porous media - värmeöverföring | värmeöverföring · 2020. 5. 8. · •porous media...
TRANSCRIPT
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Porous MediaElectrodes and electrolytes in batteries and fuel cells
Chapters 2, 8, 9 and 10
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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 layer
AFL= anode functional layer
YSZ= yttria stabilized zirconia
Ni= nickel
TPB= triple phase boundary
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Microstructure of a battery
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Transport Phenomena in general porous media
• 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 pressure
Saturation
Mass fractions
Improved models: Phase velocity and temperature
Parameters arising from averaging
Porosity
Permeability
Tortuosity
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Path lengths in a porous microstructure
𝜏 =𝑠
𝐿ε is the porosity of the porous mediumtortuosity τ
The Bruggeman correlation relates the tortuosity and porosity and reads,
𝜏𝐵𝑟𝑢𝑔𝑔𝑒𝑚𝑎𝑛2 = 𝜀1−𝛼
𝜀 =𝑣𝑜𝑖𝑑 𝑣𝑜𝑙𝑢𝑚𝑒
𝑡𝑜𝑡𝑎𝑙 𝑣𝑜𝑙𝑢𝑚𝑒
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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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Effective diffusion coefficients
• The effective diffusion coefficients Deff (for mass, ion, electrons) are related to the bulk diffusion coefficients Dbulk by
𝐷𝑒𝑓𝑓 =𝜀
𝜏2𝐷𝑏𝑢𝑙𝑘
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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 = 0.76
Tortuosity = 1.17
𝜀 =𝑣𝑜𝑖𝑑 𝑣𝑜𝑙𝑢𝑚𝑒
𝑡𝑜𝑡𝑎𝑙 𝑣𝑜𝑙𝑢𝑚𝑒
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Porous media- SOFC cathode
SOFC cathode
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Equations to be considered in the analysis
+ = Si ii
u
t x
Overall Mass Conservation Equation
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Equations to be considered in the analysis
Darcy’s law
= ii
K pu
x
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Equations to be considered in the analysis
Brinkmann’s equation
2
2 = - + ii e
i i
upu
x 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 up
t 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
Cpu u u
x
− = +
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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 T
x x x
=
Thermal Equilibrium Model
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Non-thermal equilibrium model
( )( )
f pf j f f
fe 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
Th a T T
x x
= − −
Fluid domain Solid domain