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During the development of computational methods that solve time dependent shock hydrodynamic problems, two underlying strategies have emerged that enable flow features to be resolved clearly. One, employ a numerical scheme of inherently high resolution, usually a second-order Godunov-type method. Two, locally refine the computational mesh in regions of interest. It has been demonstrated by Berger & Collela that a combination of both strategies is necessary if a solution of very high resolution is sought. The present study combines Roe's flux-difference splitting scheme with an adaptive mesh refinement algorithm developed from the ideas of Berger. The result being a general purpose scheme that can fully resolve complicated flows but which requires only modest computing power. The material in this thesis reflects three broad aims. First, to explain the methodology and intricacies of our scheme. Compared to non-adaptive methods our scheme is undeniably complicated, for it contains many elements which must be carefully co-ordinated. Second, to vindicate this complexity. To this end, computational results are presented which are comparable in resolution to Schlieren photographs, yet the calculations were performed on a small desktop workstation. Third, to give sufficient details of our implementation so as to allay the apprehensions of any person who might wish to code up the scheme.

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Adequate information is already available on flow through pipes and on flat plates under constant pressure. In pipes, where the stress does not vary along the wall, the velocity distribution is logarithmic for most of the flow region. For flat plates, where the wall stress decreases systematically in the downstream direction, the velocity profile concaves around the logarithmic law. Between these two cases remains a gap to be closed. This thesis concerns a theoretical and experimental investigation on a turbulent boundary layer where the pressure distribution is so arranged to give a constant stress along the wall as in pipes. Various sand roughnesses were used, and the distributions of mean velocity, pressure, and turbulence were measured at various sections. Chapter II concerns the theoretical and experimental study of the flow in this particular type of boundary layer, whereas in Chapter III the mean velocity distributions are examined in the light of earlier work on both rough and smooth walls, and the effect of roughness is investigated. Also a law for the velocity profile close to a smooth wall id derived, and an experiment on separation from a rough wall is reported. Chapter IV deals with turbulence measurements near rough walls, whereas Chapter V examines the usual methods of calculation for turbulent boundary layers under pressure gradients. In Chapter VI, loose sand was used for the boundary and the movement of grains was examined and compared with that in parallel flow.

This thesis presents an analytical and experimental study of the effects of a superimposed forced vortex on the flow characteristics of a circular sedimentation tank. In the analytical section, a theoretical flow through curve for a circular sedimentation tank was derived as a result of considering the flow through the tank on a diffusion basis. The theoretically derived equation was then compared with the N-formula. A new parameter for measuring the tank hydraulic efficiency was introduced, and the manner the diffusion coefficient; D of the tank affects its short-circuiting behaviour studied. With the help of Reynolds stresses and turbulent energy equations ti the effects of a superimposed forced vortex on the tank diffusion coefficient was investigated. An analysis of the problem dimensionally revealed that the tank characteristic number N was a function of Froude number and a dimensionless term wr/rg where w, v, r and g are the angular speed, kinematic viscosity, radius of the paddles and the acceleration due to gravity respectively. The experimental investigation was conducted with a model circular sedimentation tank, covering a suitable range of speeds of the paddles, and flow rates through the tank. N was found to have a relationship with Froude number and We as predicted by the dimensional analysis. The effects of the forced vortex on N and D were found to be in accordance less term where a.), 9, r and g are the angular speed, kinematic with the analytical considerations. As a result of the experimental study, the existence of critical flow rates. the optimum flow rates and the critical speeds of the paddles were revealed. The setting up of secondary currents by the forced vortex which has both beneficial and harmful effects was also studied. The present investigation have established analytically and experimentally that the effects of a forced vortex on a circular sedimentation tank are, up to a limit, to inhibit the short-circuiting of flow through the tank and to increase the tank hydraulic efficiency. Experimental results obtained with three types of inlets showed that the uniform flow inlet with baffles which was specially designed for this investigation was definitely superior to other inlets having slotted cylinder or cylindrical submerged weir diffuser. Some tracing techniques were modified and improved, especially those concerning the injection of dye and the dye concentration measurement.

Actuator disc and radial equilibrium theories have been the subject of intensive theoretical and experimental investigation in recent years. This thesis describes an examination, by means of a resin twice network analogue, of actuator disc solutions of the flow for three low-speed compressors. These solutions are compared with the radial equilibrium solutions and with aerodynamic measurements obtained from the compressors. For one of these, results of a previous worker were used, for the second, the author carried out tests on an existing compressor, and for the third, a new compressor was commissioned and tested by the author. The conclusions reached are that for some types of compressor the difference between the actuator disc and radial equilibrium solutions is small and unimportant, whilst for other designs the actuator disc approach gives an appreciably better agreement with experiment than the radial equilibrium solution does. An account of the possibilities and limitations of resistance analogues for the solution of axisymmetric flow problems is given, as well as an account of the numerous technical difficulties encountered in the analogue. An outline is given of methods of using the analogue for the solution of "thick" actuator disc problems and for compressible flow problems.

This thesis describes a photographic investigation of separated flows. The work was performed in the Imperial College hypersonic gun tunnel, mainly at a Mach number of 10 . The principal object was to gain an understanding of the mechanism of flow separation from spikes ahead of blunt bodies of revolution. A further important object was to find a method of predicting the flow pattern. On a spiked cone-cylinder configuration it is demonstrated that five different types of flow can occur, depending on the spike length and cone angle. There is an oscillatory type of flow for blunt cones with short spikes and a fully attached flow on the more slender cones. Two of the three remaining types are steady separated flows, which occur on the intermediate configurations. One has reattachment on the conical face of the body, while the other has reattachment very near the shoulder. This latter case is the most valuable with respect to the reduction of drag and heat transfer. The range of configurations for which it occurs can be extended considerably by an increase in the temperature of the body and also by injecting air into the dead air region. At the separation point, the mechanism of the interaction between the shock wave and the boundary layer is independent of the shape and size of the body. This fact is used in the derivation of a semi-empirical relation between the separation angle and the spike length ahead of the separation point. This relation, together with the geometry of the body enables the flow pattern to be predicted for the case of flows with shoulder reattachment.

This thesis is intended to provide information whereby the design of exhaust diffusers can be placed on a sounder basis. Particular emphasis has been placed upon correlating local and overall heat transfer with various possible flow patterns and associated pressure recovery. The experimental work was performed mainly on a two- dimensional model of a supersonic parallel diffuser. For a range of initial total pressures, visual observations were made of the flow patterns developed in the diffuser together with the corresponding measurements of wall static pressure distribution and local heat transfer coefficients and fluxes. The effect of varying the area of the diffuser cross-section for the same upstream generating nozzle has also been studied. The static pressure recovery across the diffuser is found to reach a maximum at the transition from a normal shock to a multiple oblique shock system of diffusion. Mach number profiles measured at sections along the diffuser show that in the presence of shock waves and a positive pressure gradient, the flow is very much underdeveloped. Following a peak value near the diffuser entry, the heat transfer, which generally follows the static pressure distribution, fluctuates about relatively low values in the region of the shock patterns, but rises steadily when the flow becomes subsonic in the downstream section of the duct. In general, the mean level of heat transfer is found to be much greater than that predicted by conventional empirical equations for subsonic pipe flows. Further, on comparison between normal and oblique shock diffusion the former is found to give the higher level of heat transfer. The method of characteristics has been used to estimate analytically the wave patterns present in this diffuser, from which predictions have been made of wall static pressure distributions which are in good agreement with those measured. At a latter stage of the work the performance of model axi-symmetrical parallel diffusers of varying area and length was studied. In general, the static pressure distributions and flow patterns are very similar to those produced by the two-dimensional diffuser, but the axi-symmetric diffusers have a wider operating range and better pressure recovery. Within wide limits the performance is independent of diffuser length.

This thesis treats a subject that of late has become deeply interesting and important not only to field engineers, who need its information for practical problems of a varied nature in river hydraulics, but also to geologists, geographers and others. As presented here it, however, treats the subject from the point of view of engineers. The thesis deals with the transport of sediment as bed-load in open channels, the formation and development of ripples and their influence on the flow resistance. A theoretical approach to the transport of sediment is presented where the bed-load is expressed as a function of the stress. The bed-load relation was found consistent with experiments on a preserved flat sand bed, where the grain speed and concentration were photographically recorded, though anomalies were apparent when applied to tests on a mobile boundary. The formation of ripples appreciably affected the transport rate through a number of actions, and entailed the introduction of a corrective factor. The speed of transport of the load is correlated to the flow and the grain concentration. The mechanistic approach to bed-load transport brought out a plausible explanation for the origin of ripples founded on experimental evidence. The thesis deals also with the main aspects of ripples, which are of special interest to river engineers. The factors governing their shape, growth, alignment and stability were discovered and criteria for their dimensions are given. It was revealed that the transport of bed-load could be inferred by simple measurements of ripple dimensions and the velocity of ripple migration. The problem of flow resistance is then discussed and it is disclosed that the bed-load transport contributes slightly to the energy loss, not due to its transport but to a change in the surface texture; whereas ripples add considerably to the energy loss. An approach for predicting the coefficient of resistance for rippled beds is given.