Dynamic structure of confined shocks undergoing sudden expansion

Abstract

The gas dynamic phenomenon associated with a normal shock wave within a tube undergoing a sudden area expansion consists of highly transient flow and diffraction that give rise to turbulent, compressible, vortical flows. These interactions can occur at time scales typically ranging from micro- to milliseconds. In this article, we review recent experimental and numerical results to highlight the flow phenomena and main physical mechanisms associated with this geometry. The topics addressed include time-accurate shock and vortex locations, flowfield evolution and structure, wall-shock Mach number, two- vs. three-dimensional sudden expansions, and the effect of viscous dissipation on planar shock-front expansions. Between axisymmetric and planar geometries, the flow structure evolves very similarly early on in the sudden expansion process (i.e., within the first two shock tube diameters). Both numerical and experimental studies confirm that the trajectory of the vortex formed at the expansion corner is convected into the flowfield faster in the axisymmetric case than the planar case. The lateral propagation of the vortices correlates very well between axisymmetric and planar geometries. In regard to the rate of dissipation of turbulent kinetic energy (TKE) for a two-dimensional planar shock undergoing a sudden expansion within a confined chamber, calculations show that the solenoidal dissipation is confined to the region of high strain rates arising from the expansion corner. Furthermore, the dilatational dissipation is concentrated mainly at the curvature of the incident, reflected, and barrel shock fronts. The multiple physical mechanisms identified, including shock–strain rate interaction, baroclinic effect, vorticity generation, and different aspects of viscous dissipation, have produced individual and collective flow structures observed experimentally.