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General remarks and models used

In a first time, we have tried to simulate the problem by entering the two fluids by the left with different velocities. In this case, we have tried to study the real physical problem. But with this configuration, instabilities don't develop without a maintained perturbation inserting by ourself like a sinusoïdal perturbation of the interface with a beater. We were not interesting by this king of instabilities because we think that instabilities mustn't be generated by an artificially maintained perturbation which is not physical. In reality, perturbations generating Kelvin-Helmholtz instabilities are little perturbations of the environment and numericaly these perturbations are due to numerical errors.
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 $ \pm \frac{U}{2}$ where $ U=U_{1}-U_{2}$ (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 ( $ 998.2 kg/m^{3}$) and fuel-oil-liquid ( $ 960 kg/m^{3}$) 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.

next up previous contents
Next: Used of batch computation Up: Modelisation of the problem Previous: Modelisation of the problem   Contents
Stephanie Terrade
Julien Delbove