Definition of the Problem














I - PRESENTATION
 
 
 
 

We can do several assumptions:


 










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 :
 
 


The general expression of Drag coefficient for two phase flows is :
 
 








Hence, we deduce :
 

         with the approximation : 
 
 
 



 
 
 
 
 
 











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