Multi-fluid stratified shear flows in pipes. Part 2. Critical conditions in the development of interfacial profiles

Abstract

Paper presented at the 5th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, South Africa, 1-4 July, 2007.The focus of this paper is on mathematical formulation and computation of critical flow conditions in horizontal or nearly horizontal pipes. Continuity and momentum equations are derived considering an arbitrary number of fluids and then rearranged so as to yield a system of ordinary differential equations. It is shown that the matrix of the system needs to be invertible so as to compute interfacial profiles. Critical conditions are recognised as those for which the matrix becomes singular and the hypothesis of gradually varied flow fails. Some well known results of linear algebra are here used to define criteria capable of discerning between geometric and kinematic conditions of the flow which are certainly noncritical and others which may or may not be critical.