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Instability of the attachment line boundary layer in a supersonic swept flow

Published online by Cambridge University Press:  23 December 2021

Alexander V. Fedorov Open the ORCID record for Alexander V. Fedorov [Opens in a new window]  and
Ivan V. Egorov Open the ORCID record for Ivan V. Egorov [Opens in a new window]
Alexander V. Fedorov*
Affiliation:
Moscow Institute of Physics and Technology (MIPT), 9 Institutsky per, Dolgoprudny, Moscow reg., 141701, Russia
Ivan V. Egorov
Affiliation:
Moscow Institute of Physics and Technology (MIPT), 9 Institutsky per, Dolgoprudny, Moscow reg., 141701, Russia Central Aerohydrodynamic Institute (TsAGI), 1 Zhukovskogo Str, Zhukovsky, Moscow reg., 140180, Russia
*
†Email address for correspondence: [email protected]
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Abstract

Theoretical analysis of attachment-line instabilities is performed for supersonic swept flows using the compressible Hiemenz approximation for the mean flow and the successive approximation procedures for disturbances. The theoretical model captures the dominant attachment-line modes in wide ranges of the sweep Mach number ${M_e}$ and the wall temperature ratio. It is shown that these modes behave similar to the first and second Mack modes in the boundary layer flow. This similarity allows us to extrapolate the knowledge gained for Mack modes to the attachment-line instabilities. In particular, we find that at sufficiently large ${M_e}$, the dominant attachment-line instability is associated with the synchronisation of slow and fast modes of acoustic nature. Point-by-point comparisons of the theoretical predictions with the experiments of Gaillard et al. (Exp. Fluids, vol. 26, 1999, pp. 169–176) demonstrate that at ${M_e} > 4$, the theory captures a significant drop of the transition onset Reynolds number, which is below the contamination criterion of Poll $({R_\mathrm{\ast }} = 250)$ at ${M_e} > 6$. This contradicts the generally accepted assumption that the attachment-line flow is stable for ${R_\mathrm{\ast }} \le 250$. The theoretical critical Reynolds numbers lie well below the experimental transition-onset Reynolds numbers. Stability computations using the Navier–Stokes mean flow and accounting for the leading-edge curvature effect do not eliminate this discrepancy. Most likely, in the experiments of Gaillard et al., we face with an unknown effect that does not fit to the concept of transition arising from linear instability.

JFM classification

Aerodynamics: High-speed flow Boundary Layers: Boundary layer stability Instability: Transition to turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 933 , 25 February 2022 , A26
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

Balakumar, P. & Trivedi, P.A. 1998 Finite amplitude stability of attachment line boundary layers. Phys. Fluids 10, 2228–2237.CrossRefGoogle Scholar
Benard, E., Gaillard, L. & Alziary de Roquefort, T. 1997 Influence of roughness on attachment line boundary layer transition in hypersonic flow. Exp. Fluids 22, 286–291. Springer-Verlag.CrossRefGoogle Scholar
Benard, E., Sidorenko, A. & Raghunathan, S. 2002 Transitional and turbulent heat transfer of swept cylinder attachment line in hypersonic flow. In 40th AIAA Aerospace Sciences Meeting and Exhibit. AIAA Paper 2002-0551. AIAA.CrossRefGoogle Scholar
Bertolotti, F.P. 1998 The influence of rotational and vibrational energy relaxation on boundary-layer stability. J. Fluid Mech. 372, 93–118.CrossRefGoogle Scholar
Bouthier, M. 1972 Stabilite lineaire des ecoulements presque paralleles. Part I. J. Mec. 11, 599–621.Google Scholar
Bouthier, M. 1973 Stabilite lineaire des ecoulements presque paralleles. Part II. La couche limite de Blasius. J. Mec. 12, 75–95.Google Scholar
Coleman, C.P., Poll, D.I.A., Laub, J.A. & Wolf, S.W.D. 1996 Leading edge transition on a 76 degree swept cylinder at Mach number 1.6. In Fluid Dynamics Conference 17 June 1996 – 20 June 1996. AIAA Paper 96-2082. AIAA.CrossRefGoogle Scholar
Creel, T.R. 1991 Effect of sweep angle and passive relaminarization devices on a supersonic swept-circular boundary layer. In 29th Aerospace Sciences Meeting. AIAA Paper 91-0066. AIAA.CrossRefGoogle Scholar
Creel, T.R., Beckwith, I.E. & Chen, F.J. 1986 Effects of wind-tunnel noise on swept-cylinder transition at Mach 3.5. In Fluid Dynamics and Co-located Conferences. AIAA Paper 86-1085. AIAA.CrossRefGoogle Scholar
Creel, T.R., Beckwith, I.E. & Chen, F.J. 1987 Transition on swept leading edges at Mach 3.5. J. Aircraft 24 (10), 710–717.CrossRefGoogle Scholar
Egorov, I.V. 1992 Influence of real gas properties on the integral aerodynamic coefficients. Fluid Dyn. 27 (4), 573–579.CrossRefGoogle Scholar
Fedorov, A. 2011 Transition and stability of high-speed boundary layers. Annu. Rev. Fluid Mech. 43 (1), 79–95.CrossRefGoogle Scholar
Fedorov, A. & Tumin, A. 2011 High-speed boundary-layer instability: old terminology and a new framework. AIAA J. 49 (8), 1647–1657.CrossRefGoogle Scholar
Gaillard, L., Benard, E. & Alziary de Roquefort, T. 1999 Smooth leading edge transition in hypersonic flow. Exp. Fluids 26 (1), 169–176.CrossRefGoogle Scholar
Gaster, M. 1967 On the flow along swept leading edges. Aeronaut. Q. 18 (Part 2), 165–184.CrossRefGoogle Scholar
Gaster, M. 1974 On the effects of boundary-layer growth on flow stability. J. Fluid Mech. 66, 465–480.CrossRefGoogle Scholar
Gennaro, E.M., Rodríguez, D., Medeiros, M.A.F. & Theofilis, V. 2013 Sparse techniques in global flow instability with application to compressible leading-edge flow. AIAA J. 51 (9), 2295–2303.CrossRefGoogle Scholar
Hall, P. & Malik, M.R. 1986 On the instability of a three-dimensional attachment line boundary layer: weakly nonlinear theory and a numerical simulation. J. Fluid Mech. 163, 257–282.CrossRefGoogle Scholar
Hall, P., Malik, M. & Poll, D. 1984 On the stability of an infinite swept attachment-line boundary layer. Proc. R. Soc. Lond. A 395, 229–245.Google Scholar
Holden, M.S. & Kolly, J.M. 1995 Attachment line transition studies on swept cylindrical leading edges at Mach numbers from 10 to 12. In Fluid Dynamics Conference 19 June 1995 – 22 June 1995. AIAA Paper 95-2279. AIAA.CrossRefGoogle Scholar
Li, F. & Choudhari, M.M. 2008 Spatially developing secondary instabilities and attachment line instability in supersonic boundary layers. In 46th AIAA Aerospace Sciences Meeting and Exhibit. AIAA paper 2008-590. AIAA.CrossRefGoogle Scholar
Lin, R.-S. & Malik, M.R. 1995 Stability and transition in compressible attachment-line boundary-layer flow. SAE Technical Paper 952041.CrossRefGoogle Scholar
Lin, R.-S. & Malik, M.R. 1996 On the stability of attachment-line boundary layers. Part 1. The incompressible swept Hiemenz flow. J. Fluid Mech. 311, 239–255.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
Mack, L.M. 1979 On the stability of the boundary layer on a transonic swept wing. In 17th Aerospace Sciences Meeting. AIAA Paper 79-0264. AIAA.CrossRefGoogle Scholar
Morkovin, M.V., Reshotko, E. & Herbert, T. 1994 Transition in open flow systems – a reassessment. Bull. Am. Phys. Soc. 39 (9), 1–31.Google Scholar
Murakami, A., Stanewsky, E. & Krogmann, P. 1996 Boundary-layer transition on swept cylinders at hypersonic speeds. AIAA J. 34 (4), 649–654.CrossRefGoogle Scholar
Nayfeh, A.H. 1980 Stability of three-dimensional boundary layers. AIAA J. 18 (4), 406–416.CrossRefGoogle Scholar
Pfenninger, W. 1965 Flow phenomena at the leading edge of swept wings. In Recent Developments in Boundary Layer Research: AGARDograph 97, Part 4.Google Scholar
Poll, D.I.A. 1979 Transition in the infinite swept attachment line boundary layer. Aeronaut. Q. 30 (4), 607–629.CrossRefGoogle Scholar
Poll, D.I.A. 1994 Implication of 3-D transition mechanisms on the performance of space vehicles. In Second European Symposium for Space Vehicles ESA. ISBN 92-9092-310-5, pp. 175–182.Google Scholar
Rechotko, E. & Beckwith, I.E. 1958 Compressible laminar boundary layer over a yawed infinite cylinder with heat transfer and arbitrary Prandtl number. NACA Tech. Rep. 1379.Google Scholar
Semisynov, A.I., Fedorov, A.V., Novikov, V.E., Semionov, N.V. & Kosinov, A.D. 2003 Stability and transition on a swept cylinder in a supersonic flow. J. Appl. Mech. Tech. Phys. 44 (2), 212–220.CrossRefGoogle Scholar
Skuratov, A.S. & Fedorov, A.V. 1991 Supersonic boundary layer transition induced by roughness on the attachment line of a yawed cylinder. Fluid Dyn. 26, 816–822.CrossRefGoogle Scholar
Spalart, P.R. 1988 Direct numerical study of leading edge contamination. AGARD CP 438.Google Scholar
Theofilis, V., Fedorov, A.V. & Collis, S.S. 2006 Leading-edge boundary layer flow (Prandtl's vision, current developments and future perspectives). In IUTAM Symposium on One Hundred Years of Boundary Layer Research. Solid Mechanics and Its Applications (ed. G.E.A. Meier, K.R. Sreenivasan & H.J. Heinemann), vol. 129, pp. 73–82. Springer.CrossRefGoogle Scholar
Theofilis, V., Fedorov, A., Obrist, D. & Dallman, U.W.E.C. 2003 The extended Görtler–Hämmerlin model for linear instability of three-dimensional incompressible swept attachment-line boundary layer flow. J. Fluid Mech. 487, 271–313.CrossRefGoogle Scholar
Tumin, A. 2006 Biorthogonal eigenfunction system in the triple-deck limit. Stud. Appl. Maths 117 (2), 165–190.CrossRefGoogle Scholar
Tumin, A.M. 2007 Three-dimensional spatial normal modes in compressible boundary layers. J. Fluid Mech. 586, 295–322.CrossRefGoogle Scholar
Tumin, A. 2011 The biorthogonal eigenfunction system of linear stability equations: a survey of applications to receptivity problems and to analysis of experimental and computational results. In 41st AIAA Fluid Dynamics Conference and Exhibit. AIAA Paper 2011-3244. AIAA.CrossRefGoogle Scholar
Whitehead, A.H. Jr. & Dunavant, J.C. 1965 A study of pressure and heat transfer over an 80° sweep slab delta wing in hypersonic flow. NASA TN D-2708.Google Scholar
Xi, Y., Ren, J. & Fu, S. 2021 Hypersonic attachment-line instabilities with large sweep Mach numbers. J. Fluid Mech. 915, A44.CrossRefGoogle Scholar