The ability of a finite roughness element to suppress the hypersonic second-mode instability on a cone is explored. A new code for simulating discrete roughness using a body-fitted grid over an analytic shape is developed. Linear stability analysis is performed on the Mach 8 meanflow of a 7 • half-angle straight cone. The resulting N-factor analysis determines the second-mode frequency of 240 kHz to most likely to lead to turbulent transition. A phase velocity plot of the hypersonic modes is obtained and the resulting synchronization location of s=0.2436 meters is determined. This led to the design and placement of a roughness element that will effectively suppress the targeted disturbance frequency. An unsteady simulation with a blowing-suction actuator, upstream of the roughness element, introduces a pulse with a nominal frequency content up to 1 MHz. FFT's of the pulse's history for a roughness case and a no-roughness case are computed and compared. Frequencies 218 kHz and higher are suppressed while lower frequencies are amplified, effectively showing that the roughness element is able to suppress the target disturbance frequency.

Recent studies by Fong et al. (2012, 2013, 2014, 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 researches 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 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.

A computational fluid dynamics study is conducted in which acoustic-like waves are observed emanating from the boundary layer of a Mach 8 slender blunt cone with a relatively low freestream enthalpy and a warm wall. The acoustic-like wave emissions are qualitatively similar to those attributed to the supersonic mode. However, the supersonic mode responsible for such emissions is often found in high-enthalpy flows with highly cooled walls, making its appearance here unexpected. Linear stability analysis on the steady-state solution reveals an unstable mode S (Mack's second mode) with a subsonic phase velocity and a stable mode F whose mode F- branch takes on a supersonic phase velocity. It is thought that the stable supersonic mode F- is responsible for the acoustic-like wave emissions. Unsteady simulations are carried out using blowing-suction actuators at two different surface locations. The analysis of the temporal data and spectral data using Fourier decomposition reveals constructive/destructive interference occurring between a primary wave packet and a satellite wave packet in the vicinity of the acoustic-like wave emissions. The constructive/destructive interference between the wave packets also appears to have a damping effect on individual frequency growth in both unsteady simulations. Based on this study's results and analysis, it is concluded that a supersonic discrete mode is not limited to high-enthalpy, cold wall flows and that it does appear in low-enthalpy, warm-wall flows; however, the mode is stable.

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