This thesis presents techniques for two and three-dimensional grid generation, grid adaptation and a finite volume procedure for solving the two-dimensional compressible Euler and Navier-Stokes equations. In two-dimensions, four grid generation techniques are discussed: a multiblock elliptic partial differential equation approach for structured grids, a Delaunay triangulation approach for unstructured grids, a hybrid grid generator using an overlapping connected approach and a technique for generating unstructured grids suitable for viscous flow simulation using advancing normals. In three-dimensions, the advancing normal technique combined with a Delaunay triangulation algorithm has been developed to generate unstructured tetrahedral grids suitable for viscous flow simulation. Adaptivity techniques developed include point enrichment, using element subdivision and source points, point derefinement and node movement, the combined use of which gives rise to an adaptation strategy in two-dimensions. The use of source points for adapting three-dimensional unstructured grids is described and examples presented of its use on realistic aerospace geometries. A Jameson finite volume, cell-centred, Runge-Kutta time stepping scheme for the solution of inviscid, viscous laminar and viscous turbulent flows is presented. This procedure includes a k-ε turbulence model.

In this thesis, consideration is given to two-dimensional isothermal incompressible flows of rheological complex materials. An introduction is provided on the background rheology and numerical schemes. A time stepping procedure is employed to solve steady state relevant partial differential equations, and in particular the equations of momentum, continuity and the Oldroyd-B constitutive equations. A Petrov Galerkin pressure correction method is used as the base finite element scheme. Model flows, considered as smooth and having analytical solutions are tested for accuracy. In contrast, complex benchmark problems, which may be smooth but with sharp velocity gradients, or alternatively non-smooth, are also solved to test stability and to contrast the quality of results against those in the literature. Despite the considerable effort devoted to establish sophisticated numerical methods to solve highly elastic complex flows of polymeric materials, the simulation of viscoelastic flows through complex geometries remains a challenge. One method that has found favour recently is the elastic-stress-splitting (EVSS) method. There are two features associated with this method, stress-splitting and recovery of velocity gradients. In this thesis, recovery and stress-splitting schemes for plane and axi-symmetric flows of non-Newtonian fluids are presented. Accuracy, stability and numerical performance issues are addressed for different schemes. It is established that recovery-based schemes are stable and superior in higher Deborah number attenuation over conventional and EVSS alternatives. Hence, it is shown that it is the recovery aspect that is responsible for improved stability behaviour. In this context, a 4:1 plane contraction and the flow past a cylinder in an infinite domain are used to analyse vortex activities for Newtonian and viscoelastic flows. Mesh convergence is also analysed.

This thesis is about standing waves on the surface of liquids. These waves have no purpose, but are the result of the action of a liquid or gas jet. Most of the work has been done on oscillations of one particular kind, i.e. asymmetrical and of mode one. An effort is made to predict amplitudes by equating energy input to energy dissipation. This leads only to a qualitative understanding of the nature of these oscillations. This is due to the fact that the energy dissipation in the waves is very small compared with viscous friction in the rest of the column. The jet plays an important role in inducing the waves. For that reason the characteristics of jet flow are investigated. 'his involves determining axial velocities and velocity profiles. The rest Its compare favourably with predictions made in the literature. Amplitudes of oscillations induced by an air jet are determined. This was done as a function of column height, diameter, density, viscosity and flowrate. It appears that it is the entrained liquid in the jet that causes the oscillations. They are therefore essentially the same waves as the ones induced by a liquid jet, plus quite often a jet is used for mixing. It was thought useful to determine how a deflector plate and a draught tube - both can be used to suppress oscillations - affect the mixing performance in a cylindrical vessel. This was achieved by changing the salinity of the jet in a stepwise fashion and measuring the response with a conductivity cell. It appears that the mixing is kept nearly ideal for a column equipped witha plate or a tube. Without these appliances - when waves are induced - the,ratio of residence times Treal/T ideal falls to 0.6.Finally a system of multiple jets was investigated. Various kinds of waves can be induced, depending on the liquid depth. The jets combine to a smaller snumber of jets to support the oscillations. Viscosity, density and flowrate have no effect on this. They do have an influence on the amplitudes.

The rheological properties of kaolin suspensions in water have been studied using a capillary tube viscometer. A method has been presented which permitted the selection , of a kaolin-water-glycerol mixture of required rheological properties. The effects of air injection into Newtonian liquids and shear-thinning suspensions have been studied in a horizontal test section of 41.7 mm internal diameter and 4.57 m long. Experimental observations entailed the measurements of flow rates of air and liquid, average pressure drops and the average and the instantaneous values of holdup. Over the range of air and liquid flow rates studied, both the plug (elongated bubble) flow and the slug flow regimes were obtained. For Newtonian liquids a 33-fold range of viscosities could conveniently be obtained; the injection of air resulted always in a monotonic increase in pressure drop whether the flow of liquid was laminar or turbulent. Results could be satisfactorily correlated by the Lockhart-Nartinelli method, incorporating the Chisholm-Sutherland correction factor where necessary. Furthermore, correlations have been developed to estimate the average liquid holdup and the average liquid holdup in the liquid slug and in the liquid film. Using the estimated values from these correlations, it has been shown that the Hubbard-Dukler slug flow model could be used to predict the average pressure drop for Newtonian liquids, initially in both laminar as well as in turbulent flow. The laminar flow of flocculated suspensions could be described adequately by the power law model, and for a range of concentrations of kaolin-water-glycerol, n' varied from 1.0 to 0.14 and K' from 0.02 to 29 Nsn'.m-2. The injection of air into these materials when in laminar flow could result in a substantial pressure drop reduction. A method has been presented to estimate the minimum pressure drop attainable at any flow rate of a liquid of given rheological properties; and also to estimate the corresponding air flow rate needed. Moreover, by modifying the Lockhart-Martinelli parameter X to take account of shear-thinning properties of liquids, it has been possible to use the same correlations as for Newtonian liquids. Hence the Hubbard-Dukler slug flow model could be used to estimate the minimum pressure drop. If the shear-thinning suspensions were initially in turbulent flow, the injection of air always resulted in an increased pressure drop. The average values of liquid holdup and of pressure drop could then be estimated from the correlation which were applicable to the flow of Newtonian liquids.

No description available.

The settling of solid particles in a flowing suspension in two-dimensional continuous sedimentation has been studied. The properties of the suspension are analysed from batch settling experiments. In analysing the properties of the suspension, an expression is presented that correlates the data of batch settling experiments. The expression includes the minimum settling parameters, initial linear rate of settling, initial porosity and the free settling velocity in gravity sedimentation. An optical technique for measuring the concentration of solid particles without disturbing the flow field of the suspension has been developed. The method is applicable to high solid particle concentration and has a reproducibility of 4% at higher concentrations of solid particles. A theory which considers forces acting in the flow of suspended solid particles in continuous sedimentation is presented. The porosity distribution measured experimentally is compared with the distribution, computed by numerical solution of the model equations. The flow patterns of both solid and liquid phase have been determined theoretically and are illustrated by streamline plots, constructed with the aid of a contour program. The experimental porosity distribution is also presented in contour form. Both theory and experimental observation show the importance of the operating conditions, that is the feed rate, feed porosity, overflow rate and underflow rate on the performance of a sedimenting system.

No description available.

No description available.

No description available.

No description available.