Dear KeJoSa2010,
First of all what do you mean by "Three Phases" you mean Liquid phase and gas/vapor phase and solid phase? i believe you don't mean it as it does not happen in reality (As far as i know), Please describe how many substances ( for example water and Acetone) and how many phases (For instance, liquid and vapor).
Second, please note that In order to calculate maximum (volumetric) flow rate you need to have Max CV value (which is nominal valve CV value) that you say you know it and also Differential Pressure (Look post No. 5). I just don't like to say Max. DP as Maximum DP is: P1-P atm (don't consider vacumm condition) and for your case it might not be applicable. So i just want to say beside having valve nominal CV value you need to have working Differential pressure. then for NORMAL cases you can easily calculate the Max. flow rate from simplified equation (for incompressible fluids) Q=CV * ( DP/(R/R0) )^1/2 where
R is the specific mass of fluid in Ib/ft3
R0 is the specific mass of water in Ib/ft3
Dp is the static pressure drop from upstream to downstream expressed in psi.
But the problem is that you are talking about probably two phase flow, if this is so, The only help i may can do is that you can send me the CV value, Differential pressure, Temperature, pipe size, valve size, substances, their vapor pressures (if they are liquid), The viscosity of each of them together with Z value and Cp/Cv value (If they are gas), so at that case i think i can calculate the max Flow rate by using software.
Have a good day.