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Tomography-based snow morphology characterization via direct and indirect approaches

Sophia Haussener

LRESE, Institute of Mechanical Engineering, EPFL, Lausanne, Switzerland

2/26Snow grain size workshop | April,.2013

• 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

Motivation


• Coupled experimental-numerical methodology

• Morphology via direct approaches

• Morphology via indirect approaches

Outline


• Aim: Use most accurate morphological representation for subsequent numerical calculations

• Experimentally obtaining exact morphology via computer tomography

• Digitalize tomographic images to get digitalized morphology tobe 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

Coupled experimental-numerical methodology

Methodology


• Volume averaging theory– Heat transfer

– Mass transfer

Coupled experimental-numerical methodology

Methodology

< mm

> cm





Outline


• Using tomography-based approaches to characterize morphology in a forward manner

• Characteristic samples

• Tomography:

Direct approaches

Methodology Direct approaches

ds (6x6x4mm3) mI (6x6x4mm3) mII (6x6x4mm3) dh (11x11x7mm3) ws (11x11x7mm3)


DA0.2490.2140.0900.1320.025

• Statistical approaches for porosity, specific surfaceTwo-point correlation function

with and

• Results

• Anisotorpy:Mean intercept length for anisotropyDegree of anisotropy (DA) = 1- lel,s/lel,l

DA ≈ 0 → isotrop

Direct approaches


*Kerbrat et al., ACP, 8, 2008.

*


• Mathematical morphology operations, i.e. opening with spherical structuring element

• Pore-size distribution Particle-size distribution

• Sizes:

Direct approaches






Outline


• Mass transfer– Permeability– Dupuit-Forchheimer coefficient

• Heat transfer– Conduction– Radiation

Morphology via indirect approaches

Methodology Direct approaches Indirect approaches


Mass transfer


Whitaker, Kulwer academic publisher, 1999.

• Theory and methodology mass transfer:

• Permeability and Forchheimer coefficient

• Methodology: Solving mass conservation, Navier-Stockes equations in the void phase by finite volume method


• Permeability for pore/particle sizes, specific surface and porosity:

Mass transfer


Zermatten et al., J. Glaciol., 2011.

ws dh mII mI ds

Conduit flow model:

Shimizu 1970 *:

Hydraulic radius model:

0.00001

0.0001

0.001

0.01

0.1

1

10

100

1000

0 0.2 0.4 0.6 0.8 1

Nor

mal

ized

per

mea

bilit

y

Porosity (-)

K/d_pore^2K/d_grain^2K*A0^2

*Shimizu, Low Temp. Sci. A, 1970.



Mass transfer



ws dh mII mI ds

Conduit flow model:

Shimizu 1970 *:

Hydraulic radius model:


0.00001

0.0001

0.001

0.01

0.1

1

10

100

1000

0 0.2 0.4 0.6 0.8 1

Nor

mal

ized

per

mea

bilit

y

Porosity (-)

K/d_pore^2K/d_grain^2K*A0^2Conduit flow modelShimizu 1970Hydraulic radius model



Mass transfer



ds mI mII dh ws

Shimizu 1970 *:


1E-12

1E-11

1E-10

1E-09

1E-08

0.0000001

0 0.0002 0.0004 0.0006 0.0008

Perm

eabi

lity

(m2 )

Grain diameter (m)

Porosity=0.854 (ds)

0.845 (mI)

0.805 (mII)

0.67 (dh)

0.384 (ws)

Direct numericalsimulations


Heat transfer


Quintard et al., AHT, 23, 1993.

• ConductionLocal 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


• Conduction – Temperature distribution

Heat transfer


3mm 8mm

Normalized temperature

1

0

mII ws


• Conduction for porosity:

Heat transfer


0.01

0.1

1

0 0.2 0.4 0.6 0.8 1

Nor

mal

ized

con

duct

ivity

Porosity (-)

Direct pore-level simulationsMaxwell boundRussel

Maxwell bound *:

Russel **:

*Maxwell, Clarendon Press, 1891.**Russel, J. Am. Cer. Soc., 1935.

ws dh mII mI dsζ=ke/ks, η=kf/ks


Heat transfer


phase iphase j

• Radiation:

• From discrete-scale to continuum-scale:

Boundary between two semi-transparent phases:


• Radiation• Averaged RTE (where ):

Postulation of:e.g.:

where:

Heat transfer


Results in:

Lipiński et al., JQSRT, 111, 2009.Lipiński et al., JQSRT, 111, 2010.


• Radiation:• 1D slab

• Absorbed radiation:

Heat transfer


qin''εr = 1 T = 0 K

mII ws


• Radiation:• Reflectance and transmittance (slab thickness: 4 cm)

Heat transfer


Collimated incident radiation

Diffuseincident radiation



Heat transfer


ds ws


• 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

Summary and outlook


Martin Schneebeli, SLFMathias Gergely, SLFEmilie Zermatten, ETHAldo Steinfeld, ETHSilvan Suter, EPFL

[email protected] http://lrese.epfl.ch

Acknowledgement

Thank you for your attention!

Questions? Comments?


• 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

• Fundamentals: Coupled multi-physics - thermal sciences, fluid dynamics, electro-magnetism, and thermo/electro/photochemistry - in complex multi-phase, multi-component media on multiple scales

LRESE competences

sustainability

renewable energy storable fuels, power and materials

novel energy conversion processes

tomography-based snow morphology characterization via ... · tomography-based snow morphology...

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