Rayleigh Taylor Instability Challenge

Objective: To conduct a Rayleigh Taylor instability simulation in an air-water multiphase setup. An RT instability is an instability occurred at the interface between two fluids of different densities. Here the heavier fluid is pushed by the lighter fluid. Examples of RT instability include the behavior of water suspended above oil in the gravity of the earth, mushroom clouds like those from volcanic eruptions and atmospheric nuclear explosions, supernova explosions in which expanding core gas is accelerated into denser shell gas, instabilities in plasma fusion reactors and inertial confinement fusion.

Solving and modeling approach: The geometry is modeled in ANSYS using the SpaceClaim module. In the geometry modeler, the shared topology is turned on so that mesh is consistent in both the surfaces and smoothly share data. To compute this setup we use a multiphase system and laminar viscous model. As it is a multiphase system the phases are patched after hybrid initialization. Finally, a volume fraction contour is created and used to obtain an animation of the similar parameter. The same setup is run for 3 different cases.

Pre-Processing:

Geometry:

The geometry is created in space claim. It is a rectangular geometry of 20mm x 40mm, which is split at the longer side. Ensure that the design has share topology active. Name the top rectangle as water and the bottom rectangle as air / user-material.

Mesh:

First, we name the four boundaries as the wall. Then the top surface as water and the bottom surface as air/user-defined material. Then click on mesh > select the sizing > and change element size to 0.5mm for the base setup and for the refined setup we change it to 0.2mm.

Setup:

Here we use the given solver settings:

We ensure that gravity is turned on and is in the negative Y-axis.

In models, the viscous model used is laminar and turn multiphase on.

Here we use two materials: Water and air/user-defined material (density 400kg/m3). In multiphase we go to the phase option and assign the surface to the phase/material.

Then initialize using hybrid initialization. After initialization is complete we patch the materials using volume fraction.

Solutions:

In the solutions, we create a contour for the volume fraction of water. Then an animation is created for the same contour.

Results:

In the base mesh, we cannot observe the plumes clearly whereas in the refined mesh the plumes are clearly visible.

The end of the animation for the base mesh has a distinct interface line whereas in the refined mesh there is a region in the middle which consists of fractions of volume of both the materials, air, and water.

The steady-state solver cannot be used for this simulation as instabilities are more vividly observed using time-dependent solvers. Also, a steady-state solver gives the end result of the simulations, and the change caused by time won't be computed.

Atwood Number: It is a dimensionless number used in the study of hydrodynamic instabilities in density stratified flow. Numerically, it is the ratio of the difference in densities between two fluids to the sum of their density.

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

Here,

`rho_1` = density of lighter liquid

`rho_2` = density of heavier liquid

For Atwood number close to 0, RT instability flows take the form of symmetric fingers of fluid; for Atwood number close to 1, the much lighter fluid below the heavier fluid takes the form of larger bubble-like plumes.

Air & water phase: 0.998

User-defined material & water phase: 0.4

Animation Files: https://drive.google.com/drive/folders/19v9LIaHUZ4V-RsBqaZ6bMjxJSk66mzDb?usp=sharing