Numerical simulation and axial stability analysis of vertical slug flow
The first part of this dissertation describes some results of a numerical simulation of vertical axisymmetric slug flow based on a front-tracking method. The liquid phase is considered incompressible. The gas phase is assumed inviscid and massless. The interface is represented as a list of marker points convected with the local liquid velocity. The bubble rising velocities, shapes, and flow field structures around the bubble nose and tail were investigated over a wide range of fluid properties and under different imposed flow rates or pressure drops.
Both single bubbles and trains of bubbles periodic in the vertical direction were investigated. For the periodic case, it is found that the bubble rising velocity remains steady even when the bubbles have an oscillating tail or a wavy interface. The rising velocity seems to be governed only by the flow in the neighborhood of the bubble nose.
For a single bubble, the sudden expansion due to a sudden pressure drop on the tube ends was simulated. In this case as well it is found that the rising velocity of the bubble is decided solely by the hydrodynamics of the nose, and is not affected by the wake.
The second part of the dissertation presents a linear analysis of the axial stability of the large bubbles encountered in slug flow. The breaking of the axial symmetry in counter-current flowing liquid was identified by solving an eigenvalue problem for two different unperturbed axisymmetric flows, an inviscid rotational flow and a potential flow. For both flows a small interface perturbation and an irrotational velocity perturbation corresponding to the symmetry-breaking mode are imposed. It is found that, under the combined effect of gravity and the pressure gradient which drives the liquid flow, the relative velocity between the bubble and the liquid decreases with increasing downflow, which diminishes the stabilizing effect of convection. The decrease of the relative velocity is accompanied by a flattening of the bubble nose, which also has a destabilizing effect.