Shock Waves (1999) 9: 1–10 Evolution of shock waves and the primary vortex loop discharged from a square cross-sectional tube Z. Jiang, O. Onodera, K. Takayama Shock Wave Research Center, Institute of Fluid Science, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan Received 29 January 1998 / Accepted 22 May 1998 Abstract. In this paper, a numerical and experimental investigation of the evolution of a transmitting shock wave and its associated primary vortex loop, which are discharged from the open end of a square cross-sectional tube, is described. The experiments were conducted in the square tube connected to a diaphragmless shock tube and the flowfield was visualized from the axial direction with diffusive holo- graphic interferometry. The numerical simulations were carried out by solving the three-dimensional Euler equations with a dispersion-controlled scheme. The numerical results were displayed in the form of inter- ferograms to compare them with experimental interferograms. Good agreement between the numerical and experimental results was obtained. More detailed numerical calculations were carried out, from which the three-dimensional transition of the shock wave configuration from an initial planar to a spherical shape and the development of the primary vortex loop from a square shaped to a three-dimensional structure were clearly observed and interpreted. Key words: Numerical simulations, Holographic interferometry, Shock tube, Numerical flow visualization, Shock waves, Vortex loop 1 Introduction During the last decade, shock-wave propagation and shock-wave/vortex interactions have been intensively in- vestigated since these phenomena are believed to be closely linked with the randomization of turbulent flows and the dissipation of the mean flow kinetic energy. How- ever, most of the work conducted in the past was limited to two-dimensional cases. This is, presumably, due to the fact that the quantitative observation of three-dimensional shock waves and their induced vortices was hard to be conducted by using conventional optical flow visualization techniques, as well as three-dimensional numerical simu- lations requiring more efficient shock-capturing schemes and powerful computers. Therefore, progress in the study of three-dimensional propagation of shock waves and the vortex motion behind them has not been, so far, achieved as much as it is expected. One of the relatively straightforward ways to obtain three-dimensional shock waves and vortices in a labora- tory is to discharge a shock wave from the open end of a square cross-sectional tube into ambient air. The shock wave, so-called as transmitting shock wave, at the open end is initially planar, but it quickly develops into a spher- ical shape via three-dimensional transition with the elapse of time. Moreover, the primary vortex loop which develops at the edge of the open end behind the transmitting shock Correspondence to: Z. Jiang wave is square and co-planar at its initial stage, but de- forms quickly into a three-dimensional configuration with the propagation of the transmitting shock wave. The evolution of the transmitting shock wave from the square cross-sectional opening was clarified first by Abe and Takayama (1989). In their work, the three-dimen- sional motion of the primary vortex loop was also visu- alized by using double exposure holographic interferom- etry. This case, from then, became a benchmark test for both shock tube experiments and numerical simulations. Some studies related to this case were reported succes- sively later, for example, by Abe (1990), and Watanabe et al. (1991) to investigate further the shock wave diffraction by viewing it from the direction perpendicular to the shock tube. Recently, Golub et al. (1996) tried to visualize a sim- ilar case by using the schlieren method but viewing from the axial direction, and Onodera et al. (1998) obtained the axial view of the flowfield by using holographic interfer- ometry. The preliminary work reported by Onodera et al. (1998) shows that the axial view provides additional in- formation not only for shock wave motion but also for the primary vortex loop evolution. The further research work described here on this topic is based on the work by On- odera et al. (1998), and more numerical simulations were carried out to investigate the evolution of the transmitting shock wave and the instability of the primary vortex loop. In the experiment, the holographic observation was con- ducted by viewing the flowfield from the axial direction, instead of the side view or the corner view like those done