Multi-fluid stratified shear flows in pipes. Part 1. Uniform flow solutions

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 uniform flow solutions in horizontal or nearly horizontal pipes. Continuity and momentum equations are derived considering an arbitrary number of fluids. Closure relationships are introduced and complete definitions of hydraulic diameters are given for co-current and countercurrent flows. A numerical procedure to compute phase holdups and pressure gradients is outlined. The iterative and direct method is shown to be robust and not limited by the choice of the friction factor correlations needed to define shear stresses. Uniform flow equations are linearized so that Newton’s methods can be applied in the search for solutions. It is given evidence that the Jacobian matrix of the shear stress functions can be used as a measure of the flow stability.