Linear nonmodal stability analysis of Core-Annular Flow

The flow of two immiscible liquid phases in a pipe has great interest in fundamental research and many important applications in industry, mainly concerning the hydraulic transportation of very viscous fluids. The concentric flow of two fluids with comparable densities in a pipe (the more viscous fluid usually lying in the core) is commonly referred to as Core-Annular Flow (CAF) and many theoretical studies have been carried out in the past aiming to characterize the stability of such a configuration, essentially in the framework of eigenvalue analysis. In this study, the classical problem of the stability of CAF is reconsidered from the point of view of linear nonmodal analysis in order to assess the effects of nonnormality of the governing operator on transient evolution of small perturbations. The investigation is directed toward the analysis of the cases in which a poor agreement between the predictions of linear modal theory and classical experiments occurs. Linear transient growths of three-dimensional perturbations are computed for physically relevant configurations, by taking into account the effects of viscosity and volume ratios between the two liquids, as well as of Reynolds number and surface tension. A detailed numerical investigation has been conducted on wide regions of the parameters space and the occurrence of substantial transient growth has been found. The main result is that in situations in which axisymmetric modes of disturbance are expected to constitute the most dangerous ones, spiral disturbances can provide higher levels of energy amplification at short times. A review of classical experimental results is reported in order to support the importance of non modal mechanisms on the instability of some typical configurations.