Physics of unsteady cylinder-induced shock-wave/transitional boundary-layer interactions

Abstract

Given the current lack of experimental data for shock waves interacting with incoming transitional boundary layers, the goal of this study was to characterize the dynamics of such an interaction to better understand the fundamental fluid physics of these complex phenomena. Here, the mean flow field and time-dependent characteristics of a three-dimensional Mach 5 cylinder-induced shock-wave/boundary-layer interaction where the upstream boundary layer is transitional, have been studied experimentally. The interactions were generated with a right circular cylinder mounted on a flat plate. Streamwise–spanwise planar laser scattering from a condensed alcohol fog and schlieren imaging were used to characterize the mean and instantaneous structure of the interaction, and fast-response wall-pressure measurements on the centreline upstream of the cylinder enabled characterization of the unsteadiness. The pressure measurements show a mean pressure profile that resembles a composite of an upstream laminar profile and a downstream turbulent profile. The upstream influence location of the transitional interaction was approximately 8.5 diameters ( $d$ ) upstream of the cylinder leading edge, which is between that of a laminar and a turbulent interaction, and is followed by a plateau region to approximately $4d$ upstream of the cylinder. The plateau region is a region with a thicker boundary layer and possible flow separation. The plateau pressure was within 7 % of the value predicted by Hill's correlation for free-interaction phenomena. Furthermore, a statistical analysis of the pressure histories suggests that the entire interaction stretches and contracts in concert. Power spectral densities of the pressure fluctuations showed unsteadiness throughout the interaction with energy content primarily centred between a region defined by a separation-length-based Strouhal number $St_{L} = 0.05\text {--}0.2$ , comparing well with other related studies of cylinder-induced interactions. Cross-correlations and coherence functions in the interaction suggest that the unsteadiness in the laminar region may be due to the entire ‘laminar’ region oscillating in response to the ‘turbulent’ unsteadiness of the intermittent region.