Computation of nozzle flow capacities for superheated steam, subcooled water, and saturated steam/water mixtures

A new computational tool models the discharge of steam, water, and saturated steam–water mixtures from safety relief valve nozzles, employing thermodynamic-property formulas derived from the Helmholtz equation and programmed into spreadsheet-based software. The computational approach maps an isentropic process from initial conditions in a series of thermodynamic states at each of which the mass flux is computed. The user can identify the maximum mass flux from the generated mass-flux pressure graphical profile. The work describes other mass-flux predictive techniques commonly used in industry and then compares the results of the proposed method against those of the others. The data indicate a very high degree of correspondence between the proposed method and the Napier equation for saturated and superheated steam. The proposed method produces saturated-liquid results consistent with those of the other methods, particularly ASME VIII/1. For the relief of saturated liquid–vapor mixtures, the proposed method increasingly overpredicts maximum mass flux relative to the HEM-based ω-method for increasing pressures and qualities. In the low-quality range, for which there is experimental data to which to compare, the proposed method severely underpredicts measured results involving flows out of nozzles of lengths less than “relaxation” length, but for flows out of longer nozzles, the underprediction is significantly less. The proposed method's subcooled-water results compared to measured data also indicates large underpredictions for sub-relaxation lengths with improved results at generally greater degrees of subcooling at greater lengths. The proposed technique shows generally good agreement with other established predictive methods within demonstrated boundaries and has advantages in stand-alone capability and versatility.