CoA. Memoranda: Aero (1964-1968)
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Item Open Access Boundary layers with suction or injection(College of Aeronautics, 1964-09) Stevenson, T. N.Approximate integral equations are derived for the compressible laminar boundary layer with arbitrary pressure gradient and arbitrary suction or injection velocity through a porous wall, Reasonable agreement is obtained when particular solutions to the integral equations are compared with solutions by previous authors. Experiments in an incompressible turbulent boundary layer over a porous surface reveal two laws for the inner and cuter regions; laws which correlate previous experimental results. The lams are used to calculate shear distributions and variations of skin friction with Reynolds number and enable Preston tubes to be used to estimate skin friction over a porous surface. The outer region theory is extended to boundary layers in small pressure gradients and at separation. The only universal functions required are obtained from zero pressure gradient flow. No other constants are used to calculate the mean velocity profiles for boundary layers in small pressure gradients, with suction or injection and at separation or reattachment. The theory agrees with the available experimental results for turbulent boundary layers in energy equilibrium. Experiments in folly developed pipe flow show haw the mean flow is altered when there is suction through a porous section of the pipe. An approximate theory for the inner region compares reasonably well with the experiments for small suction velocities.Item Open Access Non-equilibrium flow in plane expansion waves(College of Aeronautics, 1964-06) Cleaver, J. W.The non-equilibrium supersonic flow of a relaxing or reacting gas through a plane expansion has been studied from a numerical,, analytical and experimental point of view. The flow of an ideal dissociating gas in a two dimensional expansion has been solved numerically by writing the governing equations of motion in their characteristic form. In conflict with linearised theory along the wall, the numerical solutions do not asymptote to the infinite rate equilibrium values. To estimate how far the asymptotic state deviates from the infinite rate equilibrium values, a formal second order solution has been developed with the aid of transform techniques. An example has been discussed for a simplified relaxing gas model, and estimates of the asymptotic state have been obtained. An exact solution over the whole field was not possible but by treating the parameter as small, an approximate answer has been found. To understand in more detail the coupling effects of two relaxation processes, linearised theory has been extended to cope with the flow of a gas with more than one relaxing mode. An example has been discussed far Carbon Dioxide and the effect of possible coupling between the bending and stretching modes of the molecule in a plane expansion has been investigated. The Mach-Zehnder interferometer and Schlieren method have been used in conjunction with a 2" - diameter shock tube to study the density and density gradients within, and following a sharp two-dimensional expansion for shock heated Carbon Dioxide. Measurement of the density gradient at the leading edge of the expansion by quantitative Schlieren methods have allowed relaxation times to be obtained. This method has the advantage that relaxation times can be obtained for specific values of the density and temperature for only small departures from an equilibrium state.Item Open Access Optimum structures(College of Aeronautics, 1965-07) Hemp, W. S.; Chan, H. S. Y.The design of the best structure for a given purpose depends upon the criterion used for optimisation. Structures may be designed to safely transmit a given system of forces using the least weight of material.. They may also be designed to have maximum stiffness of a certain type for a given weight or alternatively to have the greatest possible fundamental frequency of vibration. These problems, although in general distinct from one another, are closely related and much can be achieved towards maximisation of stiffness and frequency by the use of minimum weight designs. In fact it can be shown that a minimum weight framework is the stiffest structure of that weight for the force system, which it is designed to carry.x The present report is concerned exclusively with the problem of the design of structures of minimum weight, which are required to transmit specified forces. Some attention will be given to frameworks because, in particular, methods of approximate numerical analysis are more readily formulated for this type of structure, but the main emphasis will be placed upon the design of structures formed from plates of variable thickness reinforced by direct load carrying members. See para,l.4Item Open Access Effect of engine, tank and propellant specific cost on single stage recoverable booster economics(College of Aeronautics, 1964) Carton, Dennis S.Reusable first stages using hydrogen-oxygen, hydrogen-fluorine and kerosine-oxygen are compared with non-reusable stages using a solid in addition to the liquid combinations. The criterion used for comparison is the minimum specific cost of the "loaded and ready for launch" stage cost per unit of stage payload mass. A closed form relationship is used in which the empty stage mass without payload is taken to scale in part proportional to propellant mass, and in part to mass flow rate. The stage specific cost is proportional to specific cost of engine (or nozzle) tank and propellant. In the second part the hydrogen-oxygen combination is consiaered,in more detail. The sensitivity of the results to changes in various specific costs including that of refurbishing are described. Throughout, the stage velocity increments are compared in the 3000-6000 metres/second range with losses.Item Open Access Shock wave structure in highly rarefied flows(College of Aeronautics, 1964-07) Battat, D.The Boltzmann equation is written in terms of two functions associated with the gain and loss of a certain type of molecule due to collisions. Its integral form is then applied to the problem of normal shock structure, and an iteration technique is used to determine the solution. The first approximation to the velocity distribution function of the Chapman-Enskog sequence, which leads to the Navier-Stokes equations, is used to initiate the iteration scheme. Expressions for the distribution function and the flow parameters pertinent to the first iteration are derived and show that the B-G-K model results can be obtained as a special case. This model is found to be valid in the continuum regime only, and is consequently limited to the study of strong shocks. In the present treatment the iteration is carried out on the distribution function and the analysis indicates that the method is equally valid for variations in both Mach and Knudsen numbers. Finally, the results of the first approximation are simplified, and expressed in a form suitable for numerical computation, and the range of their validity is discussed. The method should be equally suitable for other flow problems of linear or nonlinear nature.Item Open Access A note on the decay of aircraft trailing vortices(College of Aeronautics, 1964-03) Lilley, G. M.An elementary theory of aircraft trailing vortex decay is presented based on an assumed law for the variation of the mean eddy viscosity with distance from the wing. This law is based on the experimental data of Rose and Dee (1.963). The analysis gives results, as might be expected, in agreement with their data. The justification for the analysis must however be in doubt until more data are available covering a wide range of variables such as aircraft size, distance, incidence, etc.Item Open Access Various optimisation methods for preliminary cost and mass distribution assessment for multistage rocket vehicles(College of Aeronautics, 1964) Kalitventzeff, B.Preliminary staging studies of multi-stage space launchers are described. Both propellant and thrust scaling factors are used, and also cost parameters for propellant, propellant scaling units and thrust scaling units. The general minimum cost study, including reusable stage(s), turns out to be a generalisation of the optimisation method of the payload ratio, for specified mission requirement. Both studies lead to a velocity increment distribution between the stages, based upon optimum initial acceleration for each stage. The similarity between this analysis and that developed by Vertregt, Hall and Zambelli, and others is pointed out. Penalties for non-optimum solutions are also considered.