On the Reflection of Shock Waves from an Open End of a Duct

Abstract

The readjustment of the mean exit pressure to its steady-flow equilibrium level, following the arrival of a shock wave at an open end of a duct, has been investigated. For a cylindrical duct in which the gas is initially at rest, a solution based on acoustic theory was obtained in the form of a Fourier integral. The nature of this solution was established as a series of damped harmonic oscillations superposed on an exponential pressure decay. The actual pressure decay curve was obtained by numerical integrations. The same problem was also attacked experimentally using a shock tube of 3.23 inches i.d. From pressure records taken some distance from the open end, the ``effective'' exit pressure was derived. It was found that the exit pressure deviates appreciably from its steady-flow equilibrium value during a time in which a sound wave could travel about three duct diameters. Satisfactory agreement between theory and experiment was observed for shock pressure ratios up to about 1.9 (in air) although, near this limit, significant deviations owing to wall friction were observed toward the end of the pressure decay region. For still stronger shocks, the influence of the decay time on the phenomena inside the duct becomes unimportant while friction effects dominate. The possible significance of the lag in the establishment of steady-flow boundary conditions in practical applications is discussed, in particular, for cases where the acceleration of the gas by the reflected expansion wave may be of importance.