NUMERICAL SIMULATIONS



    The numerical study is made thanks to the software FLUENT  and the grid generator GAMBIT. The mesh used for the different studies was a 20*10 meter irregular mesh. The cell volum is decraising towards his center. It was composed of 200*100 cells. The calculation was a two-dimension one.
 
 


Mesh used.








    The simulation was made without gravity and superficial tension effects. As we did not consider the gravity, we chose two unmissible fluids: water and fuel oil liquid to simplify the results visualization.

    Studies had been made in  an unsteady laminar flow. The fuel oil liquid stream was put above the water's one.The boundary conditions are :
                                        - symmetries for the horizotal boundary.
                                        - a free stream for the outlet.
                                        - an imposed velocity at the inlet.

    The horizontal component of the two fluids inlet velocity is 0.4 m/s for fuel oil liquid and 0.2 m/s for the water. To generate the initial disturbance, we had imposed a sinusoidal vertical component to the fuel oil liquid  velocity at the inlet. Water's one was null.
 
 

    Here is the developement of a small disturbance. This instability has not developped completly and has vanished after the last picture.
 
 

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Evolution  in time of the volum fraction of fuel oil liquid (red) and water (blue).






    The next figures show the evolution of the initial disturbance in time. The step time between two figures is 4 seconds. for this simulation, the instability is completly developped. We can see the beginning of its disappearing on the last figure. We find the same solution as we had seen in the theorical part.
 
 

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Evolution  in time of the volum fraction of fuel oil liquid (red) and water (blue).








    Thanks to these simulations, we could determine the growth rate by drawing the amplitude of the instability in function of time. It should be an exponential increase.