On flow duration in low-pressure shock tubes

The severe decrease of flow duration in shock tubes operating at low pressures, previously reported by Duff, is confirmed by experiment and by an analysis of the effects of the laminar-boundary layer behind the shock wave. The latter leads to a shock tube similarity length parameter X, which depends on the tube pressure, diameter and shock Mach number, and to a flow duration parameter T. The theoretical relation T = T(X) is determined and compared with experimental results. From the theoretical result Tmax = 1, the maximum possible flow duration τm in a shock tube is determined; it increases linearly with the initial pressure and the square of the tube diameter and decreases strongly with shock Mach number.