Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-30T14:19:11.874Z Has data issue: false hasContentIssue false
  • English
  • Français

Streamwise-travelling waves of spanwise wall velocity for turbulent drag reduction

Published online by Cambridge University Press:  25 May 2009

MAURIZIO QUADRIO ,
PIERRE RICCO  and
CLAUDIO VIOTTI
MAURIZIO QUADRIO*
Affiliation:
Politecnico di Milano, Milano 20156, Italy
PIERRE RICCO
Affiliation:
King's College London, London WC2R 2LS, UK
CLAUDIO VIOTTI
Affiliation:
The University of North Carolina, Chapel Hill, NC 27516, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Waves of spanwise velocity imposed at the walls of a plane turbulent channel flow are studied by direct numerical simulations. We consider sinusoidal waves of spanwise velocity which vary in time and are modulated in space along the streamwise direction. The phase speed may be null, positive or negative, so that the waves may be either stationary or travelling forward or backward in the direction of the mean flow. Such a forcing includes as particular cases two known techniques for reducing friction drag: the oscillating wall technique (a travelling wave with infinite phase speed) and the recently proposed steady distribution of spanwise velocity (a wave with zero phase speed). The travelling waves alter the friction drag significantly. Waves which slowly travel forward produce a large reduction of drag that can relaminarize the flow at low values of the Reynolds number. Faster waves yield a totally different outcome, i.e. drag increase (DI). Even faster waves produce a drag reduction (DR) effect again. Backward-travelling waves instead lead to DR at any speed. The travelling waves, when they reduce drag, operate in similar fashion to the oscillating wall, with an improved energetic efficiency. DI is observed when the waves travel at a speed comparable with that of the convecting near-wall turbulence structures. A diagram illustrating the different flow behaviours is presented.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 627 , 25 May 2009 , pp. 161 - 178
Copyright
Copyright © Cambridge University Press 2009

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

REFERENCES

Baron, A. & Quadrio, M. 1996 Turbulent drag reduction by spanwise wall oscillations. Appl. Sci. Res. 55, 311–326.Google Scholar
Choi, K.-S., DeBisschop, J. R. & Clayton, B. R. 1998 Turbulent boundary-layer control by means of spanwise-wall oscillation. AIAA J. 36 (7), 1157–1162.CrossRefGoogle Scholar
Choi, K.-S. & Graham, M. 1998 Drag reduction of turbulent pipe flows by circular-wall oscillation. Phys. Fluids 10 (1), 7–9.CrossRefGoogle Scholar
Choi, J.-I., Xu, C.-X. & Sung, H. J. 2002 Drag reduction by spanwise wall oscillation in wall-bounded turbulent flows. AIAA J. 40 (5), 842–850.Google Scholar
Du, Y. & Karniadakis, G. E. 2000 Suppressing wall turbulence by means of a transverse traveling wave. Science 288, 1230–1234.CrossRefGoogle ScholarPubMed
Du, Y., Symeonidis, V. & Karniadakis, G. E. 2002 Drag reduction in wall-bounded turbulence via a transverse travelling wave. J. Fluid Mech. 457, 1–34.CrossRefGoogle Scholar
Gad-el Hak, M. 2000 Flow Control – Passive, Active and Reactive Flow Management. Cambridge University PressGoogle Scholar
Itoh, M., Tamano, S., Yokota, K. & Taniguchi, S. 2006 Drag reduction in a turbulent boundary layer on a flexible sheet undergoing a spanwise traveling wave motion. J. Turbul. 7 (27), 1–17.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
Karniadakis, G. E. & Choi, K.-S. 2003 Mechanisms on transverse motions in turbulent wall flows. Annu. Rev. Fluid Mech. 35, 45–62.CrossRefGoogle Scholar
Kim, J. 2003 Control of turbulent boundary layers. Phys. Fluids 15 (5), 1093–1105.Google Scholar
Kim, J. & Hussain, F. 1993 Propagation velocity of perturbations in turbulent channel flow. Phys. Fluids A 5 (3), 695–706.CrossRefGoogle Scholar
Kreplin, H.-P. & Eckelmann, E. 1979 Propagation of perturbations in the viscous sublayer and adjacent wall region. J. Fluid Mech. 95 (2), 305–322.Google Scholar
Luchini, P. & Quadrio, M. 2006 A low-cost parallel implementation of direct numerical simulation of wall turbulence. J. Comput. Phys. 211 (2), 551–571.Google Scholar
Nikitin, N. V. 2000 On the mechanism of turbulence suppression by spanwise surface oscillations. Fluid Dyn. 35 (2), 185–190.CrossRefGoogle Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Quadrio, M. & Luchini, P. 2003 Integral time-space scales in turbulent wall flows. Phys. Fluids 15 (8), 2219–2227.CrossRefGoogle Scholar
Quadrio, M. & Ricco, P. 2004 Critical assessment of turbulent drag reduction through spanwise wall oscillation. J. Fluid Mech. 521, 251–271.CrossRefGoogle Scholar
Quadrio, M., Viotti, C. & Luchini, P. 2007 Skin-friction drag reduction via steady streamwise oscillations of spanwise velocity. In Advances in Turbulence XI (ed. Palma, J. M. L. M. & Lopez, A. Silva). Springer: Pp. 659–661.CrossRefGoogle Scholar
Ricco, P. & Quadrio, M. 2008 Wall-oscillation conditions for drag reduction in turbulent channel flow. Intl J. Heat Fluid Flow 29, 601–612.Google Scholar
Ricco, P. & Wu, S. 2004 On the effects of lateral wall oscillations on a turbulent boundary layer. Exp. Therm. Fluid Sci. 29 (1), 41–52.CrossRefGoogle Scholar
Viotti, C., Quadrio, M. & Luchini, P. 2009 Streamwise oscillation of spanwise velocity at the wall of a channel for turbulent drag reduction. Phys. Fluids (submitted).Google Scholar
Zhao, H., Wu, J.-Z. & Luo, J.-S. 2004 Turbulent drag reduction by traveling wave of flexible wall. Fluid Dyn. Res. 34, 175–198.CrossRefGoogle Scholar