Week 5 - Rayleigh Taylor Instability

Aim: To Perform the Rayleigh Taylor instability simulation for 2 different mesh sizes with the base mesh being 0.5 mm and also perform a simulation with a user defined fluid of density 400kg/m# and viscocity 0.001kg/m-s.

To find the Atwood number for both the cases and to compare the results.

Some practical CFD models that have been based on the mathematical analysis of Rayleigh Taylor waves:

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 shock wave.

Kelvin-Helmholtz Instability:

The Kelvin–Helmholtz instability typically occurs when there is velocity shear in a single continues fluid, or additionally where there is a velocity difference across the interface between two fluids.

Simulation:

Geometry:

• The geometry was drawn in Space clim having dimensions of 20mm*20mm for both top and bottom liquid surface
• Then using pull option the geometry was converted to a 2-D surface
• Now, share topology was enabled between the interface edges,

Meshing:

• Being the geometry a square Quad mesh was enabled for smooth meshing.
• Mesh sizes were taken as 0.5mm and 0.2mm.

Mesh Size: 0.5mm

Mesh Size: 0.2mm

Fluent Setup:

General setting:

Viscous Model:

Multiphase Setup:

Phase Setup:

Patching:

Results:

Results –

Case 1:

Mesh size = 0.5mm

Primary phase – air

Secondary phase – water

Time step size = 0.005s

No of time steps = 1000

Link of animation: https://drive.google.com/file/d/1P7EyTnP1gTRFnlVIT9Q0Ddkg9KzAsdYn/view?usp=sharing

Case 2:

Mesh size = 0.2mm

Primary phase – air

Secondary phase – water

Time step size = 0.005s

No of time steps = 1000

Link of animation: https://drive.google.com/file/d/1NM2Y8nleHfev4x4UN7z9FmLDudTbdO4x/view?usp=sharing

Case 3:

Mesh size = 0.2mm

Primary phase – air

Secondary phase – User defined fluid

Time step size = 0.005s

No of time steps = 1000

Link of animation: https://drive.google.com/file/d/126_pfiOzbufTaum7YYSMV0KOVtZCVwVh/view?usp=sharing

Atwood number Calculation:

It is a dimensionless number that is used to study hydrodynamic instabilities in density stratified flows.

`At = (rho_1-rho_2)/(rho_1+rho_2)`

`rho_1` = Density of heavier fluid.

`rho_2` = Density of lighter fluid.

Case1:

`rho_1` = 1000`(kg)/m^3`

`rho_2` = 1.225`(kg)/m^3`

`At = (1000-1.225)/(1000+1.225)`

`At` = 0.997

Case3:

`rho_1` = 1000`(kg)/m^3`

`rho_2` = 400`(kg)/m^3`

`At = (1000-400)/(1000+400)`

`At` = 0.428

Conclusion:

• Atwood number signifies the instabilities formed due to density differences.
• Higher At represent higher difference between two mixing fluids, Thus higher rate of mixing.
• Low At number signifies lesser difference between the densities of mixing fluid, thus lower is the mixing rate
• This is evident from the video shown.