Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-19T07:40:43.916Z Has data issue: false hasContentIssue false
  • English
  • Français

Pumping or drag reduction?

Published online by Cambridge University Press:  10 September 2009

JÉRÔME HŒPFFNER  and
KOJI FUKAGATA
JÉRÔME HŒPFFNER*
Affiliation:
Department of Mechanical Engineering, Keio University, Yokohama 223-8522, Japan
KOJI FUKAGATA
Affiliation:
Department of Mechanical Engineering, Keio University, Yokohama 223-8522, Japan
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Two types of wall actuation in channel flow are considered: travelling waves of wall deformation (peristalsis) and travelling waves of blowing and suction. The flow response and its mechanisms are analysed using nonlinear and weakly nonlinear computations. We show that both actuations induce a flux in the channel in the absence of an imposed pressure gradient and can thus be characterized as pumping. In the context of flow control, pumping and drag reduction are strongly connected, and we seek to define them properly based on these two actuation examples. Movies showing the flow motion for the two types of actuation are available with the online version of this paper (journals.cambridge.org/FLM).

JFM classification

Biological Fluid Dynamics: Peristaltic pumping Flow Control: Drag reduction
Type
Papers
Information
Journal of Fluid Mechanics , Volume 635 , 25 September 2009 , pp. 171 - 187
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

Bewley, T. R. 2001 Flow control: new challenges for a new renaissance. Prog. Aerospace Sci. 37, 21–58.CrossRefGoogle Scholar
Bewley, T. R. 2009 A fundamental limit on the balance of power in a transpiration-controlled channel flow. J. Fluid Mech. 632, 443–446.CrossRefGoogle Scholar
Bewley, T. R. & Aamo, O. M. 2004 A ‘win-win’ mechanism for low-drag transients in controlled two-dimensional channel flow and its implications for sustained drag reduction. J. Fluid Mech. 499, 183–196.CrossRefGoogle Scholar
Choi, H., Moin, P. & Kim, J. 1994 Active turbulence control for drag reduction in wall-bounded flows. J. Fluid Mech. 262, 75–110.CrossRefGoogle Scholar
Fukagata, K., Iwamoto, K. & Kasagi, N. 2002 Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows. Phys. Fluids 14, L73–L76.CrossRefGoogle Scholar
Fukagata, K., Sugiyama, K. & Kasagi, N. 2009 On the lower bound of net driving power in controlled duct flows. Phys. D. 238, 1082–1086.CrossRefGoogle Scholar
Jaffrin, M. Y. & Shapiro, A. H. 1971 Peristaltic pumping. Annu. Rev. Fluid Mech. 3, 13–37.CrossRefGoogle Scholar
Joslin, R. D. 1998 Aircraft laminar flow control. Annu. Rev. Fluid Mech. 30, 1–29.CrossRefGoogle Scholar
Kasagi, N., Suzuki, Y. & Fukagata, K. 2009 Microelectromechanical systems-based feedback control of turbulence for skin friction reduction. Annu. Rev. Fluid Mech. 41, 231–251.CrossRefGoogle Scholar
Kim, J. & Bewley, T. R. 2007 A linear systems approach to flow control. Annu. Rev. Fluid Mech. 39, 383–417.CrossRefGoogle Scholar
Lighthill, Sir J. 1978 Acoustic streaming. J. Sound Vib. 61 (3), 391–418.CrossRefGoogle Scholar
Luchini, P. 2006 Acoustic streaming and lower-than-laminar drag in controlled channel flow. In Progress in Industrial Mathematics at ECMI, Mathematics in Industry, vol. 12, pp. 169–177. Springer.Google Scholar
Marusic, I., Joseph, D. D. & Mahesh, K. 2007 Laminar and turbulent comparisons for channel flow and flow control. J. Fluid Mech. 570, 467–477.CrossRefGoogle Scholar
Maslowe, S. A. 1986 Critical layers in fluid mechanics. Annu. Rev. Fluid Mech. 18, 405–432.CrossRefGoogle Scholar
Min, T., Kang, S. M., Speyer, J. L. & Kim, J. 2006 Sustained sub-laminar drag in a fully developed channel flow. J. Fluid Mech. 558, 309–318.CrossRefGoogle Scholar
Mito, Y. & Kasagi, N. 1998 DNS study of turbulence modification with streamwise-uniform sinusoidal wall-oscillation. Intl J. Heat Fluid Flow 19, 470–481.CrossRefGoogle Scholar
Mittra, T. K. & Prasad, S. N. 1974 Interaction of peristaltic motion with Poiseuille flow. Bull. Math. Biol. 36, 127–141.CrossRefGoogle ScholarPubMed
Riley, N. 2001 Steady streaming. Annu. Rev. Fluid Mech. 33, 43–65.CrossRefGoogle Scholar

Hoepffner and Fukagata supplementary movie

Movie 1. Peristalsis at Reynolds 100 and wavelength 2π for three constrictions φ. The pressure field is shown by the colormap, the streamwise velocity is shown by velocity profiles. Passive particles tracers are present to emphasize the details of the flow motion. The wall deformation in the form of a traveling wave induces a flow from regions being constricted to regions being expanded: both forward and backward. The backward flow takes place in a constricted region, where viscosity opposes the motion. This results in pumping in the direction of the wave.

Download Hoepffner and Fukagata supplementary movie(Video)
Video 9.4 MB

Hoepffner and Fukagata supplementary movie

Movie 2. Blowing and suction at wave amplitude φ=0.2 and wavelength 2π for three Reynolds numbers. The traveling wave of blowing and suction entrains particles in rotating trajectories. The backward part of this rotation takes place away from the wall, whereas the forward part of the rotation takes place close to the wall where viscosity opposes the motion. This results in pumping in the direction opposite to the wave.

Download Hoepffner and Fukagata supplementary movie(Video)
Video 8.9 MB