191443490000186
film water content: λ ═ 14.0+1.4(a-1) ═ 14.41
Film conductivity
Figure BDA0001191443490000187
Ohmic loss:
Figure BDA0001191443490000188
loss of anode activation:
Figure BDA0001191443490000189
Figure BDA00011914434900001810
(5) finally, the output voltage of the battery is obtained
Output voltage E of batteryout＝Erev-ηohm-ηact＝0.429V
Fig. 3, 4, and 5 are expected results of the study using the present modeling method:
FIG. 3 is a comparison of model prediction and experimental values under battery operating parameters, with good agreement between model simulation results and experimental results.
Fig. 4 is a graph of the effect of battery operating temperature on battery performance.
Fig. 5 is a graph of the effect of the combination of catalytic layer and microporous layer hydrophobicity (contact angle) on cell performance.

Claims (2)

1. The method for establishing the proton exchange membrane fuel cell performance prediction model is characterized in that: the constructed model comprises a one-dimensional model vertical to the polar plate direction and a 1+1+ 1-dimensional quasi-three-dimensional model, wherein the method for constructing the one-dimensional model vertical to the polar plate direction comprises the following specific steps:
(1) determining battery output voltage
Eout＝Erev-ηohm-ηact1-1
Wherein EoutRepresents the battery output voltage; erevIndicating a reversible voltage ηohmRepresenting ohmic losses of voltage ηactThe activation loss of voltage is expressed, and the ohmic loss and the activation loss include voltage loss caused by reactant concentration and water loss,
the reversible voltage is obtained by the nernst equation:
Figure FDA0002261774960000011
in the formula: erevIs a reversible voltage; Δ G is gibbs free energy variation; f is a Faraday constant; Δ S is entropy change; r is an ideal gas constant; t is the working condition temperature; t isrefIs a reference temperature;
Figure FDA0002261774960000012
respectively anode catalytic layer hydrogen pressure and cathode catalytic layer oxygen pressure;
the output voltage of the battery can be obtained from 1-1 by obtaining ohmic loss and activation loss,
(2) determination of ohmic losses
(2.1) the ohmic loss comprises the sum of ohmic losses caused by the polar plate, the porous medium layer and the proton exchange membrane, namely:
Figure FDA0002261774960000013
η thereinohm,P、ηohm,porAnd ηohm,mOhmic losses caused by the polar plate, the porous medium layer and the proton exchange membrane respectively; i is the current density;
Figure FDA0002261774960000014
the surface resistances are respectively used for transmitting electrons for the flow channel polar plate and each layer of the porous medium;
Figure FDA0002261774960000016
Figure FDA0002261774960000015
the surface resistance of the catalytic layer and the proton exchange membrane for transferring protons is respectively represented by the following solving general formula:
Ω＝L/σeff2-2
wherein L is the transmission distance, also denoted thickness; sigmaeffIn order to be of an effective electrical conductivity,
the next step is to find the effective electric conductivity of electrons in each layer and the proton electric conductivity in the catalyst layer and the proton exchange membrane,
(2.2) effective conductivity of electrons in porous dielectric layer
The effective value of the variables in the porous medium is usually corrected by Bruggemann, and the correction coefficient is 1.5:
for a diffusion layer or microporous layer or catalytic layer:
Figure FDA0002261774960000021
in the formula
Figure FDA0002261774960000022
Represents the effective conductivity of the electrons; sigmasIs the electron intrinsic conductivity; epsilon is the porosity of the porous material,
(2.3) effective conductivity of protons in the proton exchange Membrane and in the catalytic layer
Figure FDA0002261774960000023
In the formula
Figure FDA0002261774960000024
Effective conductivity for protons in the catalytic layer; xmThe volume fraction of electrolyte Nafion in the catalytic layer; sigmamIs the proton conductivity of the proton exchange membrane Nafion,
σmdepending on the water content in Nafion:
Figure FDA0002261774960000025
wherein lambda is the water content of Nafion,
Figure FDA0002261774960000026
wherein a is the water activity of the water,
for the catalytic layer:
acl＝RH+2s 2-7
wherein RH is the relative humidity of gas in the catalytic layer, and s is the volume fraction of liquid water in pores of the catalytic layer;
for theProton exchange Membrane, Water Activity aaverEqual to the average value of the water activities in the anode catalytic layer and the cathode catalytic layer:
Figure FDA0002261774960000027
(3) determination of activation loss
(3.1) analytical solution of activation loss:
Figure FDA0002261774960000028
Figure FDA0002261774960000029
η thereinact,ano，ηact,catRepresenting the activation overpotential of the anode and the cathode respectively, α is the charge transfer coefficient, n is the number of electrons transferred in unit reaction;
Figure FDA0002261774960000031
and
Figure FDA0002261774960000032
a reference hydrogen concentration and a reference oxygen concentration,
(3.2) gas concentration in the catalytic layer:
the diffusion and transmission mode of hydrogen and oxygen in the porous medium structure in the battery follows Fick's law:
Figure FDA0002261774960000033
the anode and the cathode respectively comprise four solution domains, namely a flow channel, a diffusion layer, a microporous layer and a catalytic layer,
anode catalyst layer hydrogen concentration:
Figure FDA0002261774960000034
wherein
Figure FDA0002261774960000035
Hydrogen concentration at the interface of the microporous layer and the catalytic layer;
Figure FDA0002261774960000036
hydrogen concentration at the interface of the catalyst layer and the proton exchange membrane;
Figure FDA0002261774960000037
corrected by Bruggeman for effective diffusion coefficient of hydrogen in anode catalytic layer
Figure FDA0002261774960000038
δCLThe thickness of the catalyst layer is used,
average hydrogen concentration of anode catalyst layer:
Figure FDA0002261774960000039
cathode catalyst layer oxygen concentration:
Figure FDA00022617749600000310
wherein
Figure FDA00022617749600000311
Is the oxygen concentration at the interface of the microporous layer and the catalytic layer;
Figure FDA00022617749600000312
is the oxygen concentration at the interface of the catalyst layer and the proton exchange membrane;
Figure FDA00022617749600000313
is the effective diffusion coefficient of oxygen in the cathode catalytic layer,
average oxygen concentration of cathode catalyst layer:
Figure FDA00022617749600000314
the reactant gas control equations for the flow channels, diffusion layer, microporous layer regions can be similarly set out, and then combined with the boundary conditions for hydrogen concentration in the anode flow channel and oxygen concentration in the cathode flow channel,
(4) water management
The water transmembrane transport mode comprises three modes of electroosmosis dragging, membrane state water diffusion and differential pressure diffusion,
the electroosmotic drag effect is represented by proton transport across the membrane, and at the same time, will drag a certain amount of water from the anode to the cathode, and the electroosmotic drag coefficient ndFor the number of water molecules accompanying each proton transmembrane from anode to cathode:
Figure FDA0002261774960000041
film state water diffusion coefficient DmThe calculation method of (2) is as follows:
Figure FDA0002261774960000042
for anode catalyst layer water conservation equation:
Figure FDA0002261774960000043
Figure FDA0002261774960000044
wherein JvapWater vapor transport flux; c. Cvap,MPL-CLThe water vapor concentration of the interface of the anode microporous layer and the catalytic layer; c. Cvap,CL-PEMIs the water vapor concentration of the interface of the catalyst layer and the proton exchange membrane;
Figure FDA0002261774960000045
for effective diffusion of water vapour in the catalytic layerThe scattering rate; rhodryDry film density; EW is equivalent mass of the proton exchange membrane; lambda [ alpha ]acl，λcclRespectively the anode and cathode catalytic layer membrane state water content; kmIs the permeability of the membrane;
Figure FDA0002261774960000046
respectively the liquid water pressure of the anode and cathode catalyst layers,
equation for conservation of water for the cathode catalyst layer:
Figure FDA0002261774960000047
Figure FDA0002261774960000048
where ρ islThe density of the liquid water is;
Figure FDA0002261774960000049
is the molar mass of water; kl,clIs the permeability of water in the catalyst layer; mu.slIs the kinetic viscosity of water;
Figure FDA00022617749600000410
is the hydraulic pressure of the interface of the anode catalyst layer and the proton exchange membrane;
Figure FDA00022617749600000411
is the hydraulic pressure of the interface of the cathode microporous layer and the catalytic layer; j. the design is a squarelIs the flux of the liquid water flow,
the water control equations of the diffusion layer and the microporous layer region can be similarly listed, the water vapor concentration of each anode layer and the interface hydraulic pressure of each cathode layer are obtained by assuming that no liquid water exists in the middle flow channel and combining the boundary condition that the water vapor concentration in the anode flow channel and the hydraulic pressure at the interface of the cathode flow channel and the diffusion layer are equal to one atmosphere,
obtaining capillary pressure p in the porous medium by Leverett equationcAnd liquid water volume fraction s:
Pc＝Pg-Pl4-7
Figure FDA0002261774960000051
Figure FDA0002261774960000052
wherein sigmalqA surface tension coefficient; theta is the hydraulic pressure P obtained by the contact angle of the porous mediumlThen the volume fraction s of liquid water in each part of the battery is calculated,
substituting the water distribution condition in the battery obtained in the step (4) into the step (2) and the step (3), calculating the ohmic loss and the activation loss according to the formulas 2-1, 3-1 and 3-2, substituting the ohmic loss and the activation loss into the formula 1-1, and finally calculating the battery predicted output voltage of the one-dimensional model.
2. The method for establishing the proton exchange membrane fuel cell performance prediction model according to claim 1, wherein: the 1+1+1 quasi-three-dimensional model comprises a flow channel and a rib plate, wherein the x direction is vertical to the polar plate direction, the y direction is vertical to the flow channel direction, the z direction is vertical to the flow channel and the rib plate, the 1+1+1 quasi-three-dimensional model is constructed by the superposition of the three directions, and the specific steps comprise:
(1) the establishment of the x-direction vertical plate direction one-dimensional model is the same as the 4 steps described in claim 1,
(2) the method for establishing the one-dimensional model along the flow direction in the y direction comprises the following specific steps:
two groups of battery segments are connected in parallel, the output voltage is the same, the output current density is different, the battery is divided into two parts along the flow direction,
given a first set of cell segment current densities IaThe output voltage E of the first group of battery segments is determined by the 4 steps of claim 1a,out，
Eb,out＝Ea,out5-1
Current density I of second group of battery segmentsbObtained by the following steps：
Figure FDA0002261774960000053
ηact,cat＝Erev-Eout-ηohm-ηact,ano5-3
Figure FDA0002261774960000061
Wherein
Figure FDA0002261774960000062
Respectively representing the hydrogen concentration in the anode catalytic layer and the oxygen concentration in the cathode catalytic layer of the second battery section, assuming that the current density is Iassume，
Anode catalyst layer hydrogen concentration:
Figure FDA0002261774960000063
Figure FDA0002261774960000064
cathode catalyst layer oxygen concentration:
Figure FDA0002261774960000065
Figure FDA0002261774960000066
on the boundary condition, the concentration of the hydrogen at the outlet of the anode of the first battery section is the concentration of the hydrogen at the inlet of the second battery section, and the concentration of the oxygen at the outlet of the cathode of the first battery section is the concentration of the oxygen at the inlet of the second battery section, the hydrogen concentration at the outlet of the anode of the first battery section is the concentration of the oxygen at the
Figure FDA0002261774960000067
Carry over 5-2 to obtain ηact,anoη will beact,anoCarry over 5-3 to obtain ηact,catThe current density I can be determined from 5 to 4solve，
When in use
Figure FDA0002261774960000068
When, IsolveI.e. the solved current density of the second set of cell segments,
(3) the method comprises the following steps of establishing a one-dimensional model in a direction perpendicular to a flow channel and a ribbed plate along a z direction:
the battery is divided into a first group of battery sections below the runner and a third group of battery sections below the ribbed plate along the z direction, the first group of battery sections and the third group of battery sections are connected in parallel, the output voltages are the same,
current density I of the first group of cell segmentsaThe output voltage E can be determined by the 4 steps of claim 1a,out，
Ec,out＝Ea,out6-1
Current density I of the third group of cell segmentscThe method comprises the following steps:
Figure FDA0002261774960000069
ηact,cat＝Erev-Eout-ηohm-ηact,ano6-3
Figure FDA0002261774960000071
wherein
Figure FDA0002261774960000072
Respectively shows the hydrogen concentration in the anode catalytic layer and the oxygen concentration in the cathode catalytic layer of the third group of cell segments,
the reaction gas in the third group of cell section catalytic layer comprises a reaction gas diffused by the third group of cell section microporous layer and the first group of cell section catalytic layer,
hydrogen concentration of anode catalyst layer of third group of cell segments:
Figure FDA0002261774960000073
Figure FDA0002261774960000074
oxygen concentration of cathode catalyst layer of third group of cell segments:
Figure FDA0002261774960000075
Figure FDA0002261774960000076
wherein
Figure FDA0002261774960000077
Respectively representing the hydrogen and oxygen concentrations of the interface of the microporous layer and the catalytic layer of the third group of cell sections and the interface of the catalytic layer and the proton exchange membrane;
Figure FDA0002261774960000078
respectively representing the average concentration of hydrogen and oxygen in the catalytic layer of the third group of cell segments;
Figure FDA0002261774960000079
respectively representing the average concentrations of hydrogen and oxygen in the catalyst layers of the first group of cell segments, the concentration of the reaction gas in the catalyst layers of the first group of cell segments being determined by the step (3.2) in said claim 1,
will be provided with
Figure FDA00022617749600000710
Carry over 6-2 to obtain ηact,anoη will beact,anoCarry over 6-3 to obtain ηact,catThe current density I can be determined from 6-4solve，
When in use
Figure FDA00022617749600000711
When, IsolveThe solved current density of the third group of battery segments.
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Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102264641A (en) * 2008-11-28 2011-11-30 阿克爱科蒂夫有限公司 Method for producing activated carbon material

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102264641A (en) * 2008-11-28 2011-11-30 阿克爱科蒂夫有限公司 Method for producing activated carbon material

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
高温PEMFC进气压力突变下的瞬态性能模拟;陈兴龙等;《电源技术》;20150920;第39卷(第9期);1895-1898页 *
高温质子交换膜燃料电池堆的建模与仿真;林煌等;《电源技术》;20150620;第39卷(第6期);1225-1227,1288页 *

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