LINEAR STABILITY ANALYSIS OF AIR-WATER FLOW IN A PIPELINE

Abstract

 A predictive theory is developed to investigate the instability regime of a counter-current air-water flow in a pipeline. A temporal linear stability analysis is performed to ascertain the conditions that are required for perturbations to grow over a wide range of parameters (i.e., Reynolds number, slope of the bottom of the pipeline, air-pressure factor, ratio of the air to water flow depths). Our results indicate that the air pressure effect on the instabilities is more relevant for short waves at high Reynolds numbers, whereas long waves, which dominate the instability at low Reynolds numbers, are virtually unnaffected by changes in the air pressure.