Week 5 - Rayleigh Taylor Instability

Rayleigh Taylor Instability

Instabilities in Fluid Dynamics:

1. Rayleigh Taylor instability
This interfacial instability between two phase of fluid, with different densities occurs when the lighter fluid is pushing the heavier fluid.

2. Richtmyer-Meshkov instability
This type of stability occurs when two different fluids are accelerated impulsively. It starts with disturbances of small amplitude that gradually grows with time.

3.Plateau-Rayleigh instability
This type of instability signifies the breakdown of fluid, as of their surface tension, (in a stream) of same volume but with less surface area, something like a breakdown into smaller fine particles.

Rayleigh Taylor instability:

In present case, the Rayleigh Taylor instabilty analysis is done on two different phases of fluid. The two rectangular domains are assigned with air and water, being shared a common interface. The base mesh size is kept 0.5mm and both the domains are patched such that there is only fluid with higher density at topmost part and the fluid with only less density, here air, in lower part.

Geometry approach :

The two rectangular domains are assigned with air and water, being shared a common interface as shown in the figure below

Meshing :

CASE 1 :

Mesh element size : 0.5 mm

The Transient simulation is performed as the chaotic behaviour for mixing increases with time, or say the instabilities grow with time. Gravity is given by -9.81 in y axis for the flow of fluid.

Contour are added for the surface, as shown in the figure below

Multi phase model with two phases that are air and water

• number of eulerian phases: 2
• formulation type: implicit
• volume fraction cut off: 1e-06

Result:

Run the simulation for 100 iterations at 0.005 fixed time step and record the solution animation.

Residual plot :

CASE 2 :

Refined mesh element size: 0.35

Repeat the process

The Transient simulation is performed as the chaotic behaviour for mixing increases with time, or say the instabilities grow with time. Gravity is given by -9.81 in y axis for the flow of fluid.

Contour are added for the surface, as shown in the figure below

Multi phase model with two phases that are air and water

• number of eulerian phases: 2
• formulation type: implicit
• volume fraction cut off: 1e-06

Result:

Run the simulation for 100 iterations at 0.005 fixed time step and record the solution animation.

Residual plot :

Conclusion:

• As seen in the simulation, the one with less Atwood Number has more instablities and consequenlty.
• The baseline mesh and the refined mesh can be considered as the particles in a fluid continuum in both the phases, so more refined the mesh is, the more time it could take to resolve the instabilties of mixing.
• Additionally it also depends on the density and viscosity of fluid as those fluids with high viscosity resist the deformation and mixes slowly, there are more shear forces and cycle time is more.