Skip to main content Accessibility help
×
Home

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

  • Richard E. Kennedy (a1), Stuart J. Laurence (a1), Michael S. Smith (a2) and Eric C. Marineau (a2)

Abstract

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.

Copyright

Corresponding author

Email address for correspondence: rkenn@umd.edu

References

Hide All
Berridge, D. C., Ward, C. A. C., Luersen, R. P. K., Chou, A., Abney, A. D. & Schneider, S. P.2012 Boundary-layer instability measurements in a Mach-6 quiet tunnel. AIAA Paper 2012-3147.
Casper, K. M., Beresh, S. J., Wagnild, R. M., Henfling, J. F., Spillers, R. W. & Pruett, B. O. M.2013 Simultaneous pressure measurements and high-speed schlieren imaging of disturbances in a transitional hypersonic boundary layer. AIAA Paper 2013-2739.
Chang, C. L., Vinh, H. & Malik, M. R.1997 Hypersonic boundary-layer stability with chemical reactions using PSE. AIAA Paper 1997-2012.
Chokani, N. 2005 Nonlinear evolution of Mack modes in a hypersonic boundary layer. Phys. Fluids 17, 014102.
Chou, A., Balakumar, P. & Schneider, S. P. 2017 Development of instabilities generated by freestream laser perturbations in a hypersonic boundary layer. AIAA J. 55 (3), 799807.
Grossir, G., Masutti, D. & Chazot, O.2015 Flow characterization and boundary layer transition studies in VKI hypersonic facilities. AIAA Paper 2015-0578.
Hargather, M. J. & Settles, G. S. 2012 A comparison of three quantitative schlieren techniques. Opt. Lasers Engng 50, 817.
Hofferth, J. W., Humble, R. A., Floryan, D. C. & Saric, W. S.2013 High-bandwidth optical measurements of the second-mode instability in a Mach 6 quiet tunnel. AIAA Paper 2013-0378.
Johnson, H. B. & Candler, G. V.2005 Hypersonic boundary layer stability analysis using PSE-Chem. AIAA Paper 2005-5023.
Kennedy, R. E., Laurence, S. J., Smith, M. S. & Marineau, E. C.2017 Hypersonic boundary-layer transition features from high-speed schlieren images. AIAA Paper 2017-1683.
Kimmel, R. L. & Kendall, J. M.1991 Nonlinear disturbances in a hypersonic laminar boundary layer. AIAA Paper 1991-0320.
Lafferty, J. F., Coblish, J. J., Marineau, E. C., Norris, J. D., Kurits, I., Lewis, D. R., Smith, M. C. & Marana, M.2015 The Hypervelocity Wind Tunnel No. 9 – continued excellence through improvement and modernization. AIAA Paper 2015-1340.
Laurence, S. J., Wagner, A. & Hannemann, K. 2016 Experimental study of second-mode instability growth and breakdown in a hypersonic boundary layer using high-speed schlieren visualization. J. Fluid Mech. 797, 471503.
Mack, L. M. 1975 Linear stability theory and the problem of supersonic boundary-layer transition. AIAA J. 13 (3), 278289.
Marineau, E. C., Moraru, C. G. & Daniel, D. T.2017 Sharp cone boundary-layer transition and stability at Mach 14. AIAA Paper 2017-0766.
Parziale, N. J., Shepherd, J. E. & Hornung, H. G. 2015 Observations of hypervelocity boundary-layer instability. J. Fluid Mech. 781, 87112.
Shumway, N. M. & Laurence, S. J.2015 Methods for identifying key features in schlieren images from hypersonic boundary-layer stability experiments. AIAA Paper 2015-1787.
VanDercreek, C. P., Smith, M. S. & Yu, K. H.2010 Focused schlieren and deflectometry at AEDC Hypervelocity Wind Tunnel No. 9. AIAA Paper 2010-4209.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

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

  • Richard E. Kennedy (a1), Stuart J. Laurence (a1), Michael S. Smith (a2) and Eric C. Marineau (a2)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed