So to find instabilities without forcing them we have placed ourself in the space in translation where flow is symetric from the horizontal plane y=0 with the velocity where (See Chapter 1).

To simulate this kind of flow we have used the Volume Of Fluid (VOF) model. The VOF model is a fixed grid technique designed for two or more unmiscible fluids where the position of the interface between the fluids is of interest. This method consists in solving a single set of momentum equations and tracking the volume fraction of each of the fluids throughout the domain.

We have found that this model wasn't compatible with inviscid flow, so our
simulations were made in laminar with viscous fluid.

We have also noticed that to have instabilities the densities of the fluids
had not to be too differents. Effectively with water and air there were not
instabilities. So we have chosen water (
) and fuel-oil-liquid
(
) and for these fluids instabilities could appear.

Lastly, we have changed numerical discretization schemes.

The segregated solver was used : it is the solution algorithm where the governing equations are solved sequencially.

In FLUENT, two algorithms are available for the pressure-velocity coupling : SIMPLE and SIMPLEC. For relatively uncomplicated problems (laminar flows with no additional models activated) in which convergence is limited by the pressure-velocity coupling, you can often obtain a converged solution more quickly using SIMPLEC so we have used it for our study.

For the pressure we have chosen the body-force-weighted scheme because it works well if the body forces are known a priori in the momentum equations and it is the case with buoyancy in particular.

For momentum, the QUICK scheme was used because it is recommanded when there are rotating or swirling flows inside the flow.