Porous Media - ht.energy.lth.se · • Fluid flow • Heat transfer • Mass transfer • Phase...

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Porous Media Electrodes in batteries and fuel cells, electrolytes

Transcript of Porous Media - ht.energy.lth.se · • Fluid flow • Heat transfer • Mass transfer • Phase...

Page 1: Porous Media - ht.energy.lth.se · • Fluid flow • Heat transfer • Mass transfer • Phase change ... • In the context of porous media, determining parameters is more ...

Porous MediaElectrodes in batteries and fuel cells, electrolytes

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Microstructure of CL‐PEMFC• 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;

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Illustration of Microstructure in SOFC

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

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Transport Phenomena• Fluid flow• Heat transfer• Mass transfer• Phase change• Unsaturated and multi‐phase flow• Solid‐fluid interaction• Non‐equilibrium phenomena• Chemical and electro‐chemical reactions• Ion transport• Current transport

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TerminologyVolume averaged velocity, temperature

Fluid pressureSaturation

Mass fractionsImproved models: Phase velocity and temperature

Parameters arising from averagingPorosity

PermeabilityTortuosity

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Parameter estimation

• Governing equations can be solved by FVM, FEM, or related numerical techniques.

• In the context of porous media, determining parameters is more important than solving the mass‐momentum‐energy equations.

• Porosity• Permeability (absolute, relative)• Capillary pressure• Dispersion• Inhomogeneities and anisotropy

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Complexity

• Flow path tortuos• Geometry is three dimensional and not clearly defined• Original approaches seek to relate pressure drop and flow rate, adopting a volume‐averaged perspective

• It has led to local volume‐averaging (REV) “continuum approach”• Averaging results in new model parameters

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Assumptions

• Representative elementary volume (REV)• Solid phase rigid and fixed• Closely packed arrangement• REV is larger than the pore volume• Look for solutions at a scale much larger than the REV• Porous continuum

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Dimensions

• Pore scale and particle diameter 1‐10 microns but for FCs and batteries down to nm

• REV 0.1‐1 mm

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Overview

• Porous media applications are quite a few.• Transport equations can be set up.• Simulation tools of CFD and related areas can be used.• Number of parameters is large.• Parameter estimation plays a central role in modeling and points towards need for careful experiments.

• Dependence on parameters can be reduced by carrying out multi‐scale simulations.

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Highly Porous Anode for Application in High‐Temperature Electrochemical Devices

NiO‐CGO foam after sintering

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Foam after cutting to the desired anode size and polishing to achieve a smooth surface upon which the electrolyte could be screen printed

High resolution‐SEM (scanning electron microscope) of the porous anode before (A–C) and after (D–F) reduction

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Illustration Porosity and Tortuosity

Momentum EquationVelocity field

Porosity = 0.76Tortuosity = 1.17

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Porous media‐ SOFC cathode

SOFC cathode

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Equations to be considered in the analysis

+ = Sii

i

ut x

Overall Mass Conservation Equation

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Equations to be considered in the analysis

Darcy’s law

= ii

K pux

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Equations to be considered in the analysis

Brinkmann’s equation

2

2 = - + ii e

i i

up ux K x

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Equations to be considered in the analysis

Momentum Equation

2

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

j i j

u u upt x x x K

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The Forchheimer extended Darcy's law is applied at high velocities in the porous media

air air Fi i

i

Cp u u ux

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There are two major models for the heat transfer of the foam or porous medium

1) The thermal equilibrium model

2) The non‐thermal equilibrium model (two‐equation model).

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f pf jeff

j j j

c u T Tx x x

Thermal Equilibrium Model

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Non‐thermal equilibrium model

( )f pf j f f

fe sf sf s fj j j

c u T Th a T T

x x x

0 ( )s

se sf sf s fj j

T h a T Tx x

Fluid domain Solid domain