Performance of a shock tube with a large-area contraction

An inviscid, analytical model is provided for shocktube performance when there is a large, abrupt contraction in the low-pressure side of a tube. The analysis is independent of initial high-pressure side conditions. Only the ratio of specific heats of the low-pressure gas, the large-diameter tube's incident shock Mach number, and the contraction ratio are needed for a nondimensional solution of the transmitted flow in the small-diameter tube. This solution is unique, readily evaluated, and various limits and constraints are discussed. Parametric calculations establish the increased magnitude of the transmitted shock Mach number relative to the shock Mach number for a tube without contraction. The Mach number increase, then increases the pressure and temperature downstream of the small-diameter tube's incident and reflected shocks, again relative to a tube without a contraction. Shock-tube performance, therefore, can be improved by the addition of a small-diameter tube to an existing tube's low-pressure side. The improvement can be used with a combustion-driven tube, a free-piston tube, etc.