Porous Media - ht. • Fluid flow • Heat transfer...

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  • PorousMediaElectrodesinbatteriesandfuelcells,electrolytes

  • MicrostructureofCLPEMFC Carbon: for conduction of electrons and support of the platinum nano-

    particles ;

    Ionomer: typically Nafion, for proton transport;

    Platinum: for electrochemical reactions;

    Pore: for transport of reactant and product gases;

  • IllustrationofMicrostructureinSOFC

    CFL= cathode functional layerAFL= anode functional layerYSZ= yttria stabilized zirconiaNi= nickelTPB= triple phase boundary

  • TransportPhenomena Fluidflow Heattransfer Masstransfer Phasechange Unsaturatedandmultiphaseflow Solidfluidinteraction Nonequilibriumphenomena Chemicalandelectrochemicalreactions Iontransport Currenttransport

  • TerminologyVolumeaveragedvelocity,temperature

    FluidpressureSaturation

    MassfractionsImprovedmodels:Phasevelocityandtemperature

    ParametersarisingfromaveragingPorosity

    PermeabilityTortuosity

  • Parameterestimation

    GoverningequationscanbesolvedbyFVM,FEM,orrelatednumericaltechniques.

    Inthecontextofporousmedia,determiningparametersismoreimportantthansolvingthemassmomentumenergyequations.

    Porosity Permeability(absolute,relative) Capillarypressure Dispersion Inhomogeneitiesandanisotropy

  • Complexity

    Flowpathtortuos Geometryisthreedimensionalandnotclearlydefined Originalapproachesseektorelatepressuredropandflowrate,adoptingavolumeaveragedperspective

    Ithasledtolocalvolumeaveraging(REV)continuumapproach Averagingresultsinnewmodelparameters

  • Assumptions

    Representativeelementaryvolume(REV) Solidphaserigidandfixed Closelypackedarrangement REVislargerthantheporevolume LookforsolutionsatascalemuchlargerthantheREV Porouscontinuum

  • Dimensions

    Porescaleandparticlediameter110micronsbutforFCsandbatteriesdowntonm

    REV0.11mm

  • Overview

    Porousmediaapplicationsarequiteafew. Transportequationscanbesetup. SimulationtoolsofCFDandrelatedareascanbeused. Numberofparametersislarge. Parameterestimationplaysacentralroleinmodelingandpointstowardsneedforcarefulexperiments.

    Dependenceonparameterscanbereducedbycarryingoutmultiscalesimulations.

  • HighlyPorousAnodeforApplicationinHighTemperatureElectrochemicalDevices

    NiOCGOfoamaftersintering

  • Foamaftercuttingtothedesiredanodesizeandpolishingtoachieveasmoothsurfaceuponwhichtheelectrolytecouldbescreenprinted

    HighresolutionSEM(scanningelectronmicroscope)oftheporousanodebefore(AC)andafter(DF)reduction

  • IllustrationPorosityandTortuosity

    MomentumEquationVelocityfield

    Porosity=0.76Tortuosity=1.17

  • Porousmedia SOFCcathode

    SOFCcathode

  • Equationstobeconsideredintheanalysis

    + = Si ii

    ut x

    OverallMassConservationEquation

  • Equationstobeconsideredintheanalysis

    Darcyslaw

    = ii

    K pux

  • Equationstobeconsideredintheanalysis

    Brinkmannsequation

    2

    2 = - + i

    i ei i

    up ux K x

  • Equationstobeconsideredintheanalysis

    MomentumEquation

    2

    2[ + u ] = g - + - u i i i

    j i ij i j

    u u upt x x x K

  • TheForchheimer extendedDarcy'slawisappliedathighvelocitiesintheporousmedia

    air air Fi i

    i

    Cp u u ux

  • Therearetwomajormodelsfortheheattransferofthefoamorporousmedium

    1) Thethermalequilibriummodel

    2)Thenonthermalequilibriummodel(twoequationmodel).

  • f pf jeff

    j j j

    c u T Tx x x

    ThermalEquilibriumModel

  • Nonthermalequilibriummodel

    ( )f pf j f ffe sf sf s f

    j j j

    c u T Th a T T

    x x x

    0 ( )sse sf sf s f

    j j

    T h a T Tx x

    Fluiddomain Soliddomain