Stability of Converging Cylindrical Shock Waves

Abstract

An experimental and numerical study was conducted on converging cylindrical shock waves. The goal of the present study was to clarify the nature of movement and instability in converging cylindrical shock waves. Experiments were conducted in an annular shock tube of 230mm outer diameter and 210mm inner diameter, connected to a cylindrical test section of 210mm diameter. Double-exposure holographic interferometry was used to visualize the converging cylindrical shock waves. Incident shock Mach numbers ranged from 1.1 to 2.0 in air. A numerical simulation was conducted using the total variation diminishing (TVD) finite difference scheme. It was found in the experiments that the shock wave configuration was initially cylindrical, but gradually deformed with propagation towards the center and finally showed mode-four instability. This is attributable to the existence of initial disturbances, which were introduced by the struts supporting the inner tube of the annular shock tube. This trend was significant for stronger shock waves, indicating that at the last stage of shock wave convergence each initial perturbation of the converging cylindrical shock wave was amplified to form the triple point of a Mach reflection. Numerical results correctly predicted the experimental trend.