The hydraulic analogue has no equal as a research tool in the visual study of the transient heat transfer problems. The experimental time can be designed long enough to carry out the manual adjustments of the analogue components, thus avoiding the costly automatic devices which would otherwise be built into the apparatus. The truncation error of the finite difference network and the construction error of the hydraulic analogue were investigated. The stability of the finite difference equations used in the designs were discussed, and some design parameters as guidance were suggested. An ingenious device of variable resistor for the simulation of the variation of thermal conductivity was used. The telescopic-tubes device for the variation of boundary temperature was satisfactory. Oils were found to be ideal for use, as they are free from the growth of organism and are not corrosive to the metal surfaces. Besides, suitable choice of oil can give almost any required length of experimental time. Using the shock heating problems of insulated rod and infinite plate for the comparison of hydraulic analogue accuracy, the central and end storage arrangements for the designs were also investigated. Shock heating problems of the infinite hollow cylinders of outer/inner diameter ratios of 5:1, 11:3, 15:7, 9:5, 19:11, and 27:19; and of the hollow spheres of outer/inner diameter ratios of 3:1, 2:1, and 3:2, were solved using the hydraulic analogue. In the application of the hydraulic analogue to the freezing and cooling problem of a finite cylindrical casting in a water cooled cast-iron mould, many components were designed to take into account of the latent heat, the variations of thermal conductivity, specific heat, density and boundary heat transfer coefficient, with temperature. The problem involved heat flow in two dimensions, and the mould interface temperature varied with the casting interface temperature. Salient points concluded from the results are: (1) The mould interface temperature was found more likely to vary with the casting interface temperature, and it would be a better approximation to use a reasonable relationship between the two temperatures for the boundary conditions of the casting rather than the usual assumption of constant temperature at the boundary. (2) It was found that there is a long period of partial contact between the casting and the mould during solidification, and the neglect of the conduction heat transfer would cause serious discrepancies. (3) It was found that the cooling curves within the steel casting investigated are quite accurate for use in the approximate analysis of thermal stress or solidification mechanisms of any similar casting problems.

The thesis is concerned with the vibrational characteristics of straight and pre-twisted cantilever beams of uniform rectangular and aerofoil cross-section. Two methods are presented for the solution of the differential equations of motion of pre-twisted rectangular cross-section beams neglecting shear and rotary inertia effects. The first method consists of transforming the original equations into a set of first order simultaneous equations and solving by a step-by-step finite difference procedure. The second method is a Rayleigh Ritz procedure for which two types of approximating functions are considered. The natural frequencies and mode shapes of vibration are obtained up to the fifth mode by both methods. The results are compared to each other and to the work of other investigators where available and good agreement is obtained. The Rayleigh Ritz method is extended to allow for shear and rotary inertia effects for both straight and pre-twisted rectangular cross-section beams. For straight beams good agreement is shown to exist with known solutions. The effect of variation in the value of the shear stress factor upon natural frequencies of pre-twisted rectangular cross-section beams is also examined. The transformation method has been extended to solve the equations of motion of aerofoil cross-section beams. The natural frequencies and mode shapes of vibration are obtained up to the fifth mode for both clockwise and anti-clockwise pre-twist relative to the root cross-section. The natural frequencies, for the case of zero pre-twist, are compared to results obtained by an analytical solution of the equations of motion and to standard solutions for certain special cases and good agreement is obtained. The effect of variation of the value of centre-of-flexure co-ordinates upon beam natural frequencies and mode shapes is also discussed. The natural frequencies and mode shapes of vibration are obtained by experiment for both rectangular and aerofoil cross-section beams and are compared to theoretical results.

This thesis is concerned with the vibration of a simplified compressor blade system which is stiffened by the introduction of a midspan shroud, or snubber, constraint. The initial investigation is concerned with the effect of different types of snubber interface constraint, namely: 1) Dry friction rubbing at the snubber interface. 2) Clearance at the snubber interface. 3) Viscoelastic shear joint at the snubber interface. The results of resonance tests carried out on a single blade for each type of constraint showed the viscoelastic shear joint to stiffen the structure, while giving higher damping than that of the other interface conditions. A more comprehensive experimental and theoretical investigation is carried out on this type of constraint on a single blade. The complex modulus model is used to describe the viscoelastic material properties which are treated as a function of frequency, and justification is given for its use in free vibration. The results show optimum positions for the snubber for maximum stiffening and damping and that they vary from mode to mode. The results also reveal that heavy damping may be obtained if the parameters are optimised correctly. The experiments verify the theoretical work satisfactorily. The investigation is extended to the study of a batch of five blades which are connected by a viscoelastic shear joint at the snubber interface. The theoretical analysis however fails to predict one of the five basic modes. The structure exhibits heavy damping with close natural frequencies. A survey of the methods for separating the response of individual modes from the total transient response of a structure, is carried out. It was found to be impossible to estimate the frequency anddamping for one of the heavily damped modes by any of the available techniques. Correlation between experimental and theoretical results is acceptable.

The subject of this Thesis is the performance modelling and evaluation of the Rotary Internal Combustion One-Stroke Engine specified in Patent Application number PCT/GB 84/0048. A mathematical model, capable of simulating the various changes that take place during the cycle of the engine, has been formed and applied to the engine for testing its performance. Before forming the model the dimensions of the engine were calculated by considering the stressing of the main movable parts of the engine such as the driveshaft, radial sealing wall and rotary piston, as well as the surface area to volume ratio. Also the timing and conditions under which the engine operates were speci--fied and used as input to the model. The model incorporates six subroutines namely, "DATUM" which stores all the input constants and variables, "GEOMETRY" which calculates various geometrical engine parameters, "COMBUST" and "EXPAND" which simulate the ignition delay/combustion and expansion respectively, and "PERFORMANCE" which calculates the various performance parameters of the engine. The above model was run with different sets of fuel-air ratios/speeds as input. The performance evaluated has been tabulated and a performance map of the engine drawn. Typical pressure-volume and heat flux diagrams were plotted. Further, the model was tested, with different sets of operating variables as input, to optimise the principal dimensions and timing of the engine. The model was validated by adaption to simulate a two-stroke internal combustion reciprocating piston engine and run with MAN-B&W L55GB engine data. The output was compared with the figures quoted by the engine manufacturers. The comparison was favourable. Once the model had been validated a direct comparison was made between the internal combustion rotary one-stroke engine and the MAN-B&W L55GB engine. Costs were analysed and proposals of possible methods of optimising the design of the above engine formulated.

The well-known idealised theory of the simple shock-tube predicts values of the various flow properties, many of which are in good accord with experimental observations particularly for cases involving only weak shocks. Important departures from the above predictions can occur however, both in the flows at considerable distances from the diaphragm and those in its immediate vicinity. The former are mainly attributable to the finite opening-time of the dipahrgam while the latter arise chiefly as a result of the boundary layer which develops at the walls of the tube; both these mechanisms are ignored in ideal shock-tube theory. The present work is concerned principally with the initial stages of the flow and its chief aim is to determine the influence of the dynamic behaviour of the diaphragm on the flows developing in the tube. An experimental and theoretical study has been made of the static and dynamic behaviour of shock-tube diaphragms; the information obtained from this has been incorporated into a computer-formulation of the initial flow in the tube. Experimental measurements have been made which provide confirmation of many of the computed results, particularly in regard to shock trajectories, shock-formation distances and pressure histories in the vicinity of the diaphragm during the opening process.

The hydraulic analogue has a very great potential as a research tool, it is capable of solving complex heat transfer problems for which formal mathematical solutions are difficult to obtain and where numerical solutions involve lengthy and complex calculations. The great advantage of the hydraulic analogue over other types of analogue is the comparative ease with which complex thermal conditions can be simulated. Part I of the present work describes the application of the hydraulic analogue to three-dimensional heat conduction problems. The construction of a three-dimensional hydraulic analogue is described and this analogue is used to obtain the transient temperature distributions in a cube of conducting material with three-dimensional heat flow. The analogue solution is compared with a numerical solution and a maximum total error (i.e. a constructional error and a 'lumping' error due to the finite difference approximation) of +/- 2% of the temperature range was found in the analogue solution. Before the three-dimensional problem was solved, two preliminary tests were carried out in order to investigate the constructionalaecuracy of the analogue components. These tests consisted of a one- dimensional and a two-dimensional heat conduction problem; these were solved on the three-dimensional analogue and a maximum error of +/- 2% was found in the analogue solutions. The stability and accuracy of the finite difference solutions to the heat conduction equation are discussed. Part I of this work shows therefore, that three-dimensional conduction problems can be solved with acceptable accuracy using an hydraulic analogue. The boundary conditions in the Part I problems were very simple and to show that more complex boundary conditions can be simulated by a hydraulic analogue and also to show that flow systems can be represented,the work in Part II is presented In Part 2 the geometry has cylindrical symmetry and the problems considered are one and two-dimensional only. The analogue of Part 1 is not used. Part 2 describes a new hydraulic analogue for solving the complicated heat transfer problems associated with the transient operation of regenerators. In particular, start-up flow in a tube is considered. Here, the gas stream presents complicated boundary conditions for the inside surface of the tube, varying both with time and position. The boundary conditions are simulated in the hydraulic analogue using a series of positive displacement pumps to enable the change in enthalpy of the gas stream to be represented. The disadvantage of investigating the transient temperature responses in a regenerator using the hydraulic analogue is the very long experimental time required. However, if the thermal capacity of the gas stream is ignored, then the hydraulic analogue is shown to be a very useful method. The accuracy of the finite difference approximations used in the analogue design is investigated. Using certain simplifying assumptions, the heating-up period for an actual gas flow/refractory tube sustem is analysed using an hydraulic analogue. The analogue results are compared with the actual transient temperatures obtained by direct measurement on an existing rig; the maximum discrepancy between the two solutions was +/- 6% of the maximum temperature range.

The spontaneous-ignition and ignition delays of liquid fuel droplets falling (i) on a heated surface and (ii) through heated air are investigated. The effects of fuel properties, droplet size, initial temperature, material of the surface and additives in the fuel on the ignition delays of liquid fuel droplets falling on a heated surface are studied. It is shown that for droplets falling on a heated surface, the ignition delay/temperature curves for certain fuels show minima at or slightly above the maximum boiling rate points. Two new terms namely 'the heating up delay' and the 'evaporation delay' are introduced to represent the so called 'physical delay'. The heating up delay is isolated as the truly physical part of the ignition delay and is defined as the time taken for the droplet to reach a temperature where a stoichiometric mixture can exist at or near the fuel surface. The evaporation delay is identified as partly physical and partly chemical and is defined as a function of the evaporation rates. Expressions are derived for the heating up delay and the evaporation delay for various cases (a theoretical expression is derived for the evaporation rate of a droplet in the 'spheroidal' state on a heated surface) and the experimental results for the effects of droplet size and the initial temperature of the fuel on the ignition delay are shown to be as indicated by these expressions. It is also shown that for droplets of high boiling point fuels such as kerosine and diesel fuels, in stagnant hot atmospheres or falling through heated air, the heating up delay occupies a significant proportion of the ignition delay and at high temperatures the ignition delay is virtually the heating up delay. It is shown that additives in the fuel produce significant reductions in the ignition delays of kerosine droplets falling on a heated surface and that the dosages for certain additives are critical.

The effect of pressure on the evaporation lifetime, the ignition delay, and the burning and combustion time of single liquid fuel drops on a heated surface are investigated in a pressure chamber; the fuels used are the four engine reference fuels, viz., n-Heptane, n-Hexadecane, 2,2,4-Trimethylpentane (iso-octane), and a-methylnaphthalene; the pressures used range from atmospheric pressure to 69 atmospheres. Also, the effect of pressure on the 'cleanliness' of combustion of single n-Hexadecane drops burning on a heated surface is investigated. Theoretical expressions are derived to predict the evaporation lifetime of a liquid drop on a heated surface in three important modes of evaporation, viz., true contact evaporation, evaporation in the Maximum Evaporation Rate Range and spheroidal evaporation The Transition Temperature is defined as the surface temperature at which physical and chemical factors have the same influence on the ignition delay of a fuel drop. Allowing for the variation of the S.I.T. with pressure, in no case is a Transition Temperature of the fuels used more than 100 deg.C above the S.I.T. At higher surface temperatures than a Transition Temperature, the ignition delay is largely determined by physical factors. A new theoretical concept of the spontaneous ignition and ignition delay of a fuel drop is introduced; diffusion is an integral part of this concept. This concept predicts the effect of pressure on ignition delay. Excepting spheroidal evaporation, a flame presence has a small influence on the evaporation lifetime of a drop on a heated surface. It is shown that the evaporation lifetime of a drop on a heated surface may be much less than the combustion time. Physical factors are primarily responsible for the dirty combustion of a n-Hexadecane drop. It is shown that the dirtiest combustion is obtained when the air temperature and pressure are close to and below the critical temperature and pressure of the fuel; clean combustion is obtained at reduced pressures greater than approximately four.

This thesis is concerned with the vibrational characteristics of pre-twisted cantilever beams of uniform cross-section allowing for shear deformation and rotary inertia. A method of solution of the differential equations of motion allowing for shear deformation and rotary inertia is presented which is an extension of the method developed by Dawson for the solution of the differential equations of motion of pre-twisted beams neglecting shear and rotary inertia effects. This method consists in transforming the original equations into a set of first order differential equations and solving by Runga-Kutta step-by-step integration method. The method has been programmed for an Elliot-503 computer in Algol language and the natural frequencies and mode shapes of vibration are obtained for various breadth to depth ratio beams of lengths ranging from 3 inches to 20 inches ana pre-twisted angle up to 90 degrees, for up to fifth mode of vibration. The results are compared with other investigators work where available and good agreement is obtained. The natural frequencies and mode shapes of vibration are obtained by experiment and are compared to theoretical results. The effect of the variation of the shear stress factor upon the natural frequencies and mode shapes of vibration of pre-twisted cantilever beams is also examined.

The object of this investigation was to compare the relative merits of eccentric and segmental orifice plates as a flow measurement device, and to collect sufficient experimental data to enable a national standard to be prepared. In view of the statistical aspect of the work the experimental programme had to be extensive. Some 600 flow tests involving over 1500 differential pressure readings were carried out using incompressible fluids. A number of pitot traverses and friction factor tests were made to augment the discharge coefficient data on secondary influences. Two computer programmes were devised to facilitate the processing and interpolation of the experimental data obtained. Basic discharge coefficient values were obtained for pipes of 6", 8" and 12" in diameter. In the case of eccentric orifices these values are in good agreement with the corresponding data obtained by other researchers (Beitler, West). Segmental orifices data, on the other hand, though close to Witte's results showed on average a 3% discrepancy from Lohman's and nearly 8% from Beitler's results. The effect of pipe roughness and asymmetrical velocity distribution on the value of the discharge coefficients were investigated, and found to be of the same order as in the concentric orifice plates. The major part of the investigation (over 50 pages) deals with the influence of pipe roughness on the discharge coefficients of segmental orifice plates. This aspect of flow measurement, although recognised now as of considerable importance, has not been studied extensively partly because of the complex experimental technique required to produce reliable results on naturally roughened pipes. This technique is discussed in detail, and a computer programme devised to prepare comprehensive tables of correction factors. A comparison of the two types of devices tested shows that the eccentric orifice plate:- 1. is easier to manufacture (and consequently less likely to have manufacturing errors); 2. has a more constant discharge coefficient as a function of area ratio (only 5% variation compared with over 10% for segmental); 3. has a more constant discharge coefficient as a function of pipe size (less than 1/2% variation compared with 3-4% for segmental), particularly at very low and very high area ratios. 4. provides less effective passage for solids in suspension, where errors are likely due to accumulation of material. For these reasons, eccentric orifice plates give more accurate results in most industrial applications, except in those cases where the size of particles in suspension, or extremely low velocity of flow, are likely to cause build up of material on the front face of the plate. With the addition of comprehensive data from this investigation it will now be possible to draft both a national and an international standard on the use of eccentric orifice plates for flow measurement. However, there is as yet no comparable confidence in the validity of the data on segmental orifice plates. More work will have to be completed before a reliable standard could be drafted. It is hoped, above all, that this work, in addition to providing useful data, has thrown new light on this neglected aspect of flow measurement.