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Développement d'une méthode hybride eulérienne-lagrangienne pour la modélisation numérique de la phase particulaire dans les écoulements turbulents gaz-particules

Abstract : Gas-particle flows are found in a very wide range of applications, from industrial (fluidized bed, turbomachines) to natural (pollutant dispersion, sand transport) processes. It is thus unsurprising that numerical treatments vary from one problem to another. Actually, when dealing numerically with the particle phase in gas-particle flows, the prediction can be issued in a lagrangian or an eulerian framework.

No numerical tool has yet been developped that enable a lost-cost resolution of the flow (like in an eulerian
framework) while issuing accurate predictions in the whole flow (as can be done in a lagrangian framework).
One elegant way to tackle this type of problem is the use of hybrid methods coupling approaches issued fron
different formalisms.

This work aims to develop a hybrid eulerian-lagrangian method for the numerical modeling of the disperse
phase in turbulent gas-particle flows. The spatial domain is split in sub-domains where only one of the approaches is used. Both approaches share the same description of the dispersed phase in terms of statistics, i.e. the dispersed phase is represented by the mean of a joint fluid-particle probability density function (pdf). The first approach is based on a direct resolution of the evolution equation of the pdf by a stochastic particle method. The second is based on the resolution of the eulerian equations governing the behavior of the moments (density, mean velocity and particle kinetic constraints . . . ) derived from the pdf equation, closed by additional hypothesis and discretized using finite-volume schemes.
The coupling of the two approaches is based on the kinetic description of the moments fluxes across the sub-domains interfaces, allowing the development of well-posed boundary conditions. The lagrangian boundary condition is given by the choice of the velocity distribution of ingoing particles in the lagrangian domain. This pdf is deduced from predictions of both the lagrangian and eulerian approaches. This pdf is then simulated by a statistical method called rejection method, which allows to impose the ingoing caracteristics in the lagrangian domain. The eulerian boundary conditions can be either of Dirichlet's type (computation of the lagrangian moments to be imposed) or of flux-type (splitting of the fluxes between a part given by the outgoing particles, the other part by the preceding eulerian prediction).

The two approaches, as well as the coupling methodologies, are developed in FORTRAN90, which enables validations in homogeneous flows (homogeneous shear flows) as well as inhomogeneous flows (plane
channel flows) by direct comparison with the results of numerical experiments. The hybrid method is then
applied in highly non-equilibrium flows (channel flow) where the eulerian approaches fail to accurately
predict the flow. The use of the hybrid method increase the accuracy in the prediction. The feasbility and
interest of such hybrid method is thus demonstrated.
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Contributor : Xavier Pialat <>
Submitted on : Saturday, March 22, 2008 - 3:08:01 PM
Last modification on : Friday, June 26, 2020 - 2:00:02 PM
Long-term archiving on: : Tuesday, September 21, 2010 - 3:56:52 PM


  • HAL Id : tel-00224819, version 2



Xavier Pialat. Développement d'une méthode hybride eulérienne-lagrangienne pour la modélisation numérique de la phase particulaire dans les écoulements turbulents gaz-particules. Dynamique des Fluides [physics.flu-dyn]. Ecole nationale superieure de l'aeronautique et de l'espace, 2007. Français. ⟨tel-00224819v2⟩



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