Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-28T12:39:37.189Z Has data issue: false hasContentIssue false
  • English
  • Français

Turbulent drag reduction through oscillating discs

Published online by Cambridge University Press:  04 April 2014

Daniel J. Wise  and
Pierre Ricco
Daniel J. Wise*
Affiliation:
Department of Mechanical Engineering, The University of Sheffield, Mappin Street, Sheffield S1 3JD, UK
Pierre Ricco
Affiliation:
Department of Mechanical Engineering, The University of Sheffield, Mappin Street, Sheffield S1 3JD, UK
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The changes in a turbulent channel flow subjected to sinusoidal oscillations of wall flush-mounted rigid discs are studied by means of direct numerical simulations (DNS). The Reynolds number is ${Re}_{\tau }=180$ , based on the friction velocity of the stationary-wall case and the half-channel height. The primary effect of the wall forcing is the sustained reduction of wall-shear stress, which reaches a maximum of 20 %. A parametric study on the disc diameter, maximum tip velocity, and oscillation period is presented, with the aim of identifying the optimal parameters which guarantee maximum drag reduction and maximum net energy saving, the latter computed by taking into account the power spent to actuate the discs. This may be positive and reaches 6 %. The Rosenblat viscous pump flow, namely the laminar flow induced by sinusoidal in-plane oscillations of an infinite disc beneath a quiescent fluid, is used to predict accurately the power spent for disc motion in the fully developed turbulent channel flow case and to estimate localized and transient regions over the disc surface subjected to the turbulent regenerative braking effect, for which the wall turbulence exerts work on the discs. The Fukagata–Iwamoto–Kasagi identity is employed effectively to show that the wall-friction reduction is due to two distinguished effects. One effect is linked to the direct shearing action of the near-wall oscillating-disc boundary layer on the wall turbulence, which causes the attenuation of the turbulent Reynolds stresses. The other effect is due to the additional disc-flow Reynolds stresses produced by the streamwise-elongated structures which form between discs and modulate slowly in time. The contribution to drag reduction due to turbulent Reynolds stress attenuation depends on the penetration thickness of the disc-flow boundary layer, while the contribution due to the elongated structures scales linearly with a simple function of the maximum tip velocity and oscillation period for the largest disc diameter tested, a result suggested by the Rosenblat flow solution. A brief discussion on the future applicability of the oscillating-disc technique is also presented.

JFM classification

Boundary Layers: Boundary layer control Flow Control: Drag reduction Turbulent Flows: Turbulence control
Type
Papers
Information
Journal of Fluid Mechanics , Volume 746 , 10 May 2014 , pp. 536 - 564
Copyright
© 2014 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

Abramowitz, M. & Stegun, I. A. 1964 Handbook of Mathematical Functions. National Bureau of Standards.Google Scholar
Bandyopadhyay, P. R. 2006 Stokes mechanism of drag reduction. Trans. ASME: J. Appl. Mech. 73, 483–489.CrossRefGoogle Scholar
Baron, A. & Quadrio, M. 1996 Turbulent drag reduction by spanwise wall oscillations. Appl. Sci. Res. 55, 311–326.CrossRefGoogle Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
Benney, D. J. 1964 The flow induced by a disk oscillating in its own plane. J. Fluid Mech. 18 (3), 385–391.CrossRefGoogle Scholar
Berger, T. W., Kim, J., Lee, C. & Lim, J. 2000 Turbulent boundary layer control utilizing the Lorentz force. Phys. Fluids 12 (3), 631–649.CrossRefGoogle Scholar
Canuto, C., Hussaini, M. Y., Quarteroni, A. & Zang, T. A. 2007 Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics. Springer.CrossRefGoogle Scholar
Carmi, S. & Tustaniwskyj, J. I. 1981 Stability of modulated finite-gap cylindrical Couette flow: linear theory. J. Fluid Mech. 108, 19–42.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.CrossRefGoogle Scholar
Cimarelli, A., Frohnapfel, B., Hasegawa, Y., De Angelis, E. & Quadrio, M. 2013 Prediction of turbulence control for arbitrary periodic spanwise wall movement. Phys. Fluids 25, 075102.CrossRefGoogle Scholar
Dhanak, M. R. & Si, C. 1999 On reduction of turbulent wall friction through spanwise oscillations. J. Fluid Mech. 383, 175–195.CrossRefGoogle Scholar
Di Cicca, G. M., Iuso, G., Spazzini, P. G. & Onorato, M. 2002 Particle image velocimetry investigation of a turbulent boundary layer manipulated by spanwise oscillations. J. Fluid Mech. 467, 41–56.CrossRefGoogle Scholar
Du, Y., Symeonidis, V. & Karniadakis, G. E. 2002 Drag reduction in wall-bounded turbulence via a transverse travelling wave. J. Fluid Mech. 457, 1–4.CrossRefGoogle Scholar
Duque-Daza, C. A., Baig, M. F., Lockerby, D. A., Chernyshenko, S. I. & Davies, C. 2012 Modelling turbulent skin-friction control using linearized Navier–Stokes equations. J. Fluid Mech. 702, 403–414.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 (11), 73–76.CrossRefGoogle Scholar
Gibson, J. F.2006 Channelflow: a spectral Navier–Stokes simulator in C $+\! +$ . “http://www.channelflow.org/”.Google Scholar
Gouder, K., Potter, M. & Morrison, J. F. 2013 Turbulent friction drag reduction using electroactive polymer and electromagnetically driven surfaces. Exp. Fluids 54, 1–12.CrossRefGoogle Scholar
Hinze, J. O. 1975 Turbulence. 2nd edn. McGraw Hill.Google Scholar
Iuso, G., Di Cicca, G. M., Onorato, M., Spazzini, P. G. & Malvano, R. 2003 Velocity streak structure modifications induced by flow manipulation. Phys. Fluids 15 (9), 2602–2612.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
Kang, S. & Choi, H. 2000 Active wall motions for skin-friction drag reduction. Phys. Fluids 12 (12), 3301–3304.CrossRefGoogle Scholar
Kasagi, N., Suzuki, Y. & Fukagata, K. 2009 Micromechanical systems-based feedback control of turbulence for skin friction reduction. Annu. Rev. Fluid Mech. 41, 231–251.CrossRefGoogle Scholar
Keefe, L.1998 Method and apparatus for reducing the drag of flows over surfaces. United States Patent 5,803,409.Google Scholar
Kleiser, L. & Schumann, U. 1980 Treatment of incompressibility and boundary conditions in 3-D numerical spectral simulations of plane channel flows. In Proc. 3rd GAMM Conference Numerical Methods in Fluid Mechanics (ed. Hirschel, E.), pp. 165–173. GAMM, Vieweg.CrossRefGoogle Scholar
Kuang-Chen Liu, D., Friend, J. & Yeo, L. 2010 A brief review of actuation at the micro-scale using electrostatics, electromagnetics and piezoelectric ultrasonics. Acoust. Sci. Technol. 31, 115–123.Google Scholar
Laadhari, F., Skandaji, L. & Morel, R. 1994 Turbulence reduction in a boundary layer by local spanwise oscillating surface. Phys. Fluids 6 (10), 3218–3220.CrossRefGoogle Scholar
Moarref, R. & Jovanovic, M. R. 2012 Model-based design of transverse wall oscillations for turbulent drag reduction. J. Fluid Mech. 707, 205–240.CrossRefGoogle Scholar
Panton, R. 1995 Incompressible Flow. 2nd edn. Wiley-Interscience.Google Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Pozrikidis, C. 2009 Fluid Dynamics: Theory, Computation, and Numerical Simulation. Springer.CrossRefGoogle Scholar
Quadrio, M. 2011 Drag reduction in turbulent boundary layers by in-plane wall motion. Phil. Trans. R. Soc. Lond. A 369 (1940), 1428–1442.Google ScholarPubMed
Quadrio, M., Floryan, J. M. & Luchini, P. 2007 Effect of streamwise-periodic wall transpiration on turbulent friction drag. J. Fluid Mech. 576, 424–444.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-travelling waves of spanwise wall velocity for turbulent drag reduction. J. Fluid Mech. 627, 161–178.CrossRefGoogle Scholar
Quadrio, M. & Sibilla, S. 2000 Numerical simulation of turbulent flow in a pipe oscillating around its axis. J. Fluid Mech. 424, 217–241.CrossRefGoogle Scholar
Ricco, P. & Hahn, S. 2013 Turbulent drag reduction through rotating discs. J. Fluid Mech. 722, 267–290.CrossRefGoogle Scholar
Ricco, P., Ottonelli, C., Hasegawa, Y. & Quadrio, M. 2012 Changes in turbulent dissipation in a channel flow with oscillating walls. J. Fluid Mech. 700, 77–104.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.CrossRefGoogle Scholar
Rogers, M. H. & Lance, G. N. 1960 The rotationally symmetric flow of a viscous fluid in the presence of an infinite rotating disk. J. Fluid Mech. 7 (4), 617–631.CrossRefGoogle Scholar
Rosenblat, S. 1959 Torsional oscillations of a plane in a viscous fluid. J. Fluid Mech. 6 (2), 206–220.CrossRefGoogle Scholar
Skote, M. 2011 Turbulent boundary layer flow subject to streamwise oscillation of spanwise wall-velocity. Phys. Fluids 23, 081703.CrossRefGoogle Scholar
Skote, M. 2013 Comparison between spatial and temporal wall oscillations in turbulent boundary layer flows. J. Fluid Mech. 730, 273–294.CrossRefGoogle Scholar
Trujillo, S. M., Bogard, D. G. & Ball, K. S.1997 Turbulent boundary layer drag reduction using an oscillating wall. AIAA Paper 97-1870.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 21, 115109.CrossRefGoogle Scholar
Walsh, M. J. 1990 Riblets. In Viscous Drag Reduction in Boundary Layers (ed. Bushnell, D. M. & Hefner, J. N.), Progress in Astronautics and Aeronautics, vol. 123, pp. 203–261. AIAA.Google Scholar
Wang, C. Y. 1989 Shear flow over a rotating plate. Appl. Sci. Res. 46, 89–96.CrossRefGoogle Scholar
Yoshino, T., Suzuki, Y. & Kasagi, N. 2008 Drag reduction of turbulence air channel flow with distributed micro-sensors and actuators. J. Fluid Sci. Technol. 3, 137–148.CrossRefGoogle Scholar
Zhou, D. & Ball, K. S. 2008 Turbulent drag reduction by spanwise wall oscillations. Intl J. Engng Trans. A Basics 21 (1), 85.Google Scholar