Computation of the flow with Fluent
We decided to impose the following boundaries conditions :
With the boundaries conditions on the bubble, it was
quite more difficult . Indeed, we had to impose two conditions :
We've had several problems to simulate the flow around
the air bubble. We think the problem comes from the boundary condition
on the bubble and the mesh. We have tested the symmetry condition and the
wall with specified shear stress condition. Both of them gave us wrong
results.
But, it is not so surprising. Indeed, the first one condition
of symmetry doesn't insure that the shear stress is null. Only the derivative
in r direction is null. A term with tangential composant of velocity stays
.
For the second one (boundary condition of wall with specified
shear stress), there are two problems : It is possible FLUENT considers
the shear stress in the (x,y) directions and not in the (r,teta) directions
(local reference or not); moreover, the wall boundary condition impose
that normal and tangentiel velocity are null and yet we only want
the cancellation of the normal velocity.
We think this is the reason why the two cases we have
tested gave us wrong results.
Indeed, for Re << 1, we must have :
and for Re >> 1 :
Morever, from a qualitatif point of view, our results
seems to be in "good" agreements with the theoritical prediction. Indeed,
as it is shown on the following graph, we don't observe any circulation
after the bubble. (but as boudaries conditions are not acceptable this
result has not real signification)
Graph of velocity with the bubble (Re = 1000 with v = 0.1 m/s )
Hence, we have decided to study the problem of a flow
around a solid sphere. The new boundary condition on the sphere is a wall.
As previously, our results seems to be accurate from a qualitative point
of view due to the phenomena of circulation in downstream of the air bubble.
From a quantitative point of view, the results are far from the theorical
results (a removing appears for Re=1000 while we knows it is for Re=20);
So, we deduce there is an other problem, it's not probably only the bad
boundaries conditions which gave bad results for the bubble.
Graph of velocity with the sphere (Re = 1000 with v = 0.1 m/s )