Descriptif et objectifs de l'emploi :
Heat transfer by coupled conduction, convection and radiation in high porosity materials characterized by micronic to centimetric pores play an essential role in many high temperature applications (for instance, fuel cell elements, thermal protections for satellites, catalytic combustion, first steps of core bundle degradation in a severe nuclear accident...). The derivation and the implementation of a complete macroscopic model taking into account the coupling between the conductive and convective transport phenomena and radiation is consequently a pressing challenge.
Important studies have been performed in order to derive macroscopic modeling of heat transfer in porous media without thermal equilibrium between solid and fluid phases. Most of these studies have been performed for porous media involving moderate temperatures avoiding the need of considering the coupling with radiation transfer (Quintard et al., 1997). These studies have shown the relevance of the two energy equations model and they have quantified the influence of the microstructure and the local flow on the effective transport properties. In our knowledge, this kind of up scaling approach has never been used to study heat transfer in porous media submitted to high temperatures.

The objective is to develop and validate original methods for modeling coupled heat transfer in high porosity medium, including a solid phase and a semi transparent gaseous phase. The key point is to accurately take into account the conduction, convection and radiation phenomena and their coupling in conditions of non equilibrium between the phases in a Representative Elementary Volume (R.E.V.).

From the radiative point of view, a new and original method of determination of the radiative properties of porous media, called RDFI, has been developed and validated by EM2C (Tancrez and Taine, 2004, Zeghondy et al. 2006). Its interest is to obtain these results, directly from the definition of the considered quantities, by a statistical approach using the medium morphology defined with a high spatial resolution and the medium radiative properties at local scale. Moreover, this approach allows us to quantify the validity of the obtained effective radiative properties.

The three main considered issues are:

1. to develop a macroscopic modeling of heat transfer by conduction, convection and radiation taking into account all the coupling phenomena after homogenization into each phase in non equilibrium.
   
2. to characterize all the macroscopic effective properties required, for each phase. The porous medium morphology will be determined from X ray tomographies at ESRF (European Synchrotron Radiation Facility) with a typical spatial resolution of a few micrometers and by Scanning Electron Microscopy visualization. The phase thermophysical properties, at the R.E.V. scale, will be known from data associated with the homogeneous phases, or from the measurement achieved by a partner laboratory. In practice, heat transfer by diffusion and convection will be characterized by effective conductivities, effective diffusion-dispersion coefficients, permeability and heat interfacial exchange coefficient. Radiative transfer will be characterized by conductivity tensors, associated with the two phases temperature fields, and exchange coefficients between the two phases within a R.E.V.
   
3. to apply the model developed in 1) by using the macroscopic properties obtained in 2) in a simple monodimensional test case configuration, considered as an illustration. The results will be the coupled thermal fields into the whole considered system.
   

This project is proposed within the frame of the "Fédération de Transferts Thermiques et Massiques d'Ile de France" recently labellized by the "Ministère de la Recherche et de l'Enseignement Supérieur".


M. Tancrez, J. Taine (2004) Direct identification of absorption and scattering coefficients and phase function of a porous medium by a Monte Carlo technique. IJHMT, 47, 373-383.
B. Zeghondy, E. Iacona and J. Taine (2006) Determination of the anisotropic radiative properties of a porous material by Radiative Function Distribution Identification, IJHMT, 49, 2810-2819.
B. Zeghondy, E. Iacona and J. Taine (2006) Experimental validation of the RDFI method predictions of statistically anisotropic porous medium radiative properties, IJHMT, 49, 3702-3707.


Description of the EM2C laboratory:
The Energétique Moléculaire et Macroscopique, Combustion (EM2C) Laboratory is a lab of the French Scientific Research Center (CNRS) and is located on the campus of Ecole Centrale Paris (one of the best engineering school in France). The campus is located in Châtenay-Malabry (15km south of Paris, 20min by subway). The EM2C research covers radiative transfer and coupling heat transfer, combustion and plasmas. The research programs, of high international level, are mostly motivated by industrial applications.

Contact:
Send a CV, motivation letter and list of publications in pdf format at: Jean Taine (jean.taine@ecp.fr), Estelle Iacona (estelle.iacona@ecp.fr), Nasser Darabiha (nasser.darabiha@ecp.fr).