Critical Two-Phase Flow in Pipes for Subcooled Stagnation States With a Cavity Flooding Incipient Flashing Model

Abstract

Analysis of loss of coolant accident (LOCA) scenarios in nuclear reactor safety evaluation depends on knowledge of many complex phenomena. A primary phenomenon controlling the sequence of events, by determining the residual coolant mass inventory within the primary system, is the critical flow process. Critical flow of a flashing liquid is complicated by marked departure from thermal equilibrium. Several complex models have been proposed to represent the non-equilibrium effects, including six-equation two-fluid models. Amos and Schrock (1983) developed a model based on the premise that the two-phase region is homogeneous and that thermal nonequilibrium is the dominant factor causing the departure from the homogeneous equilibrium idealization. Flashing inception was represented by a modification of the Alamgir-Lienhard (1981) pressure undershoot. Exponential relaxation of the metastable liquid was formulated as suggested by Bauer et al. (1976) and the critical flow criterion used the sound speed formulation of Kroeger (1976). Lee and Schrock (1988) extended the Amos-Schrock work by developing an improved correlation for the pressure undershoot correction factor in terms of Reynolds number and subcooling Jakob number. Improvements were also made in the relaxation constant and in the application of Kroeger’s formulation. In the present paper a new cavity flooding model is used for the evaluation of pressure undershoot at flashing inception. This model is similar to the one developed by Fabic (1964) for the evaluation of liquid superheat required for boiling on a surface subjected to transient heating. The model contains an experimentally deduced factor, which is correlated against stagnation subcooling using the experimental data of Amos and Schrock (1983, 1984), Jeandey et al. (1981), and the Marviken tests (Anon., 1979). The model was then tested against seven additional data sets and shown to be very accurate in predicted mass flux (standard deviation of 10.9 percent for all data). The cavity flooding model is thought to represent the true physics more correctly than does the earlier model, which had its origin in molecular fluctuation theory.