Modélisation et simulation de l'effet Leidenfrost dans les micro-gouttes

français

Speciality : Mathématiques Appliquées

26/11/2012 - 10:30 Mr Roland Denis (Université de Grenoble) Salle 1 - Tour IRMA

Keywords :
  • dynamique des fluides
  • changement de phase
  • tension de surface
  • méthode Level-Set
  • modélisation
The Leidenfrost effect is a special case of calefaction: when a liquid is dropped on a surface which temperature is far hotter than the liquid's boiling point, he evaporates before touching the hot plate and the produced gas forms a thin layer, under the liquid droplet, that makes it hovering and isolates it from the heat source.
This thesis deals with the modeling and the numerical simulation of this complex phenomenon. In the first part, we study a sharp interface model that supplement the Navier-Stokes equations with interfacial conditions taking into account the phase change and the surface tension. Simulating an uniform liquid layer over a vaporous film reduces the problem to one dimension. The ALE method (Arbitrary Lagrangian Eulerian) is then used to deal with the variable height of each phase. The numerical code is finally validated on a test case.
In the second part, the gas/liquid interface is captured by a Level-Set method. The interface is artificially thickened and inner regularization is applied to the thermodynamic quantities. Therefore, surface tension and phase change are approximated by volume terms. Each pure phase is supposed to be incompressible but, due to the phase change, the velocity field is not divergence-free in the interfacial zone.
The third part focusses on the discretization of this three-dimensional model, for the simulation of a motionless and rotational symmetric droplet. The problem reduces to an axisymmetric two-dimensional setting. The use of the Level-Set method requires devoted numerical algorithms which are developed: non-diffusive efficient advection scheme, reinitialization by Hamilton-Jacobi equation with global volume correction taking into account the phase change. An adapted Chorin projection algorithm is used to ensure the prescribed compressibility constraint that holds on the  interfacial fluid. In addition, we introduce a new finite difference scheme for the gradient approximation that uses a compact stencil.
The last part describes and compares our simulation results with several theoretical curves based on different droplet shape simplifications, plotting the evolution of indicators like the volume and radius of the droplet, or the height of the vapor layer.

Directors:

  • Mr Emmanuel Maitre (Professeur - Grenoble INP )
  • Mr Stéphane Labbé (Professeur - Université Joseph Fourier )

Raporteurs:

  • Mr Thierry Colin (Professeur - Univ. de Bordeaux 1 )
  • Mr Philippe Helluy (Professeur - Univ. de Strasbourg )

Examinators:

  • Mr Paul Vigneaux (Maître de Conférence - Ecole Normale Supérieure de Lyon )
  • Mr Matthieu Bonnivard (Maître de Conférence - Université Paris Diderot )
  • Mr Didier Bresch (Directeur de Recherche - Université de Savoie )