Rayleigh Taylor Instability Challenge

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

There are some practical CFD models that have been based on the mathematical analysis of Rayleigh Taylor waves:

• Kelvin–Helmholtz instability: It can occur when there is a velocity difference across the interface between two fluids. An example is a wind blowing over the water.
• Richtmyer–Meshkov instability: It occurs when two fluids of different density are impulsively accelerated. This instability can be considered the impulsive-acceleration limit of the Rayleigh–Taylor instability. An example is fuel spraying into the piston which is of high pressure with turbulence flow of hot air.
• Plateau–Rayleigh instability: often just called the Rayleigh instability, explains why and how a falling stream of fluid breaks up into smaller packets with the same volume but less surface area. An example when a small amount of water is coming out of a tap after some distance the flow will break to the small droplets This model explains this type of instabilities.

There are some practical examples that are based on the Rayleigh–Taylor instability

• mushroom cloud: It is a distinctive pyrocumulus mushroom-shaped cloud of debris/smoke and usually condensed water vapor resulting from a large explosion. Mushroom clouds result from the sudden formation of a large volume of lower-density gases at any altitude, causing a Rayleigh–Taylor instability. The buoyant mass of gas rises rapidly, resulting in turbulent vortices curling downward around its edges, forming a temporary vortex ring that draws up a central column, possibly with smoke, debris, and/or condensed water vapor to form the \"mushroom stem\" and it stops when the gases reach altitude which is no longer a low dense fluid.

Rayleigh Taylor instability simulation

In the below simulations fluids used are air and water with densities of 1.225 & 998.2kg/m^3. The method we are using is the Implicit method & we are using a volume of fluid method. There are three cases in the simulation in which above mentioned are kept constant and mesh sizes will be varied.

Case 1:

Mesh size:0.5

Nodes: 3321

Elements:3200

This is the mesh for case 1

The video link for the animations of the case 1

https://www.youtube.com/watch?v=tpAxKV4-Ajg

Case 2:

Mesh size:0.3

Nodes: 9180

Elements:8978

This is the mesh for case 2

The video link for the animations of the case 2

https://www.youtube.com/watch?v=L7AXyYmH9-0

Case3:

Mesh size:0.1

Nodes: 80601

Elements:80000

This is the mesh for case 3

The video link for the animations of the case 3

https://www.youtube.com/watch?v=_r4RMmz7GJk&feature=youtu.be

Observations made on observing cases

• In all the cases the lower dense fluid pierces into the high-density fluid as it seems to be the propagation of shock wave.
• In case 1 at the interface, we can see that some disturbances are formed as time passed the large disturbance is formed its forces into the high dense fluid like a shock wave.
• In case 2 at the interface, we can see the disturbances which are more than case 1 pushing through the high dense fluid mushroom-like structure is formed and the formation of bubbles can be seen around the mushroom structure.
• In case 3 at the interface disturbances are observed in more detail in the form of many bubbles and the formation of vortices are can be clearly seen.

This simulation cannot be run under steady-state conditions because it changes from time to time iterations so we cant achieve this simulation through this condition.

Atwood number: It is a dimensionless number in fluid dynamics used in the study of hydrodynamic instabilities in density stratified flows. It is a dimensionless density ratio defined as

where

= density of heavier fluid

= density of lighter fluid

Atwood number for the above case is

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

A=0.9975

• When the Atwood number is so high the more instability takes place in the fluid and measuring the spikes of the instability is very difficult.
• When the Atwood number is low the more stable is the fluid mixture and measuring the spikes of the instability can be done to some extent because it expresses linearity to some extent.