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RADIATION IN POROUS MEDIA: AN UPSCALING METHODOLOGY APPLIED TO A REACTOR NUCLEAR CORE

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## RADIATION IN POROUS MEDIA: AN UPSCALING METHODOLOGY APPLIED TO A REACTOR NUCLEAR CORE

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### RADIATION IN POROUS MEDIA: AN UPSCALING METHODOLOGY APPLIED TO A REACTOR NUCLEAR CORE

Energétique Moléculaire et Macroscopique, Combustion

E.M2.C

Estelle Iacona, Jean Taine and Fabien Bellet

Ecole Centrale Paris - UPR 288, CNRS

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

AXES DE RECHERCHE

COMBUSTION

NANO-OPTIQUE ET

NANO-THERMIQUE

8 ECP

Candel S.

Darabiha N.

Fiorina B.

Gicquel O.

Massot M

Rolon J.C

Richecoeur F.

Schuller Th.

4 CNRS

Ducruix S.

Laurent-Nègre F.

Veynante D.

Zimmer L.

IR CNRS:

Durox D.

Lacoste D.

Scouflaire Ph.

3 ECP1 CNRS

Greffet J.-J. Volz S.

Laroche M.

Marquier F.

PLASMAS

HORS ÉQUILIBRE

RAYONNEMENT ET

TRANSFERTS COUPLÉS

4 ECP3 CNRS

Taine J. Perrin M.Y.

Bellet F. Rivière Ph.

Goyeau B. Soufiani A.

Iacona E.

1 ECP1 CNRS

Laux Ch. Bourdon A.

IR CNRS:

Lacoste D.

EM2C

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

(porosity 0.93)

for some fuel cells (SOFC)

Mullite foam

(porosity 0.85)

for catalytic combustion

Some applications of radiation in porous mediaCombustible grape for nuclear reactor core - AREVA

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

Objectives

Up scaling method : a direct identification method

Application to real porous media

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

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)

Problem

- Medium structure statistically known
- Local radiative properties known

- Alternative : up scaling method
- model of an equivalent semi transparent continuous medium

`

=> Radiative properties ? Validity?

Diffusion

Extinction

+

Absorption

extinction coefficient :

albédo (diffusion) :

Diffusion phase function :

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 ?

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

Objectives

Up scaling method : a direct identification method

Application to real porous media

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

- 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 b
- - nonisotropic absorption coefficient k
- - scattering phase function pm
- with a direct simulation using a Monte-Carlo method.

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

Definitions and assumptions

Porous medium statistically isotropic or anisotropic

Porous medium statistically homogeneous or nonhomogeneous

Diffraction : neglected (l <<D)

Solid phase : opaque or semi transparent

Fluid phase : transparent or semi transparent

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

Statistical approach of radiation

u

r

s0

I

(semi-transparent medium)

Definition :

Extinction =absorption+scattering

At local scale: probability of reaching the interface

(non spectral, only geometric property)

linked to the cumulated distribution function of chord lengths

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

r

I

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 interface: Deduction of the scattering angle : contribution to the phase function

n

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

Statistical approach of radiation Radiation Distribution Function Identification Method(RDFI method)

0.95

ge(s,uk)

Ge(s,uk)

s (mm)

s = 0 s = 3

useful extinction optical thickness range

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

Identification criterione :

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

Objectives

Up scaling method : a direct identification method

Application to real porous media

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

mid scale (wall pores)

Local scale

Smm-1andS mm-1, pS

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

IUSTI from ESRF X ray tomography

spatial resolution of 5 m

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

Nuclear reactor core in severe accident conditions

IRNS : French Radiation and nuclear safety institute

Degradation, fusion et geometrical modification of the core

Cooling fluid leaking

Increase of temperature

T<500K

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

Degraded small scale nuclear core rod bundleGeometry obtained from ray tomography experiment FPT1, IRSN, Cadarache

3D reconstruction

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

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

Degraded small scale nuclear core rod bundleGeometry obtained from ray tomography experiment FPT1, IRSN, Cadarache

Numerical image of the whole degraded bundle

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

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

B: β=0.28

D: β=0.24

A: β=0.19

C: β=axɛ+b

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

Radiative transfer in a nuclear reactor core

For an optically thick REV from the absorption point of view

< 0. 2

Radiative conductivity model :

Calculated from the obtained radiative properties of the equivalent medium

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

General statistical approach of radiation :

- Accurate determination of Ge, Pa, Psand p for any porous medium REV

Equivalent semi-transparent media :andp

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

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