Small Perturbation Theory for Shock-Tube Attenuation and Nonuniformity

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Abstract
Closed form expressions are derived, based on the concept of self similarity, for evaluating small perturbations of shock tube flow due to the wall boundary layer. Ideal diaphragm rupture is assumed. Extensive numerical results are obtained for the perturbations induced by the boundary layer in the driven gas, assuming that the boundary layer is wholly laminar or wholly turbulent. The driven gas is taken to be air. Various driver gases are considered. Attenuation results are obtained for shock Mach numbers up to 20. It is shown that the effect of the driver gas boundary layer on perturbations in the driven gas is small for large diaphragm pressure ratios. The results indicate that a shock tube with an efficient driver, e.g., helium, should have less attenuation for a given shock Mach number than would an inefficient driver, e.g., air. The latter result disagrees with existing experimental data. The source of the discrepancy is not known.