Multiphase Homogeneous Model equations
 

Hello everybody,
i am struggling to find out the equations solved in a homogeneous model for both fluids.
Are NS solved for each fluid and a commonc velocity field is applied at interface? Exactly, which are the advantages of a euler-eluer vs lagrange model?

In a homogenous model a single velocity and pressure field is solved, and the volume fraction equation is for which phase is where. The VF equation couples to the velocity and pressure equations by controlling density (along with any other coupling, eg surface tension).

In a inhomogenous model a velocity field is solved for each phase. This means at any point different phases can have different velocities - for instance tiny bubbles rising in a stationary liquid.

Both homo- and inhomogenous models are eularian models.

Lagrange models are totally different - they track bodies (eg particles, bubbles) in a lagrangian framework where each individual body is modelled, rather than a eularian framework where "stuff" is aggregated into control volumes, and you do conservation of "stuff" in control volumes.

CFX is using the euler-euler approach by default right? Does it have specific particle tracking method?

No, the eular-eular model and lagrangian models are completely separate. e-e is chosen when you go the homogeneous/inhomogeneous route, lagrangian is chosen when you go the particle tracking route.