Week 5 - Rayleigh Taylor Instability

Aim: To perform Rayleigh Taylor instability.

Objectives:

1. What are some practical CFD models that have been based on the mathematical analysis of Rayleigh Taylor waves? In your own words, explain how these mathematical models have been adapted for CFD calculations.
2. Perform the Rayleigh Taylor instability simulation for 2 different mesh sizes with the base mesh being 0.5 mm. Compare the results by showing the animations( Attach them from your google drive). Observe the differences in the animation and explain the effect of mesh size on simulation. Also, explain why a steady-state approach might not be suitable for these types of simulation.[ Choose Air and Water for this simulation]
3. Run one more simulation with water and user-defined material(density = 400 kg/m³, viscosity = 0.001 kg/m-s) for refined mesh.
4. Define the Atwood Number. Find out the Atwood number for both the cases and explain how the variation in Atwood number in the above two cases affects the behavior of the instability.

Geometry:

• Choose Fluent from the workbench setup, edit SpaceClaim to create geometry.
• Choose the XY plane to sketch 2Dgeometry, create a square of 20mm, and select pull tool to make it a surface of that.
• Move the geometry to a new component and rename it as Air.
• Now create new geometry under the main design as water and create a square of 20mm right on top of the air square which creates an interface between the 2 boxes.
• Select the entire geometry for share prep under the workbench and select share so that the interface can face information and conformal meshing can be achieved between the 2 phases.

Meshing:

Overall Element size: 0.005m

Setup:

Solver Type	Pressure-Based
Velocity Formulation	Absolute
Time	Un-Steady
Models	Viscous model: laminar Multiphase: Volume of fluid : Implicit formulation : 2 phases
Material	Fluid type: Air : water liquid Solid-type: Aluminium
Cell zones	Fluid type: Air : water
Boundaries	Standard
Reference values	Standard
Initialization	Standard Patch: Water-surface (1 value of volume fraction of water) : Air-surface(0 value of volume fraction of water)

Results:

Residual:

Changes in flow pattern:

Animation:

https://drive.google.com/file/d/1wmCexNg_nWBc3rDV70TuLeTFnNalOPsd/view?usp=sharing

Overall Element size: 0.002m

Residual plot:

Change in flow patters:

Animation:

https://drive.google.com/file/d/1WTK4ebzNboGY7wdklG1r8wwP8cOyZsSh/view?usp=sharing

Atwood Number

The Atwood number (A) is dimensionless 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 the lighter fluid

In Rayleigh–Taylor instability, the penetration distance of heavy fluid bubbles into the lighter fluid is a function of the acceleration time scale, where g is the gravitational acceleration and t is the time.

A = `(rho_1-rho_2)/(rho_1+rho_2)` = `(998.2-1.225)/(998.2+1.225)`= 0.9975

The behavior of RT Instability on the variation of Atwood number:

RTI evolves in three distinct stages: Linear stability, mushroom head(falling) or bubble(rising) formation, long term evolution due to bubble merging and mixing. For low Atwood number, bubble and mushroom head shape is relatively symmetrical, the disturbances or perturbations are linear for a larger time. In contrast, for large Atwood number, bubble and mushroom head shape is less symmetrical, also it occurs very rapidly at an accelerating rate which leads to a nonlinear growth rate.

CONCLUSION:

• From the above cases, we observe that finer mesh captures the instability better than the coarse mesh, but it takes more time for the heavier fluid to settle down. As computational time is long but produces results with better accuracy.
• Since the simulation involves capturing instabilities that are changing in an unpredictable manner as a function of time, the transient approach is preferred over the steady-state approach.
• The Atwood no validates the CFD simulation as it is observed. In the case of water and air mixing, bubble formation takes place, whereas in the other case no bubble takes place.