A study of the effects of the location of flashing inception on maximum and minimum critical two-phase flow rates:: Part II: analysis and modelling

A general unified model is developed to predict one-component critical two-phase pipe flow. An extension of the Henry [Henry, R.E., 1970. The Two-Phase Critical Discharge of Initially Saturated or Subcooled Liquid. Nucl. Sci. Eng. 41, 336-342.] and Henry and Fauske [Henry, R.E., Fauske, H.K., 1970. The two-Phase critical Flow of One-Component Mixtures in Nozzles; Orifices and Short Tubes, ASME J. Heat Transfer, May 1970.] models to incorporate the effects of wall friction and the location of flashing inception is proposed. Modelling of the two-phase flow is accomplished by describing the evolution of the flow between the location of flashing inception and the exit (critical) plane. The model approximates the nonequilibrium phase change process via thermodynamic equilibrium paths. Included are the relative effects of varying the location of flashing inception, pipe geometry, fluid properties and length to diameter ratio. The model predicts that a range of critical mass fluxes exist and is bound by a maximum and minimum value for a given thermodynamic state. This range is more pronounced at lower subcooled stagnation states and can be attributed to the variation in the location of flashing inception. The model is based on the experimental study of critical two-phase flow rates of saturated and subcooled water through long tubes given in Part I of this work. In that study, the location of flashing inception was accurately controlled and adjusted through the use of a new device. The data obtained revealed that for fixed stagnation conditions, the maximum critical mass fluxes occurred with flashing inception located near the pipe exit; while minimum critical mass fluxes occurred with the flashing front located further upstream. The results of the present study, as well as available data since 1970 are compared with the model predictions. These data cover a wide range of conditions and include test section L/D ratios from 25 to 302 and a temperature and pressure range of 110-280°C and 0.16-6.9 Mpa, respectively. The predicted maximum and minimum critical mass fluxes show an excellent agreement with the range observed in the experimental data.