A semi-empirical approach for predicting two-phase flow discharge through branches of various orientations connected to a horizontal main pipe

The subdivision of two-phase flow in branching conduits consisting of a large horizontal main pipe with upward, downward, or lateral branches of reduced diameter is of great interest in various technological fields. For example, these conduits are important in light-water nuclear reactors (LWRs) in the case of a small break loss-of-coolant accident (SBLOCA) in a leg of the reactor's primary coolant loops, as well as for breaks or valve malfunctions in a large pipeline. In these kinds of circumstances, the relevant phenomenology often involves phase stratification coupled with possible liquid entrainment or gas pool-through phenomena. Therefore, these phenomena were studied in depth to evaluate the pressure drop across conduit elements resulting from the redistribution of flow phases and the discharged mass among them. In the past, several experiments have been performed along with studies in flow modelling. As a result, several formulae and models for branch exit quality and consequent discharge mass flow rate predictions have been proposed. In recent years, we have been engaged in extensive research on this subject, resulting in a new semi-empirical formulation to express branch exit quality in terms of the physical processes taking place in the conduits, the operating parameters and the branch geometry. In this paper, we applied these correlations to representative sets of experiments previously reported in the literature, comprising a wide range of branch-to-main-pipe diameter ratios and operating pressures, which proved our formulation to be very accurate.