Numerical and experimental study of shock waves emanating from an open-ended rectangular tube

Abstract

We examine the dynamics of a high-speed shock-induced flow near the open end of a shock tube using the particle image velocimetry (PIV) and the background oriented schlieren (BOS) methods along with two- and three-dimensional numerical simulations. In experiments, planar shock waves (\(M=1.3\)–1.6) are discharged from a rectangular (\(24\,\hbox {mm} \times 48\,\hbox {mm}\)) low-pressure section of a shock tube open to the atmosphere. Due to the rectangular exit geometry, the resulting flow is highly three-dimensional and, thus, more complicated, compared to well-studied circular/axisymmetric geometries. The study focuses on the spatio-temporal flow structure up to 1 ms after the shock wave diffraction. PIV and BOS visualization techniques share the same post-processing principle, and the iterative multi-step cross-correlation algorithm applied in the PIV software is adapted here for the calculation of background pattern displacement on the BOS images. Particular attention is given to the resolution of flow regions where sharp gradients are present, such as a diffracted shock front or embedded shocks. Computational fluid dynamic simulations of the problem are also conducted to validate the experimental results and methods and to gain more insight into the three-dimensional flow dynamics. PIV and BOS images are found to be consistent with the corresponding numerical flow visualizations.