Tomography-based snow morphology
characterization via direct and indirect
approaches
Sophia Haussener
LRESE, Institute of Mechanical Engineering, EPFL, Lausanne, Switzerland
1/26
Motivation
• Accurate characterization and quantification of the structure or
morphology of the snow is essential for many applications, including
climate modeling, hydrology, and remote sensing
• Direct approaches based on visual inspection of micrographs or
microscopic images can be used for morphological characterization but
suffer from inconsistent definitions and usually neglect the third dimension
of the snow
• Indirect approaches use the fact that snow’s heat and mass transport
properties, such as its reflectivity or permeability, are highly dependent on
its morphology. Nevertheless, the indirect method suffers from the
simplified morphology-property relations currently available
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Outline
• Coupled experimental-numerical methodology
• Morphology via direct approaches
• Morphology via indirect approaches
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Coupled experimental-numerical methodology
• Aim: Use most accurate morphological representation for subsequent
numerical calculations
• Experimentally obtaining exact morphology via computer
tomography
• Digitalize tomographic images to get digitalized morphology to
be used in subsequent direct pore-level simulations
• Direct calculations of morphological characteristics (porosity,
specific surface area, pore/particle sizes, anisotropy, …)
• Use volume-averaging theory to extract effective properties out
• Calculate heat and mass transport properties and relate them to
morphological characteristics
Methodology
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Coupled experimental-numerical methodology
• Volume averaging theory
– Heat transfer
> cm
< mm
– Mass transfer
Methodology
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Outline
• Coupled experimental-numerical methodology
• Morphology via direct approaches
• Morphology via indirect approaches
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Direct approaches
• Using tomography-based approaches to characterize morphology in a
forward manner
• Characteristic samples
• Tomography:
ds (6x6x4mm3)
Methodology
mI (6x6x4mm3)
Direct approaches
mII (6x6x4mm3)
dh (11x11x7mm3)
ws (11x11x7mm3)
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Direct approaches
• Statistical approaches for porosity, specific surface
Two-point correlation function
with
and
• Results
*
• Anisotorpy:
Mean intercept length for anisotropy
Degree of anisotropy (DA) = 1- lel,s/lel,l
DA ≈ 0 → isotrop
Methodology
Direct approaches
DA
0.249
0.214
0.090
0.132
0.025
*Kerbrat et al., ACP, 8, 2008.
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Direct approaches
• Mathematical morphology operations, i.e. opening with spherical
structuring element
• Pore-size distribution
Particle-size distribution
• Sizes:
Methodology
Direct approaches
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Outline
• Coupled experimental-numerical methodology
• Morphology via direct approaches
• Morphology via indirect approaches
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Morphology via indirect approaches
• Mass transfer
– Permeability
– Dupuit-Forchheimer coefficient
• Heat transfer
– Conduction
– Radiation
Methodology
Direct approaches
Indirect approaches
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Mass transfer
• Theory and methodology mass transfer:
• Permeability and Forchheimer coefficient
•
Methodology: Solving mass conservation, Navier-Stockes equations
in the void phase by finite volume method
Whitaker, Kulwer academic publisher, 1999.
Methodology
Direct approaches
Indirect approaches
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Mass transfer
• Permeability for pore/particle sizes, specific surface and porosity:
1000
100
Normalized permeability
Conduit flow model:
K/d_pore^2
K/d_grain^2
K*A0^2
10
Shimizu 1970 *:
1
0.1
Hydraulic radius model:
0.01
0.001
0.0001
ws
dh mII mI ds
0.00001
0
0.2
0.4
0.6
Porosity (-)
0.8
1
Zermatten et al., J. Glaciol., 2011.
*Shimizu, Low Temp. Sci. A, 1970.
Methodology
Direct approaches
Indirect approaches
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Mass transfer
• Permeability for pore/particle sizes, specific surface and porosity:
1000
100
Normalized permeability
Conduit flow model:
K/d_pore^2
K/d_grain^2
K*A0^2
Conduit flow model
Shimizu 1970
Hydraulic radius model
10
1
0.1
Shimizu 1970 *:
Hydraulic radius model:
0.01
0.001
0.0001
ws
dh mII mI ds
0.00001
0
0.2
0.4
0.6
Porosity (-)
0.8
1
Zermatten et al., J. Glaciol., 2011.
*Shimizu, Low Temp. Sci. A, 1970.
Methodology
Direct approaches
Indirect approaches
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Mass transfer
• Permeability for pore/particle sizes, specific surface and porosity:
Shimizu 1970 *:
0.0000001
ds mI mII
dh
ws
Porosity=0.854 (ds)
Permeability (m2)
1E-08
0.845 (mI)
0.805 (mII)
1E-09
0.67 (dh)
1E-10
0.384 (ws)
1E-11
Direct numerical
simulations
1E-12
0
Methodology
0.0002
0.0004
0.0006
Grain diameter (m)
Direct approaches
0.0008
Indirect approaches
Zermatten et al., J. Glaciol., 2011.
*Shimizu, Low Temp. Sci. A, 1970.
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Heat transfer
• Conduction
Local thermal equilibrium valid:
→ One-equation model, results in (steady):
Methodology: Solving steady state conduction equation in both phases
in a quasi 1D situation by finite volume technique
Quintard et al., AHT, 23, 1993.
Methodology
Direct approaches
Indirect approaches
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Heat transfer
• Conduction – Temperature distribution
mII
ws
Normalized
temperature
1
0
8mm
3mm
Methodology
Direct approaches
Indirect approaches
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Heat transfer
• Conduction for porosity:
1
ws
dh mII mI ds
Normalized conductivity
ζ=ke/ks, η=kf/ks
Maxwell bound *:
0.1
Russel **:
Direct pore-level simulations
Maxwell bound
Russel
0.01
0
0.2
0.4
0.6
Porosity (-)
0.8
1
*Maxwell, Clarendon Press, 1891.
**Russel, J. Am. Cer. Soc., 1935.
Methodology
Direct approaches
Indirect approaches
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Heat transfer
• Radiation:
• From discrete-scale to continuum-scale:
Boundary between two semi-transparent phases:
phase j
Methodology
phase i
Direct approaches
Indirect approaches
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Heat transfer
• Radiation
• Averaged RTE (where
):
Postulation of:
Results in:
e.g.:
where:
Lipiński et al., JQSRT, 111, 2009.
Lipiński et al., JQSRT, 111, 2010.
Methodology
Direct approaches
Indirect approaches
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Heat transfer
• Radiation:
• 1D slab
εr = 1
T=0K
qin''
• Absorbed radiation:
mII
Methodology
Direct approaches
Indirect approaches
ws
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Heat transfer
• Radiation:
• Reflectance and transmittance (slab thickness: 4 cm)
Diffuse
Collimated incident radiation
Methodology
Direct approaches
Indirect approaches
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Heat transfer
• Radiation:
• Reflectance and transmittance (slab thickness: 4 cm)
ds
ws
Methodology
Direct approaches
Indirect approaches
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Heat transfer
• Radiation:
• Reflectance and transmittance (slab thickness: 4 cm)
ds
ws
Methodology
Direct approaches
Indirect approaches
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Summary and outlook
• Coupled experimental-numerical approach for direct and indirect
determination of morphological properties
• Direct approaches successfully applied for the determination of:
– Porosity
– Specific surface
– Pore and particle size distributions
– Anisotropy characterization
• Indirect approaches to get a better understanding on morphology-property
relations, applied for the determination of:
– Permeability
– Conductivity
– Albedo
• Provides a powerful tool for in-depth understanding of morphology of
snow, and heat and mass transport phenomena in snow
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Acknowledgement
Martin Schneebeli, SLF
Mathias Gergely, SLF
Emilie Zermatten, ETH
Aldo Steinfeld, ETH
Silvan Suter, EPFL
[email protected]
http://lrese.epfl.ch
Thank you for your attention!
Questions? Comments?
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LRESE competences
• Laboratory of renewable energy science and engineering – LRESE
• Research interest: Efficient, sustainable, robust, and economic conversion
of renewable sources into storable fuels, materials, or chemical
commodities
sustainability
renewable energy
novel energy conversion processes
storable fuels, power and materials
• Fundamentals: Coupled multi-physics - thermal sciences, fluid dynamics,
electro-magnetism, and thermo/electro/photochemistry - in complex multiphase, multi-component media on multiple scales
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