CN110399639A - The method for establishing catalyst layer for proton exchange film fuel cell agglomeration model - Google Patents

The method for establishing catalyst layer for proton exchange film fuel cell agglomeration model Download PDF

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CN110399639A
CN110399639A CN201910521383.XA CN201910521383A CN110399639A CN 110399639 A CN110399639 A CN 110399639A CN 201910521383 A CN201910521383 A CN 201910521383A CN 110399639 A CN110399639 A CN 110399639A
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焦魁
谢彪
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Tianjin University
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Abstract

The invention discloses a kind of methods for establishing catalyst layer for proton exchange film fuel cell agglomeration model, and model includes three parts: the connection and and coupling PEMFC D beam element flow model composition for calculating Catalytic Layer unijunction block scale oxygen transmission resistance, constructing Catalytic Layer macroparameter.It is agglomerated model by establishing Catalytic Layer, and fully considers the carrying capacity of platinum and influence of the distribution situation to oxygen transmission of platinum, after coupling with Proton Exchange Membrane Fuel Cells threedimensional model, can be used for the optimization design of Catalytic Layer macroparameter.Building for unijunction block Scale Model is coupled with PEMFC D beam element flow model, can be changed the influence being embodied on battery performance to platinum carrying capacity and be verified, provide reference to be related to platinum carrying capacity optimization design research.The influence for more realistically reflecting Catalytic Layer microstructure, makes model be more in line with reality, can provide important reference for Proton Exchange Membrane Fuel Cells product development.

Description

The method for establishing catalyst layer for proton exchange film fuel cell agglomeration model
Technical field
The invention belongs to electrochemical fuel cell fields, and in particular to a kind of catalyst layer for proton exchange film fuel cell model The method of foundation.
Background technique
The features such as Proton Exchange Membrane Fuel Cells (PEMFC) is with its cold operation, quick start, high efficient energy conversion, In recent years by the favor of new energy field, it is considered to be one of most promising clean energy technology, especially in traffic Transport field has the potential quality as alternate power device.But some technical bottlenecks still hamper the commercialization of PEMFC into Journey, wherein the high cost problem of noble metal catalyst (such as platinum) bring limits always the large-scale production of PEMFC, finds cheap Alternative catalysts be also one of research hotspot, but it will be that PEMFC is urged that the excellent performance of platinum group metal, which determines it in a short time, The main source of agent, therefore how rationally to reduce the dosage of platinum and guarantee that battery performance is most important simultaneously.
Modeling and simulating is all the important technical for probing into more physical phenomenon coupled problems complicated in PEMFC all the time One of.Modeling for PEMFC Catalytic Layer generally uses the agglomeration model for considering Catalytic Layer microstructure, but tradition agglomeration mould Type is difficult to preferably embody the influence of catalyst amount variation.Actually in addition to directly affecting response area, catalyst amount The topological structure that can change Catalytic Layer is increased or decreased, and then influences the gas transport in layer, this point is being related to catalyst It is most important in the developmental research of dosage.A kind of method that the present invention proposes model for establishing Catalytic Layer agglomeration, for unijunction The analysis of oxygen transmission resistance under block scale illustrates the variation of platinum carrying capacity under micro-scale to the influence of oxygen transmission, simultaneously The macroscopic property of Catalytic Layer is also added in model, by optimizing spy to the macroparameter including catalyst amount Study carefully, important reference can be provided for Proton Exchange Membrane Fuel Cells product development.
Summary of the invention
The object of the present invention is to establish the Catalytic Layer agglomeration model for the influence that a consideration platinum carrying capacity transports oxygen, base In the true microstructure of Catalytic Layer, foundation is provided to reduce the research and development of products of PEMFC catalyst amount.
The method for establishing catalyst layer for proton exchange film fuel cell agglomeration model, including calculate Catalytic Layer unijunction block scale oxygen Gas transport resistance, the connection for constructing Catalytic Layer macroparameter, coupling PEMFC D beam element flow model three parts.Specific steps are such as Under:
(1) Catalytic Layer unijunction block scale oxygen transmission resistance is calculated
Catalytic Layer is made of pallium-on-carbon, electrolyte and hole three parts, and electrolyte is wrapped in pallium-on-carbon and forms agglomeration structure. Transport resistance of the oxygen under unijunction block scale is divided into three individual resistance items:
1) transport resistance caused by liquid water
Liquid water in Catalytic Layer hole to oxygen Catalytic Layer transport resistance Rlw:
WhereinIt is equivalent liquid water film thickness；It is diffusion coefficient of the oxygen in liquid water；S is that liquid water is full And degree；εCLIt is Catalytic Layer porosity；AimIt is the specific surface area of electrolytic thin-membrane.
2) transport resistance caused by electrolytic thin-membrane
Transport resistance R of the oxygen in electrolytic thin-membraneimIncluding dissolution resistance and diffusional resistance, dissolution resistance passes through one Coefficient links together with diffusional resistance:
Rim=Rim,disso+Rim,diffu (0.3)
Wherein δimIt is the thickness of electrolytic thin-membrane；The diffusion coefficient of oxygen in the electrolyte；k1It is dissolution resistance system Number；Aim/AptIt is the ratio between the specific surface area of electrolyte and platinum.
3) transport resistance caused by Carboplatin polymerize
WhereinIt is effective resist diffusion length；It is equivalent diffusivity；It is Michel Knuysen diffusion coefficient；rpIt is knot Block internal capillary aperture；k2It is platinum grain deposition correction factor；R is universal gas constant；T (K) is local temperature；M is gas Molal weight.
Transport resistance R caused by Carboplatin polymerizeptWhen describing oxygen and diffusing to the platinum grain surface being deposited in aperture Corresponding transmission loss, correction factor k2It is taken as average platinum carbon percentage, it is total to be meant that the quality of platinum accounts for platinum carbon catalyst The percentage of quality.
Effective resist diffusion lengthWith small aperture rpIt is related with the radius of spherical carbon carrier.
Wherein ζpt/c,iAnd χiIt is the platinum carbon percentage and mass fraction of i-th kind of catalyst, r respectivelycAnd εcIt is that carbon carries respectively The radius and porosity of body,
So far, oxygen is transmitted to total transport resistance R of catalyst surface under unijunction block scale by hole in Catalytic LayerTIt can To be obtained by above-mentioned independent loss summation:
The dosage of platinum is related to oxygen transmission resistance, and the distribution situation of platinum on the carbon carrier takes into account.
(2) it constructs and is contacted with Catalytic Layer macroparameter
The agglomeration number of unit Catalytic Layer volume is calculated by following formula:
Wherein mptIt is platinum carrying capacity；δCLIt is Catalytic Layer thickness；ρptIt is the density of platinum；ρcIt is the density of carbon, electrolyte thin film thickness Degree is calculated using the mass ratio of electrolyte and carbon.
ζim/cAnd ρimThe mass ratio I/C for being respectively electrolyte and carbon and the density under electrolyte dry state, it is possible thereby to calculate The specific surface area of electrolyte:
Aim=4 π (rc+δim)2nagg (0.15)
The specific surface area of platinum then passes through the electrochemistry effective affecting acreage parameter a of catalystECSAIt obtains:
The volume fraction that pallium-on-carbon, electrolyte and hole occupy respectively inside Catalytic Layer, by corresponding composed structure parameter It calculates.
Pallium-on-carbon:
Electrolyte:
Hole:
Wherein EW is the equivalent molal weight of dry state electrolyte, and λ is film state water content, thus establishes agglomeration micro-parameter Contacting between Catalytic Layer macroparameter improves conventional junction block models, joined the influence of platinum carrying capacity variation.
(3) coupling PEMFC D beam element flow model is constituted
The agglomeration ginseng determined by the unijunction block scale transport resistance and formula (2.5) of formula (1.12) description, (2.6), (2.7) Number is completed to build agglomeration model, and then is coupled with PEMFC D beam element flow model.The variation of platinum carrying capacity is embodied in Influence on battery performance is verified, and the conservation equation being related to thus includes:
Quality:
Momentum:
Gas component:
Energy:
Liquid water saturation:
It is hydraulic:
Wherein ε is porosity；S is liquid water saturation；ρ is density；It is superficial velocity vector；P is pressure；μ is Power viscosity；Y is the mass fraction of gas component；D is the diffusion coefficient of gas component；CpIt is specific heat capacity；keffIt is effective system Number；K is intrinsic permeability；klwIt is relative permeability, subscript g, lw and i respectively represent admixture of gas, liquid water and i-th kind Gas component.
Further include conservation equation relevant to electrochemical reaction:
Film state water:
Electron potential:
Ion electric potential:
Wherein ndIt is electric osmose drag coefficient；F is Faraday constant；It is IionIon current density；κ is conductivity；It is Potential, electrochemical reaction speed are calculated using Butler-Wall silent equation (Butler-Volmer equation).
WhereinIt is with reference to exchange current density；θTIt is temperature correction coefficient；θpt/oIt is platinum oxygen kinetics amendment system Number；CptIt is platinum surface concentrations of reactant gas；CrefIt is reference reaction gas concentration；α is transmission coefficient；η is universal gas constant；ω is Overpotential；E is the standard hydrogen electrode potential of energy parameter and cathode, and subscript a and c respectively represent anode and cathode.
Assuming that the oxygen for reaching platinum surface is consumed by electrochemical reaction immediately,
WhereinOxygen mole flux；It is concentration of the oxygen at electrolyte interface；It is that oxygen reaches platinum surface Concentration；It is the Henry's constant of oxygen in the electrolyte.
It can be by total transport resistance R in the B-V equation of cathode in PEMFC model and formula (1.12)TIt is coupled together, joint type (1.12), (3.11), (3.14), (3.15), (3.16) have:
In view of the preferable permeability of hydrogen, the B-V equation of anode is merely with Henry's constant amendment hydrogen in electrolyte circle The concentration loss in face:
WhereinFor the Henry's constant of hydrogen in the electrolyte,
The first item and transport resistance unit having the same of denominator, this resistance can be considered by electrification on the right of formula (3.17) Oxygen concentration caused by reaction is learned to lose.
The relative size of electrochemistry resistance and resistance to mass tranfer directly reflects electrochemical factors and transmission factor urges cathode The dominance for changing the electrochemical reaction that layer occurs, thus can derive the evaluation factors of mass transport losses, for characterizing mass transport losses It is whether significant:
In above formula, RTIt is total transport resistance, ReleIt is electrochemistry resistance.
To the modeling method of the invention further explanation: Catalytic Layer is made of pallium-on-carbon, electrolyte and hole three parts, point The indescribably channel of supplied for electronic transmission, ion transmission and quality (air-liquid) transmission.The model that agglomerates is abstract from the microstructure of Catalytic Layer Cell cube out --- agglomeration is agglomerated for spherical Carboplatin agglomerate, external to be wrapped up by a thin layer of dielectric film, is around aperture Biggish hole.Agglomeration is internal there is also aperture, is characterized in and applies increasingly wider high specific area carbon carrier inside shape at present At micro-pore, platinum grain can not only be embedded in carbon support, also be easy deposition and into aperture and gather, increase the biography of oxygen Defeated resistance.For the present invention, transport resistance of the oxygen under unijunction block scale is divided into three individual resistance items:
1) transport resistance caused by liquid water；
In PEMFC, the product of Cathodic oxygen reduction is water, therefore is inevitably present one in Catalytic Layer hole Operative liquid water, liquid water cause to hinder to oxygen in the transmission of Catalytic Layer first.
2) transport resistance caused by electrolytic thin-membrane；
Including dissolution resistance and diffusional resistance, dissolution resistance is generally linked together with a coefficient with diffusional resistance.
3) transport resistance caused by Carboplatin polymerize
Oxygen can be by upper by total transport resistance that hole in Catalytic Layer is transmitted to catalyst surface under unijunction block scale Individually loss summation is stated to obtain:
It can be seen that the dosage of platinum and oxygen transmission resistance are closely bound up, and the distribution situation of platinum on the carbon carrier Oxygen transmission is impacted.
Improved Catalytic Layer agglomeration model is coupled together by the present invention with PEMFC D beam element flow model, can be embodied The dosage of platinum changes the influence on battery performance, suitable for optimizing to the Catalytic Layers macroparameter such as platinum carrying capacity.
The relative size of electrochemistry resistance and resistance to mass tranfer directly reflects electrochemical factors and transmission factor urges cathode The dominance for changing the electrochemical reaction that layer occurs, thus can derive the evaluation factors of a mass transport losses, for characterizing mass transfer It whether significant loses.
It the features of the present invention and has the beneficial effect that
(1) an improved Catalytic Layer agglomeration model is established, by the oxygen transmission resistance analysis under unijunction block scale, The influence that the dosage difference of catalyst (platinum) transports oxygen is considered, by the Catalytic Layer Model coupling to PEMFC D beam element stream In model, the difference of battery performance under different platinum carrying capacity can preferably be embodied by making model integrally, to be related to the optimization of platinum carrying capacity Research provides reference.
(2) a series of macroparameters in Catalytic Layer agglomeration Model coupling Catalytic Layer configuration process, and by itself and agglomeration Micro-parameter connects, and more realistically reflects the influence of Catalytic Layer microstructure, model is made to be more in line with reality.
(3) transport resistance by the derivation of equation by oxygen in cathode catalysis layer is connected with platinum carrying capacity, and will be negative Parameter in the B-V equation of pole is divided into two parts of electrochemistry resistance and transport resistance, and the relative size of two resistance items indicates Electrochemical reaction is dominated by electrochemical factors or transmission factor, can be calculated evaluation factors by the relative scale of the two, is used for Whether significant characterize mass transport losses.
Detailed description of the invention
Fig. 1 agglomeration model and oxygen transmission resistance schematic diagram.
Fig. 2 single channel PEMFC computational domain.
Polarization curve compares under Fig. 3 difference cathode platinum carrying capacity.
The verifying analysis of Fig. 4 oxygen local transmission resistance.
The applicating example of Fig. 5 evaluation factors.
Specific embodiment
The method that model foundation of the invention is illustrated below in conjunction with attached drawing and by specific calculated examples, it should be noted that This example is the narrative explanation carried out for clear interpretation modeling procedure, is not limited the scope of protection of the present invention with this.
Initially set up Catalytic Layer agglomeration model, and fully consider platinum carrying capacity and platinum distribution situation to the shadow of oxygen transmission It rings, after coupling with Proton Exchange Membrane Fuel Cells threedimensional model, can be used for the optimization design of Catalytic Layer macroparameter.Modeling in detail Steps are as follows:
(1) Catalytic Layer unijunction block scale oxygen transmission resistance is calculated
Transport resistance of the oxygen under unijunction block scale is divided into three individual resistance items:
1) transport resistance (R caused by liquid waterlw,s m-1)
Liquid water in Catalytic Layer hole to oxygen Catalytic Layer transport resistance:
WhereinIt is equivalent liquid water film thickness；It is diffusion coefficient of the oxygen in liquid water；s It is liquid water saturation；εCLIt is Catalytic Layer porosity；Aim(m-1) be electrolytic thin-membrane specific surface area.
2) transport resistance (R caused by electrolytic thin-membraneim,s m-1)
Transport resistance R of the oxygen in electrolytic thin-membraneimIncluding dissolution resistance and diffusional resistance, dissolution resistance passes through one Coefficient links together with diffusional resistance:
Rim=Rim,disso+Rim,diffu (0.43)
Wherein δim(m) be electrolytic thin-membrane thickness；The diffusion coefficient of oxygen in the electrolyte；k1It is It dissolves resistance coefficient (present invention takes 0.15)；Aim/AptIt is the ratio between the specific surface area of electrolyte and platinum.
3) transport resistance (R caused by Carboplatin polymerizept,s m-1)
WhereinIt is effective resist diffusion length；It is equivalent diffusivity；It is Ke Nu Gloomy diffusion coefficient；rpIt is agglomeration internal capillary aperture；k2It is platinum grain deposition correction factor；R(J mol-1K-1) it is argoshield Constant；T (K) is local temperature；M(kg mol-1) it is gas molar quality.
Transport resistance R caused by Carboplatin polymerizeptWhen describing oxygen and diffusing to the platinum grain surface being deposited in aperture Corresponding transmission loss, correction factor k2It is taken as average platinum carbon percentage, it is total to be meant that the quality of platinum accounts for platinum carbon catalyst The percentage of quality:
Effective resist diffusion lengthWith small aperture rpIt is related with the radius of spherical carbon carrier,
Wherein ζpt/c,iAnd χiIt is the platinum carbon percentage and mass fraction of i-th kind of catalyst, r respectivelyc(m) and εcIt is carbon respectively The radius and porosity of carrier,
So far, oxygen is transmitted to total transport resistance R of catalyst surface under unijunction block scale by hole in Catalytic LayerT(s m-1) can be obtained by above-mentioned independent loss summation:
The dosage of platinum is related to oxygen transmission resistance, and the distribution situation of platinum on the carbon carrier takes into account.
(2) it constructs and is contacted with Catalytic Layer macroparameter
The agglomeration number of unit Catalytic Layer volume is calculated by following formula:
Wherein mpt(mg cm-2) it is platinum carrying capacity；δCLIt (m) is Catalytic Layer thickness；ρptIt is the density of platinum；ρc(kg m-3) it is carbon Density, electrolyte thin film thickness calculated using the mass ratio (I/C ratio) of electrolyte and carbon.
ζim/cAnd ρim(kg m-3) be respectively electrolyte and carbon mass ratio I/C and the density under electrolyte dry state, thus may be used To calculate the specific surface area of electrolyte:
Aim=4 π (rc+δim)2nagg (0.55)
The specific surface area of platinum then passes through the electrochemistry effective affecting acreage parameter a of catalystECSA(m2kg-1) obtain:
The volume fraction that pallium-on-carbon, electrolyte and hole occupy respectively inside Catalytic Layer, by corresponding composed structure parameter It calculates.
Pallium-on-carbon:
Electrolyte:
Hole:
Wherein EW (kg mol-1) it is the equivalent molal weight of dry state electrolyte, λ is film state water content, thus sets up and finishes Contacting between block models parameter and Catalytic Layer macroparameter improves conventional junction block models, joined the shadow of platinum carrying capacity variation It rings.
(3) coupling PEMFC D beam element flow model is constituted
The agglomeration ginseng determined by the unijunction block scale transport resistance and formula (2.5) of formula (1.12) description, (2.6), (2.7) Number is completed to build agglomeration model, and then is coupled with PEMFC D beam element flow model.The variation of platinum carrying capacity is embodied in Influence on battery performance is verified, and the conservation equation being related to thus includes:
Quality:
Momentum:
Gas component:
Energy:
Liquid water saturation:
It is hydraulic:
Wherein ε is porosity；S is liquid water saturation；ρ is (kg m-3) density；It is (m s-1) superficial velocity vector； P is (Pa) pressure；μ is (kg m-1s-1) dynamic viscosity；Y is the mass fraction of gas component；D is (m2s-1) gas component expansion Dissipate coefficient；CpIt is (J mol-1K-1) specific heat capacity；keffIt is effective thermal conductivity；K is intrinsic permeability；klwIt is (m2) it is opposite seep Saturating rate, subscript g, lw and i respectively represent admixture of gas, liquid water and i-th kind of gas component.
Further include conservation equation relevant to electrochemical reaction:
Film state water:
Electron potential:
Ion electric potential:
Wherein ndIt is electric osmose drag coefficient；F is (C mol-1) Faraday constant；It is Iion(A m-2) ion current density；κ It is (S m-1) conductivity；It is (V) is potential, electrochemical reaction speed is write from memory equation (Butler- using Butler-Wall Volmer equation) it calculates:
WhereinIt is with reference to exchange current density；θTIt is temperature correction coefficient；θpt/oIt is platinum oxygen kinetics Correction factor；CptIt is platinum surface concentrations of reactant gas；CrefIt is (mol m-3) reference reaction gas concentration；α is transmission coefficient；η is (V) Universal gas constant；ω is (kJ mol-1) overpotential；E (V) is the standard hydrogen electrode potential of energy parameter and cathode, subscript a and C respectively represents anode and cathode,
Assuming that the oxygen for reaching platinum surface is consumed by electrochemical reaction immediately,
Wherein(mol m-2s-1) it is oxygen mole flux；It is concentration of the oxygen at electrolyte interface； (mol m-3) it is the concentration that oxygen reaches platinum surface；(Pa m3mol-1) it is the Henry's constant of oxygen in the electrolyte,
It can be by total transport resistance R in the B-V equation of cathode in PEMFC model and formula (1.12)TIt is coupled together, joint type (1.12), (3.11), (3.14), (3.15), (3.16) have,
In view of the preferable permeability of hydrogen, the B-V equation of anode is merely with Henry's constant amendment hydrogen in electrolyte circle The concentration loss in face:
WhereinFor the Henry's constant of hydrogen in the electrolyte,
The first item and transport resistance unit having the same of denominator, this resistance can be considered by electrification on the right of formula (3.17) Oxygen concentration caused by reaction is learned to lose,
The relative size of electrochemistry resistance and resistance to mass tranfer directly reflects electrochemical factors and transmission factor urges cathode The dominance for changing the electrochemical reaction that layer occurs, thus derives the evaluation factors ι of mass transport losses, is for characterizing mass transport losses It is no significant:
In above formula: RT(s m-1) it is total transport resistance；ReleIt is electrochemistry resistance.
The total transport resistance R of catalyst surface is transmitted to by Catalytic Layer hole under unijunction block scaleT:
It can be seen that total transmission loss of the oxygen in Catalytic Layer is a specific surface area and platinum carbon percentage comprising platinum Function.When platinum carrying capacity reduces, the transmission path of oxygen is comparatively more tortuous, and resistance caused by electrolyte will increase；Phase Instead, when platinum carrying capacity increases, due to deposition and polymerism aggravation, also it is unfavorable for oxygen transmission to platinum surface, i.e. Carboplatin polymerization is drawn The transport resistance risen can increase.
According to above-mentioned steps, the Catalytic Layer agglomeration model that the influence by platinum carrying capacity to oxygen transmission is taken into account can be established, And be coupled in PEMFC battery model, platinum carrying capacity can be objectively responded and change the influence generated to battery performance.
Specific calculated examples:
Single channel PEMFC computational domain is as shown in Fig. 2, pole plate (BP), runner (Channel) including cathode and anode two sides, Gas diffusion layers (GDL), microporous layers (MPL), Catalytic Layer (CL) and the proton exchange membrane (MEM) of centre.Related geometric dimension Are as follows:
1) runner entrance section is wide by 0.5 × 10-3M is high by 0.7 × 10-3m；
2) pole plate total height is and overall width is 1.0 × 10-3m；
3) gas diffusion layers and microporous layer are respectively 1.8 × 10-4M and 2.0 × 10-5m；
4) anode and cathode Catalytic Layer thickness is respectively 3.0 × 10-6M and 1.0 × 10-5m；
5) flow channel length 0.1m；
6) active area 1.0 × 10-4m2；
The present embodiment selects Gore proton exchange membrane, thickness δMEMIt is 1.8 × 10-5M, dry state density pimFor 1980kg m-3, Equivalent molal weight EW is 1.1kg mol-1, permeability KMEMIt is 2.0 × 10-20m2, battery operating temperature T is 80 DEG C, anode and cathode Humidification degree is 100%, and inlet pressure is 1.5atm, and anode, cathode inlet equivalent proportion are respectively 3.0 and 4.0.
Anode, cathode catalysis layer macroparameter: platinum carrying capacity mPtRespectively 0.05mg cm-2With 0.1mg cm-2, anode platinum carbon Percentage ζpt/cIt is 20%, cathode is averaged platinum carbon percentageFor 19.3%, I/C ratio ζim/cRespectively 0.6 and 0.95.
Agglomeration model parameter: carbon carrier radius rcFor 25nm, porosity εcIt is taken as 0.05, the density p of platinum and carbonpt、ρcRespectively For 21450,2000kg m-3, hydrogen, oxygen Henry's constant be calculate by the following formula,
Electrolyte thin film thickness and unit Catalytic Layer agglomeration number can be calculated using above-mentioned parameter:
Aim=4 π (rc+δim)2nagg
The volume fraction of pallium-on-carbon, electrolyte and hole can equally calculate in Catalytic Layer:
εCL=1- εpt/c-εim
The electrochemistry effective affecting acreage parameter a of catalystECSAFor 70m2g-1, (have so as to calculate the specific surface area of platinum Effect),
The transport resistance calculating formula of oxygen are as follows:
During numerical solution, electrochemistry resistance R can be obtainedeleNumerical value, and then calculate mass transport losses judge because Son,
Reference current density in B-V equationRespectively 2.5,2.5 × 10-4A m-2, reference reaction concentration Respectively 40,3.39mol m-3, transmission coefficient αa、αc0.5 is taken, output voltage 0.6V.It gas diffusion layers, microporous layers and urges Changing layer intrinsic permeability K is respectively 1.0 × 10-12、1.0×10-12、1.0×10-13, electronic conductivity κ is respectively 8000, 5000、5000S m-1, pole plate conductivity is 20000S m-1, gas diffusion layers and microporous layers porosity are respectively 0.6,0.5.
Proton conductivity calculation formula:
Dynamic viscosity calculates formula:
μlw=2.414 × 10[247.8/(T-140)-5]
Relative permeability calculating formula:
kg=(1-s)3,klw=s3
Vaporous water and liquid water phase transformation source item:
Local steam-laden pressure gauge formula:
Vaporous water and film state water phase become source item calculating formula:
Transformation rate γv-l、γl-v、γv-dValue is respectively 5000,100,1.3s-1。
Gas effective diffusivity takes 1.5 using Bruggeman amendment (Bruggeman correction), correction factor, and Consider that the barrier action of liquid water in hole, conductivity also use similar amendment,
κeff=κ ε1.5
The body diffusion coefficient of gas component is respectively as follows:
Pole plate, gas diffusion layers, microporous layers, the specific heat capacity of Catalytic Layer and proton exchange membrane be respectively 1580,568,3300, 3300、833J kg-1K-1, pole plate, microporous layers, Catalytic Layer and proton exchange membrane effective thermal conductivity are respectively 20,1.0,1.0 and 0.95W m-1K-1, gas diffusion layers fibre bundle plane thermal conductivity is 21W m-1K-1, vertical plane direction is 1.7W m-1K-1。
So far, agglomeration Parameters in Mathematical Model can be calculated and solve the parameter that each conservation equation needs, according to above-mentioned side Method is established Catalytic Layer agglomeration model and is coupled with PEMFC threedimensional model, makes model that platinum carrying capacity integrally be added and transports influence to oxygen The considerations of, have and the Catalytic Layer macroparameter including platinum carrying capacity is optimized.
Attached drawing 3 is the comparison of simulation result and experimental data under different cathode platinum carrying capacity, and attached drawing 4 is that oxygen is being catalyzed The verifying analysis of the local transmission loss of layer, attached drawing 5 are the applicating example of evaluation factors.

Claims (1)

1. the method for establishing catalyst layer for proton exchange film fuel cell agglomeration model, including calculate Catalytic Layer unijunction block scale oxygen Transport resistance, the connection for constructing Catalytic Layer macroparameter, coupling PEMFC D beam element flow model three parts, the specific steps are as follows:
(1) Catalytic Layer unijunction block scale oxygen transmission resistance is calculated
Catalytic Layer is made of pallium-on-carbon, electrolyte and hole three parts, and electrolyte is wrapped in pallium-on-carbon and forms agglomeration structure, oxygen Transport resistance under unijunction block scale is divided into three individual resistance items:
1) transport resistance caused by liquid water
Liquid water in Catalytic Layer hole to oxygen Catalytic Layer transport resistance Rlw:
WhereinIt is equivalent liquid water film thickness；It is diffusion coefficient of the oxygen in liquid water；S is liquid water saturation； εCLIt is Catalytic Layer porosity；AimIt is the specific surface area of electrolytic thin-membrane,
2) transport resistance caused by electrolytic thin-membrane
Transport resistance R of the oxygen in electrolytic thin-membraneimIncluding dissolution resistance and diffusional resistance, dissolution resistance passes through a coefficient It links together with diffusional resistance:
Rim=RIm, disso+RIm, diffu (0.3)
Wherein RIm, dissoIt is oxygen dissolution resistance；RIm, duffuIt is oxygen diffusional resistance；δimIt is the thickness of electrolytic thin-membrane； It is the diffusion coefficient of oxygen in the electrolyte；k1It is dissolution resistance coefficient；Aim/AptIt is the ratio between the specific surface area of electrolyte and platinum,
3) transport resistance caused by Carboplatin polymerize
WhereinIt is effective resist diffusion length；It is equivalent diffusivity；It is Michel Knuysen diffusion coefficient；rpIt is in agglomeration Portion's micropore size；k2It is platinum grain deposition correction factor；R is universal gas constant；T (K) is local temperature；M is gas molar Quality,
Transport resistance R caused by Carboplatin polymerizeptIt is right that institute when oxygen diffuses to the platinum grain surface being deposited in aperture is described The transmission loss answered, correction factor k2It is taken as average platinum carbon percentage, is meant that the quality of platinum accounts for platinum carbon catalyst gross mass Percentage:
Effective resist diffusion lengthWith small aperture rpIt is related with the radius of spherical carbon carrier,
Wherein ζPt/c, iAnd χiIt is the platinum carbon percentage and mass fraction of i-th kind of catalyst, r respectivelycAnd εcIt is carbon carrier respectively Radius and porosity,
So far, oxygen is transmitted to total transport resistance R of catalyst surface under unijunction block scale by hole in Catalytic LayerTIt can be by Above-mentioned independent loss summation obtains:
The dosage of platinum is related to oxygen transmission resistance, and the distribution situation of platinum on the carbon carrier takes into account,
(2) it constructs and is contacted with Catalytic Layer macroparameter
The agglomeration number of unit Catalytic Layer volume is calculated by following formula:
Wherein mptIt is platinum carrying capacity；δCLCatalytic Layer thickness, ρptIt is the density of platinum, ρcIt is the density of carbon, electrolyte thin film thickness uses The mass ratio of electrolyte and carbon calculates,
ζim/cAnd ρimThe mass ratio I/C for being respectively electrolyte and carbon and the density under electrolyte dry state, it is possible thereby to calculate electrolysis The specific surface area of matter:
Aim=4 π (rc+δim)2nagg (0.15)
The specific surface area of platinum then passes through the electrochemistry effective affecting acreage parameter a of catalystECSAIt obtains:
The volume fraction that pallium-on-carbon, electrolyte and hole occupy respectively inside Catalytic Layer is calculated by corresponding composed structure parameter,
Pallium-on-carbon:
Electrolyte:
Hole: εCL=1- εpt/c-εim (0.19)
Wherein EW is the equivalent molal weight of dry state electrolyte, and λ is film state water content, thus establishes agglomeration model parameter and urges Change the connection between layer macroparameter,
(3) coupling PEMFC D beam element flow model is constituted
The agglomeration parameter determined by the unijunction block scale transport resistance and formula (2.5) of formula (1.12) description, (2.6), (2.7), It completes to build agglomeration model, and then is coupled with PEMFC D beam element flow model, battery is embodied in the variation of platinum carrying capacity Influence in performance is verified, and the conservation equation being related to thus includes:
Quality:
Momentum:
Gas component:
Energy:
Liquid water saturation:
It is hydraulic:
Wherein ε is porosity；S is liquid water saturation；ρ is density；It is superficial velocity vector；P is pressure；μ is that power is viscous Degree；Y is the mass fraction of gas component；D is the diffusion coefficient of gas component；CpIt is specific heat capacity；keffIt is effective thermal conductivity；K It is intrinsic permeability；klwIt is relative permeability, subscript g, lw and i respectively represent admixture of gas, liquid water and i-th kind of gas Component,
Further include conservation equation relevant to electrochemical reaction:
Film state water:
Electron potential:
Ion electric potential:
Wherein ndIt is electric osmose drag coefficient；F is Faraday constant；IionIt is ion current density；κ is conductivity；It is potential, Electrochemical reaction speed utilizes the silent equation calculation in Butler-Wall:
WhereinIt is with reference to exchange current density；θTIt is temperature correction coefficient；θpt/oIt is platinum oxygen kinetics correction factor；Cpt It is platinum surface concentrations of reactant gas；CrefIt is reference reaction gas concentration；α is transmission coefficient；η is overpotential；ω is overpotential；E(V) It is the standard hydrogen electrode potential of energy parameter and cathode, subscript a and c respectively represent anode and cathode,
Assuming that the oxygen for reaching platinum surface is consumed by electrochemical reaction immediately,
WhereinIt is oxygen mole flux；It is concentration of the oxygen at electrolyte interface；It is that oxygen reaches platinum surface Concentration；It is the Henry's constant of oxygen in the electrolyte,
By total transport resistance R in the B-V equation of cathode in PEMFC model and formula (1.12)TIt is coupled together, joint type (1.12), (3.11), (3.14), (3.15), (3.16) have,
In view of the preferable permeability of hydrogen, the B-V equation of anode is merely with Henry's constant amendment hydrogen in electrolyte interface Concentration loss:
WhereinFor the Henry's constant of hydrogen in the electrolyte,
The first item and transport resistance unit having the same of denominator, this resistance can be considered anti-by electrochemistry on the right of formula (3.17) The loss of oxygen concentration caused by answering,
The relative size of electrochemistry resistance and resistance to mass tranfer directly reflects electrochemical factors and transmission factor to cathode catalysis layer Thus the dominance of the electrochemical reaction of generation derives the evaluation factors ι of mass transport losses, for characterizing whether mass transport losses show It writes,
In above formula, RTIt is total transport resistance, ReleIt is electrochemistry resistance.
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