Scaling of cylinder-generated shock-wave/turbulent boundary-layer interactions

Abstract

Scaling parameters of shock-wave/turbulent boundary-layer interactions generated by a semi-infinite standing cylinder were explored in a combined numerical and experimental effort, consisting of Reynolds-averaged Navier–Stokes simulations and high-speed schlieren imaging. The primary interaction variable, the cylinder diameter (d), and a secondary interaction variable, the boundary-layer thickness ($$\delta $$), were varied to study the effects of the parameter $$d/\delta $$. This was found to be an appropriate scaling parameter for mean features. The characteristic interaction variables (the maximum separation distance, S, and the triple-point height, $$h_\mathrm{tp}$$) followed a linear trend when normalized as $$S/\delta $$ and $$h_\mathrm{tp}/\delta $$; however, when the boundary layer became larger than the cylinder diameter, a power law trend became more representative. The parameter $$d/\delta $$ also determined the role that viscous effects have on the strength of the interaction, where a lower $$d/\delta $$ was characterized by a greater interaction scale and lower surface pressure peaks. Moreover, the high surface pressure on the cylinder leading edge due to the Edney interaction was found to be reduced for $$d/\delta \le 0.45$$, as the boundary layer encompassed the lambda-shock structure. Trends in the shapes or peaks of the auto-spectral density function were not observed based on $$d/\delta $$, but appeared to be dominated by broadband low-frequency ($$f < 1~\hbox {kHz}$$) content. While the position and structure of the interaction may change as a result of varying $$d/\delta $$, the effects on the unsteady dynamics were minimal.