A STUDY OF NONEQUILIBRIUM DISPERSED TWO-PHASE FLOW (NUCLEAR REACTORS, VAPORIZATION NUMBER, SPRAY EQUATION, DROPLET DISTRIBUTION)

Understanding the behavior of liquid droplets in a superheated steam environment is essential to the accurate prediction of nuclear fuel rod surface temperatures during the blowdown and reflood phase of a loss-of-coolant-accident (LOCA). In response to this need, this treatise presents several original and significant contributions to the field of thermo-fluid physics. The research contained herein presents a statistical derivation of the two-phase mass, momentum and energy conservation equations using a droplet continuity equation analogous to that used in the Kinetic Theory of Gases. Unlike the Eulerian volume and time averaged conservation equations generally used to describe dispersed two-phase flow behavior, this statistical averaging approach results in an additional mass, momentum or energy term in each of the respective conservation equations. These terms take into account affects associated with the acceleration of the droplet vaporization rate as droplets travel along a heated channel. Additional terms accounting for droplet breakup and agglomeration also appear in the form of collision integrals. Further, this study demonstrates that current definitions of the volumetric vapor generation rate used in the mass conservation equation are inappropriate results under certain circumstances. The mass conservation equation derived herein is used to obtain a new definition for the volumetric vapor generation rate which overcomes the problems with existing definitions. This study also presents a new droplet size distribution function useful for predictions at a dryout or quench front. It incorporates a droplet formation coefficient which enables it to predict droplet size distributions for both the roll wave shearing mechanism and jet liquid breakup mechanism. Comparisons to experimental data show excellent agreement with the distribution function. Last, a simple two phase phenomenological model, based on the statistically averaged conservation equations, is presented and solved analytically. It is shown that the actual quality and vapor temperature, under these circumstances, depend on a single dimensionless group.