Roughness effect on hypersonic second mode instability and transition on a cone

Recent studies by Fong et al. [“Finite roughness effect on modal growth of a hypersonic boundary layer,” AIAA Paper No. 2012-1086, 2012; “Stabilization of hypersonic boundary layer waves using 2-D surface roughness,” AIAA Paper No. 2013-2985, 2013; “Numerical simulation of roughness effect on the stability of a hypersonic boundary layer,” Comput. Fluids 96, 350–367 (2014); and “Second mode suppression in hypersonic boundary layer by roughness: Design and experiments,” AIAA J. 53, 1–6 (2015)] have shown that finite roughness can attenuate Mack's second mode instability when placed at the discrete mode synchronization location for two-dimensional planar flow over a flat plate. However, more practical hypersonic flows are non-planer conical flows, and the roughness effect phenomenon in conical flows has not been extensively investigated. For that reason, this investigation research the ability of finite roughness strips to attenuate the second mode instability on a Mach 8 straight blunt cone with a freestream unit Reynolds number of 9 585 000. Two roughness configurations are studied: a single roughness strip and an array of six sequential strips. N-factor calculations determine the second mode frequency most likely to lead to turbulent transition, and the linear stability theory is used to determine the mode's synchronization location. In the unsteady simulations of the roughness configurations, a blowing-suction actuator introduces an upstream broadband Gaussian pulse. Fourier decomposition of the pulse's history shows that the single roughness strip attenuates frequencies higher than 208 kHz while lower frequencies are amplified. Likewise, the roughness array exhibits similar results, attenuating frequencies higher than 164 kHz and amplifying lower frequencies downstream. The results show that both configurations can delay second mode instability growth on a hypersonic blunt cone and possibly delay turbulent transition. However, investigations of the roughness effect's behavior downstream of the roughness configurations show that disturbance growth resumes and becomes more destabilizing to the boundary layer.