[jenssnej]

Hello community,

I am working with the twoLiquidMixingFoam Solver. Since this solver is used for mixing of multiple miscible fluids the density varies in space and time although the fluids are incompressible.
The solver uses the incompressible eddy viscosity models where the divergence of the velocity in the boussinesq approach is multiplied with a factor of 1/3 and not 2/3.
Besides the pressure equation in this solver is derivated with the assumption of a divergence free velocity field.

My problem would be solved if somebody could tell me why the solver uses the continuity equation div u = 0 which requires a constant density.

Thanks in advance, Jens

[Villo]

div(u)=0 means that your fluid is incompressible, not that your density is constant.
Your difference in density field will be take in account in the momentum equation and in the alpha equation

[jenssnej]

Originally Posted by Villo

div(u)=0 means that your fluid is incompressible, not that your density is constant.
Your difference in density field will be take in account in the momentum equation and in the alpha equation

Thanks for your answer.
But I do not understand how you get div(u)=0 with a varying density. The temporal derivation of the density in the continuity equation is not zero if the density is not constant. So you could not simplify the continuity equation to div(u)=0. Or am I wrong?

[Villo]

Originally Posted by jenssnej

Thanks for your answer.
But I do not understand how you get div(u)=0 with a varying density. The temporal derivation of the density in the continuity equation is not zero if the density is not constant. So you could not simplify the continuity equation to div(u)=0. Or am I wrong?

Here comes the point... density is varying in space and time (transient simulation with a certain distribution in your domain) but is not changing due to compression effects... that`s why continuity equation of twoLiquidMixingFoam (being a incompressible solver) respect the condition div(u)=0.
Maybe you will find strong confirmations on what i said checking the first section of http://en.wikipedia.org/wiki/Incompressible_flow
If you look in the attached file you can see that the solver take into account the spatial and temporal distribution of the density field in the momentum equation.

[jenssnej]

Originally Posted by Villo

Here comes the point... density is varying in space and time (transient simulation with a certain distribution in your domain) but is not changing due to compression effects... that`s why continuity equation of twoLiquidMixingFoam (being a incompressible solver) respect the condition div(u)=0.
Maybe you will find strong confirmations on what i said checking the first section of http://en.wikipedia.org/wiki/Incompressible_flow
If you look in the attached file you can see that the solver take into account the spatial and temporal distribution of the density field in the momentum equation.

Ok, thanks. I have got one final question: are the calculated values of the velocity and volume faction density weighted? Or is the favre filtering as well only applied in compressible flows?

[Villo]

Good question, i never check this fact... but being that`s a incompressible solver should use a time averaging

[m.Chrsitiano]

does twoLiquidMixingFoam uses boussinesq aproximation?

[alexeym]

Hi,

well, if you look at pEqn.H, you'll find these lines

...
    surfaceScalarField phig
    (
        - ghf*fvc::snGrad(rho)*rAUf*mesh.magSf()
    );

    phiHbyA += phig;
...

so I guess, the answer is "yes".

[brunotessa]

Dear alexeym, sorry for the private messege! Won't happen again!

What I can observe is that "rho" is a function of "alpha1" and since "alpha1" varies with time and space the rho calculated on all the terms in the momentum equantion also varie with time and space.

This differs from the Boussinesq Aprox since the only term that should account for density change is the gravitational term.

Again, considering my very low expirience on OF I could be wrong, what do you think?

Thanks for the reply!

[alexeym]

Hi,

You are right, my guess was wrong. It is called continuous field formulation.