Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-24T05:47:58.107Z Has data issue: false hasContentIssue false
  • English
  • Français

Characterization of instability mechanisms on sharp and blunt slender cones at Mach 6

Published online by Cambridge University Press:  17 February 2022

Richard E. Kennedy Open the ORCID record for Richard E. Kennedy [Opens in a new window] ,
Joseph S. Jewell Open the ORCID record for Joseph S. Jewell [Opens in a new window] ,
Pedro Paredes Open the ORCID record for Pedro Paredes [Opens in a new window]  and
Stuart J. Laurence Open the ORCID record for Stuart J. Laurence [Opens in a new window]
Richard E. Kennedy*
Affiliation:
BAE Systems Inc., Durham, NC 27703, USA
Joseph S. Jewell
Affiliation:
School of Aeronautics and Astronautics, Purdue University, West Lafayette, IN 47907, USA
Pedro Paredes
Affiliation:
National Institute of Aerospace, Hampton, VA 23666, USA
Stuart J. Laurence
Affiliation:
Department of Aerospace Engineering, University of Maryland, College Park, MD 20742, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Experiments are performed to investigate the effect of nose-tip bluntness on the instability mechanisms leading to boundary-layer transition on a $7^{\circ }$ half-angle cone in a Mach-6 free stream. The development of disturbances is characterized using a combination of high-speed calibrated schlieren images and pressure measurements, and the data are compared with results computed using the parabolized stability equations. The approximately 414 mm long cone model is equipped with an interchangeable nose tip ranging from sharp to 5.08 mm in radius. For nose tips with a radius $R_{N}<2.54\ {\rm mm}$, second-mode instability waves are the dominant mechanism leading to transition. Time-averaged frequency spectra computed from the calibrated schlieren visualizations and pressure measurements are used to compute the second-mode most-amplified frequencies and integrated amplification rates ($N$ factors). Good agreement is observed between the measurements and computations in the linear-growth regime for the sharp-nose configuration at each free-stream condition. Additionally, a bispectral analysis identifies quadratic phase locking of frequency content responsible for the growth of higher harmonics. For nose tips of $R_{N}\geqslant 2.54\ {\rm mm}$, the schlieren visualization region is upstream of the entropy-layer swallowing length, and second-mode waves are no longer visible within the boundary layer; instead, elongated, steeply inclined features believed to be associated with non-modal instability mechanisms develop between the entropy-layer and boundary-layer edges. Simultaneously acquired surface pressure measurements reveal high-frequency pressure oscillations similar to second-mode instability waves associated with the trailing edge of these non-modal features.

JFM classification

Boundary Layers: Boundary layer stability Compressible Flows: Hypersonic Flow Instability: Transition to turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 936 , 10 April 2022 , A39
Check for updates
Copyright
© The Author(s), 2022. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Bountin, D.A., Shiplyuk, A.N. & Maslov, A.A. 2008 Evolution of nonlinear processes in a hypersonic boundary layer on a sharp cone. J. Fluid Mech. 611, 427–442.CrossRefGoogle Scholar
Casper, K.M., Beresch, S.J., Henfling, J.F., Spillers, R.W., Pruett, B.O.M. & Schneider, S.P. 2016 Hypersonic wind-tunnel measurements of boundary-layer transition on a slender cone. AIAA J. 54 (4), 1250–1263.CrossRefGoogle Scholar
Chokani, N. 2005 Nonlinear evolution of Mack modes in a hypersonic boundary layer. Phys. Fluids 17, 014102.CrossRefGoogle Scholar
Duan, L., et al. 2019 Characterization of freestream disturbances in conventional hypersonic wind tunnels. J. Spacecr. Rockets 56 (2), 357–368.CrossRefGoogle ScholarPubMed
Dunn, D.W. & Lin, C.C. 1955 On the stability of the laminar boundary layer in a compressible fluid. J. Aeronaut. Sci. 22 (7), 455–477.CrossRefGoogle Scholar
Grossir, G., Pinna, F., Bonucci, G., Regert, T., Rambaud, P. & Chazot, O. 2014 Hypersonic boundary layer transition on a 7 degree half-angle cone at Mach 10. AIAA Paper 2014-2779.CrossRefGoogle Scholar
Grossir, G., Pinna, F. & Chazot, O. 2019 Influence of nose-tip bluntness on conical boundary-layer instabilities at Mach 10. AIAA J. 57 (9), 3859–3873.CrossRefGoogle Scholar
Hader, C., Deng, N. & Fasel, H.F. 2021 Direct numerical simulations of hypersonic boundary-layer transition for a straight cone at Mach 5. AIAA Paper 2021-0743.CrossRefGoogle Scholar
Hargather, M.J. & Settles, G.S. 2012 A comparison of three quantitative schlieren techniques. Opt. Lasers Engng 50 (1), 8–17.CrossRefGoogle Scholar
Hofferth, J.W., Humble, R.A. & Floryan, D.C. 2013 High-bandwidth optical measurements of the second-mode instability in a Mach 6 quiet tunnel. AIAA Paper 2013-0378.CrossRefGoogle Scholar
Jewell, J.S. 2014 Boundary-layer transition on a slender cone in hypervelocity flow with real gas effects. PhD thesis, California Institute of Technology.Google Scholar
Jewell, J.S., Hameed, A., Parziale, N.J. & Gogineni, S. 2019 Disturbance speed measurements in a circular jet via double focused laser differential interferometry. AIAA Paper 2019-2293.CrossRefGoogle Scholar
Jewell, J.S. & Kimmel, R.L. 2017 Boundary-layer stability analysis for Stetson's Mach 6 blunt-cone experiments. J. Spacecr. Rockets 54 (1), 258–265.CrossRefGoogle Scholar
Johnson, H.B. 2000 Thermochemical interactions in hypersonic boundary layer stability. PhD thesis, University of Minnesota.Google Scholar
Johnson, H.B. & Candler, G.V. 2005 Hypersonic boundary layer stability analysis using PSE-Chem. AIAA Paper 2005-5023.CrossRefGoogle Scholar
Johnson, H.B., Seipp, T.G. & Candler, G.V. 1998 Numerical study of hypersonic reacting boundary layer transition on cones. Phys. Fluids 10, 2676–2685.CrossRefGoogle Scholar
Kennedy, R.E. 2019 An experimental investigation of hypersonic boundary-layer transition on sharp and blunt slender cones. PhD thesis, University of Maryland, College Park.Google Scholar
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.CrossRefGoogle Scholar
Kennedy, R.E., Laurence, S.J., Smith, M.S. & Marineau, E.C. 2018 Investigation of the second-mode instability at Mach 14 using calibrated schlieren. J. Fluid Mech. 845, R2.CrossRefGoogle Scholar
Kim, Y.C. & Powers, E.J. 1979 Digital bispectral analysis and its applications to nonlinear wave interactions. IEEE Trans. Plasma Sci. 7 (2), 120–131.CrossRefGoogle Scholar
Kimmel, R.L., Borg, M.P, Jewell, J.S., Lam, K.Y., Bowersox, R.D., Srinivasan, R., Fuchs, S. & Mooney, T. 2017 AFRL Ludwieg tube initial performance. AIAA Paper 2017-0102.CrossRefGoogle Scholar
Kimmel, R.L., Demetriades, A. & Donaldson, J.C. 1996 Space-time correlation measurements in a hypersonic transitional boundary layer. AIAA J. 34 (12), 2484–2489.CrossRefGoogle Scholar
Kimmel, R.L. & Kendall, J.M. 1991 Nonlinear disturbances in a hypersonic boundary layer. AIAA Paper 1991-0320.CrossRefGoogle Scholar
Laurence, S.J., Wagner, A. & Hannemann, K. 2014 Schlieren-based techniques for investigating instability development and transition in a hypersonic boundary layer. Exp. Fluids 55, 1–17.CrossRefGoogle Scholar
Laurence, S.J., Wagner, A. & Hannemann, K. 2016 Experimental study of instability growth and breakdown in a hypersonic boundary layer using high-speed schlieren visualization. J. Fluid Mech. 797, 471–501.CrossRefGoogle Scholar
Mack, L.M. 1975 Linear stability theory and the problem of supersonic boundary-layer transition. AIAA J. 13 (3), 278–289.CrossRefGoogle Scholar
Marineau, E.C., Grossir, G., Wagner, A., Leinemann, M., Radespiel, R., Tanno, H., Chynoweth, B.C., Schneider, S.P., Wagnild, R.M. & Casper, K.M. 2019 Analysis of second-mode amplitudes on sharp cones in hypersonic wind tunnels. J. Spacecr. Rockets 56 (2), 307–318.CrossRefGoogle Scholar
Marineau, E.C., Moraru, G. & Daniel, D.T. 2017 Sharp cone boundary-layer transition and stability at Mach 14. AIAA Paper 2017-0766.CrossRefGoogle Scholar
Marineau, E.C., Moraru, G., Lewis, D.R., Norris, J.D. & Lafferty, J.F. 2014 Mach 10 boundary-layer transition experiments on sharp and blunted cones. AIAA Paper 2014-3108.CrossRefGoogle Scholar
Maslov, A.A., Shiplyuk, A.N., Bountin, D.A. & Sidorenko, A.A. 2006 Mach 6 boundary-layer stability experiments on sharp and blunted cones. J. Spacecr. Rockets 43 (1), 71–76.CrossRefGoogle Scholar
Paredes, P. 2014 Advances in global instability computations: from incompressible to hypersonic flow. PhD thesis, Technical University of Madrid.Google Scholar
Paredes, P., Choudhari, M.M. & Li, F. 2019 a Laminar-turbulent transition upstream of the entropy-layer swallowing location in hypersonic boundary layers. AIAA Paper 2019-3215.CrossRefGoogle Scholar
Paredes, P., Choudhari, M.M. & Li, F. 2020 Mechanism for frustum transition over blunt cones at hypersonic speeds. J. Fluid Mech. 894, A22.CrossRefGoogle Scholar
Paredes, P., Choudhari, M.M., Li, F., Jewell, J.S. & Kimmel, R.L. 2019 b Nonmodal growth of traveling waves on blunt cones at hypersonic speeds. AIAA J. 57 (11), 4738–4749.CrossRefGoogle Scholar
Paredes, P., Choudhari, M.M., Li, F., Jewell, J.S., Kimmel, R.L., Marineau, E.C. & Grossir, G. 2019 c Nose-tip bluntness effects on transition at hypersonic speeds. J. Spacecr. Rockets 56 (2), 369–387.CrossRefGoogle Scholar
Paredes, P., Hanifi, A., Theofilis, V. & Henningson, D. 2015 The nonlinear PSE-3D concept for transition prediction in flows with a single slowly-varying spatial direction. Procedia IUTAM 14, 35–44.CrossRefGoogle Scholar
Parziale, N.J. 2013 Slender-body hypervelocity boundary-layer instability. PhD thesis, California Institute of Technology.Google Scholar
Rotta, N.R. 1966 Effects of nose bluntness on the boundary layer characteristics of conical bodies at hypersonic speeds. Tech. Rep. NYU-AA-66-66. New York University.CrossRefGoogle Scholar
Settles, G.S. & Fulghum, M.R. 2016 The focusing laser differential interferometer, an instrument for localized turbulence measurements in refractive flows. Trans. ASME J. Fluid Engng 138 (10), 101402.CrossRefGoogle Scholar
Stetson, K.F. 1983 Nosetip bluntness effects on cone frustum boundary layer transition in hypersonic flow. AIAA Paper 1983-1763.CrossRefGoogle Scholar
Wagnild, R.M., Candler, G.V., Leyva, I.A., Jewell, J.S. & Hornung, H.G. 2010 Carbon dioxide injection for hypervelocity boundary layer stability. AIAA Paper 2010-1244.CrossRefGoogle Scholar
Wright, M.J., Candler, G.V. & Bose, D. 1998 Data-parallel line relaxation method for the Navier–Stokes equations. AIAA J. 36 (9), 1603–1609.CrossRefGoogle Scholar