e. iacona, j. taine, f. bellet laboratoire em2c - cnrs - ecp 1 radiation in porous media: an...

E. Iacona, J. Taine, F. Bellet Laboratoire EM2C - CNRS - ECP

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RADIATION IN POROUS MEDIA: AN UPSCALING METHODOLOGY APPLIED TO A

REACTOR NUCLEAR CORE

Estelle Iacona, Jean Taine and Fabien Bellet

Energétique Moléculaire et Macroscopique, Combustion

E.M2.C

Ecole Centrale Paris - UPR 288, CNRS


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AXES DE RECHERCHE

EM2C

COMBUSTIONCOMBUSTION QuickTime™ et undécompresseur GIF

sont requis pour visionner cette image.

8 ECPCandel S.Darabiha N.Fiorina B.Gicquel O.Massot MRolon J.CRichecoeur F.Schuller Th.

4 CNRS Ducruix S.Laurent-Nègre F.Veynante D.Zimmer L.

IR CNRS :Durox D.Lacoste D.Scouflaire Ph.

NANO-OPTIQUE ET NANO-THERMIQUE

NANO-OPTIQUE ET NANO-THERMIQUE

3 ECP 1 CNRS Greffet J.-J. Volz S.Laroche M.

Marquier F.

PLASMAS HORS ÉQUILIBRE

PLASMAS HORS ÉQUILIBRE

1 ECP 1 CNRS Laux Ch. Bourdon A.

IR CNRS :Lacoste D.

RAYONNEMENT ET TRANSFERTS COUPLÉS

RAYONNEMENT ET TRANSFERTS COUPLÉS

QuickTime™ et undécompresseur GIF


4 ECP 3 CNRS Taine J. Perrin M.Y.Bellet F. Rivière Ph.Goyeau B. Soufiani A.Iacona E.


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Carbon foam (porosity 0.93)

for some fuel cells (SOFC)

Mullite foam (porosity 0.85)

for catalytic combustion

Some applications of radiation in porous media

Combustible grape for nuclear reactor core - AREVA


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Outline

Objectives

Up scaling method : a direct identification method

Application to real porous media

Problem : Temperature field in the medium?

Coupled heat transfer :

- convection in pores (fluid phase)

- conduction in the fluid and in the solid phases

- radiation : Accurate calculations required in many applications high temperature applications

Local scale transfer : unaffordable (Large computer time and memory)

dz

( ) ( ) ( ) ∫−

→+−=+∂

∂ 1

1

0 ')',()'(2

)1(,,

μμμμω

ωμμ

β

μλλ

λλλλ

λ

λ

dzLPTLzLz

zL

λπ λ dµdµµzLqR ∫ ∫∞

−=

0

1

1),(2

Problem

Alternative : up scaling method model of an equivalent semi transparent continuous medium`=> Radiative properties ? Validity?

Medium structure statistically known

Local radiative properties known

dz

λ

λλ β

σω =

)''( μμλ →P

λσλκλβ +=extinction coefficient :

albédo (diffusion) :

Diffusion phase function :

Diffusion σ

Absorption κ

Extinction β

+


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parameter identification method : some drawbacks

assumed semi transparent medium model(no validity criterion)

indirect method of characterization(radiative transfer model required to analyze experiments)

accuracy on the determined radiative properties difficult to estimate

error associated with the semi transparent model ?accuracy of the radiative transfer model ?accuracy of the identification technique ?


8

Outline

Objectives




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Objectives

From the statistical knowledge of the porous medium structure and its local radiative properties:

• calculate the radiative properties of a potentially equivalent semi-transparent medium :

- nonisotropic extinction coefficient β- nonisotropic absorption coefficient κ- scattering phase function pμ

• with a direct simulation using a Monte-Carlo method.


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Definitions and assumptions

Porous medium statistically isotropic or anisotropic

Porous medium statistically homogeneous or nonhomogeneous

Diffraction : neglected (λ <<D)Solid phase : opaque or semi transparentFluid phase : transparent or semi transparent


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Definition : Extinction =absorption+scattering At local scale: probability of reaching the interface(non spectral, only geometric property)

Statistical approach of radiation

u

r

I

s0

(semi-transparent medium)

linked to the cumulated distribution function of chord lengths


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Monte-Carlo method

Typically 109 ramdom rays

• any ray : • 1 random original point r into the fluid phase• 1 random direction impact at the solid interface

Calculation of the extinction distance : s0=rI Calculation of : the normal vector

the impact angle at the solid interfaceDeduction of the scattering angle : contribution to the phase function

u

r

I

n


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Identification criterion e :

Statistical approach of radiation

Radiation Distribution Function Identification Method

(RDFI method)

ge(s,uk)

Ge(s,uk)

s (mm)

0.95

useful extinction optical thickness range

β s = 0 β s = 3

Extinction coefficients calculated from identification of Ge(s) with ge(s) with mean square method


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Outline

Objectives




15IUSTI from ESRF X ray tomography

spatial resolution of 5 μm

3D Numerical image of a mullite foam sample issued from a tomography

Tomography resolution

mid scale (wall pores) Local scale

βSmm-1

andκSmm-1, pS


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IRNS : French Radiation and nuclear safety institute

Cooling fluid leaking

Increase of temperatureDegradation, fusion et geometrical modification of the core

T<500K

Nuclear reactor core in severe accident conditions


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2D of a cross section (density scale in g/cm3)

Degraded small scale nuclear core rod bundleGeometry obtained from ray tomography

experiment FPT1, IRSN, Cadarache

QuickTime™ et undécompresseur Vidéo 1 Microsoft


3D reconstruction


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Numerical image of the whole degraded bundle

Walls assumed opaque at local scale : = 0.8 (Chalopin et al., 2008)

z

Degraded small scale nuclear core rod bundleGeometry obtained from ray tomography

experiment FPT1, IRSN, Cadarache


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A: β=0.19D: β=0.24

Bain fondu + cavité

C: β=axɛ+b

B: β=0.28


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Radiative transfer in a nuclear reactor core

Calculated from the obtained radiative properties of the equivalent medium

Radiative conductivity model :

< 0. 2

For an optically thick REV from the absorption point of view

λπ λ dµdµµzLqR ∫ ∫∞

−=

0

1

1),(2


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conclusions

General statistical approach of radiation :

Accurate determination of Ge, Pa, Ps and p for any porous medium REV

Equivalent semi-transparent media : βκσandp by the Radiative Distribution Function Identification (RDFI) method

Validity of the semi transparent medium model : all porous media can’t be modeled by semi transparent media

Direct determination method radiative properties directly obtained from their definitions,

without use of a radiative transfer model

based on the knowledge of- the porous medium morphology (tomography)

- the radiative properties at the local scale (less than the spatial tomography resolution)

e. iacona, j. taine, f. bellet laboratoire em2c - cnrs - ecp 1 radiation in porous media: an...

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