Rayleigh Instability

Abstract: This study focuses on Rayleigh Taylor Instability for different mesh under transient approach. Here practical CFD models applicable to Rayleigh instability is explained. Atwood number is calculated and explained.

Introduction:

Rayleigh Instability:

The instability of a heavy fluid layer supported by a light one is generally known as Rayleigh-Taylor (RT) instability. It can occur under gravity and, equivalently, under an acceleration of the fluid system in the direction toward the denser fluid. The first experiments by Lewis have shown three subsequent stages in the evolution of an unstable air-water interface. The initial phase of exponential growth is followed, first, by a transition phase of bubble formation and then by an asymptotic stage of rising air columns.

Potential Flow Model:

A two dimensional incompressible potential flow in a vertical cylinder with a initially flat free under surface. This is Rayleigh-Taylor unstable with an Atwood number A=1. The velocity potential must satisfy Beroulli\'s equation in cylindrical polar coordinates.

Rayleigh Instability studied for different Mesh sizes.

In this study initially water in the top air at bottom as time passes Rayleigh Instability is observed for different mesh sizes.

Mesh Size of 0.5mm:

Mesh Size of 0.3mm:

Mesh Size of 0.2mm:

Atwood Number:

It is a dimensionless number that describes the density difference between two adjacent fluid with common interface.

`Aunderset(t)()=(rhounderset(w)()-rhounderset(a)())/(rhounderset(w)()+rhounderset(a)())=(1000-1.25)/(1000+1.25)=0.9975`