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The flow behaviour of shallow gas-fluidised beds was studied. experimentally using a rotational viscometer, and an inclined open channel. Initially, tests were carried out with the viscometer in order to establish qualitative trends in the flow properties of a variety of materials over a wide range of fluidising conditions. Also, a technique was developed which enabled quantitative viscosity data to be extracted from the experimental results. The flow properties were found to be sensitive to the size, size-range and density of the fluidised material, the type of distributor used, and the moisture content of the fluidising gas. Tests in beds up to 120 mm deep showed that the fluidity of the bed improves with reduction in depth; and indicated a range of flow behaviour from shear-thinning to Newtonian, depending chiefly on fluidising velocity. Later, an apparatus was built which provided for a steady, continuous flow of fluidised material down an inclined open channel of 3m length x 0.15m square, up to a mass flowrate of 10 kg/s (35 ton/hr). This facility has enabled data to be obtained that is of practical value in industrial applications; which is otherwise difficult in view of the present limited understanding of the true mechanism of fluidised flow. A correlation has been devised, based on analogy with laminar liquid flow, which describes the channel flow behaviour with reasonable accuracy over the whole range of shear-rates used. 1he channeI results indicated that at low fluidiising velocities the flow was adversely affected by settlement of a stagnant layer of particles on to the distributor, which gave rise to increased flow resistance. Conversely, at higher fluidising velocities the resistance at the distributor appeared to be less than at the walls. In view of this, and also because of the disparity in shear-rates between the two types of apparatus, it is not possible as yet to predict exactly the flow behaviour in an open channel from small-scale viscometer tests.

This thesis reports on the results of the analyses of certain aspects of sampling inspection plans. The investigation has been confined to attributes (as distinct from variables) plans and in this respect.the analyses have been concerned with two main aspects of single and double plans. These are:- (i) the Average Outgoing Quality Limit (AOQL) of the plan. (ii) the Average Sample Number (ASN) of the plan. In the former connection the investigation has been concerned with the evaluation of the AOQL analytically and the determination of the fraction defective of the incoming material to give the AOQL. The analyses have been applied to both single and double sampling plans, In the latter connection the investigation has been concerned with the evaluation of the maximum ASN analytically and the determination of the fraction defective of the incoming material to give the maximum value of ASN. The analyses have been confined only to double sampling plans because in the case of single sampling the ASN is constant and is equal to n, the sample size.

Experirnental data and theoretical calculation on the heat transfer performance of extended surface submerged: in shallow air fluidized beds ~ less than 150 mm, are presented. Energy t;ransferrence from the bed material was effected by water cooled tubes passing through the fins. The extended surface tested was either manufactured from square or radial copper fins silver soldered to a circular basic tube or commercially supplied, being of the crimped or extruded helical fin type. Performances are compared, for a wide range of geometric variables, bed configurations and fluidized materials, with plain and oval tubes operating under similar experimental conditions. A statistical analysis of all results, using a regression technique, has shown the relative importance of each significant variable. The bed to surface heat transfer coefficients are higher than those reported in earlier published work using finned tubes in much deeper beds and the heat transfer to the whole of the extended surface is at least as good as that previously reported for un-finned tubes. The improved performance is attributed partly to the absence of large bubbles in shallow beds and it is suggested that the improved circulation of the solids when constrained in the narrow passages between adjacent fins may be a contributory factor. Flow visualisation studies between a perspex extended surface and a fluidized bed using air at ambient temperatures, have demonstrated the effect of too small a fin spacing. Fin material and the bonding to the basic tube are more important in the optimisation of performance than in conventional convective applications because of the very much larger heat fluxes involved. A theoretical model of heat flow for a radial fin surface, provides data concerning the maximum heat transfer and minimum metal required to fulfil a given heat exchange duty. Results plotted in a series of charts aim at assisting the designer of shalJow fluidized beds.

In the bulge test, a sheet metal specimen is clamped over a circular hole in a die and formed into a bulge by the hydraulic pressure on one side of the specirnen. As the unsupported part of the specimen is deformed in this way, its area is increased, in other words, the material is generally stretched and its thickness generally decreased. The stresses causing this stretching action are the membrane stresses in the shell generated by the hydraulic pressure, in the same way as the rubber in a toy balloon is stretched by the membrane stresses caused by the air inside it. The bulge test is a widely used sheet metal test, to determine the "formability" of sheet materials. Research on this forming process (2)-(15)* has hitherto been almost exclusively confined to predicting the behaviour of the bulged specimen through the constitutive equations (stresses and strains in relation to displacements and shapes) and empirical work hardening characteristics of the material as determined in the tension test. In the present study the approach is reversed; the stresses and strains in the specimen are measured and determined from the geometry of the deformed shell. Thus, the bulge test can be used for determining the stress-strain relationship in the material under actual conditions in sheet metal forming processes. When sheet materials are formed by fluid pressure, the work-piece assumes an approximately spherical shape, The exact nature and magnitude of the deviation from the perfect sphere can be defined and measured by an index called prolateness. The distribution of prolateness throughout the workpiece at any particular stage of the forming process is of fundamental significance, because it determines the variation of the stress ratio on which the mode of deformation depends. It is found. that, before the process becomes unstable in sheet metal, the workpiece is exactly spherical only at the pole and at an annular ring. Between the pole and this annular ring the workpiece is more pointed than a sphere, and outside this ring, it is flatter than a sphere. In the forming of sheet materials, the stresses and hence the incremental strains, are closely related to the curvatures of the workpiece. This relationship between geometry and state of stress can be formulated quantitatively through prolateness. The determination of the magnitudes of prolateness, however, requires special techniques. The success of the experimental work is due to the technique of measuring the profile inclination of the meridional section very accurately. A travelling microscope, workshop protractor and surface plate are used for measurements of circumferential and meridional tangential strains. The curvatures can be calculated from geometry. If, however, the shape of the workpiece is expressed in terms of the current radial (r) and axial ( L) coordinates, it is very difficult to calculate the curvatures within an adequate degree of accuracy, owing to the double differentiation involved. In this project, a first differentiation is, in effect, by-passed by measuring the profile inclination directly and the second differentiation is performed in a round-about way, as explained in later chapters. The variations of the stresses in the workpiece thus observed have not, to the knowledge of the author, been reported experimentally. The static strength of shells to withstand fluid pressure and their buckling strength under concentrated loads, both depend on the distribution of the thickness. Thickness distribution can be controlled to a limited extent by changing the work hardening characteristics of the work material and by imposing constraints. A technique is provided in this thesis for determining accurately the stress distribution, on which the strains associated with thinning depend. Whether a problem of controlled thickness distribution is tackled by theory, or by experiments, or by both combined, the analysis in this thesis supplies the theoretical framework and some useful experimental techniques for the research applied to particular problems. The improvement of formability by allowing draw-in can also be analysed with the same theoretical and experimental techniques. Results on stress-strain relationships are usually represented by single stress-strain curves plotted either between one stress and one strain (as in the tension or compression tests) or between the effective stress and effective strain, as in tests on tubular specimens under combined tension, torsion and internal pressure. In this study, the triaxial stresses and strains are plotted simultaneously in triangular coordinates. Thus, both stress and strain are represented by vectors and the relationship between them by the relationship between two vector functions. From the results so obtained, conclusions are drawn on both the behaviour and the properties of the material in the bulge test. The stress ratios are generally equal to the strain-rate ratios (stress vectors collinear with incremental strain vectors) and the work-hardening characteristics, which apply only to the particular strain paths are deduced. Plastic instability of the material is generally considered to have been reached when the oil pressure has attained its maximum value so that further deformation occurs under a constant or lower pressure. It is found that the instability regime of deformation has already occurred long before the maximum pressure is attained. Thus, a new concept of instability is proposed, and for this criterion, instability can occur for any type of pressure growth curves.

The work presented involves the theoretical and experimental studies of the kinematic and dynamic effects of bearing clearance in linkage mechanisms. In the test mechanism developed a six-bar linkage, having a test plain bearing, is oscillated at amplitude of 17.5 mm within the frequency range 4-7 Hz. A transducer assembly is used to measure the impact accelerations which are related to clearance size, mass distribution, spring load and excitation configuration, ( the vibrators are independently phased ). The motion-analysis of the test mechanism including clearance at a bearing is described using Lagrangian mechanics. The behaviour of the system is obtained by solving the coupled time-dependent equations using Kutta-Merson integration procedure. The method proves to be lengthy in computation time and not easily applied in design. Further, it is shown that there is little difference, in a gross sense, between the results so found and results obtained assuming no bearing clearance. An empirical formula relating the three parameters, clearance size, the rate of change of contact position and the corresponding minimum reaction force is derived from the no-clearance analysis. The. variation of this empirical relationship with excitation frequency is found to be similar to that obtained for the experimental impact levels. Thus it may be used to describe the impact accelerations and its numerical significance as a design criterion is suggested. The experimental work also demonstrates that the pattern of the impact levels remains unchanged when the bearing is oil film lubricated. Some simple design guides using the empirical relationship on a four-bar chain are suggested and general application from a practical point of view is discussed.

Previously, specifications for mechanical properties of casting alloys were based on separately cast test bars. This practice provided consistently reproducible results; thus, any change in conditions was reflected in changes in the mechanical properties of the test coupons. These test specimens, however, did not necessarily reflect the actual mechanical properties of the castings they were supposed to represent'. Factors such as section thickness and casting configuration affect the solidification rate and soundness of the casting thereby raising or lowering its mechanical properties in comparison with separately cast test specimens. In the work now reported, casting shapes were developed to investigate the variations of section thickness, chemical analysis and heat treatment on the mechanical properties of a high strength Aluminium alloy under varying chilling conditions. In addition, an insight was sought into the behaviour of chills under more practical conditions. Finally, it was demonstrated that additional information could be derived from the radiographs which form an essential part of the quality control of premium quality castings. As a result of the work, it is now possible to select analysis and chilling conditions to optimize the as cast and the heat treated mechanical properties of Aluminum 7% Silicon 0.3% Magnesium alloy.

Measurements were carried out to determine local coefficients of heat transfer in short lengths of horizontal pipe, and in the region of an discontinuity in pipe diameter. Laminar, transitional and turbulent flow regimes were investigated, and mixtures of propylene glycol and water were used in the experiments to give a range of viscous fluids. Theoretical and empirical analyses were implemented to find how the fundamental mechanism of forced convection was modified by the secondary effects of free convection, temperature dependent viscosity, and viscous dissipation. From experiments with the short tube it was possible to determine simple empirical relationships describing the axial distribution of the local 1usselt number and its dependence on the Reynolds and Prandtl numbers. Small corrections were made to account for the secondary effects mentioned above. Two different entrance configurations were investigated to demonstrate how conditions upstream could influence the heat transfer coefficients measured downstream In experiments with a sudden contraction in pipe diameter the distribution of local 1u3se1t number depended on the Prandtl number of the fluid in a complicated way. Graphical data is presented describing this dependence for a range of fluids indicating how the local Nusselt number varied with the diameter-ratio. Ratios up to 3.34:1 were considered. With a sudden divergence in pipe diameter, it was possible to derive the axial distribution of the local Nusse1t number for a range of Reynolds and Prandtl numbers in a similar way to the convergence experiments. Difficulty was encountered in explaining some of the measurements obtained at low Reynolds numbers, and flow visualization techniques wore used to determine the complex flow patterns which could lead to the anomalous results mentioned. Tests were carried out with divergences up to 1:3.34 to find the way in which the local Nusselt number varied with the diameter ratio, and a few experiments were carried out with very large ratios up .to 14.4. A limited amount of theoretical analysis of the 'divergence' system was carried out to substantiate certain explanations of the heat transfer mechanisms postulated.

It is well established that hydrodynamic journal bearings are responsible for self-excited vibrations and have the effect of lowering the critical speeds of rotor systems. The forces within the oil film wedge, generated by the vibrating journal, may be represented by displacement and velocity coefficient~ thus allowing the dynamical behaviour 0f the rotor to be analysed both for stability purposes and for anticipating the response to unbalance. However, information describing these coefficients is sparse, misleading, and very often not applicclble to industrial type bearinjs. Resu'its of a combined analytical and experimental investigation into the hydrodynamic oil film coefficients operating in the laminar region are therefore presented, the anal,lsis being applied to a 120 degree partial journal bearing having a 5.0 in diameter journal and a LID ratio of 1.0. The theoretical analysis shows that for this type of popular bearing, the eight linearized coefficients do not accurately describe the behaviour of the vibrating journal based on the theory of small perturbations, due to them being masked by the presence of nonlinearity. A method is developed using the second order terms of Taylor expansion whereby design charts are provided which predict the twentyeight force coefficients for both aligned, and for varying amounts of journal misalignment. The resulting non-linear equations of motion are solved using a modified Newton-Raphson method whereby the whirl trajectories are obtained, thus providing a physical appreciation of the bearing characteristics under dynamically loaded conditions.

A mathematical model of a large coal-fired fluidized bed boiler for power generation is synthesised. The effect of variations in the main parameters of the model on variables such as the background carbon concentrations in the bed, and the transient response of heat evolution are studied. The mechanisms of solids mixing within the bed, combustion and the flow of heat to the boiler tubes are shown to result in a characteristic dynamic response, knowledge of which is essential for the proper control and regulation of a practical system.

The deformation of plastics and metals is discussed with, reference to the effect of the rate of strain. A review of the impact of solids is made, including elastic and plastic wave propagation and the effect of the reflection and superposition of the waves on the progress of the impact. An account of the concepts underlying the Hertz theory of impact is given, together with a consideration of its applicability to the present work. The various theories proposed for liquid-solid impact are reviewed and discussed with reference to recent experimental evidence. An air gun and velocity measuring apparatus were constructed for producing impacts and the theory and practice of the optical techniques used for the examination and measurement of the resultant surface distortions is reviewed. The damage sites produced by the impact of solid spheres, deformable pellets and water drops on Perspex and metals arc studied, at striking velocities up to 1250 ft./sec (850 m.p.h.). This enables the complex process of the impact of a deformable solid (or liquid) to be compared with that of a hard solid. The main quantitative results obtained for all the impact phenomena investigated relate to the variation of the diameter and volume of the damaged region with the velocity of impact. In the case of steel ball impact on Perspex the diameter/velocity relation is similar to that calculated, for elastic solid impact using Hertz's theory. For steel ball on Duralumin the volume of the indentation is proportional to the kinetic energy of the impactor. The nature of the damage produced by polythene pellets and water drops is similar, but the rate of size increase with velocity is much greater than in solid-solid impact. This rapid variation is discussed in relation to the dynamic properties of the liquid and the solid. A detailed examination of the surface damage is made including a measurement of the depths of the cracks in Perspex. Single and multiple drop impact are compared by studying a specimen subjected to artificial rain. The changes in the type of depression observed when Perspex is impacted at different temperatures are analysed.

A wide-band, short duration, pulse technique has been used to investigate the nature of stress wave propagation in straight rods and helical springs. The stress pulses were initiated by means of electromechanical transducers and the distortion of the pulses, due to dispersion, was investigated by recording the surface strain at various points along the waveguides using small ceramic strain gauges. Two types of generating transducer were used, one employing the electrostrietive properties of PT-5 ceramic, supplied by Brush Clevite Company, and the other employing the magnetostrictive properties of nickel wire. The latter was used for all the quantitative experimental results obtained. The surface strain gauges were made from the P3T-5 ceramic. The signal from the strain gauge was amplified and displayed on an oscilloscope screen from which direct measurements were taken. The oscilloscope traces were also photographed. Some of the mathematical theories used to describe the propagation of flexural waves along a straight rod have been outlined; these include the exact and three approximate theories, namely an elementary theory, an improved theory due to Rayleigh and the more accurate Timoshenko theory. Approximate theories for helical springs and plane rings, which are comparable with the Timoshenko theory for a straight rod, are now available and these theories were investigated in this work. The accuracy of the approximate theories has been assessed by obtaining the corresponding dispersion curves and then comparing the theoretical predictions, according to Kelvin's method of stationary phase, with the experimental results. The comparison indicates that the approximate theories investigated give a good indication of the dispersion characteristics for the lowest longitudinal, torsional and flexural modes in a helical spring over the frequency range considered.

An experimental and theoretical investigation of the turbulent free convection boundary layer on a vertical plane surface in air has been conducted. The experimental investigation comprised observations of both the streamwise development from a laminar state to a 'fully developed' turbulent flow and the lateral structure of the turbulent flow at Grashof numbers up to 7x 1010. Measurements were taken of the probability density distributions of temperature and streamwise velocity as well as power spectra of these quantities. The results show that a periodic flow structure, present in the early stages of the transition, disappears as the intensities of temperature and velocity increase to a maximum in the midstage of the transition and then decay. Observations in the 'fully turbulent' flow suggest that the flow has a lateral structure similar to that of a forced convection flow: a viscous sublayer with mean temperature profiles linearly dependent on the distance from the plate, a buffer layer which includes the maximum of mean velocity profiles, and a turbulent layer where the power spectra of temperature and velocity contain an inertial subrange. The theoretical investigation comprised a study of the governing equations and the application of several turbulence hypotheses to the prediction of the boundary layer flow. Solutions for lateral profiles and for the streamwise development of velocity and temperature fields agreed reasonably well with experimental data although there was some disagreement on the heat-transfer rates. Energy balances of the mean kinetic energy and turbulence kinetic energy of the turbulent flow were also predicted. Measurements of the flow were performed with a hot-wire anemometer and thermocouple sensor in conjunction with digital data processing. A large part of the work was devoted to the development of suitable data processing techniques.