Calibration of a shock tube by analysis of the particle trajectories




Whitten, Brian Thomas

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It can be shown that for the complete description of all the physical parameters in the flow behind an imtermediate strength unsteady shock, a knowledge of the particle trajectories within the flow is sufficient. This principle has been applied to determine the variation of the physical parameters throughout the length of a conventional shock tube. The particle trajectories were obtained by the high speed photography of cigarette smoke tracers, placed at 10 cm. intervals along the tube. By applying the conservation of mass equation to the particle trajectory data, the density variation was obtained throughout the flow including the rarefaction wave from the end of the compression chamber and behind the first reflected shock from the closed end of the expansion chamber. By means of the Rankine-Hugoniot relation, the pressures immediately behind the incident and reflected shock fronts were calculated, and by assuming isentropic flow between shocks along any particle trajectory, the complete pressure variation was determined. The temperature and local sound speed were subsequently calculated at all points and the particle velocities were determined from the time derivative of the particle trajectories. A complete mapping of all the parameters in the shock tube was thus obtained using a single photographic technique, which is simpler than previous methods.



particle trajectory, shock tube, Rankine-Hugoniot equation