Browsing by Author "Cleaver, J. W."

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    Ablation studies of low melting point bodies in a pre-heated supersonic air stream
    (College of Aeronautics, 1960-02) Cleaver, J. W.
    This report is an investigation into the melting of axi-symmetric and two-dimensional bogies at a Mach No. of M[infinity] = 1.78 and stagnation temperatures up to 550 [degrees]K. In this temperature range, the most suitable material for the models was found to be an eutectic tin-lead alloy a melting point of 456 [degrees]K. For the cone and hemisphere-cone models two distinct modes of melting were observed. In cases where the estimated equilibrium surface temperature (Tw)o was approximately equal to the material melting temperature Tm, melting occurred only at the stagnation point of the model and was such that a flat surface normal to the gas stream always resulted. If the average rate of heat transfer at the air-liquid interface be defined as qi = LmPm x, where Lm is the latent heat of fusion, Pm is the density of the material and x is the rate of recession of the flat surface, it is found that qi decreases with increase of the radius of the flat nose. A very approximate theory is found to show some agreement with the experimental rates of heat transfer. When (Tw)o was considerably greater than Tm the flat surface was no longer preserved and the resulting steady ablating shape was paraboloidal in nature. When this occurred x was usually constant. This allowed some average steady state heat transfer rates to be evaluated and compared with theory. Preliminary tests were also made with a two-dimensional wedge model.
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    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.
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    The two-dimensional flow of an ideal dissociating gas
    (College of Aeronautics, 1959-12) Cleaver, J. W.
    By neglecting viscosity, heat conduction and diffusion, a method for investigating the effect of dissociaion on the two dimensional flow of a high temperature supersonic gas stream has been examined. The ideal ‘oxygen-like’ gas introduced by Lighthill (1957) has been used and in all cases the internal modes of the molecules are assumed to be instantaneously adjusted to be in equilibrium with each other. A brief introduction to the ideal dissociating gas and the rate equation is given and then the partial differential equations governing the motion of this ideal gas are treated by a standard characteristic method. Due to the entropy production associated with the chemical reactions, analytical solutions are not possible, and a numerical step-by-step method is used to obtain a solution. As an application of the method developed the flow field around a sharp corner of an ideal dissociating gas is examined and a limited investigation of the free stream conditions and expansion angle on the resulting relaxation zone has been given.