Continuing on from the wall post:

I have a multiphaseTurbulence class inherited by mixture/singlePhase/twoPhase turbulence classes which are then split into the specific models. So far k-Epsilon/realisable/RNG are in there, but I haven't looked into any turbulence models where equations for both dispersed and continuous phases are solved for.

As Lamb/Heisenberg said, "When I meet God, I am going to ask him two questions: Why relativity? And why turbulence? I really believe he will have an answer for the first."

What do you think of the turbulence transport equations in the twoPhaseEulerFoam? (shown below for k)



I think it is missing the volume fraction in the convection and diffusion terms. Something like:



However, I've tried a few different formulations to this effect, but they all caused major stability problems with phase separation. I think a phase-intensive treatment - similar to the one used for the momentum equations - might be a good choice.

I use mixture turbulence models because my flow separates.

If anything, I'd suggested removing the beta altogether? I've just had a quick look at the fluent manual;

my.fit.edu/itresources/manuals/fluent6.3.../html/ug/node910.htm

and it looks perhaps like in the openfoam derivation perhaps the div() and laplacian() terms have been expanded. Maybe check that derivation (it'll be similar to the one going from a conservative to non-conservative momentum equation).

Laurence McGlashan wrote:
I use mixture turbulence models because my flow separates.

If anything, I'd suggested removing the beta altogether? I've just had a quick look at the fluent manual;

my.fit.edu/itresources/manuals/fluent6.3.../html/ug/node910.htm

and it looks perhaps like in the openfoam derivation perhaps the div() and laplacian() terms have been expanded. Maybe check that derivation (it'll be similar to the one going from a conservative to non-conservative momentum equation).

Of course, the mixture is more robust as it doesn't have the volume fraction in it, but in that case I think the mixture density should be included in the flux as it is no longer constant.

The Fluent formulation for the continuous phase(Equation (23.5-98) in your link) seems to be the same as I proposed in my previous post, but without the constant density.

I'm thinking out loud here. Say you start with

ddt(beta k)
+ div(beta U_b k)
= ...

This can be expanded to:

beta ddt(k) + k ddt(beta)
+ (beta U_b) . grad(k) + k beta div(U_b) + (k U_b) . grad(beta)
= ...

then

beta ddt(k) + k ddt(beta)
+ (beta U_b) . grad(k) + k div(beta U_b)
= ...

then due to continuity:

beta ddt(k)
+ (beta U_b) . grad(k)
= ...

You can divide through by beta now. I'm not sure why beta is still in the time derivative in the code?

For the mixture model I used similar arguments to the above and I have the k equation as:



I'm not so sure if that's actually equivalent to not dividing by rho_mixture anymore.

To me it seems that either the volume fraction should be included in the convection and diffusion terms, or the whole equation should be divided by the volume fraction i.e. the "phase-intensive" formulation. Note that in the current formulation, the volume fraction is also included in the source terms.