Rayleigh Taylor Instability Challenge
Q1 Ans: Some of the models are:
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 shockwave. The development of the instability begins with small amplitude perturbations which initially grow linearly with time.
Viscous vortex single-mode bubble evolution model: -
It tells about the viscous effects of early stages of Rayleigh Taylor waves at low atwood number.
Savart–Plateau–Rayleigh instability of a water column: -
It explains why and how a falling stream of fluid breaks up into smaller packets with the same volume but less surface area. The penetration distance of heavy fluid bubbles into the light fluid is a function of acceleration time scale.
K-L turbulence model:
It described the self-similar growth of the Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities.The model describes the dominant eddies in the mixing zone with evolutionary equations for their characteristic dimension L and energy per unit mass K≡V2∕2.
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.
Q2Ans Solver: Solution is done with the pressure based type in transient time. Two fluids are assigned for this problem : Air and Water. Laminar Model is used. Patching is done after standard initialization. After that it is initialized and calculated with animations at 200 time steps and 0.005 time step size.
Results:
Meshing Analysis:
(a) Mesh size : 0.05
No. of Nodes :3321
No of Elements:3200
Residual Plot:
Animation :
(b) Mesh Size : 0.04
No. of Nodes :5151
No. of Elements:5000
Residual Plot :
Animation:
(c) Mesh Size : 0.03
No. of Nodes :9180
No. of Elements:8978
Residual Plot:
Animation:
Q3 Ans Atwood Number: Atwood number, abbreviated as A, is a dimensionless number that describes density difference between two adjacent fluids with a common interface.
(Density of heavier fluid taken, water = 997kg per metre cube.
Density of lighter fluid taken , air = 1.225kg per metre cube.)
Penetration distance of heavy fluid in bubbles in light fluid is given by
Pd=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.