Geometrical impedance matching for weak shock waves at shock tube end wall

When a shock wave encounters an interface with a medium of different acoustic impedance, a reflected wave is generated. It is a shock wave if the medium has a higher acoustic impedance or an expansion fan if the impedance is lower. When the acoustic impedances are perfectly matched, no wave is reflected—a phenomenon known as “impedance matching.” This study aims to achieve a similar effect by varying the geometry of the shock tube exit. Assuming a steady-state, quasi-one-dimensional and subsonic post flow, we derived the exit geometry condition under which neither shock waves nor expansion waves are reflected. To validate this condition, we conducted shock tube experiments with shock Mach numbers up to approximately 1.07, and found that the shock wave reflection behavior is influenced not only by the cross-sectional area ratio of the tube but also by the specific shape of the orifice. In tests with a simple converging orifice shape, a pressure spike occurred due to the leading reflected shock wave before the pressure stabilized. The overpressure of this spike was reduced to 7×10−3 times the pressure ahead of the spike by installing perforated sections and a porous metal body on the sidewall just upstream of the orifice. This study offers a new approach to suppress post-shock pressure fluctuations in practical applications such as high-speed trains entering tunnels and within exhaust pipes of internal combustion engines, as well as to extend the test duration of shock tube experiments.