A Study of the Shape of Low Amplitude Shock Waves in a Shock Tube

Abstract

A simple form of the shock tube consists of two pieces of tubing separated by a thin air-tight diaphragm. After a pressure difference is created across the diaphragm, it is ruptured. The resulting rush of air from the high pressure side (compression section) into the low-pressure side (expansion section) forms a one-dimensional shock wave. Simple acoustic theory predicts that the shock wave will be twice the length of the compression section, half the pressure difference in amplitude, and propagate unattenuated in the tube. However, a theory of shock waves based on dynamic relationships independently developed by Rankine and Hugoniot predicts that the front of the pulse will travel with supersonic speed into the undisturbed gas, while the tail of the pulse will travel with the small signal sound speed of the medium. As a result, the wave becomes distorted as it propagates. To investigate some of the phenomena described by these theories, a simple shock tube was constructed with which the speed of the shock front, and the shape of the shock wave, could be recorded for the same pulse. Basically, the Rankine-Hugoniot based theory was confirmed the shape of the shock wave did distort as it propagated. It was also found that the initial pulse length was dependent upon the pressure difference established across the diaphragm before it ruptured, and that the pulse strength did attenuate as it propagated.