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The waves propagating from an oscillating plane piston into a vibrationally relaxing gas are calculated by an exact numerical method ignoring viscosity and heat conduction. Secondary effects due to the starting of the piston from rest and to acoustic streaming can be eliminated from the calculated flows, leaving a truly periodic progressive wave which can be analysed and compared with approximate solutions. It is found that for moderate amplitude waves nonlinearity is only important as a convective effect which produces higher harmonics, whereas dissipation is adequately described by linear theory.
Jets from notched nozzles are investigated by schlieren photography and pressure traverses. It is demonstrated that the dominant feature of the flow which determines the structure far downstream is the trailing vortices shed from the swept edges of the notches.
The method of characteristics is used to calculate the supersonic flow past a wedge of small angle with non-equilibrium effects. The wave decay and development distances are presented in a concise similarity form which permits accurate extrapolation to very weak waves. The numerical solutions are compared with shock-tube flows of CO2 and N2O.
A method is presented for determining the swirling compressible flow through a nozzle, given conditions at a reference section. The principal assumption is that changes in the nozzle cross-sectional area are sufficiently gradual for the radial velocity component to be neglected at each section, i e, the usual assumption of one-dimensional compressible flow theory. This method is used to determine choked-flow conditions in the case where there is solid-body rotation at the throat for a range of swirl intensities with the ratio of the specific heats taking various values. Mass-flux coefficients and impulse functions are determined. Sonic surfaces, velocity profiles and other characteristics of interest are also presented. An approximate analysis valid for low swirl intensities is developed and analytical formulae are derived for most quantities of interest. The main conclusion of practical importance is that the introduction of swirl to compressible nozzle flows need not lead to a significant reduction in specific thrust. Further exploration of the possible effects of swirl on noise during the relatively short take-off and landing periods cannot therefore be ruled out on the grounds that swirl would lead to excessive thrust losses.
An approximate expression is given for the thickness of weak fully dispersed shock waves. Using available data on the thermodynamic properties of air, it is shown that shocks of the strength expected in sonic bangs are fully dispersed. Estimated relaxation times for dry and humid air lead to wide variations in possible thickness, varying from millimetres to metres.
The one-dimensional problem of shock-wave reflexion with relaxation is treated numerically by combining the shock-wave, characteristic, and Rayleigh-line equations. The theoretical results are compared with pressure and density measurements in CO2, and the agreement is found to be excellent.
Rotating-Drum (or mirror) cameras have often been used in conjunction with schlieren apparatus to investigate the performance of shock tubes. In the conventional arrangement the working section is viewed through a slit parallel to the axis of the tube, which is also parallel to the drum axis. The photographic record obtained on a film attached to the drum represents the distance-time (x, t) diagram of the propagation of (density) disturbances in the working section. The quantitative information obtainable from such records is usually limited to the speed of propagation of such disturbances.
The detailed structure of the relaxation region in shock waves in oxygen was investigated using Blackman's experimental results. Oxygen was found to display a behaviour similar in many ways to that found previously for carbon dioxide with the relaxation frequency, as defined by the simple relaxation equation, depending on the departure from equilibrium as well as on temperature. The previous results for carbon dioxide were further analysed by means of a separate relaxation equation for each mode.