Generalized Quazi-One-Dimensional Model of Non-Homogeneous Two-Phase Flow and Criterion for Density Wave Oscillation in Parallel Channels With Riser

Abstract

A one-dimensional analytical model (with quasi-1D (or q1D) corrections to the homogeneous flow representation) estimated in a lumped parameter fashion has been developed to describe the threshold of density wave oscillations (DWO) in a parallel heated channel with riser. The heated channel consists of a single-phase part occurring up to the point of bubble detachment and a two-phase part comprising the riser. The two-phase region is described by the drift-flux model that accounts for drift velocity and subcooled boiling. In the proposed model, corre- sponding pressure drops include friction, acceleration, drift, and local pressure drops linked with the inlet and the outlet of the system, respectively. Using perturbation theory, we have linearized conservation law equations around the steady-state operating conditions. The result is a set of two ordinary differential equations with coefficients representing physical proper- ties and model parameters. Using the theory of linear attenuating oscillator, generalized ex- pression (criterion) is obtained for the stability thresholds of DWO for wide range regime and geometric conditions. The current study shows that this generalized criterion is a function of not only traditional homogeneous parameters represented in the classical studies (e.g., Moro- zov-Gerliga, Ishii-Zuber, Guido et al.), but also new parameters, such as q1D corrections, riser effect, and density, enthalpy, and pressure drop, which are described with drift effects and phase-shift of the model parameters. It is shown here that the new generalized criterion approaches the classical ones in the limiting cases.