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Analysis of the hypersonic cross-flow instability with experimental wavenumber distributions

  • Harrison B. Yates (a1), Matthew W. Tufts (a2) and Thomas J. Juliano (a1)


Stationary cross-flow vortex N-factors were calculated over the surface of a yawed circular cone using computationally predicted and experimentally observed wavenumber distributions. Surface heat-flux data were obtained on a $7^{\circ }$ half-angle circular cone to investigate the behaviour of the stationary waves at different angles of attack and Reynolds numbers at Mach 6 under quiet-flow conditions in the Boeing/AFOSR Mach-6 Quiet Tunnel at Purdue University. A wavelet analysis was conducted on the experimental surface heat-flux data to construct a spatial mapping of the local largest amplitude wavenumbers of the stationary cross-flow waves, which were between 40 and 80 per circumference. Significant axial and azimuthal variation was observed. The results from the wavelet analysis were used to inform the stability analysis. The computed integration marching directions demonstrated very good agreement with the experimentally observed paths. N-factors were first calculated by integrating the local amplification rate corresponding to the most amplified experimental wavenumbers. The calculations were repeated based on non-dimensional computationally varying wavenumber ratios, which were dimensionalized by the experimental data. The computed N-factors showed good agreement between the two techniques. N-factors were also computed using the computationally predicted most unstable wavenumbers. The results showed decreased agreement with the other two cases, suggesting that this assumption does not properly model the cross-flow transition process.


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Adams, J. C. & Martindale, W. R.1973 Hypersonic lifting body windward surface flowfield analysis for high angles of incidence. Tech. Rep. 73-2. Arnold Engineering Development Center.
Balakumar, P. & Owens, L. R.2009 Stability of supersonic boundary layers on a cone at an angle of attack. AIAA Paper 2009-3555.
Balakumar, P. & Owens, L. R.2010 Stability of hypersonic boundary layers on a cone at an angle of attack. AIAA Paper 2010-4718.
Boyd, C. F. & Howell, A.1994 Numerical Investigation of One-Dimensional Heat-Flux Calculations. Tech. Rep. NSWCDD/TR-94/114. Dahlgren Division Naval Surface Warfare Center.
Cerasuolo, S.2016 Heat flux measurements by infrared thermography in the Boeing/AFOSR Mach-6 Quiet Tunnel. Master’s thesis, University of Naples Federico II.
Chang, C.2003 The Langley stability and transition analysis code (LASTRAC): LST, linear & nonlinear PSE for 2-D, axisymmetric, and infinite swept wing boundary layers. AIAA Paper 2003-0974.
Chang, C.2004a The langley stability and transition analysis code (LASTRAC) version 1.2 user manual. NASA Tech. Rep. 2004-213233. Langley Research Center.
Chang, C.2004b LASTRAC.3d: transition prediction in 3D boundary layers. AIAA Paper 2004-2542.
Chang, C.-L., Malik, M., Erlebacher, G. & Hussaini, M.1993 Linear and Nonlinear PSE for Compressible Boundary Layers. NASA Contractor Rep. 191537. ICASE Rep. No. 93-70. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center.
Chynoweth, B. C.2015 A new roughness array for controlling the nonlinear breakdown of second-mode waves at Mach 6. Master’s thesis, Purdue University, West Lafayette, IN.
Daubechies, I. 1990 The wavelet transform time-frequency localization and signal analysis. IEEE Trans. Inf. Theory 36 (5), 9611004.
Dinzl, D. J. & Candler, G. V. 2017 Direct simulation of hypersonic crossflow instability on an elliptic cone. AIAA J. 55 (6), 17691782.
Edelman, J. B.2019 Nonlinear growth and breakdown of the hypersonic crossflow instability. PhD thesis, Purdue University, West Lafayette, IN.
Hirschen, C. & Gülhan, A. 2009 Infrared thermography and pitot pressure measurements of a scramjet nozzle flowfield. J. Propul. Power 25 (5), 11081120.
InfraTec2016 Infrared-thermographic camera image IR. User Manual. InfraTec GmbH.
Juliano, T. J., Adamczak, D. & Kimmel, R. L.2014 HIFiRE-5 flight test heating analysis. AIAA Paper 2014-0076.
Juliano, T. J., Paquin, L. A. & Borg, M. P. 2019 Measurement of HIFiRE-5 boundary-layer transition in a Mach-6 quiet tunnel with infrared thermography. AIAA J. 57 (5), 20012010.
Juliano, T. J., Schneider, S. P. & Aradag, S. 2008 Quiet-flow Ludwieg tube for hypersonic transition research. AIAA J. 46 (7), 17571763.
Kuehl, J. J.2016 Görtler modified mack-modes on a hypersonic flared cone. AIAA Paper 2016-0849.
Kuehl, J. J., Perez, E. & Reed, H. L.2012 JoKHeR: NPSE simulations of hypersonic crossflow instability. AIAA Paper 2012-0921.
Li, F., Choudhari, M., Chang, C. & White, J.2010 Analysis of instabilities in non-axisymmetric hypersonic boundary layers over cones. AIAA Paper 2010-4643.
Lilly, J. M. & Olhede, S. C. 2012 Generalized Morse wavelets as a superfamily of analytic wavelets. IEEE Trans. Signal Process. 60 (11), 60366041.
Malik, M. R. & Balakumar, P.1992 Instability and transition in three-dimensional supersonic boundary layers. AIAA Paper 1992-5049.
Moyes, A. J., Kocian, T. S., Mullen, D. & Reed, H. L.2017 Boundary layer stability analysis of HIFiRE-5b flight geometry. AIAA Paper 2017-4301.
Perez, E., Reed, H. L. & Kuehl, J. J.2013 Instabilities on a hypersonic yawed cone. AIAA Paper 2013-2879.
Running, C. L., Sakaue, H. & Juliano, T. J. 2019 Stability and transition of three-dimensional boundary layers. Exp. Fluids 60, 23.
Running, C. L., Thompson, M. J., Juliano, T. J. & Sakaue, H.2017 Boundary-layer separation detection for a cone at high angle of attack in Mach 4.5 flow with pressure-sensitive paint. AIAA Paper 2017-3120.
Saric, W. S., Reed, H. L. & White, E. B. 2003 Stability and transition of three-dimensional boundary layers. Annu. Rev. Fluid Mech. 35 (1), 413440.
Schneider, S. P. 2008 Development of hypersonic quiet tunnels. J. Spacecr. Rockets 45 (4), 641664.
Schuele, C. Y.2011 Control of stationary crossflow modes using stationary patterned roughness and DBD plasma actuators at Mach 3.5. PhD thesis, University of Notre Dame, Notre Dame, IN.
Schuele, C. Y., Corke, T. & Matlis, E. 2013 Control of stationary crossflow modes in a Mach 3.5 boundary layer using patterned passive and active roughness. J. Fluid Mech. 718, 538.
Torrence, C. & Compo, G. 1997 A practical guide to wavelet analysis. Bull. Am. Meteorol. Soc. 79 (1), 6178.
van der Vegt, A. K. 1999 From Polymers to Plastics, 3rd edn. Delft Academic Press.
Ward, C. A. C.2014 Crossflow instability and transition on a circular cone at angle of attack in a Mach-6 quiet tunnel. PhD thesis, Purdue University, West Lafayette, IN.
Willems, S., Gülhan, A., Juliano, T. J., Kimmel, R. L. & Schneider, S. P.2014 Laminar to turbulent transition on the HIFiRE-1 cone at Mach 7 and high angle of attack. AIAA Paper 2014-0428.
Yates, H. B., Juliano, T. J., Matlis, E. H. & Tufts, M. W.2018 Plasma-actuated flow control of hypersonic crossflow-induced boundary-layer transition in a Mach-6 quiet tunnel. AIAA Paper 2018-1076.
Yates, H. B., Juliano, T. J., Matlis, E. H. & Tufts, M. W.2019 Crossflow transition acceleration with plasma actuators in hypersonic quiet flow. AIAA Paper 2019-1909.
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Analysis of the hypersonic cross-flow instability with experimental wavenumber distributions

  • Harrison B. Yates (a1), Matthew W. Tufts (a2) and Thomas J. Juliano (a1)


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