Rayleigh Taylor s Instability

Practical CFD models :

I) Rayleigh Taylor instability

It is an instability of an interface between two fluids of different densities when the lighter fluid is pushing the heavier fluid.Example include the behavior of water suspended above oil. For A close to 0, RT instability flows take the form of symmetric \"fingers\" of fluid; for A close to 1, the much lighter fluid \"below\" the heavier fluid takes the form of larger bubble-like plumes.

II) Richtmyer Meshkov instability

The Richtmyer–Meshkov instability (RMI) occurs when two fluids of different density are impulsively accelerated. Normally this is by the passage of a shock wave. The development of the instability begins with small amplitude perturbations which initially grow linearly with time. This is followed by a nonlinear regime with bubbles appearing in the case of a light fluid penetrating a heavy fluid, and with spikes appearing in the case of a heavy fluid penetrating a light fluid. This instability can be considered the impulsive-acceleration limit of the Rayleigh Taylor instability.

III) Kelvin Helmholtz instability

The Kelvin–Helmholtz instability can occur when there is velocity shear in a single continous fluid, or where there is a velocity difference across the interface between two fluids. An example is wind blowing over water, the instability manifests in waves on the water surface.

IV) Plateau Rayleigh instability

The 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. It is related to the and is part of a greater branch of fluid dynamics concerned with fluid thread break-up. This fluid instability is exploited in the design of a particular type of ink jet technology whereby a jet of liquid is perturbed into a steady stream of droplets.The driving force of the Plateau–Rayleigh instability is that liquids, by virtue of their surface tension, tend to minimize their surface area. A considerable amount of work has been done recently on the final pinching profile by attacking it with self similar solutions.

Rayleigh Taylor instability

Geometry

We create 2 squares and move it into the same component, we delete the common edge and ensure that we have share topology.

Mesh

We mesh the geometry with three cases that are :case 1)0.233mm, case 2)0.5mm and case 3)0.1mm respectively.

Set-up

We use a pressure based solver ,with transient step and absolute velocity formation. We also need gravity so the y- value is defined as -9.81m/s.

In physics, we use multiphase volume of fluid, we add new fluid material i.e water.

We standard initialize the solution, we patch the water and air values and create the contours and animations.

Solution:

Case (I)

Case (II)

Case (III)

• Steady state cannot be used because we need to see the mixing of the two fluids rather than just the end product.
• So we use Transient state with proper time steps so that we can capture the mixing.

Atwood number

It is a dimensionless number used for studying hydrodynamic instabilities in density.

A = `(rho1-rho2)/(rho1+rho2`

where A = Atwood number

`rho1` = density of heavier fluid`

`rho2` = density of lighter fluid`

Here,

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

A = 0.997