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Simulation of Viscous Fingering Instability by the Lattice Boltzmann Method

Communication avec acte
Author
VIENNE, Lucien
134975 Laboratoire de Dynamique des Fluides [DynFluid]
MARIE, Simon
134975 Laboratoire de Dynamique des Fluides [DynFluid]
300351 Conservatoire National des Arts et Métiers [Cnam] [Cnam]
GRASSO, Francesco
134975 Laboratoire de Dynamique des Fluides [DynFluid]
300351 Conservatoire National des Arts et Métiers [Cnam] [Cnam]

URI
http://hdl.handle.net/10985/19696
DOI
10.2514/6.2019-3432
Date
2019

Abstract

The viscous fingering instability is successfully simulated within a lattice Boltzmann framework. Each species of the mixture is governed by its own kinetic equation and a force takes into account the diffusion between species. The influence of the porous medium is mimicked by using the gray lattice Boltzmann model or the Brinkman force model. In this study, both representations of the porous medium yield equivalent results. Then a physical analysis of the instability is performed and two different dynamical behaviour are stated and discussed. Finally, it is observed that a high Péclet number intensify the instability and the viscous dissipation stemming from the Darcy-Brinkman equations delay the development of the fingers in the case of large effective viscosity.

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