NUCLEATION AND FLASHING IN NOZZLES .1. A DISTRIBUTED NUCLEATION MODEL

It is well known that both the number and size of bubbles must be accu rately determined for the initial calculation of flashing void develop ment downstream of flashing inception in ducts, nozzles and restrictio ns. This paper presents a new method of accurately determining both fo r small geometries with water, which results in accurate calculation o f the downstream void development. A wall cavity model is described fo r use in the calculation of nucleation rates and bubble number densiti es at flashing inception, and subsequently in the calculation of the v oid development downstream of minimum area zones in nozzles. The model is based on the physics of the nucleation phenomena in flashing and c onsiders transient conduction to be the sole means of heat transfer fr om the superheated liquid to the vapor bubble. The activation criterio n developed for site nucleation is one-sided, due to the uniform super heat, rather than two-sided as in boiling. A figure of merit for the p articular fluid solid combination is then determined which yields the minimum nucleation surface energy per site. Characteristic site nuclea tion frequencies and the number densities of nucleation sites of given sizes are then obtained from the data, providing the first link betwe en a surface-characteristic-based nucleation and evaporation model and global behavior. Throat void fractions for all data found in the lite rature are < 1%, confirming earlier assumptions. A bubble transport eq uation is used to predict the number density and size of bubbles at th e throat. Throat superheats are then calculated for all throat superhe ats 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 previ ous correlations by more than 3 orders of magnitude. As a result, flow rates can be calculated to within 3% of measured values using a combi nation of single-phase theory and accurate calculation of the throat p ressure under critical conditions. This provides a valuable consistenc y check to independent critical flow predictions.