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On the receptivity of a NACA0008 airfoil to high free-stream turbulence levels

Published online by Cambridge University Press:  04 September 2025

Diego C.P. Blanco*
Affiliation:
Divisão de Engenharia Aeroespacial, Instituto Tecnológico de Aeronáutica, São José dos Campos, São Paulo 12228-900, Brazil
José M. Faúndez Alarcón
Affiliation:
FLOW Turbulence Lab., Department of Engineering Mechanics, KTH Royal Institute of Technology, Sweden
André V.G. Cavalieri
Affiliation:
Divisão de Engenharia Aeroespacial, Instituto Tecnológico de Aeronáutica, São José dos Campos, São Paulo 12228-900, Brazil
Ardeshir Hanifi
Affiliation:
FLOW Turbulence Lab., Department of Engineering Mechanics, KTH Royal Institute of Technology, Sweden
Dan S. Henningson
Affiliation:
FLOW Turbulence Lab., Department of Engineering Mechanics, KTH Royal Institute of Technology, Sweden
*
Corresponding author: Diego C.P. Blanco, diegodcpb@ita.br

Abstract

This work investigates the receptivity mechanisms of a NACA0008 airfoil to a $\textit{Tu}=2.5\,\%$ level of free-stream turbulence (FST) through a direct numerical simulation (DNS) and an associated linearised simulation on the same mesh. By comparing velocity perturbation fields between the two simulations, the study reveals that the streaky structures that degenerate into turbulent spots are predominantly influenced by nonlinear convective terms, rather than the linear amplification of inflow perturbations around the laminar base flow. A power spectral analysis shows differences in the energy distribution between the DNS and linearised simulation, with the DNS containing more energy at higher wavenumbers, for structures located near the airfoil’s leading edge. Representative wavenumbers are identified through modal analysis, revealing a dynamics dominated by streak-like structures. The study employs the Nek5000 numerical solver to distinguish between linear and nonlinear receptivity mechanisms over the NACA0008 airfoil, highlighting their respective contributions to the amplification of perturbations inside the boundary layer. In the high FST case studied, it is observed that the energy of the incoming turbulence is continuously transferred into the boundary layer along the length of the wing. The nonlinear interactions generate streaks with higher spanwise wavenumbers compared with those observed in purely linearised simulations. These thinner streaks align with the spanwise scales identified as susceptible to secondary instabilities. Finally, the procedures presented here generalise the workflow of previous works, allowing for the assessment of receptivity for simulations with arbitrary mesh geometries.

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Type
JFM Papers
Copyright
© The Author(s), 2025. Published by Cambridge University Press

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References

Andersson, P., Berggren, M. & Henningson, D.S. 1999 Optimal disturbances and bypass transition in boundary layers. Phys. Fluids 11 (1), 134150.10.1063/1.869908CrossRefGoogle Scholar
Antoni, J. & Schoukens, J. 2009 Optimal settings for measuring frequency response functions with weighted overlapped segment averaging. IEEE Trans. Instrum. Meas. 58 (9), 32763287.CrossRefGoogle Scholar
Berlin, S., Wiegel, M. & Henningson, D.S. 1999 Numerical and experimental investigations of oblique boundary layer transition. J. Fluid Mech. 393, 2357.10.1017/S002211209900511XCrossRefGoogle Scholar
Blaisdell, G., Spyropoulos, E. & Qin, J. 1996 The effect of the formulation of nonlinear terms on aliasing errors in spectral methods. Appl. Numer. Maths 21 (3), 207219.10.1016/0168-9274(96)00005-0CrossRefGoogle Scholar
Blanco, D.C., Hanifi, A., Henningson, D.S. & Cavalieri, A.V. 2024 Linear and nonlinear receptivity mechanisms in boundary layers subject to free-stream turbulence. J. Fluid Mech. 979, A31.10.1017/jfm.2023.1035CrossRefGoogle Scholar
Blanco, D.C., Martini, E., Sasaki, K. & Cavalieri, A.V. 2022 Improved convergence of the spectral proper orthogonal decomposition through time shifting. J. Fluid Mech. 950, A9.CrossRefGoogle Scholar
Borée, J. 2003 Extended proper orthogonal decomposition: a tool to analyse correlated events in turbulent flows. Exp. Fluids 35 (2), 188192.10.1007/s00348-003-0656-3CrossRefGoogle Scholar
Brandt, L. 2014 The lift-up effect: the linear mechanism behind transition and turbulence in shear flows. Eur. J. Mech. B Fluids 47, 8096.CrossRefGoogle Scholar
Brandt, L., Schlatter, P. & Henningson, D.S. 2004 Transition in boundary layers subject to free-stream turbulence. J. Fluid Mech. 517, 167198.CrossRefGoogle Scholar
Brockie, N. & Baker, C. 1990 The aerodynamic drag of high speed trains. J. Wind Engng Indust. Aerodyn. 34 (3), 273290.CrossRefGoogle Scholar
Bucci, M.A., Cherubini, S., Loiseau, J.-C. & Robinet, J.-C. 2021 Influence of freestream turbulence on the flow over a wall roughness. Phys. Rev. Fluids 6, 063903.10.1103/PhysRevFluids.6.063903CrossRefGoogle Scholar
Bushnell, D.M. 2003 Aircraft drag reduction – a review. Proc. Inst. Mech. Engnrs Part G: J. Aerosp. Engng 217 (1), 118.10.1243/095441003763031789CrossRefGoogle Scholar
Butler, K.M. & Farrell, B.F. 1992 Three-dimensional optimal perturbations in viscous shear flow. Phys. Fluids A: Fluid Dyn. 4 (8), 16371650.10.1063/1.858386CrossRefGoogle Scholar
Dalili, N., Edrisy, A. & Carriveau, R. 2009 A review of surface engineering issues critical to wind turbine performance. Renew. Sustain. Energy Rev. 13 (2), 428438.CrossRefGoogle Scholar
De Vincentiis, L., Henningson, D.S. & Hanifi, A. 2022 Transition in an infinite swept-wing boundary layer subject to surface roughness and free-stream turbulence. J. Fluid Mech. 931, A24.CrossRefGoogle Scholar
Délery, J., Marvin, J.G. & Reshotko, E. 1986 Shock-wave boundary layer interactions. Tech. Rep. AGARD-AG-280, Advisory Group for Aerospace Research and Development, NATO.Google Scholar
Ðurović, K., De Vincentiis, L., Simoni, D., Lengani, D., Pralits, J., Henningson, D.S. & Hanifi, A. 2021 Free-stream turbulence-induced boundary-layer transition in low-pressure turbines. J. Turbomach. 143 (8), 081015.10.1115/1.4050450CrossRefGoogle Scholar
Ðurović, K., Hanifi, A., Schlatter, P., Sasaki, K. & Henningson, D.S. 2024 Direct numerical simulation of transition under free-stream turbulence and the influence of large integral length scales. Phys. Fluids 36 (7), 074105.CrossRefGoogle Scholar
Ellingsen, T. & Palm, E. 1975 Stability of linear flow. Phys. Fluids 18 (4), 487488.10.1063/1.861156CrossRefGoogle Scholar
Faúndez Alarcón, J.M., Cavalieri, A.V., Hanifi, A. & Henningson, D.S. 2024 Role of streak secondary instabilities on free-stream turbulence-induced transition. J. Fluid Mech. 988, A6.10.1017/jfm.2024.433CrossRefGoogle Scholar
Faúndez Alarcón, J.M., Morra, P., Hanifi, A. & Henningson, D.S. 2022 Disturbance growth on a NACA0008 wing subjected to free stream turbulence. J. Fluid Mech. 944, A44.CrossRefGoogle Scholar
Fedorov, A.V. 2003 Receptivity of a high-speed boundary layer to acoustic disturbances. J. Fluid Mech. 491, 101129.10.1017/S0022112003005263CrossRefGoogle Scholar
Fischer, P.F., Lottes, J.W. & Kerkemeier, S.G. 2008 nek5000 Web page. https://nek5000.mcs.anl.gov.Google Scholar
Gustavsson, L.H. 1991 Energy growth of three-dimensional disturbances in plane Poiseuille flow. J. Fluid Mech. 224, 241260.10.1017/S002211209100174XCrossRefGoogle Scholar
Hack, M.J.P. & Zaki, T.A. 2014 Streak instabilities in boundary layers beneath free-stream turbulence. J. Fluid Mech. 741, 280315.CrossRefGoogle Scholar
Henningson, D. 1996 Comment on ‘Transition in shear flows. Nonlinear normality versus non-normal linearity’ [Phys. Fluids 7, 3060 (1995)]. Phys. Fluids 8 (8), 22572258.10.1063/1.869011CrossRefGoogle Scholar
Henningson, D.S., Lundbladh, A. & Johansson, A.V. 1993 A mechanism for bypass transition from localized disturbances in wall-bounded shear flows. J. Fluid Mech. 250 (1), 169207.10.1017/S0022112093001429CrossRefGoogle Scholar
Hinze, J. 1959 Turbulence: An Introduction to Its Mechanism and Theory, McGraw-Hill series in mechanical engineering, McGraw-Hill Book Company.Google Scholar
Hultgren, L.S. & Gustavsson, L.H. 1981 Algebraic growth of disturbances in a laminar boundary layer. Phys. Fluids 24 (6), 10001004.10.1063/1.863490CrossRefGoogle Scholar
Hunt, J. & Durbin, P. 1999 Perturbed vortical layers and shear sheltering. Fluid Dyn. Res. 24 (6), 375404.10.1016/S0169-5983(99)00009-XCrossRefGoogle Scholar
Hunt, J.C.R. & Carruthers, D.J. 1990 Rapid distortion theory and the ‘problems’ of turbulence. J. Fluid Mech. 212, 497532.10.1017/S0022112090002075CrossRefGoogle Scholar
Hwang, Y. & Cossu, C. 2010 Linear non-normal energy amplification of harmonic and stochastic forcing in the turbulent channel flow. J. Fluid Mech. 664, 5173.CrossRefGoogle Scholar
Johnson, M.W. & Pinarbasi, A. 2014 The effect of pressure gradient on boundary layer receptivity. Flow, Turbul. Combust. 93 (1), 124.10.1007/s10494-014-9529-5CrossRefGoogle Scholar
Jovanović, M.R. & Bamieh, B. 2005 Componentwise energy amplification in channel flows. J. Fluid Mech. 534, 145183.10.1017/S0022112005004295CrossRefGoogle Scholar
Karban, U., Martini, E., Cavalieri, A., Lesshafft, L. & Jordan, P. 2022 Self-similar mechanisms in wall turbulence studied using resolvent analysis. J. Fluid Mech. 939, A36.10.1017/jfm.2022.225CrossRefGoogle Scholar
Kendall, J. 1998 Experiments on boundary-layer receptivity to freestream turbulence. In 36th AIAA Aerospace Sciences Meeting and Exhibit, pp. 530, American Institute of Aeronautics and Astronautics, Inc.10.2514/6.1998-530CrossRefGoogle Scholar
Landahl, M.T. 1980 A note on an algebraic instability of inviscid parallel shear flows. J. Fluid Mech. 98 (2), 243251.10.1017/S0022112080000122CrossRefGoogle Scholar
Luchini, P. 2000 Reynolds-number-independent instability of the boundary layer over a flat surface: optimal perturbations. J. Fluid Mech. 404, 289309.CrossRefGoogle Scholar
Maday, Y. & Patera, A.T. 1989 Spectral element methods for the incompressible Navier–Stokes equations. In State-of-the-Art Surveys On Computational Mechanics (A90-47176 21-64), pp. 71143.Google Scholar
Malm, J., Schlatter, P., Fischer, P.F. & Henningson, D.S. 2013 Stabilization of the spectral element method in convection dominated flows by recovery of skew-symmetry. J. Sci. Comput. 57 (2), 254277.10.1007/s10915-013-9704-1CrossRefGoogle Scholar
Mans, J., De Lange, H. & Van Steenhoven, A. 2007 Sinuous breakdown in a flat plate boundary layer exposed to free-stream turbulence. Phys. Fluids 19 (8), 088101.10.1063/1.2750684CrossRefGoogle Scholar
Martini, E., Cavalieri, A.V.G., Jordan, P. & Lesshafft, L. 2020 Accurate frequency domain identification of odes with arbitrary signals. arXiv: 1907.04787.Google Scholar
Matsubara, M. & Alfredsson, P.H. 2001 Disturbance growth in boundary layers subjected to free-stream turbulence. J. Fluid Mech. 430, 149168.10.1017/S0022112000002810CrossRefGoogle Scholar
McKeon, B.J. & Sharma, A.S. 2010 A critical-layer framework for turbulent pipe flow. J. Fluid Mech. 658, 336382.10.1017/S002211201000176XCrossRefGoogle Scholar
Moffatt, H.K. 2014 Note on the triad interactions of homogeneous turbulence. J. Fluid Mech. 741, R3.CrossRefGoogle Scholar
Morkovin, M.V. 1969 On the many faces of transition. In Viscous Drag Reduction (ed. C.S. Wells), pp. 131. Springer.Google Scholar
Morkovin, M.V. 1985 Bypass transition to turbulence and research desiderata. In Transition in Turbines, pp. 161204. NASA. Lewis Research Center.Google Scholar
Morkovin, M.V., Reshotko, E. & Herbert, T. 1994 Transition in open flow systems – a reassessment. B. Am. Phys. Soc. 39, 1882.Google Scholar
Morra, P., Nogueira, P.A.S., Cavalieri, A.V.G. & Henningson, D.S. 2021 The colour of forcing statistics in resolvent analyses of turbulent channel flows. J. Fluid Mech. 907, A24.10.1017/jfm.2020.802CrossRefGoogle Scholar
Nagarajan, S., Lele, S.K. & Ferziger, J.H. 2007 Leading-edge effects in bypass transition. J. Fluid Mech. 572, 471504.10.1017/S0022112006001893CrossRefGoogle Scholar
Nogueira, P.A.S., Morra, P., Martini, E., Cavalieri, A.V.G. & Henningson, D.S. 2021 Forcing statistics in resolvent analysis: application in minimal turbulent Couette flow. J. Fluid Mech. 908, A32.CrossRefGoogle Scholar
Reed, H.L., Saric, W.S. & Arnal, D. 1996 Linear stability theory applied to boundary layers. Annu. Rev. Fluid Mech. 28 (1), 389428.10.1146/annurev.fl.28.010196.002133CrossRefGoogle Scholar
Reshotko, E. 1984 Disturbances in a laminar boundary layer due to distributed surface roughness. In Turbulence and Chaotic Phenomena in Fluids. Proceedings of the International Symposium: held in Kyoto, 3946. Elsevier Science Ltd.Google Scholar
Saric, W.S., Reed, H.L. & Kerschen, E.J. 2002 Boundary-layer receptivity to freestream disturbances. Annu. Rev. Fluid Mech. 34 (1), 291319.10.1146/annurev.fluid.34.082701.161921CrossRefGoogle Scholar
Sasaki, K., Cavalieri, A.V.G., Hanifi, A. & Henningson, D.S. 2022 Parabolic resolvent modes for streaky structures in transitional and turbulent boundary layers. Phys. Rev. Fluids 7, 104611.10.1103/PhysRevFluids.7.104611CrossRefGoogle Scholar
Schlatter, P., Brandt, L., de Lange, H.C. & Henningson, D.S. 2008 On streak breakdown in bypass transition. Phys. Fluids 20 (10), 101505.CrossRefGoogle Scholar
Schmid, P.J., Henningson, D.S., Khorrami, M.R. & Malik, M.R. 1993 A study of eigenvalue sensitivity for hydrodynamic stability operators. Theor. Comput. Fluid Dyn. 4 (5), 227240.10.1007/BF00417929CrossRefGoogle Scholar
Schrader, L.-U., Brandt, L. & Henningson, D.S. 2009 Receptivity mechanisms in three-dimensional boundary-layer flows. J. Fluid Mech. 618, 209241.10.1017/S0022112008004345CrossRefGoogle Scholar
Schrader, L.-U., Brandt, L., Mavriplis, C. & Henningson, D.S. 2010 Receptivity to free-stream vorticity of flow past a flat plate with elliptic leading edge. J. Fluid Mech. 653, 245271.10.1017/S0022112010000376CrossRefGoogle Scholar
Schubauer, G.B. & Skramstad, H.K. 1947 Laminar boundary-layer oscillations and stability of laminar flow. J. Aeronaut. Sci. 14 (2), 6978.CrossRefGoogle Scholar
Sirovich, L. 1987 Turbulence and the dynamics of coherent structures part i: coherent structures. Q. Appl. Math. 45 (3), 561571.10.1090/qam/910462CrossRefGoogle Scholar
Sovran, G. 2012 Aerodynamic Drag Mechanisms of Bluff Bodies and Road Vehicles. Springer Science & Business Media.Google Scholar
Suder, K.L., Obrien, J.E. & Reshotko, E. 1988 Experimental study of bypass transition in a boundary layer. In Mathesis NASA-TM-100913. NASA, Lewis Research Center.Google Scholar
Towne, A., Schmidt, O.T. & Colonius, T. 2018 Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis. J. Fluid Mech. 847, 821867.CrossRefGoogle Scholar
Trefethen, L.N., Trefethen, A.E., Reddy, S.C. & Driscoll, T.A. 1993 Hydrodynamic stability without eigenvalues. Science 261 (5121), 578584.10.1126/science.261.5121.578CrossRefGoogle ScholarPubMed
Vaughan, N.J. & Zaki, T.A. 2011 Stability of zero-pressure-gradient boundary layer distorted by unsteady Klebanoff streaks. J. Fluid Mech. 681, 116153.10.1017/jfm.2011.177CrossRefGoogle Scholar
Walker, G.J. 1993 The role of laminar–turbulent transition in gas turbine engines: a discussion. J. Turbomach. 115 (2), 207216.10.1115/1.2929223CrossRefGoogle Scholar
Webber, J.B.W. 2012 A bi-symmetric log transformation for wide-range data. Meas. Sci. Technol. 24 (2), 027001.CrossRefGoogle Scholar
Welch, P.D. 1967 The use of fast fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms. IEEE Trans. Audio Electroacoust. 15 (2), 7073.10.1109/TAU.1967.1161901CrossRefGoogle Scholar
Zaki, T.A. & Durbin, P.A. 2005 Mode interaction and the bypass route to transition. J. Fluid Mech. 531, 85111.10.1017/S0022112005003800CrossRefGoogle Scholar