CN106407621A - Method for establishing two-dimensional finite element model of solid oxide fuel cell - Google Patents
Method for establishing two-dimensional finite element model of solid oxide fuel cell Download PDFInfo
- Publication number
- CN106407621A CN106407621A CN201611019937.9A CN201611019937A CN106407621A CN 106407621 A CN106407621 A CN 106407621A CN 201611019937 A CN201611019937 A CN 201611019937A CN 106407621 A CN106407621 A CN 106407621A
- Authority
- CN
- China
- Prior art keywords
- interface
- model
- sofc
- finite element
- fuel cell
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
Abstract
The invention discloses a method for establishing a two-dimensional finite element model of a solid oxide fuel cell. The method comprises the following steps: S01, model assumption and geometrical setting; S02, model establishment with COMSOL software; and S03, analysis on the model result. Studied in the model are five solid oxide fuel cell units having different anode electrolyte geometrical interfaces, which are respectively a planar interface, a rectangular interface a triangular interface, a first elliptical interface and a second elliptical interface. The two-dimensional finite element model of the solid oxide fuel cell is established based on the practical operating parameters and laws of the fuel cell, the internal physical and chemical laws of the model are further studied, several different geometrical interface shapes are studied by numerical simulation to obtain an interface with optimal performance, and the law of performance improvement is tried to analyzed to explore the reason, which has great significance for manufacturing of the solid oxide fuel cell and is beneficial to improving the cost performance of the solid oxide fuel cell.
Description
Technical field
The invention belongs to fuel cell field is and in particular to a kind of SOFC two-dimensional finite element model
Method for building up.
Background technology
SOFC (Solid Oxide Fuel Cell, i.e. SOFC) runs in high temperature environments
The fuel cell of complete solid-state structure, is also one of five kinds of fuel cells generally acknowledging at present.Fill with current others energy production
Put and compare, it has following significant advantage：(1) SOFC operating temperature highest can reach 1000 DEG C, system itself
Just have very high energy conversion efficiency.If reusing heat recovery technology to carry out cogeneration of heat and power generating, in this kind of system, it
Aggregate efficiency can reach 70%-80%, be highest in all generation technologies.(2) SOFC has very strong fuel-flexible degree.
It can utilize the inside reforming of inside battery Hydrocarbon to react, and (carry out under the high operating temperature of SOFC is a series of
Complicated chemical change procedure) hydrogen and carbon monoxide are obtained, thus can be natural gas, the coal being easier in actual life obtain
Gas, biomass gas etc. are directly as the unstripped gas of fuel cell, and make its raw material be not limited only to H2Scope.(3) SOFC adopts
It is all solid state battery component, the such as burn into bringing due to liquid electrolyte therefore can be avoided to reveal, block reaction
The technical problems such as thing transmission channel, also imply that there is higher motility in battery structure design simultaneously.(4) due to SOFC
High operating temperature, its existing very high output, and without using urging as the desired precious metal of other fuel cells
Agent, can be using more cheap Metal catalyst materials (Ni).SOFC is due to its efficient, environmental protection etc.
Speciality and very big development potentiality is had on future source of energy market.But current, because the items that hot operation brings are chosen
War, its development is subject to lifetime of system and the dual of high cost to keep in check, and its cost performance still far lags behind other generating approach,
Therefore present need exist for research and development energetically.For first, there are a lot of modes can improve soild oxide combustion at present
The cost performance of material battery, the interface attempting modifying wherein electrode and electrolyte is admissible to seek more preferably battery performance
One of method.Either experiment or analog end, has had a considerable amount of documents all to demonstrate because increasing interface to battery table
Now bring castering action.However, in those articles, only little interface shape by as object of study, and to boundary
The tortuous in face lack clearly conclusion with the relation of performance, bring a lot of queries to being systematically carried out modifying interface.
Content of the invention
It is an object of the invention to, a kind of method for building up of SOFC two-dimensional finite element model is provided,
With fuel cell actual operation parameters, rule for relying on, set up model and study further in it physical chemistry rule, right
The manufacture of SOFC has a great deal of practical meanings, and is beneficial to SOFC cost performance
Lifting.
Technical scheme：A kind of method for building up of SOFC two-dimensional finite element model, including
Following steps：
S01, model hypothesis and geometry set；
S02, set up model using COMSOL software；
S03, the analysis of model result.
In the method for building up of aforesaid SOFC two-dimensional finite element model, this solid oxide fuel electricity
The target area of pond modeling is the repetitives of an anode supporting type solid oxide fuel cell, is combined the moon by LSM/YSZ
Pole, YSZ ceramic electrolyte and Ni/YSZ cermet anode composition.
In the method for building up of aforesaid SOFC two-dimensional finite element model, in described step S01, model
Assume and geometry setting is as follows：
A, all parameter values not time to time change；
Temperature in b, unit is unified to be 800 DEG C；
C, porous electrode are the continuuies that three components are uniformly constituted；
D, be passed through anode gas composition be volume fraction 97% H2+ 3% O2, negative electrode is 21% O2+ 79%
N2；
In e, electrode, electron potential is equal everywhere；
F, the Butler-Volmer electrochemical kinetics process of standard are set up.
In the method for building up of aforesaid SOFC two-dimensional finite element model, in described model, have studied five
Kind there is the SOFC unit at different anodolyte geometry interfaces, be respectively planar interface, rectangular interfaces,
Triangle interface, the first oval interface and the second oval interface.
In the method for building up of aforesaid SOFC two-dimensional finite element model, utilize in described step S02
COMSOL software is set up model and is comprised the following steps：
The input of S021, constant and expression formula, constant and expression formula are inputted in COMSOL software,
S022, set up geometric figure after, carry out solve domain setting, border setting；
S023, set up network, carry out stress and strain model, subsequently row operation is entered to model by computer；
Carry out post processing using the instrument that COMSOL carries after S024, computing, existed by the value changing Model Parameter
COMSOL Script is programmed being circulated computing to model, probes into single parameter to solid-oxide fuel battery performance
Impact.
In the method for building up of aforesaid SOFC two-dimensional finite element model, described rectangular interfaces, described
Triangle interface, the described first oval interface, the electric current density at the described second oval interface are all higher than described planar interface
The electric current density of SOFC.
In the method for building up of aforesaid SOFC two-dimensional finite element model, the described second oval interface
Electric current density be more than described rectangular interfaces, described triangle interface, the electric current density at described first oval interface.
Compared with prior art, the present invention has the advantages that：
(1) present invention, with fuel cell actual operation parameters, rule for relying on, sets up SOFC two dimension
FEM (finite element) model, and study further in it physical chemistry rule, by several different geometry circle of numerical simulation study
Face shape simultaneously draws the interface with optimum performance, and analyze the rule of such performance boost, and spy is traced it to its cause, and this will be to solid
The manufacture of oxide fuel cell has a great deal of practical meanings, and is beneficial to carrying of SOFC cost performance
Rise.
(2) present invention has inquired into five kinds of anode-electrolyte interfaces with different interfaces expansion factor to battery performance
Impact, draws with respect to another four kinds of interface batteries, under fixed voltage, the second oval interface (i.e. relatively deep ellipse interface) energy
Obtain maximum average current density；Average current density-the voltage curve of different batteries confirms its performance comparison, in addition,
Larger ion electric potential change around cell electrolyte illustrates ion ohmic loss very greatly, and the following electrolyte thickness that reduces is
Feasible improvement；Optimization further to the second oval interface (i.e. relatively deep ellipse interface) shows, it is in anode/electrolyte
Interface is deeper, more intensive, and the total performance of battery is better, and planar interface battery compares, and ideally can obtain maximum
The lifting of 32% electric current density.
Brief description
Fig. 1 is the knot of the SOFC of the second oval interface (i.e. relatively deep ellipse interface) of the present invention
Structure schematic diagram；
Fig. 2 is the structural representation of the SOFC of rectangular interfaces of the present invention；
Fig. 3 is the knot of the SOFC of the first oval interface (i.e. compared with shallow elliptical shape interface) of the present invention
Structure schematic diagram；
Fig. 4 is the structural representation of the SOFC of planar interface of the present invention；
Fig. 5 is the structural representation of the SOFC at triangle interface of the present invention；
Fig. 6 is the electric current density of the present invention and the relation schematic diagram of interface expansion factor；
Fig. 7 is molar concentration (E=0.7V) schematic diagram of the anode hydrogen gas of the present invention；
Fig. 8 is molar concentration (E=0.7V) schematic diagram of the anode vapor of the present invention；
Fig. 9 is the I-V curve comparison diagram of five kinds of different interfaces batteries of the present invention；
Figure 10 is the ion electric potential distribution schematic diagram along cell interface of the present invention；
Figure 11 is the ion electric potential sectional view along Figure 10 vertical y direction of the present invention；
Figure 12 is second oval interface (the i.e. relatively deep ellipse interface) anode of the present invention and electrolyte geometry shows
It is intended to.
Specific embodiment
With reference to embodiment, the present invention is further illustrated, but is not intended as the foundation that the present invention is limited.
A kind of method for building up of SOFC two-dimensional finite element model, comprises the following steps：
S01, model hypothesis and geometry set；
S02, set up model using COMSOL software；
S03, the analysis of model result.
Further, the target area of this SOFC modeling is an anode supporting type solid oxide
The repetitives of fuel cell, are made up of LSM/YSZ composite cathode, YSZ ceramic electrolyte and Ni/YSZ cermet anode.
Further, in described step S01, model hypothesis and geometry setting are as follows：
A, all parameter values not time to time change；
Temperature in b, unit is unified to be 800 DEG C；
C, porous electrode are the continuuies that three components are uniformly constituted；
D, be passed through anode gas composition be volume fraction 97% H2+ 3% O2, negative electrode is 21% O2+ 79%
N2；
In e, electrode, electron potential is equal everywhere；
F, the Butler-Volmer electrochemical kinetics process of standard are set up.
Further, have studied five kinds of soild oxide combustions with different anodolyte geometry interfaces in described model
Material battery unit, is planar interface, rectangular interfaces, triangle interface, the first oval interface and the second oval interface respectively.
Further, set up model using COMSOL software in described step S02 to comprise the following steps：
The input of S021, constant and expression formula, constant and expression formula are inputted in COMSOL software,
S022, set up geometric figure after, carry out solve domain setting, border setting；
S023, set up network, carry out stress and strain model, subsequently row operation is entered to model by computer；
Carry out post processing using the instrument that COMSOL carries after S024, computing, existed by the value changing Model Parameter
COMSOL Script is programmed being circulated computing to model, probes into single parameter to solid-oxide fuel battery performance
Impact.
Further, described rectangular interfaces, described triangle interface, the described first oval interface, described second ellipse
The electric current density at shape interface is all higher than the electric current density of described planar interface SOFC.
Further, the electric current density at described second oval interface be more than described rectangular interfaces, described triangle interface,
The electric current density at the described first oval interface.
The method for building up of SOFC two-dimensional finite element model is specific as follows：
1.1 model hypothesis and geometry set
Because this paper purpose is the result of inspection Different electrodes/electrolyte geometry effect of the interface battery performance, in order that mould
Type is more brief, establish in literary composition several through simplification do not lose again rational it is assumed that as follows：
1) limit：System has reached steady operational status, i.e. all parameter values not time to time change.
2) temperature in unit is unified is 800 DEG C, is isothermal within this range.
3) porous electrode is the continuum that three components are uniformly constituted, and such as anode is Ni, and YSZ and pore form.
4) the gas composition being passed through anode is the H of volume fraction 97%2+ 3% O2, negative electrode is then 21% O2+ 79%
N2, thus can get boundary condition at electrode surface for the gas composition.
5) in electrode, electron potential is equal everywhere.In this model, anode current potential is 0, and cathode potential is then
It is the working voltage E of battery.Due to the electronic conductivity of anode Ni and negative electrode LSM 4 numbers bigger than the ionic conductivity of YSZ
Magnitude, also implies that the electron potential reduced value in certain electric current bottom electrode is compared with ion electric potential and is negligible,
Therefore this assumes to set up.
6) the Butler-Volmer electrochemical kinetics process of standard is set up, as the processes such as absorption, dissociation and migration are neglected
Slightly.That is it is adaptable to electric current is relatively small and said process can be with ignored situation.
Have studied five kinds of SOFC units with different anodolyte geometry interfaces in model, point
It is not plane, rectangle, triangle, first oval (i.e. compared with shallow elliptical shape) and second oval (i.e. relatively deep oval) interface,
Specifically as Figure 1-Figure 5.
The size at Fig. 1-Fig. 5 intermediate cam shape interface marks, in detail using the example as other several geometry interfaces.Actual
On for four kinds of geometry interfaces in addition to planar interface, the depth that the bottom of their electrolyte is absorbed in electrode is all 100 μm.It
Compare with planar interface situation and have extra electrolyte portion to insert in anode, the electrolyte that this part has more may result in
Bigger ohmic loss, therefore, in order to ensure the concordance of various situations, for planar condition between its embedded anode and cathode
Complete electrolyte thickness has 100 μm, and anode thickness is then accordingly reduced to 480 μm.And under other geometry interfaces, such as in triangle
Shown in surface chart, the electrolyte thickness more than 500 μm of base anodes is 80 μm.
For different geometry interfaces, a geometric parameter can be defined to weigh its enlarged degree to interface, its quilt
It is referred to as interface expansion factor λ, its formula is：
Wherein horizontal direction anode-electrolyte length is exactly the length of planar interface, as 800 μm as Figure 1-Figure 5.
In the complex figures such as ellipse, λ can be obtained by the calculating of COMSOL software.
It is noted that all do not account for the effect of connector in monocell in Fig. 1-Fig. 5, this is because this model
Purpose is the interface optimization of electrode and electrolyte, and for different geometry interfaces, the difference of its performance and connector are not directly
Relation, therefore, model will never consider that the monocell angle of connector effect comprises to SOFC inside
The module of electrode and electrolyte carries out theoretical investigation and optimizes, and its result is equally applicable under having connector effect.Or
It is also assumed that there are electrode two ends herein is that electrical conductivity is very high, contact resistance and electronic resistance can be ignored, right
Battery performance affect very little metallic interconnection materials.
1.2 models and math equation
All of SOFC parameter integration is specifically taught how to get up to set up numerical model.Summarize
For, need to consider the conservation of electric charge and gas and anode tap hydrogen is oxidized and cathode terminal oxygen is reduced electrochemistry mistake
Journey.
1.2.1 ion and electric transmission model
The simple ionic conductivity of YSZ and the electronic conductivity (unit of electrode material：S/m) can by formula (1-2),
(1-3) obtain with (1-4)：
They may certify that the value of electronic conductivity is significantly larger than ionic conductivity.Due in hypothesis before, in electrode
Electron potential keeps constant, and only ion electric potential is just different in the electrodes, thus in model practical application only ion
Conductivity.In porous electrode, actual YSZ resistance than formula more larger because it is than the volume fraction of phase pure material
Little, particle twisting coefficient is bigger, so, in order to more accurate, effective conductivity should be used wherein
Wherein τYSZAnd VYSZRepresent YSZ particle twisting coefficient in the electrodes and volume fraction respectively.Table 1-1 shows simulation
In anode used and negative electrode micro-parameter.
The composition of table 1-1 electrode and tortuosity
| Porosity | VYSZ | VNiOr VLSM | τ | |
| Anode | 0.333 | 0.333 | 0.333 | 3 |
| Negative electrode | 0.5 | 0.25 | 0.25 | 3 |
Can be described by unified formula (1-6) in the transmission of electrolyte and electrode intermediate ion：
Wherein u is ion electric potential, ivIt is the volumetric reaction speed in male or female, B is the parameter according to part and change.
Specifically, in electrolyte, B is equal to 0, during anode B be equal to -1 and during negative electrode B be equal to 1.Above-mentioned formula is actually fixed with ohm
Rule has same physical significance (but in Ohm's law, electric current is not the volumetric energy as shown in formula), and it shows
Ion electric potential in electrode is closely related with the process of electric charge transfer.
1.2.2 gas transmission model
Dusty gas model is used for describing transmission in porous electrode for the gas.As described above, it considers Knudson
Diffusion and the VISCOUS FLOW of gas, are the extensions of Stefan-Maxwell model.For anode and negative electrode, unified gas
Body transmission equation is represented by：
For a binary system, above-mentioned equation can be deformed into according to the conservation of every component：
Wherein, subscript 1 represents the H of anode tap2Or the O of cathode terminal2, R is ideal gas constant, and T is the absolute temperature of work
Degree, PtIt is the total gas pressure intensity of certain point, PiIt is the pressure of gas i at certain point.It should be noted that for ideal gases Pi=
ciRT keeps setting up.SctIt is mole generation or the consumption of electrochemical reaction.
In above-mentioned equation, xiIt is the molar fraction of reactant i, μ is the coefficient of viscosity of mixed gas, its calculating formula
For：
Wherein μiIt is the coefficient of viscosity of gas i, MiIt is the molecular weight of gas.
K is the permeability of porous electrode, it is possible to use Blake-Kozeny empirical relation is representing：
Wherein dpIt is average pore diameter.Under typical sintering environment, average pore diameter is equal to the straight of average grain
Footpath.So, in a model, according to the report of document, the diameter of average pore and granule is set to 2 μm.ε is the hole of electrode
Porosity and τ are the twisting coefficients of pore.
WithIt is the effective diffusivity in binary gas diffusion and Knudson diffusibility, they can be defined
For：
DijAnd DI, KIt is binary and Knudson diffusion coefficient respectively, formula is as follows：
Wherein MiIt is the molecular weight of gas i, ViIt is special Fuller diffusion volume parameter, its value is as shown in table 1-2.
The diffusion volume of the various gas of table 1-2
1.2.3 electrochemical model
H2Oxidation and O2Reduction reaction be respectively occurring in anode and negative electrode, their reduction kinetics can be passed through
Butler-Volmer relation is indicated.(it describes and is controlled by charge transfer process when electrochemical reaction, rather than
When gas transmission controls, that is, mean electric current less, and E-Eeq=ηact)
Wherein ivIt is the unit volume electric current density of electrode, ηactIt is the activation overpotential of this position, β is transfer ratio, lead to
A symmetrical electric transmission is all assumed that, so the value of β is set to 0.5 for often.N is the electron number participating in electrochemical reaction
Mesh, itpbIt is the exchange current density of unit TPB length, ltpbIt is the TPB density in electrode.Therefore for anode and negative electrode,
Butler-Volmer equation is：
Empirical equation can be used to calculate the i of anode and negative electrodetpb：
Assessment l attempted in a lot of articlestpbValue, using focused ion beam scanning ultramicroscope (FIB-SEM) technology
After carrying out the three-dimensional directly observation to porous electrode, ltpbAnd VYSZValue can more reasonably obtain.Herein with reference to several
L after piece documenttpbIt is taken as 1.8 × 1012m/m3.
As we can find out from Butler-Volmer equation, in order to obtain particular location electrochemical reaction rate, need
Know this position activation overpotential.The activation overpotential of anode and negative electrode each position is respectively defined as
WhereinIt is electron potential,It is the ion electric potential of electrode diverse location.WithRepresent anode and the moon respectively
The equilibrium potential of pole.From the point of view of from document, three kinds of methods are mainly had to set up the electron potential side of electrode equilibrium potential and electrode
The model of boundary's condition, respectively shown in following 1,2 and 3：
Boundary condition：φe,a=0 (1-33)
Wherein E represents working voltage, ENernstIt is energy nernst voltage, in cell, it is equal to open-circuit voltage EOCV, under
Mark a and c represents anode and negative electrode respectively, and tpb represents at electrode three phase boundary.
Boundary condition：φe,a=0 (1-37)
φe,c=E (1-38)
Boundary condition：φe,a=ENernst(1-41)
φe,c=E (1-42)
After a series of calculating, may certify that above-mentioned three kinds of definition are substantially equivalent.Because they are corresponding
Do not change the value of activation overpotential in calculating.Use second definition in the model of this paper, be set to all
ValueBring into, can obtain activation overpotential can be write as：
Due to polarity effect, the working voltage of battery is always less than its reversible voltage, that is,：
E=EOCV-ηact-ηohm-ηcon(1-45)
And concentration polarization is represented by：
Wherein cI, tpbThe molar concentration of gas, c in electrodeI, bIt is the molar concentration in air inlet for the gas.
In model, electromotive force can this special formula formula can be represented by standard：
WhereinIt is relevant with temperature open-circuit voltage under normal pressure.
Electric current density along unit can be obtained by equation below：
Wherein S is the area of anode, lcellIt is the length of repetitives, as 800 μm.To sum up, the polarization curve of battery
Can be obtained by calculating corresponding electric current density under different working voltages.
1.3 operating modes and boundary condition
Table 1-3 illustrates the working condition being applied in model.It should be noted that 480 μm of anode thickness is only applicable to
The situation of planar interface.
Design conditions in table 1-3 model
| Parameter | Value | Unit |
| Anode thickness | 480 | μm |
| Electrolyte thickness | 100 | μm |
| Cathode thickness | 50 | μm |
| Temperature (T) | 1073 | K |
| Pressure (P) | 101325 | Pa |
| Running voltage (E) | 0.7 | V |
| Element length (lcell) | 800 | μm |
| Particle diameter (dp) | 2 | μm |
| TPB density (ltpb) | 1.8×1012 | m/m3 |
Table 1-4 then shows the boundary condition in model.Due to the gas at electrode and electrolyte interface, do not fixed
The boundary condition of bulk concentration value etc., is therefore the boundary condition of electrode surface herein.Subscript in table represents that electrode is gentle
The gas concentration on road surface.Noteworthy point is that, for ion electric potential, except on some borders, its gradient is equal to zero
In addition, actually significantly do not constrain.And finally we can obtain its concrete numerical value, this is because along solid
Its electric current of oxide fuel cell battery is being constant in same circuit, and this just can be applied with to the gradient of ion electric potential
The constraint of effect.Further, since the every aspect in model as gas transmission so is directly or indirectly all distributed with ion electric potential
Relation, so it is considered to after all these constraint, ion electric potential distribution after the simulation of accurate software calculates can be successful
Obtain.
Boundary condition in table 1-4 model
All equatioies discussed above and constraint all input in COMSOL Multiphysics (version 3 .5.0.494), always
Have four kinds of patterns to have connected whole system.1st, ion-conductance potential field, 2, electron potential field, 3, the gas distribution in anode, 4, cloudy
Gas distribution in extremely.Comprise the partial differential equations with regard to independent variable of mistake presented hereinbefore in each pattern, characterize
The physical field rule meeting in SOFC.
This model use COMSOL emulation basic process, need in physical analysis constant and expression formula (include
Overall expression formula, solves domain expression formula etc.) after Input Software, geometric construction can be carried out, then in succession carry out solving domain setting
Put, border is arranged, to set up multiple physical field coupling model.Carry out stress and strain model afterwards it is notable that grid division
When, near its grid of region of electrode and electrolyte interface should arrange more more dense, because electric charge can occur at this
Transfer reaction, the value of independent variable is it may happen that very big change.Subsequently just row operation can be entered to model by computer, in model
The number of degree of freedom is 17874, and relative tolerance is 1e-6, the foundation of judgement in calculating, can be restrained as model.Can after computing
Post processing is carried out with the instrument carrying using COMSOL, the acquisition including datagrams such as equipotential line, exterior view, profiles and to change
The post processing operations such as amount integration.Hereafter, thus it is possible to vary Model Parameter (such as geometric parameter, SOFC operating mode
Parameter etc.) value be programmed being circulated computing to model in COMSOL Script, single parameter can be probed into deeper into ground
Impact to solid-oxide fuel battery performance.
1.4 results and analysis
1.4.1 the contrast at different geometry interfaces
Table 1-5 list under the constant battery operation voltage for 0.7V the electric current density of different geometry interfaces battery and it
Respective interface expansion factor.From result it is found that either any geometry interface, they are than planar interface solid oxygen
Compound fuel cell has bigger electric current density.This phenomenon shows to expand the property that interfacial contact area can improve battery really
Energy.Moreover it is possible to find that depth ellipse interface has the electric current density of maximum in all boundary elements：2114A/m2.Change sentence
Talk about, compare with plane battery, due to the expansion at its interface, its electric current density improves 10.86%.Therefore, this shape will
It is the core subsequently optimizing further.
Additionally, remaining in table 1-5, when we compare interface expansion factor and electric current density, it can be found that
The positive correlation having between them.In order to make it more more readily apparent, specifically show its mutual relation in figure 6.Overall
On, the interface of anode and electrolyte is bigger, and under fixed voltage, the electric current density of this battery is also bigger.Big in view of their value
In the current density value of plane battery, it can therefore be concluded that going out, bigger interfacial area can increase electrode and electrolyte circle
Three phase boundary near face, thus results in less activation polarization losses and more preferably battery performance.However, it is also noticeable
Be, deeper oval situation there is certain exception although its interface expansion factor be not maximum but its electric current density but
It is maximum.This situation is likely due to this kind of shape interface and rectangular interfaces compare bigger effective interface, therefore
Bigger three phase boundary region can be provided around interface.
The analog result at the different interface of five kinds of table 1-5
1.4.2 battery behavior
After model completes in COMSOL, the parameters of battery and performance can accordingly obtain.In the figure 7, show
The distribution situation of hydrogen in relatively deep ellipse anode.Can see and compare hydrogen with electrolyte interface end with anode surface in anode
Amount significantly reduce, by the 11.015mol/m of air flue electrode surface3It is reduced to 10.907mol/m3, this is due in the anode
The hydroxide reaction occurring is so that the amount of hydrogen consumes and is gradually reduced, and produces corresponding concentration polarization.Vapor
Concentration distribution then shows in fig. 8, contrary with hydrogen, and as the product of hydroxide reaction, its partial pressure is with closer to anode electricity
Solve matter interface and all the more increase, its peak value can reach 0.541mol/m3.Likewise, the gas distribution of cathode terminal is also and anode
End is similar, is constantly consuming close to catholyte interface oxygen and nitrogen proportion then constantly rises.
Fig. 9 shows the current density voltage curve figure of different interfaces battery obtained by simulation.This figure is by changing electricity
Pond working voltage (0.1,0.2,0.4,0.6,0.7,0.9 and 1.1V), obtain its under each voltage corresponding electric current density and
Get.Consistent by the battery performance that can be seen that in Fig. 9 previously in running under 0.7V voltage, from plane, shallower ellipse
Shape, rectangle is arrived at triangle interface again, relatively deep ellipse interface, and its I-V curve is gradually increasing.I.e. under any running voltage, its
Electric current density is all the relation being gradually increasing.Under all of voltage, the battery at relatively deep ellipse interface suffers from bigger electricity
Current density, the conclusion that also and above it has optimum performance is identical.Therefore, this conclusion further demonstrates with interface
The change of shape, the corresponding chemical property of SOFC unit also can occur to change accordingly.
Figure 10 shows the ion electric potential distribution along battery cross sectional.Ion electric potential has in electrolyte area and significantly subtracts
Less it is seen that due to larger dielectric substrate thickness, the ohmic loss along electrolyte area is than larger.
What Figure 11 represented is situation to be changed stepwise along cell thickness direction ion electric potential, and it is actually Figure 10's
On the basis of, the value of fixing horizontal direction x, obtained by the value of the lower ion electric potential of different y values.It can be found that in most anode
Region, ion electric potential value is very stable, because this area charge mainly exists as electrons.But near electrolysis
The anode region at matter interface, due to there is charge transfer reaction, (i.e. electronics and ion are anti-as the electrochemistry of a portion
Should), its value can substantially reduce.In dielectric substrate, ion electric potential linearly reduces in the presence of Ohm's law.Merit attention
, as shown in Figure 11, it is greater than in electrolyte corresponding gradient in the gradient of ion electric potential in the anode region at interface.
This is because, in the presence of pore etc., the effective ion resistivity of these positions is greater than pure YSZ dielectric substrate, leads to leaning on
At the anode of nearly electrolyte, the slope of ion electric potential will larger, afterwards with the consumption of ion populations, and this slope is gradually reduced
And finally to zero.For cathode terminal, similar conclusion equally can also be obtained.
1.4.3 the geometry optimization at oval interface
Drawn from above, relatively deep oval structure has maximum current density under fixed voltage.Due to limiting in a model
Made include battery fragment length, a lot of size such as interface depth, therefore, if again this little parameter is adjusted optimize,
Can be had the Interface Construction of best electrochemical performance in theory.
But from unlike model parameter before, herein will be using a kind of simpler model.Due to periodicity bar
The presence of part, object of study can concentrate in the repeatability unit of one piece of very little of battery, that is, this element only need to contain
One such as rectangle, oval such irregular interface.In order to reach the purpose typically describing an oval interface,
As shown in figure 12, set three geometric parameters characterizing oval sizes, this three parameters are Distance respectively, Length and
Height, wherein Distance and Length can be used for weighing the proportion that oval interface accounts in the horizontal direction, this repetitive
Length be 2 (Distance+Length), Height is used for weighing the depth at oval interface.Due to cathode conditions in simulation
Keep constant, therefore in this schematic diagram, eliminate cathode portion.
Table 1-6 is used for the relatively deep ellipse interface parameter value of loop computation
| Parameter | Value (μm) |
| Distance | 10,50 |
| Length | 10,50,100 |
| Height | 50,100,200 |
It is provided with three groups of different values firstly, for this three geometry variables, as shown in table 1-6.Its value is to consider
Show that deeper ellipse has better performance in 1.4.1, therefore the parameter setting of Height is obtained higher.In addition, it is theoretical
The upper chemical property saying the more intensive battery in oval interface also can be better, the therefore cycle values of parameter Distance and Length
All substantially little than before 800 μm of element length.
It is assumed that SOFC working voltage is 0.7V, by being circulated fortune in COMSOL Script
Calculate, it is possible to obtain respective electric current density under various geometric combination, to obtain the oval interface knot with optimum performance
Structure.Under its various combination obtain current density value as shown in table 1-7, it can be found that working as Distance, Length and Height
Value respectively reach 10 μm, when 10 μm and 200 μm electric current density obtain maximum.In other words, when this oval boundary
In the case that the density in face is ideally high, can obtain being about 2500A/m2Electric current density.According to simulation before
Structure, is 1885A/m as its electric current density of plane interface with reference to situation2That is to say, that electric current density in such cases
32% lifting can be obtained.This conclusion and before chemical property and interface expansion factor have the conclusion kiss of positive relation
Close, because more intensive with contact surface, electrolyte more gos deep in electrode, is accordingly obtained in that bigger interface expansion factor,
Just it is obtained in that bigger electric current density.But it is contemplated that actual manufacture difficulty and the cost that median surface is processed, this kind to be obtained
Groove interface deep enough is also technically extremely difficult.But, conclusion above remains able to provide to us
Valuable information, that is, manufacture containing comparatively dense and can increase the SOFC battery of electrode electrolyte contact surface
Can have and improve its chemical property to a certain extent.
Idens under table 1-7 difference elliptic geometry parameter
1.5 brief summary
Establishing two dimension to the anode supporting type solid oxide fuel cell repetitives having larger electrolyte thickness has
Limit meta-model, describes the respective equation of multiple physical field and the process of modeling in detail, has inquired into and has had the expansion of different interfaces
The impact to battery performance for the five kinds of anode-electrolyte interfaces of the factor, has obtained to draw a conclusion：
1) with respect to another four kinds of interface batteries, under fixed voltage, relatively deep oval interface energy obtains the average of maximum
Electric current density, such as under 0.7V working voltage, its average current density exceeds 10.86% than plane interface battery.
2) the interface expansion factor being defined herein and the performance of battery generally have positively related relation.
3) average current density-voltage curve of different batteries confirms its performance comparison, in addition, in cell electrolyte week
Enclose larger ion electric potential change and illustrate ion ohmic loss very greatly, the following electrolyte thickness that reduces is feasible improvement.
4) optimization further to relatively deep ellipse interface shows, it is deeper in anode/electrolyte interface, more intensive,
The total performance of battery is better, and planar interface battery compares, and ideally can obtain maximum 32% the carrying of electric current density
Rise.
5) manufacture containing comparatively dense and the SOFC battery of electrode electrolyte contact surface can be increased can have
Improve its chemical property to a certain extent.
The above is the preferred embodiment of the present invention, certainly can not limit the right model of the present invention with this
Enclose it is noted that for the professional and technical personnel of the art, under the premise without departing from the principles of the invention, also may be used
To make some improvement and to change, these improve and variation is also considered as protection scope of the present invention.
Claims (7)
1. a kind of method for building up of SOFC two-dimensional finite element model is it is characterised in that comprise the following steps：
S01, model hypothesis and geometry set；
S02, set up model using COMSOL software；
S03, the analysis of model result.
2. SOFC two-dimensional finite element model as claimed in claim 1 method for building up it is characterised in that
The target area of this SOFC modeling is the repetition list of an anode supporting type solid oxide fuel cell
Unit, is made up of LSM/YSZ composite cathode, YSZ ceramic electrolyte and Ni/YSZ cermet anode.
3. SOFC two-dimensional finite element model as claimed in claim 1 method for building up it is characterised in that
In described step S01, model hypothesis and geometry setting are as follows：
A, all parameter values not time to time change；
Temperature in b, unit is unified to be 800 DEG C；
C, porous electrode are the continuuies that three components are uniformly constituted；
D, be passed through anode gas composition be volume fraction 97% H2+ 3% O2, negative electrode is 21% O2+ 79% N2；
In e, electrode, electron potential is equal everywhere；
F, the Butler-Volmer electrochemical kinetics process of standard are set up.
4. SOFC two-dimensional finite element model as claimed in claim 1 method for building up it is characterised in that
Have studied five kinds of SOFC units with different anodolyte geometry interfaces in described model, be respectively
Planar interface, rectangular interfaces, triangle interface, the first oval interface and the second oval interface.
5. SOFC two-dimensional finite element model as claimed in claim 1 method for building up it is characterised in that
Set up model using COMSOL software in described step S02 to comprise the following steps：
The input of S021, constant and expression formula, constant and expression formula are inputted in COMSOL software,
S022, set up geometric figure after, carry out solve domain setting, border setting；
S023, set up network, carry out stress and strain model, subsequently row operation is entered to model by computer；
Carry out post processing using the instrument that COMSOL carries, by changing the value of Model Parameter in COMSOL after S024, computing
Script is programmed being circulated computing to model, probes into the impact to solid-oxide fuel battery performance for the single parameter.
6. SOFC two-dimensional finite element model as claimed in claim 4 method for building up it is characterised in that
Described rectangular interfaces, described triangle interface, described first oval interface, the described second oval interface electric current density equal
Electric current density more than described planar interface SOFC.
7. SOFC two-dimensional finite element model as claimed in claim 6 method for building up it is characterised in that
The electric current density at the described second oval interface is more than described rectangular interfaces, described triangle interface, the described first oval boundary
The electric current density in face.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201611019937.9A CN106407621A (en) | 2016-11-21 | 2016-11-21 | Method for establishing two-dimensional finite element model of solid oxide fuel cell |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201611019937.9A CN106407621A (en) | 2016-11-21 | 2016-11-21 | Method for establishing two-dimensional finite element model of solid oxide fuel cell |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN106407621A true CN106407621A (en) | 2017-02-15 |
Family
ID=58069000
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201611019937.9A Pending CN106407621A (en) | 2016-11-21 | 2016-11-21 | Method for establishing two-dimensional finite element model of solid oxide fuel cell |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN106407621A (en) |
Cited By (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108875145A (en) * | 2018-05-25 | 2018-11-23 | 中国电子科技集团公司第十八研究所 | Manufacturing method of solid-state lithium battery based on COMSO L model |
| CN109244510A (en) * | 2018-09-26 | 2019-01-18 | 电子科技大学 | A kind of solid oxide fuel cell control method based on Unmarried pregnancy compensation |
| CN109448799A (en) * | 2018-09-03 | 2019-03-08 | 岭东核电有限公司 | Metal cools down FBR metallic fuel multiple physical field Model coupling method |
| CN110993035A (en) * | 2019-11-22 | 2020-04-10 | 华中科技大学鄂州工业技术研究院 | Two-dimensional steady-state model establishment method for proton exchange membrane electrolytic cell characteristic analysis |
| CN111506999A (en) * | 2020-04-17 | 2020-08-07 | 华中科技大学鄂州工业技术研究院 | Performance analysis method and device of solid oxide fuel cell |
| CN112578008A (en) * | 2020-12-03 | 2021-03-30 | 江苏科技大学 | Performance analysis method for three-dimensional microstructure of ternary composite electrode of proton ceramic fuel cell |
| CN113420483A (en) * | 2021-06-30 | 2021-09-21 | 哈尔滨工业大学（深圳） | Method for establishing SOFC/SOEC electrode microstructure electrochemical model |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101324908A (en) * | 2008-08-01 | 2008-12-17 | 重庆大学 | Multi-dimension analogy method of solid-oxide fuel battery |
| CN102011140A (en) * | 2010-10-27 | 2011-04-13 | 清华大学 | Electrolyte/oxygen electrode interface microstructure modification method for solid oxide electrolytic cell |
-
2016
- 2016-11-21 CN CN201611019937.9A patent/CN106407621A/en active Pending
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101324908A (en) * | 2008-08-01 | 2008-12-17 | 重庆大学 | Multi-dimension analogy method of solid-oxide fuel battery |
| CN102011140A (en) * | 2010-10-27 | 2011-04-13 | 清华大学 | Electrolyte/oxygen electrode interface microstructure modification method for solid oxide electrolytic cell |
Non-Patent Citations (1)
| Title |
|---|
| 欧阳健: "固体氧化物燃料电池阳极电解质界面的建模和分析", 《万方数据库-学位论文库》 * |
Cited By (10)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108875145A (en) * | 2018-05-25 | 2018-11-23 | 中国电子科技集团公司第十八研究所 | Manufacturing method of solid-state lithium battery based on COMSO L model |
| CN108875145B (en) * | 2018-05-25 | 2022-09-06 | 中国电子科技集团公司第十八研究所 | Manufacturing method of solid-state lithium battery based on COMSOL model |
| CN109448799A (en) * | 2018-09-03 | 2019-03-08 | 岭东核电有限公司 | Metal cools down FBR metallic fuel multiple physical field Model coupling method |
| CN109244510A (en) * | 2018-09-26 | 2019-01-18 | 电子科技大学 | A kind of solid oxide fuel cell control method based on Unmarried pregnancy compensation |
| CN109244510B (en) * | 2018-09-26 | 2021-07-13 | 电子科技大学 | Solid oxide fuel cell control method based on unmodeled dynamic compensation |
| CN110993035A (en) * | 2019-11-22 | 2020-04-10 | 华中科技大学鄂州工业技术研究院 | Two-dimensional steady-state model establishment method for proton exchange membrane electrolytic cell characteristic analysis |
| CN110993035B (en) * | 2019-11-22 | 2022-07-15 | 华中科技大学鄂州工业技术研究院 | Two-dimensional steady-state model establishment method for proton exchange membrane electrolytic cell characteristic analysis |
| CN111506999A (en) * | 2020-04-17 | 2020-08-07 | 华中科技大学鄂州工业技术研究院 | Performance analysis method and device of solid oxide fuel cell |
| CN112578008A (en) * | 2020-12-03 | 2021-03-30 | 江苏科技大学 | Performance analysis method for three-dimensional microstructure of ternary composite electrode of proton ceramic fuel cell |
| CN113420483A (en) * | 2021-06-30 | 2021-09-21 | 哈尔滨工业大学（深圳） | Method for establishing SOFC/SOEC electrode microstructure electrochemical model |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN106407621A (en) | Method for establishing two-dimensional finite element model of solid oxide fuel cell | |
| Ni et al. | Mathematical modeling of the coupled transport and electrochemical reactions in solid oxide steam electrolyzer for hydrogen production | |
| Yin et al. | A coupled three dimensional model of vanadium redox flow battery for flow field designs | |
| Khazaeli et al. | Numerical investigation and thermodynamic analysis of the effect of electrolyte flow rate on performance of all vanadium redox flow batteries | |
| Ni | Computational fluid dynamics modeling of a solid oxide electrolyzer cell for hydrogen production | |
| Li et al. | Theoretical modeling of air electrode operating in SOFC mode and SOEC mode: The effects of microstructure and thickness | |
| Konno et al. | A corrugated mesoscale structure on electrode–electrolyte interface for enhancing cell performance in anode-supported SOFC | |
| Iwai et al. | Power generation enhancement of solid oxide fuel cell by cathode–electrolyte interface modification in mesoscale assisted by level set-based optimization calculation | |
| CN106383977A (en) | Rectangular electrode/electrolyte interface based SOFC (solid oxide fuel cell) simulation method | |
| Ni et al. | Electrochemistry modeling of proton exchange membrane (PEM) water electrolysis for hydrogen production | |
| AlZahrani et al. | A performance assessment study on solid oxide fuel cells for reduced operating temperatures | |
| Sahli et al. | Optimization study of the produced electric power by SOFCs | |
| Moreno-Blanco et al. | On the effect of gas channels-electrode interface area on SOFCs performance | |
| Modestino et al. | Integrated microfluidic test-bed for energy conversion devices | |
| Chinda et al. | Microscale Modeling of an Anode‐Supported Planar Solid Oxide Fuel Cell | |
| van Gorp et al. | Bottom-up design of porous electrodes by combining a genetic algorithm and a pore network model | |
| Wang et al. | Analysis of overpotential in discharge process associated with precipitation for vanadium-manganese flow battery | |
| Wang et al. | Boosting the performance and durability of heterogeneous electrodes for solid oxide electrochemical cells utilizing a data-driven powder-to-power framework | |
| CN114300713A (en) | Cross-flow SOEC galvanic pile two-dimensional dynamic model construction method and application thereof | |
| Ouyang et al. | Performance evaluation and mechanism study of a dual-electrolyte self-pumping microfluidic fuel cell | |
| Silva et al. | Impact of the catalytic activity of carbon nanotubes in the performance of Li-O2 batteries | |
| Khalid et al. | Model development and analysis of a novel high-temperature electrolyser for gas phase electrolysis of hydrogen chloride for hydrogen production | |
| CN110993035B (en) | Two-dimensional steady-state model establishment method for proton exchange membrane electrolytic cell characteristic analysis | |
| Pianko-Oprych et al. | Simulation of the steady-state behaviour of a new design of a single planar Solid Oxide Fuel Cell | |
| Wang et al. | Two-phase analytical modeling and intelligence parameter estimation of proton exchange membrane electrolyzer for hydrogen production |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| C06 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| RJ01 | Rejection of invention patent application after publication | ||
| RJ01 | Rejection of invention patent application after publication |
Application publication date: 20170215 |