Multi-fluid stratified shear flows in pipes. Part 3. Linear stability analysis

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 linear stability analysis of steady state solutions developing in horizontal or nearly horizontal pipes. Continuity and momentum equations for incompressible and isothermal flows are derived considering an arbitrary number of fluids. It is shown that the linearization of the governing equations around the steady state solutions and the assumption of a particular form of the perturbations yield an eigen-value problem, the roots of which represent complex wave speeds of the perturbations. The coefficients of the eigenvalue problem are derived for the most general case and given in analytical form. The effects of inertia of the fluids, gravity, interfacial tensions, shear stresses and wave length are included explicitly in the stability coefficients. Some general properties of the eigen-value problem are outlined.