[Simbelmynë]

Hi,

Assuming we have two incompressible fluids where a mass transfer is happening between the phases. How can this be implemented with the VOF model in a mass conservative way?

A simple example: Assume that we have 50% oxygen and 50% water in a computational cell. Lets assume that all oxygen dissolves into the water, much faster than the computational time-step.

As the VOF is formulated we still have essentially the same mixture density before and after the mass transfer.

If water is the primary phase then:
The oxygen volume fraction goes to zero, which in turn leads to the water volume fraction going to one.

If oxygen is the primary phase then:
The oxygen mass transfer to the water leads to a negligible increase in water volume fraction, which in turn leads to no change in the oxygen volume fraction.

So the questions are:
1. Is it impossible to conserve mass during mass transfer under the above conditions?
2. To minimize the error, we should use the light phase as the primary phase?


Cheers!

[holgerbre]

I think your problem is just becoming stiff because your phase change happens on a smaller time scale than the flow. So reducing the computational time step will allow oxygen from the surrounding cells to flow into the cell where the phase change happens (assuming you run a density variable VOF code).

[Simbelmynë]

I do not agree. Reducing the time-step will not help.

Example:

Instead of having 100% of the Oxygen in the cell dissolve into the water we now have a smaller fraction, e.g. 50% of the oxygen, that dissolves, in half the time.

If Oxygen is the primary phase then you will increase the total Oxygen content in the computational cell by 50% of it's original mass in the cell.

The next time-step you will increase it by another 50% of it's original mass.

This is the same situation as if you take a time-step twice as big.

The flux into and out of the cell will not be affected since the VOF density is the same regardless of time-step taken.

[holgerbre]

that's why I wrote I assume you use a density variable VOF code. Then the density and the pressure will decrease and consequently oxygen will flow into the cell.
I do not see how it can work if the density of both phases is each constant. But this problem is not VOF specific. If you compute an evaporating droplet in a Lagrangian manner, you need a density variable code for the gaseous phase. Otherwise you loose the evaporated liquid mass...

[Simbelmynë]

OK, since I wrote two incompressible fluids in the original post I assumed you meant variable density, without coupling through an equation of state. If you mean that we should change one phase to being compressible then the problem statement is very different.

I do not know how a mixed compressible/incompressible VOF simulation would look like so I can only speculate. If there is only one continuity equation for the mixture density, then I don't see how the problem would go away by declaring the gas phase to be compressible.

Also, an Euler-Lagrange approach is quite different compared to the VOF method. Sure, if we are solving a reacting compressible gas flow with liquid particles in a Lagrangian manner we might see the flow effects of the dissolution as you state, but that is because we do not solve for the mixture density in the cells as in the VOF case.