Two phase problems and two phase flow
In section 1 of this thesis a two-dimensional mathematical model is used to investigate the circulation in a gas-bubble agitation system of a cylindrical vessel for the case of an orifice located at the centre of the base. The two-phase (liquid/gas) region is assumed to be confined to a cone-shaped region and is investigated using Wallis' Drift Flux Model. In the single-phase (liquid) region the turbulent Navier-Stokes equations, written in terms of the stream function, are used for the mathematical model. The analysis in the two-phase region yields the boundary conditions on the two-phase/single-phase boundary. The velocity field in the two-phase region is solved analytically giving results in closed form. A numerical algorithm is developed for calculating liquid flow in the single phase region, and numerical results are presented graphically in terms of the stream function. In section 2 two moving interface problems are investigated. Small time analytic solutions are found for three-dimensional inward solidification of a half space initially at fusion temperature in the first problem. In the second problem, perturbation solutions for melting of a cylindrical annulus with constant heat flux on inner surface are given. In both problems the interface immobilization technique is used. Interface locations at various times are calculated for the inward solidification problem and the results shown in three-dimensional graphs. First and second perturbation terms for the interface location are given for the second problem and graphs of each are presented for a particular case.