Taylor bubble rise in circular tubes: steady-states and linear stability analysis

Slug flow is one of the flow regimes that is encountered in two-phase gas-liquid flows in pipes. The flow regime is of great interest in many applications such as hydrocarbons production in oil wells and their transportation in pipelines, conventional and nuclear power generation plants, heat an mass transfer operations between gas and liquid in chemical reactors, among many others. Slug flow in vertical tubes is characterised by periodic rise of large bullet-shaped bubbles known as Taylor bubbles separated by pockets of liquids, known as liquid slugs. While numerous studies have been carried out in the areas of estimation of steady state hydrodynamics features of a single Taylor bubble rising in liquids, not much has been done in understanding some of the transitions featuring in this flow. This dissertation focuses on studying the transitions encountered in the dynamics of a rising Taylor bubble. A particular attention is given to the understanding of the mechanism governing the transition of the bubble from symmetric to asymmetric shape in downward liquid flow. This involves three basic steps; computing the steady state solution, examining the stability of the steady state solution and carrying out energy analysis on the stability results. For different flow conditions, characterised by dimensionless Eotvos number (Eo), inverse viscosity number (Nf) and centreline liquid velocity Froude number (Um), we compute the steady state solution of a rising two-dimensional axisymmetric Taylor bubble. The linear stability of the steady state solutions to three-dimensional infinitesimal perturbations are then investigated. The analysis enable us to determine the region in the dimensionless parameters space at which a Taylor bubble transitioned from symmetric to asymmetric shape. To understand the mechanism that govern the instability, we carried out energy budget analysis to isolate the most dominant energy term that drives the instability. The analysis showed that the mechanism that drives the instability is different depending on whether the effect of surface tension can be neglected or not. For region of negligible surface tension effect, the instability originates from inside the bubble and the dominant source of energy that drives the instability is the bubble pressure, while for region where surface tension has strong effect, the instability originates from the liquid phase and the dominant source of energy that drives the instability is the tangential stress.Open Acces