Modelling 2phased expansion valve

Jun 2018

I am currently trying to model a 2phased expansion valve in Simscape (matlab - simulink). They already have a Variable Local Restriction for a 2Phased model ( which I would like to use for my model.

This Variable Local Restriction can calculate the Pressure drop of the Orifice according to its Throat Area. This is what I am also interested in to control.... If I determine what the desired pressure drop is then I would like to calculate the needed throat area to send as control signal to the Variable Local Restriction.

However to calculate the Throat Area I will need to rewrite the Pressure Drop Eq (Capture1.png) and I will need to know the v_R (specific volume of the restricted area). I believe this value should come from the energy balance Eq (Capture2.png), but I only know the values of the A and B port (pressure, temperature, internal energy, specific volume, etc...). I don't know the pressure, internal energy or specific volume of the restricted area...

So my question is, does any one know how the determine the Specific Volume of the Restricted Area of an Orifice when the Pressure and Temperature of the inlet and outlet are known?