Diffraction of a Shock Wave by a Cylinder

Abstract

The propagation of plane shock waves around cylinders of various radii was recorded with shadowgrams using a Cranz-Schardin multiple spark camera and with single Mach-Zehnder interferograms. The range of the incident shock Mach numbers extends from 1.04 to 2.2. Regular reflection and transition to Mach reflection are seen as the incident shock proceeds. From shadowgrams made at about 1 μsec intervals during this process the critical angle of transition was measured. The limiting angle of two shock theory fails to agree with the measured value. A theory of Whitham which requires the critical angle as well as the incident shock Mach number as initial values was applied to predict the triple point locus and the contour of the Mach stems. Numerical calculations using both the theoretical and the measured value of the critical angle for a fixed shock Mach number produced triple point loci lying close together. The predicted contour of the Mach stem and the density jump across it agree with the observations to within experimental error.