Shock propagation through a local constriction

Abstract

The interaction of a moving shock wave with a localised constriction in a straight conduit is studied using large-eddy simulations, validated against time-resolved schlieren imaging and wall-pressure measurements from shock-tube experiments. The blockage ratio (0.35–0.75) and the normalised constriction length (0.25–2) are varied independently for two limiting geometric families, an abrupt rectangular constriction and a smoothly contoured sinusoidal constriction, at incident Mach numbers of 1.4 and 1.8. The start-up process within the constriction develops over time scales one to two orders of magnitude longer than the shock passage time, and in the sinusoidal family it follows two distinct pathways: shock-induced separation of an attached transonic flow in longer constrictions and acceleration of a separated jet in shorter ones. Despite these differences, the late-time reflected and transmitted shock strengths depend primarily on the blockage ratio, with constriction length and contour acting as secondary modifiers. We attribute this regularity to choking at an effective sonic area, and show that this condition supplies the closure required to predict both reflected and transmitted asymptotic shock-wave strengths, recovering reduced-order models developed here as limiting forms. The contraction coefficients required by this closure follow from the constriction geometry and the local flow analysis, without fitting. The predictions agree with the simulations to within approximately 1 % for the reflected shock and a few per cent for the transmitted shock. A reflection-corrected geometrical shock-dynamics formulation, closed by the same condition, reproduces the approach of the transmitted shock front to this asymptote for the smooth contours.