Hostname: page-component-848d4c4894-2xdlg Total loading time: 0 Render date: 2024-06-19T14:29:35.319Z Has data issue: false hasContentIssue false
  • English
  • Français

How spanwise travelling transversal surface waves change the near-wall flow

Published online by Cambridge University Press:  23 February 2023

Esther Mäteling Open the ORCID record for Esther Mäteling [Opens in a new window] ,
Marian Albers Open the ORCID record for Marian Albers [Opens in a new window]  and
Wolfgang Schröder Open the ORCID record for Wolfgang Schröder [Opens in a new window]
Esther Mäteling*
Affiliation:
Institute of Aerodynamics, RWTH Aachen University, Wüllnerstraße 5a, 52062 Aachen, Germany
Marian Albers
Affiliation:
Institute of Aerodynamics, RWTH Aachen University, Wüllnerstraße 5a, 52062 Aachen, Germany
Wolfgang Schröder
Affiliation:
Institute of Aerodynamics, RWTH Aachen University, Wüllnerstraße 5a, 52062 Aachen, Germany JARA Center for Simulation and Data Science, RWTH Aachen University, Seffenter Weg 23, 52074 Aachen, Germany
*
†Email address for correspondence: e.maeteling@aia.rwth-aachen.de
Get access Rights & Permissions [Opens in a new window]

Abstract

The alteration of the near-wall flow field of a turbulent boundary layer flow subjected to spanwise travelling transversal surface waves at a friction Reynolds number $Re_\tau \approx 1525$ is investigated. The results of a spatial noise-assisted multivariate empirical mode decomposition reveal that this flow control method periodically induces near-wall large-scale bursts while simultaneously lowering the energetic content of small-scale features. The increasing occurrence of intense large-scale ejections in the near-wall region is of particular importance for reducing the wall-shear stress since these ejections balance large-scale sweeps originating from the outer layer. Thus, they corrupt the outer-layer impact on the near-wall dynamics and, consequently, the overall fluctuation intensity at the wall is attenuated. This disturbed top-down momentum exchange is highlighted by an inner–outer interaction analysis, which further reveals an increased bottom-up communication provoked by the large-scale ejections. Moreover, it is shown that the periodic secondary flow field induced by the actuation interferes with the quasi-streamwise vortices in the near-wall region. The velocity gradients of the secondary flow field deform the vortices’ cross-section into an elliptic shape, which yields an unstable vortex state resulting in vortex disintegration. In combination with the effect of the large-scale ejections, the reduced number of quasi-streamwise vortices compared with the undisturbed boundary layer flow results in a decreased wall-normal momentum exchange and the widening and weakening of near-wall streaks. This yields a reduced fluctuation intensity in the near-wall region that lowers the overall wall-shear stress level.

JFM classification

Boundary Layers: Boundary layer control Flow Control: Drag reduction Turbulent Flows: Turbulence control
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 957 , 25 February 2023 , A30
Check for updates
Copyright
© The Author(s), 2023. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Adrian, R.J., Christensen, K.T. & Liu, Z.-C. 2000 Analysis and interpretation of instantaneous turbulent velocity fields. Exp. Fluids 29 (3), 275–290.CrossRefGoogle Scholar
Agostini, L. & Leschziner, M. 2014 On the influence of outer large-scale structures on near-wall turbulence in channel flow. Phys. Fluids 26 (7), 075107.CrossRefGoogle Scholar
Agostini, L. & Leschziner, M. 2018 The impact of footprints of large-scale outer structures on the near-wall layer in the presence of drag-reducing spanwise wall motion. Flow Turbul. Combust. 100, 1037–1061.CrossRefGoogle Scholar
Agostini, L. & Leschziner, M. 2021 Statistical analysis of outer large-scale/inner-layer interactions in channel flow subjected to oscillatory drag-reducing wall motion using a multiple-variable joint-probability-density function methodology. J. Fluid Mech. 923, A25.CrossRefGoogle Scholar
Albers, M., Meysonnat, P.S., Fernex, D., Semaan, R., Noack, B.R. & Schröder, W. 2020 Drag reduction and energy saving by spanwise traveling transversal surface waves for flat plate flow. Flow Turbul. Combust. 105, 125–157.CrossRefGoogle Scholar
Corino, E.R. & Brodkey, R.S. 1969 A visual investigation of the wall region in turbulent flow. J. Fluid Mech. 37 (1), 1–30.CrossRefGoogle Scholar
Cornish, J.J. III & Boatwright, D.W. 1960 Application of full scale boundary layer measurements to drag reduction of airships. Tech. Rep. 28. Mississippi State University.CrossRefGoogle Scholar
Cossu, C. & Hwang, Y. 2017 Self-sustaining processes at all scales in wall-bounded turbulent shear flows. Phil. Trans. R. Soc. Lond. A 375 (2089), 20160088.Google ScholarPubMed
Dhanak, M.R. & Marshall, M.P. 1993 Motion of an elliptical vortex under applied periodic strain. Phys. Fluids A 5 (5), 1224–1230.CrossRefGoogle Scholar
Dritschel, D.G. 1989 Strain-induced vortex stripping. In Mathematical Aspects of Vortex Dynamics (ed. R.E. Caflisch), pp. 107–119. SIAM.Google Scholar
Dritschel, D.G. 1990 The stability of elliptical vortices in an external straining flow. J. Fluid Mech. 210, 223–261.CrossRefGoogle Scholar
Fernex, D., Semaan, R., Albers, M., Meysonnat, P.S., Schröder, W. & Noack, B.R. 2020 Actuation response model from sparse data for wall turbulence drag reduction. Phys. Rev. Fluids 5 (7), 073901.CrossRefGoogle Scholar
Ganapathisubramani, B., Hutchins, N., Monty, J.P., Chung, D. & Marusic, I. 2012 Amplitude and frequency modulation in wall turbulence. J. Fluid Mech. 712, 61–91.CrossRefGoogle Scholar
Gatti, D. & Quadrio, M. 2013 Performance losses of drag-reducing spanwise forcing at moderate values of the Reynolds number. Phys. Fluids 25 (12), 125109.CrossRefGoogle Scholar
Gatti, D. & Quadrio, M. 2016 Reynolds-number dependence of turbulent skin-friction drag reduction induced by spanwise forcing. J. Fluid Mech. 802, 553–582.CrossRefGoogle Scholar
Hamilton, J.M., Kim, J. & Waleffe, F. 1995 Regeneration mechanisms of near-wall turbulence structures. J. Fluid Mech. 287, 317–348.CrossRefGoogle Scholar
Hussain, A.K.M.F. & Reynolds, W.C. 1970 The mechanics of an organized wave in turbulent shear flow. J. Fluid Mech. 41 (2), 241–258.CrossRefGoogle Scholar
Hutchins, N. & Marusic, I. 2007 Large-scale influences in near-wall turbulence. Phil. Trans. R. Soc. Lond. A 365 (1852), 647–664.Google ScholarPubMed
Jeong, J., Hussain, F., Schoppa, W. & Kim, J. 1997 Coherent structures near the wall in a turbulent channel flow. J. Fluid Mech. 332, 185–214.CrossRefGoogle Scholar
Jiménez, J. & Moin, P. 1991 The minimal flow unit in near-wall turbulence. J. Fluid Mech. 225, 213–240.CrossRefGoogle Scholar
Jiménez, J. & Pinelli, A. 1999 The autonomous cycle of near-wall turbulence. J. Fluid Mech. 389, 335–359.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
Kida, S. 1981 Motion of an elliptic vortex in a uniform shear flow. J. Phys. Soc. Japan 50 (10), 3517–3520.CrossRefGoogle Scholar
Koh, S.R., Meysonnat, P., Statnikov, V., Meinke, M. & Schröder, W. 2015 Dependence of turbulent wall-shear stress on the amplitude of spanwise transversal surface waves. Comput. Fluids 119, 261–275.CrossRefGoogle Scholar
Koshel, K.V., Ryzhov, E.A. & Carton, X.J. 2019 Vortex interactions subjected to deformation flows: a review. Fluids 4 (1), 14.CrossRefGoogle Scholar
Laadhari, F., Skandaji, L. & Morel, R. 1994 Turbulence reduction in a boundary layer by a local spanwise oscillating surface. Phys. Fluids 6 (10), 3218–3220.CrossRefGoogle Scholar
Li, W., Roggenkamp, D., Hecken, T., Jessen, W., Klaas, M. & Schröder, W. 2018 Parametric investigation of friction drag reduction in turbulent flow over a flexible wall undergoing spanwise transversal traveling waves. Exp. Fluids 59 (6), 1–18.CrossRefGoogle Scholar
Li, W., Roggenkamp, D., Paakkari, V., Klaas, M., Soria, J. & Schroeder, W. 2020 Analysis of a drag reduced flat plate turbulent boundary layer via uniform momentum zones. Aerosp. Sci. Technol. 96, 105552.CrossRefGoogle Scholar
Lu, S.S. & Willmarth, W.W. 1973 Measurements of the structure of the Reynolds stress in a turbulent boundary layer. J. Fluid Mech. 60 (3), 481–511.CrossRefGoogle Scholar
Mariotti, A., Legras, B. & Dritschel, D.G. 1994 Vortex stripping and the erosion of coherent structures in two-dimensional flows. Phys. Fluids 6 (12), 3954–3962.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), 1–8.CrossRefGoogle ScholarPubMed
Marusic, I. & Heuer, W.D.C. 2007 Reynolds number invariance of the structure inclination angle in wall turbulence. Phys. Rev. Lett. 99 (11), 114504.CrossRefGoogle ScholarPubMed
Marusic, I., Mathis, R. & Hutchins, N. 2010 High Reynolds number effects in wall turbulence. Intl J. Heat Fluid Flow 31 (3), 418–428.CrossRefGoogle Scholar
Mäteling, E., Klaas, M. & Schröder, W. 2020 Detection of small-scale/large-scale interactions in turbulent wall-bounded flows. Phys. Rev. Fluids 5 (11), 114610.CrossRefGoogle Scholar
Mäteling, E. & Schröder, W. 2022 Analysis of spatiotemporal inner-outer large-scale interactions in turbulent channel flow by multivariate empirical mode decomposition. Phys. Rev. Fluids 7, 034603.CrossRefGoogle Scholar
Moore, D.W. & Saffman, P.G. 1971 Structure of a line vortex in an imposed strain. In Aircraft Wake Turbulence and its Detection (ed. J.H. Olsen, A. Goldburg, M. Rogers), pp. 339–354. Springer.CrossRefGoogle Scholar
Nagib, H.M., Chauhan, K.A. & Monkewitz, P.A. 2007 Approach to an asymptotic state for zero pressure gradient turbulent boundary layers. Phil. Trans. R. Soc. Lond. A 365 (1852), 755–770.Google Scholar
Quadrio, M., Ricco, P. & Viotti, C. 2009 Streamwise-travelling waves of spanwise wall velocity for turbulent drag reduction. J. Fluid Mech. 627, 161–178.CrossRefGoogle Scholar
Ricco, P., Skote, M. & Leschziner, M. 2021 A review of turbulent skin-friction drag reduction by near-wall transverse forcing. Prog. Aerosp. Sci. 123, 100713.CrossRefGoogle Scholar
Robinson, A.C. & Saffman, P.G. 1984 Three-dimensional stability of an elliptical vortex in a straining field. J. Fluid Mech. 142, 451–466.CrossRefGoogle Scholar
Roidl, B., Meinke, M. & Schröder, W. 2013 A reformulated synthetic turbulence generation method for a zonal RANS–LES method and its application to zero-pressure gradient boundary layers. Intl J. Heat Fluid Flow 44, 28–40.CrossRefGoogle Scholar
Schoppa, W. & Hussain, F. 2002 Coherent structure generation in near-wall turbulence. J. Fluid Mech. 453, 57–108.CrossRefGoogle Scholar
Skote, M. 2022 Drag reduction of turbulent boundary layers by travelling and non-travelling waves of spanwise wall oscillations. Fluids 7 (2), 65.CrossRefGoogle Scholar
Tamano, S. & Itoh, M. 2012 Drag reduction in turbulent boundary layers by spanwise traveling waves with wall deformation. J. Turbul. 13, N9.CrossRefGoogle Scholar
Tomiyama, N. & Fukagata, K. 2013 Direct numerical simulation of drag reduction in a turbulent channel flow using spanwise traveling wave-like wall deformation. Phys. Fluids 25 (10), 105115.CrossRefGoogle Scholar
Tomkins, C.D. & Adrian, R.J. 2003 Spanwise structure and scale growth in turbulent boundary layers. J. Fluid Mech. 490, 37–74.CrossRefGoogle Scholar
Touber, E. & Leschziner, M.A. 2012 Near-wall streak modification by spanwise oscillatory wall motion and drag-reduction mechanisms. J. Fluid Mech. 693, 150–200.CrossRefGoogle Scholar
Vessey, H.F. 1935 Skin friction drag: the practical importance of reduction in profile and fuselage drag. Aircr. Engng Aerosp. Tec. 7, 173–174.CrossRefGoogle Scholar
Weske, J.R. 1939 Reduction of skin-friction on a flat plate through boundary layer control. J. Aeronaut. Sci. 6 (7), 289–291.CrossRefGoogle Scholar
Zhou, J., Adrian, R.J., Balachandar, S. & Kendall, T.M. 1999 Mechanisms for generating coherent packets of hairpin vortices in channel flow. J. Fluid Mech. 387, 353–396.CrossRefGoogle Scholar

Mäteling et al. Supplementary Movie

See "Mäteling et al. Supplementary Movie Captions"

Download Mäteling et al. Supplementary Movie(Video)
Video 9.7 MB
Supplementary material: PDF

Mäteling et al. Supplementary Movie Caption

Mäteling et al. Supplementary Movie Caption

Download Mäteling et al. Supplementary Movie Caption(PDF)
PDF 11.7 KB