On the critical flow of two-phase one-component mixtures

In the field of light water reactor safety a large number of studies is devoted to the critical flow phenomenon of a two-phase one-component mixture. The present work is aimed at giving a contribution in this field, through the development of a theoretical model for the critical flow of such mixtures in a dutch with friction and adiabatic walls. This model is based on the assumptions of one-dimensional motion, thermodynamic equilibrium and slip between the phases. In order to define the expansion law of the mixture in the duct, the assumption is made that the entropic flowrate, compatibly with the energy equation, is maximum with respect to the void fraction in all sections of the duct. Besides, it is assumed that critical flow conditions occur at the duct outlet and that the mixture expansion there is isoentropic. This allows to evaluate the critical flowrate and critical conditions at the tube outlet versus the mixture conditions at the inlet, as well as to determine the flowrate as a function of critical conditions. The model is applied to steam-water mixtures, and plots are obtained giving the specific critical flowrate versus the local properties of mixtures at the tube outlet in the 0,6-160 bar pressure range and in the 0-1 quality range