Definition of the Problem

I - PRESENTATION

We can do several assumptions:

• the flow is stationnary and axisymmetric
• the bubble stays motionless and spheric

We suppose mass transfert across bubble-air interface is null. Therefore, the corresponding boundary condition is :

Moreover, the viscosity of water is much more important than the viscosity of air, it involves :

This means the shear stress vanishes on the air - water interface.

The definition of the two following numbers allows  to classify the different types of diphasic flows :

For a flow of liquid around a gas particle,  we have :

(indeed, it is equal to 0.017)

II - THEORICAL RESULTS

In order to verify (or not) validity of FLUENT computation, we  use some theorical results.

We can define Reynold's number with  following characteristics :

• Re <<1 : Stocke's solution:
The general expression of Drag coefficient for two phase flows is :

Hence, we deduce :

with the approximation :

• Re = or < 1 : Weak inertial effects:

• Re>1 : Major inertial effects - potential flow :

Comment: Contrary to a flow around a  solid sphere, a flow around a spheric bubble don't remove for any Re. We hope this result will be verified.

III- PHYSICAL PARAMETERS