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Instability evolution in the hypersonic boundary layer over a wavy wall

Published online by Cambridge University Press:  06 June 2022

W.K. Zhu
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, Collaborative Innovation Center for Advanced Aero-Engines, Peking University, Beijing 100871, PR China
D.W. Gu
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, Collaborative Innovation Center for Advanced Aero-Engines, Peking University, Beijing 100871, PR China
W.F. Si
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, Collaborative Innovation Center for Advanced Aero-Engines, Peking University, Beijing 100871, PR China
M.J. Zhang
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, Collaborative Innovation Center for Advanced Aero-Engines, Peking University, Beijing 100871, PR China
S.Y. Chen
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, Collaborative Innovation Center for Advanced Aero-Engines, Peking University, Beijing 100871, PR China
C.R. Smith
Affiliation:
Department of Mechanical Engineering and Mechanics, Lehigh University, 19 Memorial Drive West, Bethlehem, PA 18015, USA
Y.D. Zhu*
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, Collaborative Innovation Center for Advanced Aero-Engines, Peking University, Beijing 100871, PR China
C.B. Lee*
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, Collaborative Innovation Center for Advanced Aero-Engines, Peking University, Beijing 100871, PR China
*
Email addresses for correspondence: [email protected], [email protected]
Email addresses for correspondence: [email protected], [email protected]

Abstract

The effects of a wavy wall on the stability of a hypersonic boundary layer on a flared cone are investigated by detailed experimental measurements and direct numerical simulations. The non-contact optical measurement method of focused laser differential interferometry is used to measure the disturbance development within the wavy region. The measurement results show that the second mode for the wavy wall is suppressed significantly compared with the smooth wall, and that multiple disturbances at low frequencies appear within the wavy region. Numerical corroboration against experimental measurements reveals good quantitative agreement. It is found that the disturbances at $f=360$ kHz on the wavy wall are suppressed appreciably, which are very significant on the smooth wall. And the disturbances at $f=140$ kHz and $f=260$ kHz develop within the wavy region, and increase considerably. Also, the disturbances achieve a significant increase over the first half of a wavy trough and become more stable over the second half of a wavy trough. The physical mechanism is found to be due to the change in wall geometry and is attributed to the spatially modulated mean flow. The disturbance growth rate is closely related to the level of the mean-flow distortion.

Type
JFM Papers
Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

REFERENCES

Benitez, E.K., Esquieu, S., Jewell, J.S. & Schneider, S.P. 2020 Instability measurements on an axisymmetric separation bubble at Mach 6. AIAA Paper 2020-3072.CrossRefGoogle Scholar
Bountin, D.A., Chimitov, T., Maslov, A.A., Novikov, A.V., Egorov, I.V., Fedorov, A.V. & Utyuzhnikov, S. 2013 Stabilization of a hypersonic boundary layer using a wavy surface. AIAA J. 51 (5), 12031210.CrossRefGoogle Scholar
Brès, G.A. & Colonius, T. 2008 Three-dimensional instabilities in compressible flow over open cavities. J. Fluid Mech. 599, 309339.CrossRefGoogle Scholar
Butler, C.S. & Laurence, S.J. 2021 Interaction of second-mode disturbances with an incipiently separated compression-corner flow. J. Fluid Mech. 913, R4.CrossRefGoogle Scholar
Casper, K.M., Wagner, J.L., Beresh, S.J., Spillers, R.W., Henfling, J.F. & Dechant, L.J. 2018 Spatial distribution of pressure resonance in compressible cavity flow. J. Fluid Mech. 848, 660675.CrossRefGoogle Scholar
Diwan, S.S. & Ramesh, O.N. 2009 On the origin of the inflectional instability of a laminar separation bubble. J. Fluid Mech. 629, 263298.CrossRefGoogle Scholar
Dong, M. & Li, C. 2021 Effect of two-dimensional short rectangular indentations on hypersonic boundary-layer transition. AIAA J. 59 (7), 23682381.CrossRefGoogle Scholar
Dong, M., Liu, Y. & Wu, X. 2020 Receptivity of inviscid modes in supersonic boundary layers due to scattering of free-stream sound by localised wall roughness. J. Fluid Mech. 896, A23.CrossRefGoogle Scholar
Dong, M. & Zhao, L. 2021 An asymptotic theory of the roughness impact on inviscid Mack modes in supersonic/hypersonic boundary layers. J. Fluid Mech. 913, A22.CrossRefGoogle Scholar
Dovgal, A.V., Kozlov, V.V. & Michalke, A. 1994 Laminar boundary layer separation: instability and associated phenomena. Prog. Aeosp. Sci. 30 (1), 6194.CrossRefGoogle Scholar
Egorov, I.V., Novikov, A.V. & Fedorov, A.V. 2006 Numerical modeling of the disturbances of the separated flow in a rounded compression corner. Fluid Dyn. 41 (4), 521530.CrossRefGoogle Scholar
Egorov, I.V., Novikov, A.V. & Fedorov, A.V. 2010 Direct numerical simulation of supersonic boundary layer stabilization using grooved wavy surface. AIAA Paper 2010-1245.CrossRefGoogle Scholar
Fedorov, A. 2003 Receptivity of hypersonic boundary layer to acoustic disturbances scattered by surface roughness. AIAA Paper 2003-373.CrossRefGoogle Scholar
Fedorov, A. 2011 Transition and stability of high-speed boundary layers. Annu. Rev. Fluid Mech. 43, 7995.CrossRefGoogle Scholar
Fujii, K. 2006 Experiment of the two-dimensional roughness effect on hypersonic boundary-layer transition. J. Spacecr. Rockets 43 (4), 731738.CrossRefGoogle Scholar
Hader, C. & Fasel, H.F. 2018 Towards simulating natural transition in hypersonic boundary layers via random inflow disturbances. J. Fluid Mech. 847, R3.CrossRefGoogle Scholar
Haller, G., Hadjighasem, A., Farazmand, M. & Huhn, F. 2016 Defining coherent vortices objectively from the vorticity. J. Fluid Mech. 795, 136173.CrossRefGoogle Scholar
Kendall, J.M. 1975 Wind tunnel experiments relating to supersonic and hypersonic boundary-layer transition. AIAA J. 13 (3), 290299.CrossRefGoogle Scholar
Lee, C. & Chen, S. 2018 Recent progress in the study of transition in the hypersonic boundary layer. Natl Sci. Rev. 6, 155170.CrossRefGoogle Scholar
Lee, C. & Jiang, X. 2019 Flow structures in transitional and turbulent boundary layers. Phys. Fluids 31 (11), 111301.Google Scholar
Li, X.L., Fu, D.X. & Ma, Y.W. 2008 Direct numerical simulation of hypersonic boundary layer transition over a blunt cone. AIAA J. 46 (11), 28992913.CrossRefGoogle Scholar
Li, X.L., Fu, D.X. & Ma, Y.W. 2010 Direct numerical simulation of hypersonic boundary layer transition over a blunt cone with a small angle of attack. Phys. Fluids 22 (2), 025105.CrossRefGoogle Scholar
Liu, Y., Dong, M. & Wu, X. 2020 Generation of first Mack modes in supersonic boundary layers by slow acoustic waves interacting with streamwise isolated wall roughness. J. Fluid Mech. 888, A10.CrossRefGoogle Scholar
Lugrin, M., Beneddine, S., Leclercq, C., Garnier, E. & Bur, R. 2021 Transition scenario in hypersonic axisymmetrical compression ramp flow. J. Fluid Mech. 907, A6.CrossRefGoogle Scholar
Ma, Y. & Zhong, X. 2003 Receptivity of a supersonic boundary layer over a flat plate. Part 2. Receptivity to free-stream sound. J. Fluid Mech. 488, 79121.CrossRefGoogle Scholar
Mack, L.M. 1984 Boundary-layer linear stability theory. AGARD Rep. 709.Google Scholar
Marxen, O., Iaccarino, G. & Shaqfeh, S.E.G. 2010 Disturbance evolution in a Mach 4.8 boundary layer with two-dimensional roughness-induced separation and shock. J. Fluid Mech. 648, 435469.CrossRefGoogle Scholar
Marxen, O., Iaccarino, G. & Shaqfeh, S.E.G. 2014 Nonlinear instability of a supersonic boundary layer with two-dimensional roughness. J. Fluid Mech. 752, 497520.CrossRefGoogle Scholar
Morkovin, M.V. 1994 Transition in open flow systems – a reassessment. Bull. Am. Phys. Soc. 39, 1882.Google Scholar
Nayfeh, A.H., Ragab, S.A. & Al-Maaitah, A.A. 1988 Effect of bulges on the stability of boundary layers. Phys. Fluids 31 (4), 796806.CrossRefGoogle Scholar
Park, D. & Park, S.O. 2013 Linear and non-linear stability analysis of incompressible boundary layer over a two-dimensional hump. Comput. Fluids 73, 8096.CrossRefGoogle Scholar
Pruett, C.D. & Chang, C.-L. 1998 Direct numerical simulation of hypersonic boundary-layer flow on a flared cone. Theor. Comput. Fluid Dyn. 11 (1), 4967.CrossRefGoogle Scholar
Raposo, H., Mughal, S. & Ashworth, R. 2018 Acoustic receptivity and transition modeling of Tollmien–Schlichting disturbances induced by distributed surface roughness. Phys. Fluids 30 (4), 044105.CrossRefGoogle Scholar
Raposo, H., Mughal, S. & Ashworth, R. 2019 An adjoint compressible linearised Navier–Stokes approach to model generation of Tollmien–Schlichting waves by sound. J. Fluid Mech. 877, 105129.CrossRefGoogle Scholar
Raposo, H., Mughal, S., Bensalah, A. & Ashworth, R. 2021 Acoustic-roughness receptivity in subsonic boundary-layer flows over aerofoils. J. Fluid Mech. 925, A7.CrossRefGoogle Scholar
Sawaya, J., Sassanis, V., Yassir, S., Sescu, A. & Visbal, M. 2018 Assessment of the impact of two-dimensional wall deformation shape on high-speed boundary-layer disturbances. AIAA J. 56 (12), 47874800.CrossRefGoogle Scholar
Schmid, P.J., Henningson, D.S. & Jankowski, D.F. 2002 Stability and transition in shear flows. Applied mathematical sciences. Appl. Mech. Rev. 55 (3), B57B59.CrossRefGoogle Scholar
Si, W.F., Huang, G.L., Zhu, Y.D., Chen, S.Y. & Lee, C.B. 2019 Hypersonic aerodynamic heating over a flared cone with wavy wall. Phys. Fluids 31, 051702.Google Scholar
Smith, C.R. 2021 Aerodynamic heating in hypersonic flows. Phys. Today 74 (11), 6667.CrossRefGoogle Scholar
Smith, C.R. & Metzler, S.P. 1983 The characteristics of low-speed streaks in the near-wall region of a turbulent boundary layer. J. Fluid Mech. 129 (1), 2754.CrossRefGoogle Scholar
Stetson, K., Thompson, E., Donaldson, J. & Siler, L. 1983 Laminar boundary layer stability experiments on a cone at Mach 8. Part 1: sharp cone. AIAA Paper 1983-1761.CrossRefGoogle Scholar
Sun, B.H. & Oran, E.S. 2018 New principle for aerodynamic heating. Natl Sci. Rev. 5 (5), 606607.CrossRefGoogle Scholar
Tang, Q., Zhu, Y.D., Chen, X. & Lee, C.B. 2015 Development of second-mode instability in a Mach 6 flat plate boundary layer with two-dimensional roughness. Phys. Fluids 27 (6), 064105.CrossRefGoogle Scholar
Thomas, C., Mughal, S. & Ashworth, R. 2017 Development of Tollmien–Schlichting disturbances in the presence of laminar separation bubbles on an unswept infinite wavy wing. Phys. Rev. Fluids 2, 043903.CrossRefGoogle Scholar
Thomas, C., Mughal, S.M., Gipon, M., Ashworth, R. & Martinez-Cava, A. 2016 Stability of an infinite swept wing boundary layer with surface waviness. AIAA J. 54 (10), 30243038.CrossRefGoogle Scholar
Torrence, C. & Compo, G.P. 1998 A practical guide to wavelet analysis. Bull. Am. Meteorol. Soc. 79 (1), 6178.2.0.CO;2>CrossRefGoogle Scholar
Wie, Y.-S. & Malik, M.R. 1998 Effect of surface waviness on boundary-layer transition in two-dimensional flow. Comput. Fluids 27 (2), 157181.CrossRefGoogle Scholar
Wu, X. 2011 On generation of sound in wall-bounded shear flows: back action of sound and global acoustic coupling. J. Fluid Mech. 689, 279316.CrossRefGoogle Scholar
Wu, X. & Dong, M. 2016 A local scattering theory for the effects of isolated roughness on boundary-layer instability and transition: transmission coefficient as an eigenvalue. J. Fluid Mech. 794, 68108.CrossRefGoogle Scholar
Xiong, Y.D., Yu, T., Lin, L.Q., Zhao, J.Q. & Wu, J. 2020 Nonlinear instability characterization of hypersonic laminar boundary layer. AIAA J. 58 (12), 52545263.CrossRefGoogle Scholar
Xu, H., Mughal, S.M., Gowree, E.R., Atkin, C.J. & Sherwin, S.J. 2017 Destabilisation and modification of Tollmien–Schlichting disturbances by a three-dimensional surface indentation. J. Fluid Mech. 819, 592620.CrossRefGoogle Scholar
Xu, H., Sherwin, S.J., Hall, P. & Wu, X.S. 2016 The behaviour of Tollmien–Schlichting waves undergoing small-scale localised distortions. J. Fluid Mech. 792, 499525.CrossRefGoogle Scholar
Zhao, L., Dong, M. & Yang, Y. 2019 Harmonic linearized Navier–Stokes equation on describing the effect of surface roughness on hypersonic boundary-layer transition. Phys. Fluids 31 (3), 034108.Google Scholar
Zhao, Y.M., Yang, Y. & Chen, S.Y. 2016 Evolution of material surfaces in the temporal transition in channel flow. J. Fluid Mech. 793, 840876.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
Zhu, Y.D., Gu, D.W., Zhu, W.K., Chen, S.Y., Lee, C.B. & Oran, E.S. 2021 Dilatational-wave-induced aerodynamic cooling in transitional hypersonic boundary layers. J. Fluid Mech. 911, A36.CrossRefGoogle Scholar
Zhu, Y.D., Lee, C.B., Chen, X., Wu, J.Z., Chen, S.Y. & Gad-el-Hak, M. 2018 Newly identified principle for aerodynamic heating in hypersonic flows. J. Fluid Mech. 855, 152180.CrossRefGoogle Scholar