Investigation of Shock Front Topography in Shock Tubes

Citation

Bowman, Robert Marcus (1966) Investigation of Shock Front Topography in Shock Tubes. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/XPM1-ZZ53. https://resolver.caltech.edu/CaltechETD:etd-12082005-105038

Abstract

An experimental investigation of the shape of shock waves in a circular shock tube is conducted. It is found that there are three distinct regimes governed, in a given tube, by the initial pressure in the test section.

At very low pressures, where the shock thickness is greater than about half the tube radius, the axial extent (deviation from a plane) of the shock is roughly constant and dominated by the viscous interaction between the "shock", the boundary layer, and the driving piston of gas. This range of pressures is called the viscosity-dominated regime.

At intermediate pressures, the shape of the shock is very nearly that predicted by the theory of de Boer, the shock curvature being produced by the boundary layer and the axial extent being roughly inversely proportional to the square root of the initial pressure. This is the boundary layer regime. de Boer's work is extended and the shock shapes for both the two-dimensional and axisymmetric cases are computed and plotted.

At high pressures, the shape of the shock is complex and varies periodically down the tube. This shape is determined by transverse waves produced at the diaphragm (or other upstream disturbance) and reflecting back and forth across the tube, decaying with the square root of the distance down the tube. In this transverse wave regime, the axial extent of the shock is essentially independent of initial pressure and is much greater than had been expected.

The square root decay of the transverse wave disturbances is in contrast to the 3/2 power decay predicted by Freeman and apparently verified by Lapworth. The experimental data of Lapworth is re-plotted and it is shown that if this data is analyzed in a slightly different manner it appears to exhibit square root decay.

It is shown that the shock perturbations which exist in the transverse wave regime are absent at lower pressures. The transition region where these disturbances suddenly disappear seems to correspond approximately to the initial pressure at which the boundary layer (appropriately defined) at the disturbance fills the tube.

A rule of thumb is developed from which it should be possible to predict the transition initial pressure (which separates the transverse wave and boundary layer regimes) in any given shock tube. This pressure occurs when the quantity L/p₁R² is of order one, the tube dimensions being in millimeters and the initial pressure in millimeters of mercury. This rule of thumb is used to analyze the results of several shock tube experiments published by other researchers.

Using this rule of thumb as an important constraint, a low pressure shock tube design chart is developed, from which, given the type of experiments contemplated and the nature of the instrumentation available, the proper shock tube dimensions and operating pressures may be determined.

Finally, avenues of future research are suggested, wherein it may be possible to design a new type of "hi-fi" shock tube, capable of producing more nearly plane shock fronts for use in shock structure and relaxation time studies, especially where methods such as integrated schlieren, optical reflectivity, or electron beam scattering are to be used.

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