Rayleigh Taylor Instability problem (Multiphase)

Aim: Perform the transient simulation on Rayleigh Taylor Instability of different mesh sizes.

Define the Atwood Number. Find out the Atwood number for both the cases and explain how the variation in Atwood numbers in the above two cases affects the behaviour of the instability. 

Software Used: Ansys Fluent

Rayleigh Taylor Instability:

The Rayleigh–Taylor instability, or RT instability, is an instability of an interface between two fluids of different densities which occurs when the lighter fluid is pushing the heavier fluid.

Geometry Creation:

First create 2 rectangle having dimensions 20mmX20mm. one for lighter density and another for heavier density fluid.

After creating the rectangles use pull option for creating the surface.

After enable the share topology option, Click workbench in space claim.

In workbench click the share option for conformal mesh.

The Upper square is represent as water and lower square is represent as air.

Mesh(Size= 0.5mm):

Setup:

Solver:

Models:

Phases:

Materials:

Air:

Water:

Initialization:

use patch option in initialization:

Water:

Air:

Residual Plot:

Contour:

Mesh 2 (size = 0.2mm):

Residual Plot:

Countour:

Mesh Size 0.2 and User defined material instead of Air:

Properties:

user-defined material(density = 400 kg/m³, viscosity = 0.001 kg/m-s)

Materials:

user defined:

Water:

Phases:

Residual plot:

Contours:

it is observed that more we can refine the mesh, The simulation results get smoother about the irregularities that take place at interface of two fluids.

Reason for using Transient Approach rather than steady -state:

The steady -state gives only the final results of the solution, therefore we can't able to analyse the physics that happened in as small time during the simulation.

In transient-state we can see what is happening over time and we can visualize how high density fluid dominates the light fluid. 

Transient simulation helps to see the irregularities are forming when two fluids are mixed under the effect of gravity.

In this problem we are observing that steady state is more into capture the final results but transient we can see the behaviour o the solution and every instant such that capturing bubbles, vortex and shockwaves. so transient state is more suitable for this kind of simulations.

Atwood Number:

Definition: In fluid dynamics, the Atwood number (A) is a dimensionless-number. The Atwood  number is defined as a dimensionless density ratio it is  given as:/

Formula:  

For Case1:

density of water = 998.2

density of air = 1.225

A = (998.2-1.225)/(998.2+1.225)

   = 0.997

For Case 2:

density of water = 998.2

density of user-defined material = 400

A = (998.2-400)/(998.2+400)

   = 0.427