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RADIATION IN POROUS MEDIA: AN UPSCALING METHODOLOGY APPLIED TO A REACTOR NUCLEAR CORE. E nergétique M oléculaire et M acroscopique, C ombustion E.M2.C. Estelle Iacona, Jean Taine and Fabien Bellet. Ecole Centrale Paris - UPR 288, CNRS. AXES DE RECHERCHE. COMBUSTION. NANO-OPTIQUE ET

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radiation in porous media an upscaling methodology applied to a reactor nuclear core

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
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

some applications of radiation in porous media

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

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

slide4

Outline

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

dz

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

dz

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
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

slide8

Outline

Objectives

Up scaling method : a direct identification method

Application to real porous media

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

slide9

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 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
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

slide11

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

monte carlo method

u

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

slide13

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 criterione :

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

slide14

Outline

Objectives

Up scaling method : a direct identification method

Application to real porous media

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

slide15

Tomography resolution

mid scale (wall pores)

Local scale

Smm-1andS 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
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

slide17
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

slide18

z

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

slide19

Bain fondu + cavité

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
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

slide21

conclusions

General statistical approach of radiation :

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

Equivalent semi-transparent media :andp

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