Simpson Two-phase Nozzle
Lets take an example case from Larry Simpson's article. "Estimating Two-phase Flow in Safety Relief Devices". This is a classical case of how to perform a two-phase flow design for a relief nozzle based on a required relief rate and how to determine the maximum gas flux (Gmax) based on utilizing a two-point HEM direct integration method.
Larry Simpson provides the physical property data at Set (State A), to be 100 psia and at "State B" to be 80 psia. He also provides the mass fraction of vapor at Set to be 0.00. The relieving pressure is 102 psia. He provides the user with the physical properties at these conditions and performs a direct integration of the VdP integral after performing a regression analysis to generate psudo-equations of state for the specific volume of the liquid, specific volume of vapor, and the vapor mass fractions.
The Mach II uses the same methodology by taking his physical property data and performing a regression analysis to generate pseudo-equations of state that can be integrated over the pressure range to calculate the mass flux until it reaches a maximum (Gmax).
Larry Simpson will then use this maximum mass flux (Gmax) and the provided two-phase relief rate of 400,000 lbs./hr. to calculate the required relief orifice area based on a discharge coefficient of 0.62.
We will also use this discharge coefficient to replicate his results but DIERS research has shown that it is best to use a vapor discharge coefficient when the fluid is choked and a liquid discharge coefficient when it does not choke.
Mach II input data for Simpson Nozzle
Select Rigorous HEM, Design mode, API orifice, Equilibrium, and no slip. The calculation type will be User input two-phase (400,000 lbs/hr) and the Relieving pressure (102 psia), and heat of vaporization of 802.2 Btu/lboF. Since Mr. Simpson has provided the two-phase relief rate, the only reason to provide a heat of vaporization would be to calculate a vapor only single-phase relief rate for comparison.