Two-phase Flashing Flow
DIERS performed a saris of benchmark test on several different relief calculations to include nozzles and piping.
There were 17 different relief cases that were investigated such as, vapor flow, two-phase flashing flow, hybrid flow, frozen flow, churn-turbulent, and bubbly flow. Within the categories of two-phase flashing flow, hybrid flow, and frozen flow were added low viscosity, medium viscosity, high viscosity, and very high viscosity cases.
The purpose of the benchmarks was to compare different computer programs results to determine consistency and identify errors or limitation of different methods. Several individuals participated in the benchmarks and their results were published in an article by Harold Fisher and Shawn P. Adair, entitled, "Benchmarking Two-phase Flow Through Safety Relief Valves and Pipe".
Two-phase Flashing Flow Download
For the DIERS two-phase flashing flow a two-phase fluid (steam), at a relieving pressure of 72.5 psia and a quality of 0.01 is allowed to flash as it flows through the inlet pipe, entering the nozzle ( 4 P 6), and exiting through the discharge pipe. The Mach II uses the direct integration(HDI), of the VdP integral to calculate the maximum fluid flux(Gmax) through the relief nozzle which sets the basis for the relief design. Below you can view the results of nozzle and you can view a snap shot of the direct integration table along with a graph showing the flow rate as a function of pressure. The flow reaches a maxim at the maximum flux(Gmax) which can be seen from the integration table and also as the point of discontinuity on the graph.
For the inlet and outlet piping you can view the output results for the 4 X 6 piping from the direct integrating table and graph. Notice on the green line that the outlet flow rate maximum is only 91,618 lbs/hr which is less than the nozzle flow rate. This means that there is too much back-pressure on the discharge pipe and it will have to be increased to eight(8) inches. After re-runnig the Mach I after the change in outlet pipie size, the direct integration shows a match for the flow rate of the outlet pipe equals the flow rate of the nozzle on the green line.
Mach II Input Data and Nozzle Results
Flow rate (lbs/hr) Choke(psia) Quality inept dP / %Pset Outlet dP /%Pset Piping
95,044 59.0 0.0248 -------- ------- nozzle
93,309 57.8 0.0261 0.81 / 1.5 3.9 / 7.4 6 X 8