VOF is a multiphase model. "Only one of the phases can be compressible" in the manual mean that if you have more than 2 phases in your system, only 1 of them can be set as compressible. I found something about the compressible vof, but I am not sure if they are useful to you.

1.http://www.math.ntu.edu.tw/~shyue/mytalks/kmshyue1_iapcm2011.pdf

2.http://hdl.handle.net/11370/2b216d61-196e-4392-976a-36705ed3b5ff

3. fluent manual:25.2.4. Modeling Compressible Flows;25.3.6. Defining the Phases for the VOF Model

Hello,

I had a look at the manual but couldn't find the governing equation for advection of phase parameter alpha.

Will it be different  from incompressible case?

Thanks

17.3.4. Volume Fraction Equation

If  you are talking about the equation as attached, then this is the equation of continuity and not the phase parameter equation.

(P.S: sorry,I don't have the save manual version as you may be referring)

Moreover, I would like to know if one of the phase is considered compressible, then there would a state equation available for that phase.

But since this is single fluid model, then how that EOS is applied to only that particular phase. Any suggestions?

Thanks