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Link between subsonic stall and transonic buffet on swept and unswept wings: from global stability analysis to nonlinear dynamics

Published online by Cambridge University Press:  04 December 2020

Frédéric Plante Open the ORCID record for Frédéric Plante [Opens in a new window] ,
Julien Dandois Open the ORCID record for Julien Dandois [Opens in a new window] ,
Samir Beneddine Open the ORCID record for Samir Beneddine [Opens in a new window] ,
Éric Laurendeau  and
Denis Sipp Open the ORCID record for Denis Sipp [Opens in a new window]
Frédéric Plante*
Affiliation:
DAAA, ONERA, Université Paris Saclay, 8 rue des Vertugadins, 92190Meudon, France Department of Mechanical Engineering, Polytechnique Montréal, Montréal H3T 1J4, Canada
Julien Dandois
Affiliation:
DAAA, ONERA, Université Paris Saclay, 8 rue des Vertugadins, 92190Meudon, France
Samir Beneddine
Affiliation:
DAAA, ONERA, Université Paris Saclay, 8 rue des Vertugadins, 92190Meudon, France
Éric Laurendeau
Affiliation:
Department of Mechanical Engineering, Polytechnique Montréal, Montréal H3T 1J4, Canada
Denis Sipp
Affiliation:
DAAA, ONERA, Université Paris Saclay, 8 rue des Vertugadins, 92190Meudon, France
*
†Email address for correspondence: frederic.plante@polymtl.ca
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Abstract

This paper examines the three-dimensional cellular patterns appearing on wings in subsonic stall and transonic buffet conditions. Unsteady Reynolds-averaged Navier–Stokes simulations are carried out for three-dimensional infinite swept configurations closed by periodic boundary conditions in the spanwise direction. In both flow conditions the occurrence of stall/buffet cells is observed, as well as their convection at a speed proportional to the sweep angle. In transonic buffet conditions, this phenomenon is superimposed to the well-documented two-dimensional buffet instability. These results indicate that the discrepancies between two-dimensional and three-dimensional buffet are caused by the occurrence of buffet cells and that this phenomenon is similar to the one observed at low speed. These phenomena are then studied using global linear stability analysis with the assumption of a periodic flow in the spanwise direction. From these analyses a mode coherent with the two-dimensional buffet is obtained, as well as a mode coherent with two-dimensional vortex shedding in stall conditions. In addition, in both flow conditions an unstable mode reminiscent of stall/buffet cells is observed.

JFM classification

Instability: Instability Aerodynamics: Aerodynamics Turbulent Flows: Turbulent Flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 908 , 10 February 2021 , A16
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

REFERENCES

Åkervik, E., Brandt, L., Henningson, D. S., Hoepffner, J., Marxen, O. & Schlatter, P. 2006 Steady solutions of the Navier–Stokes equations by selective frequency damping. Phys. Fluids 18 (6), 068102.CrossRefGoogle Scholar
Barkley, D., Gomes, M.-G.-M. & Henderson, R. 2002 Three-dimensional instability in flow over a backward-facing step. J. Fluid Mech. 473, 167–190.CrossRefGoogle Scholar
Bayly, B., Orszag, S.-A. & Herbert, T. 1988 Instability mechanism in shear-flow transition. Annu. Rev. Fluid Mech. 20 (1), 359–391.CrossRefGoogle Scholar
Beneddine, S. 2017 Characterization of unsteady flow behavior by linear stability analysis. PhD thesis, Paris-Saclay.Google Scholar
Benoit, B. & Legrain, I. 1987 Buffeting prediction for transport aircraft applications based on unsteady pressure measurements. AIAA Paper 1987-2356.CrossRefGoogle Scholar
Bertagnolio, F., Sørensen, N. N. & Rasmussen, F. 2005 New insight into the flow around a wind turbine airfoil section. Trans. ASME: J. Sol. Energy 127 (2), 214–222.Google Scholar
Bourgault-Côté, S., Ghasemi, S., Mosahebi, A. & Laurendeau, É. 2017 Extension of a two-dimensional Navier–Stokes solver for infinite swept flow. AIAA J. 55 (2), 662–667.CrossRefGoogle Scholar
Brion, V., Dandois, J., Abart, J.-C. & Paillart, P. 2017 Experimental analysis of the shock dynamics on a transonic laminar airfoil. Prog. Flight Phys. 9, 365–386.CrossRefGoogle Scholar
Broeren, A. P. & Bragg, M. B. 2001 Spanwise variation in the unsteady stalling flowfields of two-dimensional airfoil models. AIAA J. 39 (9), 1641–1651.CrossRefGoogle Scholar
Brunet, V. & Deck, S. 2008 Zonal-detached eddy simulation of transonic buffet on a civil aircraft type configuration. AIAA Paper 2008-4152.CrossRefGoogle Scholar
Busquet, D., Marquet, O., Richez, F., Juniper, M. P. & Sipp, D. 2017 Global stability analysis of turbulent flows around an airfoil near stall. In EUROGEN 2017. Madrid, Spain.Google Scholar
Cambier, L., Heib, S. & Plot, S. 2013 The Onera elsA CFD software: input from research and feedback from industry. Mech. Ind. 14 (3), 159–174.CrossRefGoogle Scholar
Chabert, T., Dandois, J. & Garnier, É. 2016 Experimental closed-loop control of separated-flow over a plain flap using extremum seeking. Exp. Fluids 57 (3), 37.CrossRefGoogle Scholar
Christodoulou, K. N. & Scriven, L. E. 1988 Finding leading modes of a viscous free surface flow: an asymmetric generalized eigenproblem. J. Sci. Comput. 3 (4), 355–406.CrossRefGoogle Scholar
Crouch, J. D., Garbaruk, A., Magidov, D. & Travin, A. 2009 Origin of transonic buffet on aerofoils. J. Fluid Mech. 628, 357.CrossRefGoogle Scholar
Crouch, J. D., Garbaruk, A. & Strelets, M. 2018 Global instability analysis of unswept and swept-wing transonic buffet onset. AIAA Paper 2018-3229.CrossRefGoogle Scholar
Crouch, J. D., Garbaruk, A. & Strelets, M. 2019 Global instability in the onset of transonic-wing buffet. J. Fluid Mech. 881, 3–22.CrossRefGoogle Scholar
Dandois, J. 2016 Experimental study of transonic buffet phenomenon on a 3D swept wing. Phys. Fluids 28 (1), 016101.CrossRefGoogle Scholar
Deck, S. 2005 Numerical simulation of transonic buffet over a supercritical airfoil. AIAA J. 43 (7), 1556–1566.CrossRefGoogle Scholar
Deck, S. & Renard, N. 2020 Towards an enhanced protection of attached boundary layers in hybrid RANS/LES methods. J. Comput. Phys. 400, 108970.CrossRefGoogle Scholar
Dell'Orso, H. & Amitay, M. 2018 Parametric investigation of stall cell formation on a NACA 0015 airfoil. AIAA J. 56 (8), 1–13.Google Scholar
Edwards, J. 1993 Transonic shock oscillations calculated with a new interactive boundary layer coupling method. AIAA Paper 1993-0777.CrossRefGoogle Scholar
Fukushima, Y. & Kawai, S. 2018 Wall-modeled large-eddy simulation of transonic airfoil buffet at high Reynolds number. AIAA J. 56 (6), 1–18.CrossRefGoogle Scholar
Gallaire, F., Marquille, M. & Ehrenstein, U. 2007 Three-dimensional transverse instabilities in detached boundary layers. J. Fluid Mech. 571, 221–233.CrossRefGoogle Scholar
Gallay, S. & Laurendeau, E. 2015 Nonlinear generalized lifting-line coupling algorithms for pre/poststall flows. AIAA J. 53 (7), 1784–1792.CrossRefGoogle Scholar
Garnier, E. & Deck, S. 2010 Large-eddy simulation of transonic buffet over a supercritical airfoil. In Turbulence and Interactions (ed. M. Deville, T.-H. Lê & P. Sagaut), pp. 135–141. Springer.CrossRefGoogle Scholar
Ghasemi, S., Mosahebi, A. & Laurendeau, É. 2014 A two-dimensional/infinite swept wing Navier–Stokes solver. AIAA Paper 2014-0557.CrossRefGoogle Scholar
Giannelis, N. F., Levinski, O. & Vio, G. A. 2018 Influence of Mach number and angle of attack on the two-dimensional transonic buffet phenomenon. Aerosp. Sci. Technol. 78, 89–101.CrossRefGoogle Scholar
Giannelis, N. F., Vio, G. A. & Levinski, O. 2017 A review of recent developments in the understanding of transonic shock buffet. Prog. Aerosp. Sci. 92, 39–84.CrossRefGoogle Scholar
Goncalves, É. & Houdeville, R. 2004 Turbulence model and numerical scheme assessment for buffet computations. Intl J. Numer. Meth. Fluids 46 (11), 1127–1152.CrossRefGoogle Scholar
Gregory, N., Quincey, V. G., O'Reilly, C. L. & Hall, D. J. 1971 Progress report on observations of three-dimensional flow patterns obtained during stall development on aerofoils, and on the problem of measuring two-dimensional characteristics. Tech. Rep. C.P. No. 1146. Aeronautical Research Council.Google Scholar
Gross, A., Fasel, H. F. & Gaster, M. 2015 Criterion for spanwise spacing of stall cells. AIAA J. 53 (1), 272–274.CrossRefGoogle Scholar
Grossi, F., Braza, M. & Hoarau, Y. 2014 Prediction of transonic buffet by delayed detached-eddy simulation. AIAA J. 52 (10), 2300–2312.CrossRefGoogle Scholar
He, W., Gioria, R. S., Pérez, J. M. & Theofilis, V. 2017 Linear instability of low Reynolds number massively separated flow around three NACA airfoils. J. Fluid Mech. 811, 701–741.CrossRefGoogle Scholar
He, W. & Timme, S. 2020 Triglobal shock buffet instability study on infinite wings. AIAA Paper 2020-1986.CrossRefGoogle Scholar
Huang, J., Xiao, Z., Liu, J. & Fu, S. 2012 Simulation of shock wave buffet and its suppression on an OAT15A supercritical airfoil by IDDES. Sci. China Phys. Mech. Astron. 55 (2), 260–271.CrossRefGoogle Scholar
Huerre, P. & Monkewitz, P. A. 1990 Local and global instabilities in spatially developing flows. Annu. Rev. Fluid Mech. 22 (1), 473–537.CrossRefGoogle Scholar
Iorio, M. C., González, L. M. & Ferrer, E. 2014 Direct and adjoint global stability analysis of turbulent transonic flows over a NACA0012 profile. Intl J. Numer. Meth. Fluids 76 (3), 147–168.CrossRefGoogle Scholar
Iovnovich, M. & Raveh, D. E. 2012 Reynolds-Averaged Navier–Stokes study of the shock-buffet instability mechanism. AIAA J. 50 (4), 880–890.CrossRefGoogle Scholar
Iovnovich, M. & Raveh, D. E. 2015 Numerical study of shock buffet on three-dimensional wings. AIAA J. 53 (2), 449–463.CrossRefGoogle Scholar
Ishida, T., Hashimoto, A., Ohmichi, Y., Aoyama, T. & Takekawa, K. 2017 Transonic buffet simulation over NASA-CRM by unsteady-FaSTAR code. AIAA Paper 2017-0494.CrossRefGoogle Scholar
Ishida, T., Ishiko, K., Hashimoto, A., Aoyama, T. & Takekawa, K. 2016 Transonic buffet simulation over supercritical airfoil by unsteady-FaSTAR code. AIAA Paper 2016-1310.CrossRefGoogle Scholar
Jacquin, L., Molton, P., Deck, S., Maury, B. & Soulevant, D. 2009 Experimental study of shock oscillation over a transonic supercritical profile. AIAA J. 47 (9), 1985–1994.CrossRefGoogle Scholar
Jordi, B. E., Cotter, C. J. & Sherwin, S. J. 2014 Encapsulated formulation of the selective frequency damping method. Phys. Fluids 26 (3), 034101.CrossRefGoogle Scholar
Jordi, B. E., Cotter, C. J. & Sherwin, S. J. 2015 An adaptive selective frequency damping method. Phys. Fluids 27 (9), 094104.CrossRefGoogle Scholar
Kamenetskiy, D. S., Bussoletti, J. E., Hilmes, C. L., Venkatakrishnan, V., Wigton, L. B. & Johnson, F. T. 2014 Numerical evidence of multiple solutions for the Reynolds-Averaged Navier–Stokes equations. AIAA J. 52 (8), 1686–1698.CrossRefGoogle Scholar
Kitsios, V., Rodríguez, D., Theofilis, V., Ooi, A. & Soria, J. 2009 Biglobal stability analysis in curvilinear coordinates of massively separated lifting bodies. J. Comput. Phys. 228 (19), 7181–7196.CrossRefGoogle Scholar
Koike, S., Ueno, M., Nakakita, K. & Hashimoto, A. 2016 Unsteady pressure measurement of transonic buffet on NASA common research model. AIAA Paper 2016-4044.CrossRefGoogle Scholar
Le Balleur, J. C. & Girodroux-Lavigne, P. 1989 Viscous-inviscid strategy and computation of transonic buffet. In Symposium Transsonicum III (ed. J. Zierep & H. Oertel), pp. 49–63. Springer.CrossRefGoogle Scholar
Lee, B. H. K. 1990 Oscillatory shock motion caused by transonic shock boundary-layer interaction. AIAA J. 28 (5), 942–944.CrossRefGoogle Scholar
Liu, D. & Nishino, T. 2018 Numerical analysis on the oscillation of stall cells over a NACA 0012 aerofoil. Comput. Fluids 175, 246–259.CrossRefGoogle Scholar
Manni, L., Nishino, T. & Delafin, P.-L. 2016 Numerical study of airfoil stall cells using a very wide computational domain. Comput. Fluids 140, 260–269.CrossRefGoogle Scholar
Marquet, O., Lombardi, M., Chomaz, J.-M., Sipp, D. & Jacquin, L. 2009 Direct and adjoint global modes of a recirculation bubble: lift-up and convective non-normalities. J. Fluid Mech. 622, 1–21.CrossRefGoogle Scholar
Masini, L., Timme, S. & Peace, A. J. 2020 Analysis of a civil aircraft wing transonic shock buffet experiment. J. Fluid Mech. 884, A1.CrossRefGoogle Scholar
McDevitt, J. B. & Okuno, A. F. 1985 Static and dynamic pressure measurements on a NACA 0012 airfoil in the Ames High Reynolds Number Facility. Tech. Rep. NASA-TP-2485. NASA Ames Research Center, Moffett Field, California, United States.Google Scholar
Mettot, C., Renac, F. & Sipp, D. 2014 Computation of eigenvalue sensitivity to base flow modifications in a discrete framework: application to open-loop control. J. Comput. Phys. 269, 234–258.CrossRefGoogle Scholar
Moss, G. F. & Murdin, P. M. 1971 Two-dimensional low-speed tunnel tests on the NACA 0012 section including measurements made during pitching oscillations at the stall. Tech. Rep. C.P. No. 1145. Aeronautical Research Council.Google Scholar
Ohmichi, Y., Ishida, T. & Hashimoto, A. 2018 Modal decomposition analysis of three-dimensional transonic buffet phenomenon on a swept wing. AIAA J. 56 (10), 3938–3950.CrossRefGoogle Scholar
Paladini, E. 2018 Insight on transonic buffet instability: evolution from two-dimensional aerofoils to three-dimensional swept wings. PhD thesis, École Nationale Supérieure d'Arts et Métiers, Paris, France.CrossRefGoogle Scholar
Paladini, E., Beneddine, S., Dandois, J., Sipp, D. & Robinet, J.-Ch. 2019 a Transonic buffet instability: from two-dimensional airfoils to three-dimensional swept wings. Phys. Rev. Fluids 4 (10), 103906.CrossRefGoogle Scholar
Paladini, E., Dandois, J., Sipp, D. & Robinet, J.-Ch. 2019 b Analysis and comparison of transonic buffet phenomenon over several three-dimensional wings. AIAA J. 57 (1), 379–396.CrossRefGoogle Scholar
Paul, R. C. & Gopalarathnam, A. 2014 Iteration schemes for rapid post-stall aerodynamic prediction of wings using a decambering approach. Intl J. Numer. Meth. Fluids 76 (4), 199–222.CrossRefGoogle Scholar
Picella, F., Loiseau, J.-Ch., Lusseyran, F., Robinet, J.-Ch., Cherubini, S. & Pastur, L. 2018 Successive bifurcations in a fully three-dimensional open cavity flow. J. Fluid Mech. 844, 855–877.CrossRefGoogle Scholar
Plante, F., Dandois, J., Beneddine, S., Sipp, D. & Laurendeau, É. 2019 a Numerical simulations and global stability analyses of transonic buffet and subsonic stall. In 54th 3AF International Conference on Applied Aerodynamics. FP63-AERO2019-plante.Google Scholar
Plante, F., Dandois, J. & Laurendeau, E. 2019 b Similarities between cellular patterns occurring in transonic buffet and subsonic stall. AIAA J. 58 (1), 1–14.Google Scholar
Plante, F. & Laurendeau, É. 2019 Simulation of transonic buffet using a time-spectral method. AIAA J. 57 (3), 1–13.CrossRefGoogle Scholar
Ribeiro, A. F. P., Singh, D., König, B., Fares, E., Zhang, R., Gopalakrishnan, P., Li, Y. & Chen, H. 2017 Buffet simulations with a Lattice–Boltzmann based transonic solver. AIAA Paper 2017-1438.CrossRefGoogle Scholar
Richez, F., Leguille, M. & Marquet, O. 2016 Selective frequency damping method for steady RANS solutions of turbulent separated flows around an airfoil at stall. Comput. Fluids 132, 51–61.CrossRefGoogle Scholar
Robinet, J.-Ch. 2007 Bifurcations in shock-wave/laminar-boundary-layer interaction: global instability approach. J. Fluid Mech. 579, 85–112.CrossRefGoogle Scholar
Rodríguez, D. & Theofilis, V. 2010 Structural changes of laminar separation bubbles induced by global linear instability. J. Fluid Mech. 655, 280–305.CrossRefGoogle Scholar
Rodríguez, D. & Theofilis, V. 2011 On the birth of stall cells on airfoils. Theor. Comput. Fluid Dyn. 25, 105–117.CrossRefGoogle Scholar
Roos, F. 1985 The buffeting pressure field of a high-aspect-ratio swept wing. AIAA Paper 1985-1609.CrossRefGoogle Scholar
Sartor, F., Mettot, C. & Sipp, D. 2015 Stability, receptivity, and sensitivity analyses of buffeting transonic flow over a profile. AIAA J. 53, 1980–1993.CrossRefGoogle Scholar
Sartor, F. & Timme, S. 2016 Mach number effects on buffeting flow on a half wing-body configuration. Intl J. Numer. Meth. Heat Fluid Flow 26 (7), 2066–2080.CrossRefGoogle Scholar
Sartor, F. & Timme, S. 2017 Delayed detached–Eddy simulation of shock buffet on half wing–body configuration. AIAA J. 55 (4), 1230–1240.CrossRefGoogle Scholar
Schewe, G. 2001 Reynolds-number effects in flow around more-or-less bluff bodies. J. Wind Engng Ind. Aerodyn. 89 (14–15), 1267–1289.CrossRefGoogle Scholar
Schmid, P. J., de Pando, M. F. & Peake, N. 2017 Stability analysis for $n$-periodic arrays of fluid systems. Phys. Rev. Fluids 2 (11), 113902.CrossRefGoogle Scholar
Sipp, D., Marquet, O., Meliga, P. & Barbagallo, A. 2010 Dynamics and control of global instabilities in open-flows: a linearized approach. Appl. Mech. Rev. 63 (3), 030801.CrossRefGoogle Scholar
Sorensen, D. C. 1992 Implicit application of polynomial filters in a k-step Arnoldi method. SIAM J. Matrix Anal. Appl. 13 (1), 357–385.CrossRefGoogle Scholar
Spalart, P. R. 2014 Prediction of lift cells for stalling wings by lifting-line theory. AIAA J. 52 (8), 1817–1821.CrossRefGoogle Scholar
Sugioka, Y., Koike, S., Nakakita, K., Numata, D., Nonomura, T. & Asai, K. 2018 Experimental analysis of transonic buffet on a 3D swept wing using fast-response pressure-sensitive paint. Exp. Fluids 59 (6), 1–20.CrossRefGoogle Scholar
Taira, K., Brunton, S. L., Dawson, S. T. M., Rowley, C. W., Colonius, T., McKeon, B. J., Schmidt, O. T., Gordeyev, S., Theofilis, V. & Ukeiley, L. S. 2017 Modal analysis of fluid flows: an overview. AIAA J. 55 (12), 4013–4041.CrossRefGoogle Scholar
Theofilis, V. 2011 Global linear instability. Annu. Rev. Fluid Mech. 43 (1), 319–352.CrossRefGoogle Scholar
Theofilis, V., Hein, S. & Dallmann, U. 2000 On the origins of unsteadiness and three-dimensionality in a laminar separation bubble. Phil. Trans. R. Soc. Lond. A 358 (1777), 3229–3246.CrossRefGoogle Scholar
Thiery, M. & Coustols, E. 2006 Numerical prediction of shock induced oscillations over a 2D airfoil: influence of turbulence modelling and test section walls. Intl J. Heat Fluid Flow 27 (4), 661–670.CrossRefGoogle Scholar
Timme, S. 2018 Global instability of wing shock buffet. arXiv:1806.07299.Google Scholar
Timme, S. 2019 Global shock buffet instability on NASA common research model. San Diego, California. AIAA Paper 2019-0037.Google Scholar
Timme, S. 2020 Global instability of wing shock-buffet onset. J. Fluid Mech. 885, A37.CrossRefGoogle Scholar
Wales, C., Gaitonde, A. L., Jones, D. P., Avitabile, D. & Champneys, A. R. 2012 Numerical continuation of high Reynolds number external flows. Intl J. Numer. Meth. Fluids 68 (2), 135–159.CrossRefGoogle Scholar
Winkelmann, A. E. & Barlow, J. B. 1980 Flowfield model for a rectangular planform wing beyond stall. AIAA J. 18 (8), 1006–1008.CrossRefGoogle Scholar
Yon, S. A. & Katz, J. 1998 Study of the unsteady flow features on a stalled wing. AIAA J. 36 (3), 305–312.CrossRefGoogle Scholar
Zaman, K. B. M. Q., McKinzie, D. J., Rumsey, C. L. 1989 A natural low-frequency oscillation of the flow over an airfoil near stalling conditions. J. Fluid Mech. 202, 403–442.CrossRefGoogle Scholar
Zhang, W. & Samtaney, R. 2016 Biglobal linear stability analysis on low-Re flow past an airfoil at high angle of attack. Phys. Fluids 28 (4), 044105.CrossRefGoogle Scholar
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