Drift-flux correlation disengagement models: Part II — Shape-based correlations for disengagement prediction via churn-turbulent drift-flux correlation

Abstract

In Part I of this work the theoretical foundation was laid for predicting disengagement via volumetric gas production and an axial void fraction profile. Earlier work indicated for non-foaming systems one of the two drift-flux correlations can be chosen on the basis of viscosity. Herein, for the churn-turbulent drift-flux correlation (low-viscosity system), the dependence average void fraction and dimensionless superficial vapor velocity [1] on vessel shape (e.g., vertical cylinder, horizontal cylinder, or sphere) is explored. There is very little shape dependence and it is quantified below. A simple two-constant correlation is suggested, which satisfies the conditions at low and high dimensionless superficial vapor velocity conditions. Constants are given for vertical cylinders, horizontal cylinders, and spheres for the churnturbulent drift-flux correlation. The disengagement model is based on a constant energy generation per unit mass of liquid. Thus, the application to runaway reaction with vaporization is straightforward. The application of the correlation to reactive systems producing gas (i.e., gassy systems) and to those both producing gas and involving vaporization (i.e., hybrid systems) in non-constant cross-sectional area vessels is clarified here. Rating calculation equations are developed, and the calculations are illustrated. For a rating calculation, the maximum gas rate (based on vent capacity) is known. The calculation of maximum average void fraction (i.e., 1-fill ratio) and gas generation per unit of liquid is straightforward. Thus, the rate of reaction (i.e., gas generation) must be found to assure that the vent capacity is sufficient