Experimental investigation of the Chester problem with weak shock waves propagating in converging ducts with quasi-steady flow

Abstract

The Chester problem (Adv. Appl. Mech. 6:119–152, 1960) introduces a quasi-one-dimensional (quasi-1D) analytical solution developed by Chester based on Chester–Chisnell–Whitham (CCW) theory (Proc. R. Soc. Lond. A 232:350–370, 1955; Lond. Edinb. Philos. Mag. 45:1293–1301, 1954; J. Fluid Mech. 2:286–298, 1957; J. Fluid Mech. 4:337–360, 1958) addressing the interaction between a steady flow within a converging–diverging duct and a shock wave entering from the converging section. Although Chester’s solution provided approximate results for both weak and strong shock waves, this study derives a solution without limitations on the shock Mach number. Additionally, experiments were conducted using a three-channel shock tube, equipped with two diaphragms with adjustable relative rupture timings, to investigate the interaction between the flow and weak shock waves (shock Mach number 1.01–1.10) in the converging section, where the lower wall is flat. The shock wave reflects off the converging upper wall; however, at particularly low shock Mach numbers, the arrival of the reflected wave at the lower wall is delayed. In such cases, the shock wave near the lower wall, which remains unaffected by duct compression, diverges from the quasi-1D solution, and the pressure behind the shock wave is reduced by the upstream co-directional flow. These findings confirm that the shock wave can be attenuated by the non-turbulent, steady upstream flow.