Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-28T16:17:38.813Z Has data issue: false hasContentIssue false

Transition mechanisms in cross-flow-dominated hypersonic flows with free-stream acoustic noise

Published online by Cambridge University Press:  04 June 2020

Adriano Cerminara*
Affiliation:
Aerodynamics and Flight Mechanics Research Group, Southampton, HampshireSO16 7QF, UK
Neil Sandham*
Affiliation:
Aerodynamics and Flight Mechanics Research Group, Southampton, HampshireSO16 7QF, UK
*
Email addresses for correspondence: [email protected], [email protected]
Email addresses for correspondence: [email protected], [email protected]

Abstract

Transition to turbulence in high-speed flows is determined by multiple parameters, many of which are not fully understood, leading to problems in developing physics-based prediction methods. In this contribution, we compare transition mechanisms in configurations with unswept and swept leading edges that are exposed to free-stream acoustic disturbances. Direct numerical simulations are run at a Mach number of six with the same free-stream noise, consisting of either fast or slow acoustic disturbances, with two different amplitudes to explore the linear and nonlinear aspects of receptivity and transition. For the unswept configuration, receptivity follows an established mechanism involving synchronisation of fast acoustic disturbances with boundary-layer modes. At high forcing amplitudes, transition proceeds via the formation of streaks and their eventual breakdown. In the swept case, the process of streak-induced transition is modified by the presence of a cross-flow instability in the leading-edge region. Linear stability analysis confirms the presence of a cross-flow mode as well as weaker first and second mode waves. Both fast and slow types of forcing independently stimulate an unusual transition mechanism involving significantly narrower streaks than those arising from the cross-flow instability behind the swept leading edge or those induced nonlinearly in the unswept case. In the observed transition process, the cross-flow mode leads to a thin layer of streamwise vorticity that breaks up under the influence of high spanwise wavenumber disturbances. These disturbances first appear in the leading-edge region.

Type
JFM Papers
Copyright
© The Author(s), 2020. 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

Andersson, P., Brandt, L., Bottaro, A. & Henningson, D. S. 2001 On the breakdown of boundary layer streaks. J. Fluid Mech. 428, 2960.CrossRefGoogle Scholar
Balakumar, P. 2009 Receptivity of a supersonic boundary layer to acoustic disturbances. AIAA J. 47 (5), 10691078.CrossRefGoogle Scholar
Balakumar, P. & King, R. A. 2012 Receptivity and stability of supersonic swept flows. AIAA J. 50 (7), 14761489.CrossRefGoogle Scholar
Balakumar, P. & Owens, L. 2010 Stability of hypersonic boundary layers on a cone at an angle of attack. In 40th Fluid Dynamics Conference and Exhibit, AIAA Paper 2010-4718. AIAA.Google Scholar
Bartkowicz, M., Subbareddy, P. & Candler, G. 2010 Simulation of boundary layer transition on elliptic cones in hypersonic flow. In 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, AIAA Paper 2010-1064. AIAA.Google Scholar
Berlin, S. & Henningson, D. S. 1999 A nonlinear mechanism for receptivity of free-stream disturbances. Phys. Fluids 11 (12), 37493760.CrossRefGoogle Scholar
Bippes, H. 1999 Basic experiments on transition in three-dimensional boundary layers dominated by crossflow instability. Prog. Aerosp. Sci. 35 (4), 363412.CrossRefGoogle Scholar
Borg, M. P., Kimmel, R. L. & Stanfield, S. 2015 Traveling crossflow instability for the hifire-5 elliptic cone. J. Spacecr. Rockets 52 (3), 664673.CrossRefGoogle Scholar
Brandt, L. & Henningson, D. S. 2002 Transition of streamwise streaks in zero-pressure-gradient boundary layers. J. Fluid Mech. 472, 229261.CrossRefGoogle Scholar
Carpenter, M. H., Nordström, J. & Gottlieb, D. 1999 A stable and conservative interface treatment of arbitrary spatial accuracy. J. Comput. Phys. 148 (2), 341365.CrossRefGoogle Scholar
Cerminara, A.2017 Boundary-layer receptivity and breakdown mechanisms for hypersonic flow over blunt leading-edge configurations. PhD thesis, University of Southampton.Google Scholar
Cerminara, A., Durant, A., André, T., Sandham, N. D. & Taylor, N. J. 2019 Receptivity to freestream acoustic noise in hypersonic flow over a generic forebody. J. Spacecr. Rockets 56 (2), 447457.CrossRefGoogle Scholar
Cerminara, A. & Sandham, N. 2015 Leading-edge receptivity to acoustic waves for high-speed flows over a blunt wedge. In 45th AIAA Fluid Dynamics Conference, AIAA Paper 2015-3078. AIAA.Google Scholar
Cerminara, A. & Sandham, N. D. 2017 Acoustic leading-edge receptivity for supersonic/hypersonic flows over a blunt wedge. AIAA J. 55 (12), 42344244.CrossRefGoogle Scholar
Choudhari, M. 1994 Roughness-induced generation of crossflow vortices in three-dimensional boundary layers. Theor. Comput. Fluid Dyn. 6 (1), 130.CrossRefGoogle Scholar
Choudhari, M., Chang, C.-L., Jentink, T., Li, F., Berger, K., Candler, G. & Kimmel, R. 2009 Transition analysis for the hifire-5 vehicle. In 39th AIAA Fluid Dynamics Conference, AIAA Paper 2009-4056. AIAA.Google Scholar
Choudhari, M. M., Li, F., Chang, C.-L., Carpenter, M., Streett, C., Malik, M. R. & Duan, L. 2013 Towards bridging the gaps in holistic transition prediction via numerical simulations. In 21st AIAA Computational Fluid Dynamics Conference, AIAA Paper 2013-2718. AIAA.Google Scholar
Craig, S. A. & Saric, W. S. 2016 Crossflow instability in a hypersonic boundary layer. J. Fluid Mech. 808, 224244.CrossRefGoogle Scholar
Crouch, J. D. & Ng, L. L. 2000 Variable n-factor method for transition prediction in three-dimensional boundary layers. AIAA J. 38 (2), 211216.CrossRefGoogle Scholar
De Tullio, N., Paredes, P., Sandham, N. D. & Theofilis, V. 2013 Laminar–turbulent transition induced by a discrete roughness element in a supersonic boundary layer. J. Fluid Mech. 735, 613646.CrossRefGoogle Scholar
De Tullio, N. & Sandham, N. D. 2015 Influence of boundary-layer disturbances on the instability of a roughness wake in a high-speed boundary layer. J. Fluid Mech. 763, 136165.CrossRefGoogle Scholar
Dinzl, D. J. & Candler, G. V. 2017 Direct simulation of hypersonic crossflow instability on an elliptic cone. AIAA J. 55 (6), 17691782.CrossRefGoogle Scholar
Duan, L., Choudhari, M. M. & Wu, M. 2014 Numerical study of acoustic radiation due to a supersonic turbulent boundary layer. J. Fluid Mech. 746, 165192.CrossRefGoogle Scholar
Ducros, F., Ferrand, V., Nicoud, F., Weber, C., Darracq, D., Gacherieu, C. & Poinsot, T. 1999 Large-eddy simulation of the shock/turbulence interaction. J. Comput. Phys. 152 (2), 517549.CrossRefGoogle Scholar
Durant, A., André, T., Schneider, S. P. & Chynoweth, B. 2015 Mach 6 quiet tunnel laminar to turbulent investigation of a generic hypersonic forebody. In 20th AIAA International Space Planes and Hypersonic Systems and Technologies Conference, AIAA Paper 2015-3575. AIAA.Google Scholar
Egorov, I. V., Sudakov, V. G. & Fedorov, A. V. 2006 Numerical modeling of the receptivity of a supersonic boundary layer to acoustic disturbances. Fluid Dyn. 41 (1), 3748.Google Scholar
Estorf, M., Radespiel, R., Schneider, S., Johnson, H. & Hein, S. 2008 Surface-pressure measurements of second-mode instability in quiet hypersonic flow. In 46th AIAA Aerospace Sciences Meeting and Exhibit, AIAA Paper 2008-1153. AIAA.Google Scholar
Fedorov, A. 2011 Transition and stability of high-speed boundary layers. Annu. Rev. Fluid Mech. 43, 7995.CrossRefGoogle Scholar
Fedorov, A. & Tumin, A. 2011 High-speed boundary-layer instability: old terminology and a new framework. AIAA J. 49 (8), 16471657.CrossRefGoogle Scholar
Fedorov, A. V. 2003 Receptivity of a high-speed boundary layer to acoustic disturbances. J. Fluid Mech. 491, 101129.CrossRefGoogle Scholar
Fedorov, A. V. & Khokhlov, A. P. 2001 Prehistory of instability in a hypersonic boundary layer. Theor. Comput. Fluid Dyn. 14 (6), 359375.CrossRefGoogle Scholar
Gaster, M. 1962 A note on the relation between temporally-increasing and spatially-increasing disturbances in hydrodynamic stability. J. Fluid Mech. 14 (2), 222224.CrossRefGoogle Scholar
Goldstein, M. E. & Hultgren, L. S. 1989 Boundary-layer receptivity to long-wave free-stream disturbances. Annu. Rev. Fluid Mech. 21 (1), 137166.CrossRefGoogle Scholar
Juliano, T. J., Borg, M. P. & Schneider, S. P. 2015 Quiet tunnel measurements of hifire-5 boundary-layer transition. AIAA J. 53 (4), 832846.CrossRefGoogle Scholar
Kohama, Y. 1987 Some expectation on the mechanism of cross-flow instability in a swept wing flow. Acta Mechanica 66 (1–4), 2138.CrossRefGoogle Scholar
Li, F., Choudhari, M., Paredes, P. & Duan, L. 2016 High-frequency instabilities of stationary crossflow vortices in a hypersonic boundary layer. Phys. Rev. Fluids 1 (5), 053603.CrossRefGoogle Scholar
Li, F., Choudhari, M. M., Duan, L. & Chang, C.-L. 2014 Nonlinear development and secondary instability of traveling crossflow vortices. Phys. Fluids 26 (6), 064104.CrossRefGoogle Scholar
Ma, Y. & Zhong, X. 2003a Receptivity of a supersonic boundary layer over a flat plate. Part 1. Wave structures and interactions. J. Fluid Mech. 488, 3178.CrossRefGoogle Scholar
Ma, Y. & Zhong, X. 2003b Receptivity of a supersonic boundary layer over a flat plate. Part 2. Receptivity to free-stream sound. J. Fluid Mech. 488, 79121.CrossRefGoogle Scholar
Ma, Y. & Zhong, X. 2005 Receptivity of a supersonic boundary layer over a flat plate. Part 3. Effects of different types of free-stream disturbances. J. Fluid Mech. 532, 63109.CrossRefGoogle Scholar
Mack, L. M.1984 Boundary-layer linear stability theory. Special course on stability and transition of laminar flows. California Inst. of Technology, JPL, AGARD Rep. 709, Pasadena, CA, pp. 3.1–81.Google Scholar
Malik, M. R. 1990 Numerical methods for hypersonic boundary layer stability. J. Comput. Phys. 86 (2), 376413.CrossRefGoogle Scholar
Malik, M. R. & Balakumar, P. 2007 Acoustic receptivity of Mach 4.5 boundary layer with leading-edge bluntness. Theor. Comput. Fluid Dyn. 21 (5), 323342.CrossRefGoogle Scholar
Malik, M. R., Li, F., Choudhari, M. M. & Chang, C.-L. 1999 Secondary instability of crossflow vortices and swept-wing boundary-layer transition. J. Fluid Mech. 399, 85115.CrossRefGoogle Scholar
Masutti, D., Spinosa, E., Chazot, O. & Carbonaro, M. 2012 Disturbance level characterization of a hypersonic blowdown facility. AIAA J. 50 (12), 27202730.CrossRefGoogle Scholar
McKenzie, J. F. & Westphal, K. O. 1968 Interaction of linear waves with oblique shock waves. Phys. Fluids 11 (11), 23502362.CrossRefGoogle Scholar
Nishioka, M. & Morkovin, M. V. 1986 Boundary-layer receptivity to unsteady pressure gradients: experiments and overview. J. Fluid Mech. 171, 219261.CrossRefGoogle Scholar
Paredes, P., Choudhari, M. M. & Li, F. 2016a Nonlinear transient growth and boundary layer transition. In 46th AIAA Fluid Dynamics Conference, AIAA Paper 2016-3956. AIAA.Google Scholar
Paredes, P., Choudhari, M. M., Li, F. & Chang, C.-L. 2016b Optimal growth in hypersonic boundary layers. AIAA J. 54 (10), 30503061.CrossRefGoogle Scholar
Paredes, P., Choudhari, M. M., Li, F. & Chang, C.-L. 2016c Transient growth analysis of compressible boundary layers with parabolized stability equations. In 54th AIAA Aerospace Sciences Meeting, AIAA Paper 2016-0051. AIAA.Google Scholar
Paredes, P., Gosse, R., Theofilis, V. & Kimmel, R. 2016d Linear modal instabilities of hypersonic flow over an elliptic cone. J. Fluid Mech. 804, 442466.CrossRefGoogle Scholar
Paredes, P. & Theofilis, V. 2015 Centerline instabilities on the hypersonic international flight research experimentation hifire-5 elliptic cone model. J. Fluids Struct. 53, 3649.CrossRefGoogle Scholar
Parziale, N. J., Shepherd, J. E. & Hornung, H. G. 2014 Free-stream density perturbations in a reflected-shock tunnel. Exp. Fluids 55 (2), 1665.CrossRefGoogle Scholar
Reed, H. L. & Saric, W. S. 1989 Stability of three-dimensional boundary layers. Annu. Rev. Fluid Mech. 21 (1), 235284.CrossRefGoogle Scholar
Reshotko, E. 1976 Boundary-layer stability and transition. Annu. Rev. Fluid Mech. 8 (1), 311349.CrossRefGoogle Scholar
Sandham, N. D., Li, Q. & Yee, H. C. 2002 Entropy splitting for high-order numerical simulation of compressible turbulence. J. Comput. Phys. 178 (2), 307322.CrossRefGoogle Scholar
Sansica, A.2015 Stability and unsteadiness of transitional shock-wave/boundary-layer interactions in supersonic flows. PhD thesis, University of Southampton.Google Scholar
Saric, W. S., Reed, H. L. & Kerschen, E. J. 2002 Boundary-layer receptivity to freestream disturbances. Annu. Rev. Fluid Mech. 34 (1), 291319.CrossRefGoogle Scholar
Schneider, S. P. 2001 Effects of high-speed tunnel noise on laminar-turbulent transition. J. Spacecr. Rockets 38 (3), 323333.CrossRefGoogle Scholar
Schneider, S. P. 2008 Development of hypersonic quiet tunnels. J. Spacecr. Rockets 45 (4), 641664.CrossRefGoogle Scholar
Schneider, S. P. 2015 Developing mechanism-based methods for estimating hypersonic boundary-layer transition in flight: the role of quiet tunnels. Prog. Aerosp. Sci. 72, 1729.CrossRefGoogle Scholar
Stetson, K. F., Thompson, E. R., Donaldson, J. C. & Siler, L. G. 1984 Laminar boundary layer stability experiments on a cone at Mach 8. II. Blunt cone. In American Institute of Aeronautics and Astronautics, Aerospace Sciences Meeting, 22nd, Reno, NV.Google Scholar
Wagner, A., Schülein, E., Petervari, R., Hannemann, K., Ali, S. RC., Cerminara, A. & Sandham, N. D. 2018 Combined free-stream disturbance measurements and receptivity studies in hypersonic wind tunnels by means of a slender wedge probe and direct numerical simulation. J. Fluid Mech. 842, 495531.CrossRefGoogle Scholar
Ward, C., Henderson, R. & Schneider, S. P. 2015 Secondary instability of stationary crossflow vortices on an inclined cone at Mach 6. In 45th AIAA Fluid Dynamics Conference, AIAA Paper 2015-2773. AIAA.Google Scholar
White, E. B. & Saric, W. S. 2005 Secondary instability of crossflow vortices. J. Fluid Mech. 525, 275308.CrossRefGoogle Scholar
Yee, H. C., Sandham, N. D. & Djomehri, M. J. 1999 Low-dissipative high-order shock-capturing methods using characteristic-based filters. J. Comput. Phys. 150 (1), 199238.CrossRefGoogle Scholar
Zhong, X. 2001 Leading-edge receptivity to free-stream disturbance waves for hypersonic flow over a parabola. J. Fluid Mech. 441, 315367.CrossRefGoogle Scholar
Zhong, X. & Ma, Y. 2006 Boundary-layer receptivity of Mach 7.99 flow over a blunt cone to free-stream acoustic waves. J. Fluid Mech. 556, 55103.CrossRefGoogle Scholar
Zhong, X. & Wang, X. 2012 Direct numerical simulation on the receptivity, instability, and transition of hypersonic boundary layers. Annu. Rev. Fluid Mech. 44, 527561.CrossRefGoogle Scholar