Simulation of the two-dimensional Rayleigh-Taylor instability problem by using diffuse-interface model

Saher Akmal Khan,Abdullah Shah

doi:10.1063/1.5100791

Abstract

The purpose of this paper is to simulate a two-dimensional Rayleigh-Taylor instability problem using the diffuse-interface formulation of the incompressible Navier-Stokes equations. The governing equations consist of a system of coupled nonlinear partial differential equations for conservation of mass, momentum and phase transport. The Boussinesq approximation is introduced in the momentum equation to relax the complexity of variable density formulation. Due to the simplicity, this approximation can be used for small density variations in simulating two-phase flows. The numerical scheme is based on an artificial compressibility formulation with a finite difference scheme for the space discretization. To validate the method, the penetration of a heavier fluid into the lighter one is computed and illustrated graphically.

Highlights

In two-phase flow, the dynamic variables like the velocity, viscosity, pressure, and density are normally used to explain the movement of fluids
One of the presumptions among other is, the Boussinesq approximation1,2 which is utilized for buoyancy-driven flows
The RT instability due to the gravitational field was initially proposed by Rayleigh3 and subsequently has been applied to all fluids by Taylor

Summary

Introduction

In two-phase flow, the dynamic variables like the velocity, viscosity, pressure, and density are normally used to explain the movement of fluids. The RT instability due to the gravitational field was initially proposed by Rayleigh and subsequently has been applied to all fluids by Taylor.. The RT instability due to the gravitational field was initially proposed by Rayleigh and subsequently has been applied to all fluids by Taylor.4 This instability has been applied to a wide range of problems, including the mushroom clouds like volcanic eruptions and atmospheric nuclear explosions, plasma fusion reactors instability and inertial confinement fusion, Oceanographic and supernova explosions in which the expanding core gas is accelerated into a denser shell gas. Several numerical techniques have been suggested to study the relatively short time RT instability phenomena including boundary integral methods, front tracking methods, volume of fluid methods, level set methods and phase-field methods.. Complete separation time is one of the crucial factors in designing the separator.

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