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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. 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

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  1. 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

  2. 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

  3. 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

  4. Outline Objectives Up scaling method : a direct identification method Application to real porous media E. Iacona, J. Taine, F. Bellet Laboratoire EM2C - CNRS - ECP

  5. 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)

  6. 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 :

  7. 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

  8. Outline Objectives Up scaling method : a direct identification method Application to real porous media E. Iacona, J. Taine, F. Bellet Laboratoire EM2C - CNRS - ECP

  9. 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

  10. 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

  11. 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

  12. 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

  13. 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

  14. Outline Objectives Up scaling method : a direct identification method Application to real porous media E. Iacona, J. Taine, F. Bellet Laboratoire EM2C - CNRS - ECP

  15. 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

  16. 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

  17. 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

  18. 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

  19. 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

  20. 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

  21. 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

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