[mostanad]

Dear OpenFOAM users,

I am working with the compressibleMultiphaseInterFOAM solver, which handles N compressible phases with thermophysical properties. I have successfully derived the equations for and pressure, according to this thread Formulation in compressibleInterFoam, but something has been bothering me—I believe there must be some physical reasoning behind it.

If we look at the derivation for , it should simply be as follows:



However, based on the concept of defining dgdt as compressibility:
https://github.com/OpenFOAM/OpenFOAM...am/pEqn.H#L106

We rewrite the ​ equation by incorporating other phases compressibilities, as follows:


Mathematically, this expression is equivalent to the one in the first image.

But my question is: Why? The first expression seems more straightforward to me.

[mostanad]

No idea about this?

[mostanad]

Well, I think I’ve kind of found the answer to my question. Including the compressibility of other phases in one phase's void fraction equation is important because the phase needs to account for how the compressibility of other phases affects its volume fraction.
In other words, this form of the equation allows the phase to consider its own compressibility while also incorporating the effects of other phases' compressibility, specifically at the interface, which is crucial for maintaining a homogeneous and closed system of equations.

[Tobermory]

Originally Posted by mostanad

Well, I think I’ve kind of found the answer to my question. Including the compressibility of other phases in one phase's void fraction equation is important because the phase needs to account for how the compressibility of other phases affects its volume fraction.
In other words, this form of the equation allows the phase to consider its own compressibility while also incorporating the effects of other phases' compressibility, specifically at the interface, which is crucial for maintaining a homogeneous and closed system of equations.

Sounds good to me! Thanks for taking the time to share.