Investigation of the second-mode instability at Mach 14 using calibrated schlieren

• Published in: Journal of fluid mechanics Vol. 845
• Main Authors: Kennedy, Richard E., Laurence, Stuart J., Smith, Michael S., Marineau, Eric C.
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 25.06.2018
• Subjects: Amplification; Bispectral analysis; Boundary layer; Boundary layers; Calibration; Computation; Density profiles; Experiments; Field of view; Fluid flow; Fluid mechanics; Hypersonic boundary layer; Instability; Interactions; JFM Rapids; Mach number; Mathematical models; Parabolized stability equations; Pressure; Reynolds number; Sensors; Solutions; Stability; Transducers; Tunnels; Visualization; United States > US; high-speed flow; boundary layer stability; transition to turbulence
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/jfm.2018.269

Second-mode wave growth within the hypersonic boundary layer of a slender cone is investigated experimentally using high-speed schlieren visualizations. Experiments were performed in AEDC Tunnel 9 over a range of unit Reynolds number conditions at a Mach number of approximately 14. A thin lens with a known density profile placed within the field of view enables calibration of the schlieren set-up, and the relatively high camera frame rates employed allow for the reconstruction of time-resolved pixel intensities at discrete streamwise locations. The calibration in conjunction with the reconstructed signals enables integrated spatial amplification rates ( $N$ factors) to be calculated for each unit Reynolds number condition and compared to $N$ factors computed from both pressure transducer measurements and linear parabolized stability equation (PSE) solutions. Good agreement is observed between $N$ factors computed from the schlieren measurements and those computed from the PSE solutions for the most-amplified second-mode frequencies. The streamwise development of $N$ factors calculated from the schlieren measurements compares favourably to that calculated from the pressure measurements with slight variations in the $N$ factor magnitudes calculated for harmonic frequencies. Finally, a bispectral analysis is carried out to identify nonlinear phase-coupled quadratic interactions present within the boundary layer. Multiple interactions are identified and revealed to be associated with the growth of disturbances at higher harmonic frequencies.