Stability of converging cylindrical shock waves.

Abstract

This paper reports primarily a study of cylindrical shock wave convergence in an annular shock tube. The goal of the present study is to clarify experimentally and numerically the instability of converging cylindrical shock waves. Experiments were conducted in the annular shock tube having 230mm o.d. and 210mm i.d. and a cylindrical converging test section of 210mm diameter. Optical flow visualization was carried out by double-exposure holographic interferometry. Shock Mach numbers range between 1.1∼2.0 in air. The numerical simulation was also conducted using the TVD finite difference scheme. It is found that although the initial shock configuration appeared perfectly cylindrical, the shock configuration was gradually deformed with propagation and showed mode-4 instability. This is attributable to the initial disturbances from the four struts which support the inner tube of the annular shock tube. This trend was even significant for larger shock Mach numbers. This revealed that large linear deformation of the converging cylindrical shock front results in the generation of the triple point of Mach reflection. The numerical results agreed with the experimental trend.