Equations of motion for two-phase flow in a pin bundle of a nuclear reactor

Abstract

By performing Eulerian area averaging over a channel area of the local continuity, momentum and energy equations for single phase turbulent flow, assuming each phase in two-phase flows to be continuum but coupled by the appropriate “jump” conditions at the interface, the corresponding axial macroscopic balances for two-fluid model in a pin bundle are obtained. To determine the crossflow, a momentum equation in transverse (to the gap between the pins) direction is obtained for each phase by carrying out Eulerian segment averaging of the local momentum equation, where the segment is taken parallel to the gap. By considering the mixture as a whole, a diffusion model based on drift-flux velocity is formulated. In axial direction it is expressed in terms of three mixture conservation equations of mass, momentum and energy with one additional continuity equation for the vapor phase. For the determination of crossflow, transverse momentum equation for a mixture is obtained. It is discussed that the previous formulation of the two-phase flow based on the “slip” flow model and integral subchannel balances using finite control volumes is inadequate in the following respects: (a) The model is heuristic and a priori assumes the order of magnitude of the terms. An excellent example of this provided by the manner in which the form of transverse momentum equation has evolved since its first crude form. (b) The model is incomplete and incorrect when applied to two-phase mixtures in thermal non-equilibrium such as during accidental depressurization of a water cooled reactor. It is demonstrated that the governing equations presented here are based on very formal and sound physical basis and are indispensable if physically correct methods are desired for analyzing two-phase flows in a pin bundle.