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.
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