NONEQUILIBRIUM PHASE CHANGE—1. Flashing Inception, Critical Flow, and Void Development in Ducts

This chapter will introduce the first concepts of nonequilibrium with emphasis on nucleation and flashing in nozzles, and subsequent void development. Both number and size of bubbles must be accurately determined for initial calculation of flashing void development downstream of restrictions. Void development upstream of a restriction is negligible if the inlet is subcooled. A new method is presented of accurately determining number of nuclei and their size, and shows this results in accurate calculation of downstream void development. The activation criterion developed for site nucleation, different from that developed for subcooled boiling, is one sided due to the uniform superheat. A priactical method of utilizing the activation criterion is then identified. A defined figure-of-merit for the particular fluid solid combination yields minimum nucleation surface energy per site, and allows characteristic site nucleation frequencies, and number densities of nucleation sites of given sizes to be obtained from data. A bubble transport equation is used to predict the number density and size of bubbles at the throat. Throat superheats are calculated with a standard deviation of 1.9K for throat superheats up to ˜100K and expansion rates between 0.2 bar/s to over 1 Mbars, extending previous correlations by more than three orders of magnitude. Throat void fractions for all data found in the literature are less than 1% confirming earlier assumptions and allowing nozzle critical flow rates to be calculated with an accuracy of ˜3%. Accurate calculation of throat superheats allows for correct calculation of throat pressures up to ˜70 bars below saturation, a critical factor in calculating choked flows. A quasi-one-dimensional, five-equation model, developed on a microcomputer, was used to calculate the behavior of flowing, initially subcooled, flashing liquids. Equations for mixture and vapor mass conservation, mixture momentum conservation, liquid energy conservation, and bubble transport were discretized and linearized semi-implicitly, and solved using a successive iteration Newton method. Closure was obtained through simple constitutive equations for friction and spherical bubble growth, and a new nucleation model for wall nucleation in small nozzles combined with an existing model for bulk nucleation in large geometries. Good qualitative and quantitative agreement with experiment confirms the adequacy of the nucleation models in determining both initial size and number density of nuclei. It is shown that bulk nucleation becomes important as the volume-to-surface ratio of the geometry is increased.