Rayleigh Taylor Instability Challenge

RT instability:

It is the interpenetration of materials that occurs whenever a light fluid pushes on a heavy fluid. It is a dynamic process where the two fluids seek to reduce their combined potential energy. It occurs under the effect of gravity and fluid system accelerates towards the denser fluid. The fluid interchange decreases the potential energy content of the system which is the cause of the instability.tem which is the cause of instability.

Examples:

• The behaviour of water suspended above oil in the gravity of earth.
• Clouds from the volcanic eruptions.
• Supernova explosions.
• Instabilities in plasma fusion reactors, etc.

Geometry: the required geometry for analysis is modelled as shown in fig. using SpaceClaim tool. In order to generate conformal mesh the SharePrep tool is used to share the topology of geometry.

Meshing:

Few simulations are tried using different mesh sizes.

Case1:

Element Sizing: 0.5 mm

Number of elements: 3200

Number of Nodes: 3321

As only quadrilateral call are used to mesh domain hence the quality of cells is good.

Solver Settings:

Solver: Pressure based,Transient

Models:

Viscous: - Laminar

Multiphase: - Volume of Fluid (VOF) with implicit formulation.

Materials:

Air: Low density (1.225 kg/m²)

Water: high density (1000 kg/m²)

Time step: 0.005 s.

Number of iterations: 1500.

Results:

Residuals:

Solution Animation:

solution animation for case 1 can be accessed from link given below:

https://drive.google.com/file/d/1-NYr1QabtNLwH4gDgwBIZen1nmYvLnJ1/view?usp=sharing

Case 2:

element size 0.25 mm

Mesh:

Element Size: 0.25 mm

Number of elements: 12800

Residuals:

Solution Animation:

solution animation for case 2 can be accessed from link given below:

https://drive.google.com/file/d/1nYkvpTIqtSUhdVSdv4WuIxxaqO_mn5s9/view?usp=sharing

Case 3:

Element Size: 10 mm

Mesh:

Element size: 0.10 mm

Number of Elements:80000

Materials:

Water

User Defined Material

Density: 400 kg/m3

Viscosity: 0.001 kg-m/s

Results:

Residual:

Solution Animation:

solution animation for case 3 can be accessed from link given below:

https://drive.google.com/file/d/1EnATIm7FIafDcIriihvTpzbUyfYmwNXZ/view?usp=sharing

Here in this case the defined material is more viscous than the water. High viscosity decreases the growth rate of instability i.e. it slows down the rate of mixing. High viscosity keeps the Reynolds number low and prevents turbulence.

Atwood Number:

A dimensionless number used for study of hydrodynamic instabilities in density stratified flows. It is density ratio of heavier and lighter fluid (Difference in densities divided by sum of densities). It is an important number for study of RT instability. In Rayleigh–Taylor instability, the penetration distance of heavy fluid bubbles into the light fluid is a function of acceleration time scale.

Atwood Number for water-air iterface:

`A=(ρ_Water-ρ_air)/(ρ_water+ρ_air )`

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

`A=0.9975`

Atwood Number for water- user fluid interface:

`A=(ρ_Water-ρ_fluid)/(ρ_water+ρ_fluid )`

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

`A=0.4285`

as we can see from the results in animation that the instability grows with time as Atwood number increases and refined mesh captures the instability better than coarse mesh.

For the case of small Atwood number, the density difference between the two sides of the interface is small, and the density distribution of the upper and lower layers is nearly symmetrical. The initial density stratification plays a dominant role, and the expansion-compression effect has little influence. With the increase in the Atwood number, the stabilization effect of initial density stratification decreases, and the instability caused by the expansion-compression effect becomes more significant. The flow structures of bubbles and spikes are quite different at medium Atwood number. The effect of compressibility on the bubble velocity is strong at large A_t.