Rayleigh Taylor Instability Model

Introduction:

Rayleigh Taylor instability is observed at the interface of two different density fluids interacting with each other. This mixing example can be water suspended over air under the effect of gravity., where the air will penetrate the water forming bubbles and instability is observed.

Some Practical CFD models are:

• Mass diffusion model.
• Single Fluid Model:
  1. Potential Flow model.
  2. Buoyancy Drag model.
• Multi Fluid model:
  1. K-L turbulence model (Two equation)
  2. K-L turbulence model (Three equation)
  3. K-L turbulence model (Four equation)

CFD analysis of Rayleigh Taylor instability:

In the current study, 3 different cases are analyzed. For each case, the mesh is refined for getting better mixing results. Volume of Fluid (VOF) method is used for multiphase fluid flow problems along with an implicit solver.

Case1:

Mesh Size: 0.5 mm

No of elements: 3200

Time step size: 0.005

No. of time steps: 300

Case2:

Mesh Size: 0.25 mm

No of elements: 12800

Time step size: 0.004

No. of time steps: 500

Case3:

Mesh Size: 0.125 mm

No of elements: 51200

Time step size: 0.004

No. of time steps: 500

Observations:

• Steady-state analysis cannot be performed in such a case as we need to see the behavior during mixing rather than the end results after mixing. Thus, transient analysis with an appropriate time step is chosen.
• With refined mesh, the instabilities are observed precisely but solution time increases significantly.

Atwood No.

It is a dimensionless no used for studying hydrodynamic instabilities in density stratified flow field.

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

Where,

A = Atwood No.

`rho1`= Density of Heavier fluid

`rho2`= Density of lighter fluid

For our case,

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

A = 0.997

For Atwood No near to 1, the lighter fluid enters heavier fluid forming bubble plumes. This can be observed in our case and also Atwood No is close to 1 hence our case is validated.