On some aspects of the use of shock tubes in aerodynamic research

Abstract

Interest has recently been revived in an apparatus which was first developed fifty years ago. This apparatus, which is known today as a shock tube, consists of a simple duct which may be closed or open at one end, and closed at the other end. A diaphragm divides this duct into two compartments which initially contain gases at different pressures. When the diaphragm is ruptured, an unsteady gas motion ensues. A survey of existing shock tube theory and experimental results has been conducted; particular emphasis was placed on the features of actual shock tube flow which diverged from ideal non-viscous theory. A basic ideal shock tube theory has been formulated in detail; using those parameters which have greatest practical significance, and subsequently, performance charts affording a rapid method for the aerodynamic design of shock tubes using air as the working fluid have been developed. Experimental results diverge from the simple ideal theory mentioned above, principally because viscous effects are present in actual shock tube flow. Careful analysis of available experimental data yielded a series of important parameters which should be incorporated in any modified theory of shock tube flow. A new analytical approach led to the development of a theory of shock tube flow which included the effects of boundary layer growth on the walls of the shock tube and explained severaI features of the actual flow patterns which are at variance with ideal non-viscous theory. As presented herein, the theory is restricted to shock tube flows where the shock wave is weak, and the boundary layers on the walls of the tube are laminar and incompressible. The complete Solution of shock tube flow including the effects of viscosity is a formidably difficult problem, but it is hoped that the present analysis may be a useful first step towards the full solution. As a parallel study with the above theoretical work, the design and construction of a shock tube installation was undertaken. Low cost was one of the main criteria of this design, and a shock tube made of mahogany was finally selected. (The Bristol shock tube is believed to be the first employing wooden construction.) Ancillary equipment was developed for the installation, and particular attention was given to the optical and electronic equipment. The development of the apparatus, and principally that of the electronic instrumentation, took considerable time; but a detailed calibration of the shock tube was ultimately carried out. Finally, timed photographs of the transient diffraction of a shock wave over a wedge were obtained; this illustrated one main. application of the shock tube, that is, the study of unsteady flows. In conclusion, the probable future development and uses of shock tubes in aerodynamic research is discussed in the light of recent experimental and theoretical work.