Coherent turbulence and entrainment in a supersonic, axisymmetric, separated/reattaching shear layer

The influence of coherent turbulent structures on the entrainment characteristics of a separated shear layer in a Mach-2.49 longitudinal cylinder wake is investigated using stereoscopic particle image velocimetry (SPIV). Three thousand non-time-correlated velocity field measurements, acquired along a plane coincident with the central axis, were decomposed into modes using the snapshot proper orthogonal decomposition (POD) method. The second and third POD modes identified high-energy velocity fluctuations aligned with consistent directions in the separated shear layers, near the boundaries of the recirculation region. Previous work by the authors has demonstrated, using tomographic PIV, that these directionally consistent velocity fluctuations identified by the POD modes are caused by three-dimensional (3D) coherent upright and inverted hairpin vortex structures in this flow. The SPIV velocity field snapshots were conditionally sorted based on the value of their corresponding POD amplitude coefficients, and conditional statistics from these subsets of snapshots were used to derive results in the current work. It is demonstrated that a higher statistical prevalence of upright hairpin vortices in the shear layer directly correlates with reduced shear layer growth rates, and a subsequent increase in the reattachment length. Conversely, a higher statistical prevalence of inverted hairpin vortices correlates with increased shear layer growth rates, and a subsequent reduction in the reattachment length. Comparisons of conditional statistics for the SPIV data are drawn with previous laser Doppler velocimetry measurements acquired in a 5 degrees boat-tailed cylinder configuration of this flow. These comparisons demonstrate clear similarities of important features between the two flows, such as an increase in the reattachment length when compared to the unconditional blunt-based cylinder flow, which is indicative of higher cylinder base pressures and subsequently reduced pressure drag.