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Aerodynamic performance of a transonic airfoil with spanwise forcing

Published online by Cambridge University Press:  09 May 2025

Niccolò Berizzi Open the ORCID record for Niccolò Berizzi [Opens in a new window] ,
Davide Gatti Open the ORCID record for Davide Gatti [Opens in a new window] ,
Giulio Soldati Open the ORCID record for Giulio Soldati [Opens in a new window] ,
Sergio Pirozzoli Open the ORCID record for Sergio Pirozzoli [Opens in a new window]  and
Maurizio Quadrio Open the ORCID record for Maurizio Quadrio [Opens in a new window]
Niccolò Berizzi
Affiliation:
Dipartimento di Scienze e Tecnologie Aerospaziali, Politecnico di Milano, Via La Masa 34, Milano 20156, Italy
Davide Gatti
Affiliation:
Institute of Fluid Mechanics, Karlsruhe Institute of Technology, Kaiserstraße 10, Karlsruhe 76131, Germany
Giulio Soldati
Affiliation:
Dipartimento di Meccanica e Aeronautica, Università di Roma ‘La Sapienza’, Via Eudossiana 18, Roma 00184, Italy
Sergio Pirozzoli
Affiliation:
Dipartimento di Meccanica e Aeronautica, Università di Roma ‘La Sapienza’, Via Eudossiana 18, Roma 00184, Italy
Maurizio Quadrio*
Affiliation:
Dipartimento di Scienze e Tecnologie Aerospaziali, Politecnico di Milano, Via La Masa 34, Milano 20156, Italy
*
Corresponding author: Maurizio Quadrio, [email protected]
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Abstract

Spanwise wall forcing in the form of streamwise-travelling waves is applied to the suction side of a transonic airfoil with a shock wave to reduce aerodynamic drag. The study, conducted using direct numerical simulations, extends earlier findings by Quadrio et al. (J. Fluid Mech. vol. 942(R2), 2022, pp. 1–10) and confirms that the wall manipulation shifts the shock wave on the suction side towards the trailing edge of the profile, thereby enhancing its aerodynamic efficiency. A parametric study over the parameters of wall forcing is carried out for the Mach number set at 0.7 and the Reynolds number at 300 000. Similarities and differences with the incompressible plane case are discussed; for the first time, we describe how the interaction between the shock wave and the boundary layer is influenced by flow control via spanwise forcing. With suitable combinations of control parameters, the shock is delayed, which results in a separated region whose length correlates well with friction reduction. The analysis of the transient process following the sudden application of control is used to link flow separation with the intensification of the shock wave.

JFM classification

Turbulent Flows: Compressible turbulence Turbulent Flows: Turbulence control
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1010 , 10 May 2025 , A18
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© The Author(s), 2025. Published by Cambridge University Press

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References

Abbas, A., de Vicente, J. & Valero, E. 2013 Aerodynamic technologies to improve aircraft performance. Aerosp. Sc & Tech. 28 (1), 100–132.CrossRefGoogle Scholar
Auteri, F., Baron, A., Belan, M., Campanardi, G. & Quadrio, M. 2010 Experimental assessment of drag reduction by traveling waves in a turbulent pipe flow. Phys. Fluids 22 (11), 115103–115114.CrossRefGoogle Scholar
Banchetti, J., Luchini, P. & Quadrio, M. 2020 Turbulent drag reduction over curved walls. J. Fluid Mech. 896, 1–23.CrossRefGoogle Scholar
Bird, J., Santer, M. & Morrison, J.F. 2018 Experimental control of turbulent boundary layers with in-plane travelling waves. Flow Turbul. Combust. 100 (4), 1015–1035.CrossRefGoogle ScholarPubMed
Délery, J. & Marvin, J.G. 1986 Shock-Wave Boundary Layer Interactions. (ed. Reshotko, E.) AGARDograph 280. Advisory Group for Aerospace Research for Development, NATO, p. 224.Google Scholar
Doerffer, P., Flaszynski, P., Dussauge, J.-P., Babinsky, H., Grothe, P. & Petersen, A. 2021 Transition Location Effect on Shock Wave Boundary Layer Interaction: Experimental and Numerical Findings from the TFAST Project, In Notes on Numerical Fluid Mechanics and Multidisciplinary Design. (ed. Billard, F.), vol. 144. Springer International Publishing.Google 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), 517–549.CrossRefGoogle Scholar
Fang, J., Zheltovodov, A., Yao, Y., Moulinec, C. & Emerson, D. 2020 On the turbulence amplification in shock-wave/turbulent boundary layer interaction. J. Fluid Mech. 897, A32.CrossRefGoogle Scholar
Frohnapfel, B., Hasegawa, Y. & Quadrio, M. 2012 Money versus time: evaluation of flow control in terms of energy consumption and convenience. J. Fluid Mech. 700, 406–418.CrossRefGoogle Scholar
Fumarola, I., Santer, M. & Morrison, J. 2024 Simultaneous measurements of surface spanwise waves and velocity in a turbulent boundary layer. Flow Turbul. Combust. 113 (1), 139–158.CrossRefGoogle Scholar
Gallorini, E. & Quadrio, M. 2024 Spatial discretization effects in spanwise forcing for turbulent drag reduction. J. Fluid Mech. 982, A11.CrossRefGoogle Scholar
Gattere, F., Zanolini, M., Gatti, D., Bernardini, M. & Quadrio, M. 2024 Turbulent drag reduction with streamwise-travelling waves in the compressible regime. J. Fluid Mech. 987, A30.CrossRefGoogle Scholar
Gatti, D., Güttler, A., Frohnapfel, B. & Tropea, C. 2015 Experimental assessment of spanwise-oscillating dielectric electroactive surfaces for turbulent drag reduction in an air channel flow. Exp. Fluids 56 (5), 1–15.CrossRefGoogle Scholar
Gatti, D. & Quadrio, M. 2016 Reynolds-number dependence of turbulent skin-friction drag reduction induced by spanwise forcing. J. Fluid Mech. 802, 553–558.CrossRefGoogle Scholar
Graver, B., Zhang, K. & Rutherford, D. 2019 CO2 emissions from commercial aviation, 2018, Tech. Rep.International Council on Clean Transportion.Google Scholar
Jameson, A., Schmidt, W. & Turkel, E. 1981 Numerical solution of the Euler equations by finite volume methods using Runge Kutta time stepping schemes, In 14th Fluid and Plasma Dynamics Conference. American Institute of Aeronautics and Astronautics.CrossRefGoogle Scholar
Jung, W.J., Mangiavacchi, N. & Akhavan, R. 1992 Suppression of turbulence in wall-bounded flows by high-frequency spanwise oscillations. Phys. Fluids A 4 (8), 1605–1607.CrossRefGoogle Scholar
Kasagi, N., Hasegawa, Y. & Fukagata, K. 2009 Towards cost-effective control of wall turbulence for skin-friction drag reduction. In Advances in Turbulence XII, (ed. Eckhardt, B.), vol. 132, pp. 189–200. Springer.CrossRefGoogle Scholar
Knoop, M.W., Hartog, F.H., Schrijer, F.F.J., van Campenhout, O.W.G., van Nesselrooij, M. & van Oudheusden, B.W. 2024 Experimental assessment of square-wave spatial spanwise forcing of a turbulent boundary layer. Exp. Fluids 65 (5), 65.CrossRefGoogle Scholar
Laflin, K.R., Klausmeyer, S.M., Zickuhr, T., Vassberg, J.C., Wahls, R.A., Morrison, J.H., Brodersen, O.P., Rakowitz, M.E., Tinoco, E.N. & Godard, J.-L. 2005 Data summary from second AIAA computational fluid dynamics drag prediction workshop. J. Aircraft 42 (5), 1165–1178.CrossRefGoogle Scholar
Liu, X.D., Osher, S. & Chan, T. 1994 Weighted essentially non-oscillatory schemes. J. Comp. Phys. 115, 200–212.CrossRefGoogle Scholar
Marusic, I., Chandran, D., Rouhi, A., Fu, M.K., Wine, D., Holloway, B., Chung, D. & Smits, A.J. 2021 An energy-efficient pathway to turbulent drag reduction. Nat. Commun. 12 (1), 5805.CrossRefGoogle ScholarPubMed
Mele, B., Tognaccini, R. & Catalano, P. 2016 Performance assessment of a transonic wing-body configuration with riblets installed. J. Aircraft 53 (1), 129–140.CrossRefGoogle Scholar
Memmolo, A., Bernardini, M. & Pirozzoli, S. 2018 Scrutiny of buffet mechanisms in transonic flow. Intl J. Numer. Meth. Fluids 28 (5), 1031–1046.CrossRefGoogle Scholar
Pirozzoli, S. 2011 Numerical methods for high-speed flows. Annu. Rev. Fluid Mech. 43 (1), 163–194.CrossRefGoogle Scholar
Pirozzoli, S., Bernardini, M. & Grasso, F. 2010 Direct numerical simulation of transonic shock/boundary layer interaction under conditions of incipient separation. J. Fluid Mech. 657, 361–393.CrossRefGoogle Scholar
Placek, R. & Ruchala, P. 2018 The flow separation development analysis in subsonic and transonic flow regime of the laminar airfoil. Transp. Res. Proc. 29, 323–329.Google Scholar
Quadrio, M., Chiarini, A., Banchetti, J., Gatti, D., Memmolo, A. & Pirozzoli, S. 2022 Drag reduction on a transonic airfoil. J. Fluid. Mech. 942, 1–10.CrossRefGoogle Scholar
Quadrio, M. & Ricco, P. 2004 Critical assessment of turbulent drag reduction through spanwise wall oscillations. J. Fluid Mech. 521, 251–271.CrossRefGoogle Scholar
Quadrio, M. & Ricco, P. 2011 The laminar generalized Stokes layer and turbulent drag reduction. J. Fluid Mech. 667, 135–157.CrossRefGoogle Scholar
Quadrio, M., Ricco, P. & Viotti, C. 2009 Streamwise-traveling waves of spanwise wall velocity for turbulent drag reduction. J. Fluid Mech. 627, 161–178.CrossRefGoogle Scholar
Russo, S. & Luchini, P. 2017 A fast algorithm for the estimation of statistical error in DNS (or experimental) time averages. J. Comput. Phys. 347, 328–340.CrossRefGoogle Scholar
Schlatter, P. & Örlü, R. 2012 Turbulent boundary layers at moderate Reynolds numbers: inflow length and tripping effects. J. Fluid Mech. 710, 5–34.CrossRefGoogle Scholar
Skote, M. 2012 Temporal and spatial transients in turbulent boundary layer flow over an oscillating wall. Intl J. Heat Fluid Flow 38, 1–12.CrossRefGoogle Scholar
Smits, A.J. & Dussauge, J.P. 2006 Turbulent Shear Layers in Supersonic Flow. Springer.Google Scholar
Spalart, P. & Allmaras, S. 1992 A one-equation turbulence model for aerodynamic flows, In 30th Aerospace Sciences Meeting and Exhibit. American Institute of Aeronautics and Astronautics.CrossRefGoogle Scholar
Szubert, D., Asproulias, I., Grossi, F., Duvigneau, R., Hoarau, Y. & Braza, M. 2016 Numerical study of the turbulent transonic interaction and transition location effect involving optimisation around a supercritical aerofoil. Eur. J. Mech. ( B/ Fluids) 55, 380–393.CrossRefGoogle Scholar
Trettel, A. & Larsson, J. 2016 Mean velocity scaling for compressible wall turbulence with heat transfer. Phys. Fluids 28 (2), 026102.CrossRefGoogle Scholar
Venkatakrishnan, V. 1995 Convergence to steady state solutions of the Euler equations on unstructured grids with limiters. J. Comput. Phys. 118 (1), 120–130.CrossRefGoogle Scholar
Xu, D., Ricco, P. & Duan, L. 2023 Decomposition of the skin-friction coefficient of compressible boundary layers. Phys. Fluids 35 (3), 035107.CrossRefGoogle Scholar
Yao, J. & Hussain, F. 2019 Supersonic turbulent boundary layer drag control using spanwise wall oscillation. J . Fluid Mech. 880, 388–429.CrossRefGoogle Scholar
Yudhistira, I. & Skote, M. 2011 Direct numerical simulation of a turbulent boundary layer over an oscillating wall. J. Turbul. 12 (9), 1–17.CrossRefGoogle Scholar
Zauner, M., De Tullio, N. & Sandham, N.D. 2019 Direct numerical simulations of transonic flow around an airfoil at moderate Reynolds numbers. AIAA J. 57 (2), 597–607.CrossRefGoogle Scholar
Supplementary material: File

Berizzi et al. supplementary material movie 1

Transient of flow case C10. On the left: time histories of the spanwise-averaged mean friction coefficient between x = 0.3 and x = 0.4 (top), the shock position (center) and the length of the recirculation bubble (bottom), after sudden activation of StTW. The horizontal lines show the mean asymptotic value (coloured) and the mean value of the REF flow case (black). On the right: magnitude of the pressure gradient on a (x, y) plane, shortly after the control activation (t = 1.7), and at a later time (t = 16.6).
Download Berizzi et al. supplementary material movie 1(File)
File 10 MB
Supplementary material: File

Berizzi et al. supplementary material movie 2

Transient of flow case C13. On the left: time histories of the spanwise-averaged mean friction coefficient between x = 0.3 and x = 0.4 (top), the shock position (center) and the length of the recirculation bubble (bottom), after sudden activation of StTW. The horizontal lines show the mean asymptotic value (coloured) and the mean value of the REF flow case (black). On the right: magnitude of the pressure gradient on a (x, y) plane, shortly after the control activation (t = 1.7), and at a later time (t = 16.6).
Download Berizzi et al. supplementary material movie 2(File)
File 9.9 MB