International Journal of Multiphase Flow, Vol.19, No.6, 943-964, 1993
Nucleation and Flashing in Nozzles .1. A Distributed Nucleation Model
It is well known that both the number and size of bubbles must be accurately determined for the initial calculation of flashing void development downstream of flashing inception in ducts, nozzles and restrictions. This paper presents a new method of accurately determining both for small geometries with water, which results in accurate calculation of the downstream void development. A wall cavity model is described for use in the calculation of nucleation rates and bubble number densities at flashing inception, and subsequently in the calculation of the void development downstream of minimum area zones in nozzles. The model is based on the physics of the nucleation phenomena in flashing and considers transient conduction to be the sole means of heat transfer from the superheated liquid to the vapor bubble. The activation criterion developed for site nucleation is one-sided, due to the uniform superheat, rather than two-sided as in boiling. A figure of merit for the particular fluid solid combination is then determined which yields the minimum nucleation surface energy per site. Characteristic site nucleation frequencies and the number densities of nucleation sites of given sizes are then obtained from the data, providing the first link between a surface-characteristic-based nucleation and evaporation model and global behavior. Throat void fractions for all data found in the literature are < 1%, confirming earlier assumptions. A bubble transport equation is used to predict the number density and size of bubbles at the throat. Throat superheats are then calculated for all throat superheats up to approximately 100 K and expansion rates between 0.2 bar/s to over 1 Mbar/s, with a standard deviation of 1.9 K. This extends previous correlations by more than 3 orders of magnitude. As a result, flow rates can be calculated to within 3% of measured values using a combination of single-phase theory and accurate calculation of the throat pressure under critical conditions. This provides a valuable consistency check to independent critical flow predictions.
Keywords:FLOW