Rayleigh Taylor Instability simulation   (ANSYS Fluent, Skill Lync, Easy)

Aim:

• To learn analysis of multiphase flows in ANSYS Fluent
• To simulate the Rayleigh Taylor instability problem

Introduction:

A Rayleigh Taylor instability is an instability of an interface between two fluids of different densities which occurs typically when the heavy fluid is supported by lighter one. As the RT instability develops, the initial perturbations progress from a linear growth phase into a non-linear growth phase, eventually developing "plumes" flowing upwards and "spikes" falling downwards. In this instability surface tension plays an important role. The initial perturbations of small magnitude are damped out due to surface tension and the separation line remains stable till large magnitude of force imbalance is formed.

Atwood Number (At): The ratio of difference of fluid densities to the sum of fluid densities is called Atwood number. It used for predicting the shape of instability flow. For At = 0, RT instability flows take the form of symmetric "fingers" of fluid & for A close to 1, the much lighter fluid "below" the heavier fluid takes the form of larger bubble-like plumes.

Some other types of instabilities that are similar to Rayleigh Taylor instability:

• The Kelvin–Helmholtz instability

This can occur when there is velocity shear in a single continuous fluid, or where there is a velocity difference across the interface between two fluids. Here, the similarity is that both analyze the interface stability and the only difference is the cause of instability. Here, velocity difference leads to formation of small vortices at the interface of fluids.

• The Richtmyer–Meshkov instability

This occurs when two fluids of different density are impulsively accelerated. This instability can be considered the impulsive-acceleration limit of the Rayleigh–Taylor instability.

• The Plateau–Rayleigh instability

This instability refers to explanation of breaking of fluid flow into smaller packets due to surface tension at the interface.

Analysis:

Here, a transient simulation of Rayleigh Taylor instability is created for interface of water column above air column.

1) Geometry:

A 2D geometry is considered suitable for simulation where 2 squares, one above other, of 20 mm side length are used. At initial state, the upper square is considered to be water and lower one is considered to be air. For this problem, both generated square surfaces need to have a continuity in mesh, so a conformal mesh is generated by sharing the topology between both squares.

2) Mesh:

Here, 3 meshes with different element sizes are used. This is done to identify the effect of refining the mesh on the fluid flow.

Element sizes used = 0.5 mm, 0.3 mm, 0.2 mm.

Corresponding number of elements = 3200, 8978, 20000

(It might appear that elements are not square shaped but this is due to the graphic display of all elements. If zoomed to an appropriate level, all elements look perfectly square shaped.)

3) Setup:

Analysis type: 2D Transient state

Solver type: Pressure based

Operating conditions: Gravity in Y direction = -9.81 m/s²

Viscous model: Laminar

Multiphase model: Volume of fluid (VOF) model with 2 Eulerian phases, Implicit formulation and sharp interface modelling

Phase Materials: Air and Liquid Water. (From Fluent Database)

Phase Interactions: Surface tension modelling with surface tension coefficient of water = 0.0728 N-m

Patch: After standard initialization, upper square is patched with volume fraction of water = 1 and lower square is patched with volume fraction of water = 0.

Total simulation time: 5 sec

Time Step size: 0.005 sec, 0.002 sec, 0.001 sec (Respectively)

4) Results:

These are the animation videos of all three cases. In each video, there is volume fraction plot on the left of screen and velocity plot on the left. This kind of display is provided to show how the fluid flows.

(The animation frames for all 3 cases are taken at appropriate times such that each case would generate 500 images in total.)

Here, Atwood number is (997 - 1.225)/(997 + 1.225) = 0.9975. Therefore, we can expect a plume and spike type flow here.

• Case 1: (Element size = 0.5 mm)

We can see the formation of a large plume of air rising from center and water spikes falling along walls. The Atwood number predicted this behavior and it seems to be correct. The water falling from above splashes and small water droplets are thrown away. Also, a tiny droplet of water sticks to the top wall. These all effects are due to surface tension modelling. Also, we can see the interface getting stable after sometime.

In the velocity plot, we can see that there is formation of vortices inside the fluid.

• Case 2: (Element size = 0.3 mm)

As the mesh gets fine, we can see more detailed view of splashing of water and release of bubbles of air from the bottom. The interface appears more distinct than the previous case.

• Case 3: (Element size = 0.2 mm)

Here, the water falls from center and air rises from top. This difference is due to finer mesh. The flow pattern looks most real in this case, with formation of number of small bubbles. The interface appears as a clear separate line.

(A steady state study for this kind of problem is not of use as we would directly see the final state of air over water. Even if we try to perform steady state study in ANSYS Fluent, the state changes automatically to pseudo-transient state.)

5) Conclusion:

The simulation of multiphase flow is learnt by taking example of Rayleigh Taylor instability.