Reflection of a weak shock wave from a perforated plug

Abstract

A plane shock wave is assumed to be incident upon a solid surface that is perforated by a number of closely spaced holes of length L and radius a, where a/L≪1, and the problem is to determine the character of the reflected wave field. The latter is essentially determined when the rate of inflow from the ambient atmosphere to the perforated plug is known, and the majority of the effort in this paper is devoted to the evaluation of this quantity. The assumption that the incident wave is weak is made throughout. Results show how the reflected wave field depends upon L and a and upon the acoustic-impedance ratio of the ambient air and the air within the slender tubes; the latter may be influenced by the distensibility of the tubes, although this matter is not pursued here. It is theoretically possible for reflected-shock strengths to exceed the solid-wall value for short intervals of time. Qualitative comparisons of the present theory with some existing observations of rather strong-shock reflection from perforated plugs lend support to the predictions, especially in the situation for which viscous effects are slight.