Rayleigh Taylor waves

Problem Statement: -

Q1. 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

Q2. Perform the Rayleigh Taylor instability simulation for 3 different mesh sizes with the base mesh being 0.5 mm. Compare the results by showing the animations(Attach them from your google drive). Also, explain why a steady state approach might not be suitable for these types of simulation.

Q3. Define the Atwood Number. Find out the Atwood number for this case and explain how the variation in Atwood number affects the behaviour of the instability. How can we use the Atwood number to validate our simulation result?

Objective: -

• To Study Rayleigh Taylor wave
• Simulate the freefall flow for Rayleigh Taylor instability solution for water and air combination
• To Study the effect of Different size meshing
• To study Atwood number and significance in instability simulations.

Specification of Geometry: -

Practical CFD Models Based on Rayleigh’s Taylor Wave

Richtmyer–Meshkov instability: -

• This instability occurs when two fluid with different density are accelerated impulsively.
• Magnetized target fusion, formation of material in the cores of stars(cobalt 56) are the example of this type of instability.

iscous vortex single-mode bubble evolution model: -

• Explains Viscous effect of early stages of Rayleight taylor wave for low Atwood number.

Savart–Plateau–Rayleigh instability of a water column: -

• column of liquid spontaneously breaks up into droplets under the influence of surface tension

K-L turbulence model for the self-similar growth of the Rayleigh-Taylor and Richtmyer-Meshkov instabilities

• Used to simulate turbulence model or turbulent boundary conditions.

Rayleigh Taylor Instability

• Instability between two fluid with different densities which results due to lighter fluid pushes heavier fluid.
• Can be used to find solution of CFD analysis with Turbulent Models.

Mesh Sensitivity Analsysis:-

To check RTI we are performing experiment with above specified geometry.upper domain is of water wheras lower domain is of air.In order get intermedient results we have to use transient analysis as we are not intersted in direct end results.

Mesh: -0.5

Number of Element: -3200

Number of Nodes: -3321

Solution: -

To solve this type of problem we have to choose Multiphase, Transient option in physics and we are using volume of fraction method to define the problem. initialisation is done using standard method after that we have to define which surface is defined as air and which surface as water using Patch control. The problem is solved for 0.005 sec time step size with 1500 no of timesteps.

Residual Graph: -

Animation: -

Mesh: -0.25

Number of Element: -12800

Number of Nodes: -13041

Residual Graph: -

Animation: -

Mesh: -0.15

Number of Element: -35378

Number of Nodes: -35778

Residual Graph: -

Animation: -

Atwood Number:

• Atwood number is dimensionless number used to study hydrodynamic instability.
• To calculate number we can use below formulae

• Penetration distance of heavy fluid in baubles in light fluid is given by

P_d=Agt²

A=Atwood Number

g=gravity

t=time

From the observation of fraction of water content animation, we can clearly see that water is fully penetrated in air which results in bubble formation. Calculation Atwood number is closer to 1 shows bubble formation takes place. Hence our simulation is valid.