In VOF methods for interface capturing schemes: it is assumed that the flow solved is incompressible div U =0 and the effective density is computed as

rho = rho_liquid*gamma+(1-gamma)*rho_gas

this value of rho is used in computation of variables and can be easily seen to vary between the liquid and gas densities in a given cell.

Since the density in a given cell is varying as a function of time (since gamma = gamma (t) ) how good is the assumption that flow is incompressible?

does div U = 0 a good assumption ? since we eliminate the density from the continuity equation?

CFDtoy

Well..., in fact, you don't have the fluid density varying in time. Note that you'll be solving a two phase problem where each fluid has its own properties (density and viscosity) what are assumed not to be varying in time.

Hope it helps.

Renato.

Hello Renato:

the conventional VOF scheme method doesnt do that. It solves one set of momentum equations for both the phases and tracks the interface !!! So, my question is since the overall momentum equation uses a density which is a function of time varying gamma quantitiy...why is the change in density as a function of time not there in the mass conservation equaton?

The method you talk about is the eulerian method for different phases and finally use matching condition at the interface.

CFDtoy

>>> It solves one set of momentum equations for both the phases and tracks the interface !!! <<<

So, How is the interface tracked? I understand that we need a marking function (a step function in VOF) to determine the interface position.

let me put it in other words:

In Interface Capturing methods like VOF and LS we employ a marking function to define where the interface is. VOF and LS methods are quite similar in their concepts, the main difference is in the marking function employed. For VOF, we use a step function ranging from 0 to 1 (or 0% to 100% of water, for example) where the interface is captured by the cells with transition values (not completely filled with fluid). In these cells, the marking function will correspond to the fraction of fluid filling the cell. Note that these marking functions (in VOF or LS) are transported with an advection transport equation using a velocity field obtained from a two-phase incompressible fluid flow. By this way, you need to solve both problems (fluid flow and transport), generally, in a staggered way. Furthermore, when solving the incompressible fluid flow, since you'll have two (immiscible) fluids, you'll have different properties for each fluid, but these properties will not be changing in time. It's easier to understand if you imagine two incompressible and immiscible fluids flowing independently of each other. Both flows will need to satisfy the mass conservation condition at the same time, even flowing together.

This is what I understand by VOF methods concepts. Of course, I could have misunderstood the papers I've already read about it, but the ideas that I've cited above make sense for me -- at least... up to now ;o)

Regards

Renato.