Week 5 - Rayleigh Taylor Instability

Aim: to perform Rayleigh Tayler CFD analysis.

Introduction: The instability of a heavy fluid layer is supported by a light fluid or air is called as Rayleigh Taylor instability. It is occurred due to effect of gravity. Two different fluids with different densities are intersecting over each other.

Theory:

Multiphase: it is simultaneous or parallel flow of materials with different states or phases (liquid-gas). It is a flow of materials with different chemicals properties but in the same state or phase(liquid-liquid).

Types of phases in multiphase

1. Separated phase: it is defined as one or more immiscible fluid is a continuous phase separated by an interface.
2. Mixed phase: it is defined as phase in which one or more fluids mixed together. It contains both separate and dispersed phase.
3. Dispersed phase: it is defined as phase in which the finite number of phases are spread in continuous phase.

VOF method

VOF stands for volume of fluid. Volume of fluid method is a surface tracking method. It is designed to find out the position of interface between two or more immiscible flids. The volume fraction of each fluid in each of the cell through out domain can be tracked by using this method. Single set of momentum equation is shred only by the fluids.

In this method, all the control volume must be filled with single phase or combination of phases. Application of VOF model include stratified flow, free surface flow, filling, sloshing, the motion of large bubbles in liquid, motion of liquid after a dam break, prediction of jet breakup (surface tension) and the steady or transient tracking of any liquid-gas interface.

For example: let us consider

= phase 1

= phase 2

Then VOF + = 1

Transient state:

1. Explicit scheme: it offers time accurate data but timestep size has to be taken ensuring that the courant number is satisfied.
2. Implicit scheme: it will offer speed of steady state but we need a time varying solution. It is unconditionally stable (timestep size is not constraint) and is the default scheme in ANSYS fluent.

Courant number:

It is a non-dimensional number that tells how fast information travels through our discretised domain. It is ratio of these two lengths or fraction of cell that the flow moves across in a time step. For explicit time integration, time step size must be less than a certain value or solution would be false.

CFL < 1

Geometry

For this analysis I have developed the geometry in two different phases. Upper part is used for water and lower part is used for air. These two bodies are different by using share topology tool.

Mesh

For better analysis I have done tetrahedron type of mesh. It is 2D type of mesh. For getting better result here the mesh element size is 0.5mm.

Model: for this analysis here, I used laminar type of viscous model. And multiphase part, 2 phase part is used.

For element size 0.4 mm

FOR UDF

Atwood number: It is dimensionless number that is used to study for hydrodynamic instabilities in different densities flows.

A =

= Density of heavier fluid

= Density of lighter fluid

For air and water

A =

= 0.998

For UDF and water

A =

= 0.428

Conclusion

From the above Atwood number values for both cases, it is clearly seen that for higher Atwood number, disturbance is very much linear for larger value. And for smaller Atwood number, disturbance is very un-uniform shaped with higher accelerating rate.