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Spanwise reflection symmetry breaking and turbulence control: plane Couette flow

Published online by Cambridge University Press:  19 March 2014

G. Chagelishvili ,
G. Khujadze ,
H. Foysi  and
M. Oberlack
G. Chagelishvili
Affiliation:
Abastumani Astrophysical Observatory, Ilia State University, Tbilisi 0160, Georgia M. Nodia Institute of Geophysics, Tbilisi State University, Tbilisi 0128, Georgia Chair of Fluid Dynamics, Technische Universität Darmstadt, Darmstadt 64287, Germany
G. Khujadze*
Affiliation:
Abastumani Astrophysical Observatory, Ilia State University, Tbilisi 0160, Georgia Chair of Fluid Mechanics, Universität Siegen, Paul-Bonatz-Str. 9-11, 57068 Siegen, Germany
H. Foysi
Affiliation:
Chair of Fluid Mechanics, Universität Siegen, Paul-Bonatz-Str. 9-11, 57068 Siegen, Germany
M. Oberlack
Affiliation:
Chair of Fluid Dynamics, Technische Universität Darmstadt, Darmstadt 64287, Germany GS Comp. Engineering, Technische Universität Darmstadt, Darmstadt 64287, Germany
*
†Email address for correspondence: george.khujadze@uni-siegen.de
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Abstract

We propose and analyse a new strategy of shear flow turbulence control that can be realized by the following steps: (i) imposing specially designed seed velocity perturbations, which are non-symmetric in the spanwise direction, at the walls of a flow; (ii) the configuration of the latter ensures a gain of shear flow energy and the breaking of turbulence spanwise reflection symmetry: this leads to the generation of spanwise mean flow; (iii) that changes the self-sustained dynamics of turbulence and results in a considerable reduction of the turbulence level and the production of turbulent kinetic energy. In fact, by this strategy the shear flow transient growth mechanism is activated and the formed spanwise mean flow is an intrinsic, nonlinear composition of the controlled turbulence and not directly introduced in the system. In the present paper, a weak near-wall volume forcing is designed to impose the velocity perturbations with required characteristics in the flow. The efficiency of the proposed scheme has been demonstrated by direct numerical simulation using plane Couette flow as a representative example. A promising result was obtained: after a careful parameter selection, the forcing reduces the turbulence kinetic energy and its production by up to one-third. The strategy can be naturally applied to other wall-bounded flows, e.g. channel and boundary-layer flows. Of course, the considered volume force is theoretical and hypothetical. Nevertheless, it helps to gain knowledge concerning the design of the seed velocity field that is necessary to be imposed in the flow to achieve a significant reduction of the turbulent kinetic energy. This is convincing with regard to a new control strategy, which could be based on specially constructed blowing/suction or riblets, by employing the insight gained by the comprehension of the results obtained using the investigated methodology in this paper.

JFM classification

Flow Control: Flow Control Turbulent Flows: Turbulence control Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 745 , 25 April 2014 , pp. 300 - 320
Copyright
© 2014 Cambridge University Press 

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References

Bewley, T. R. 2001 Flow control: new challenges for a new renaissance. Prog. Aerosp. Sci. 37, 21–53.Google Scholar
Canuto, C., Hussaini, M. Y., Quarteroni, A. & Zang, Th. A. 2006 In Spectral Methods Fundamentals in Single Domains, Springer.Google Scholar
Choi, H., Moin, P. & Kim, J. 1993 Direct numerical simulation of turbulent flow over riblets. J. Fluid Mech. 255, 503–539.Google Scholar
Craik, A. D. D. & Criminale, W. O. 1986 Evolution of wavelike disturbances in shear flows: a class of exact solutions of the Navier–Stokes equations. Proc. R. Soc. Lond. A 406, 13–26.Google Scholar
Dean, B. & Bhushan, B. 2010 Shark-skin surfaces for fluid-drag reduction in turbulent flow: a review. Phil. Trans. R. Soc. A 368, 4775–4806.Google Scholar
Farrell, B. F. & Ioannou, P. J. 1993 Optimal excitation of three-dimensional perturbations in viscous constant shear flow. Phys. Fluids A 5, 1390–1400.Google Scholar
Farrell, B. F. & Ioannou, P. J. 2000 Transient and asymptotic growth of two-dimensional perturbations in viscous compressible shear flow. Phys. Fluids 12 (11), 3021–3028.CrossRefGoogle Scholar
Gad-el-Hak, M. 2000 Passive, Active and Reactive Flow. Cambridge University. Press.Google Scholar
Garcia-Mayoral, R. & Jimenez, J. 2011 Hydrodynamic stability and breakdown of the viscous regime over riblets. J. Fluid Mech. 678, 317–347.CrossRefGoogle Scholar
Goldstein, D., Handler, R. & Sirovich, L. 1995 Direct numerical simulation of turbulent flow over a modelled riblet covered surface. J. Fluid Mech. 302, 333–376.Google Scholar
Karniadakis, G. E. & Choi, K. -S. 2003 Mechanisms on transverse motions in turbulent wall flows. Annu. Rev. Fluid Mech. 35, 45–62.Google Scholar
Kim, J. 2003 Control of turbulent boundary layers. Phys. Fluids 15, 1093–1105.Google Scholar
Kim, J. 2011 Physics and control of wall turbulence for drag reduction. Phil. Trans. R. Soc. A 369, 1396–1411.Google Scholar
Komminaho, J., Lundbladh, A. & Johansson, A. V. 1996 Very large structures in plane turbulent couette flow. J. Fluid Mech. 320, 259–285.Google Scholar
Lee, M. J. & Kim, J. 1991 The structure of turbulence in a simulated plane couette flow. In Eight Symp. on Turbulent Shear Flow pp. 5.3.1–5.3.6. Technical University of Munich.Google Scholar
Lundbladh, A., Henningson, D. & Johansson, A. V.2004 An efficient spectral integration method for the solution of the navier-stokes equations. Tech. Rep., Department of Mechanics, KTH, S-100 44, Stockholm, Sweden.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.Google Scholar
Ricco, P., Ottoneli, C., Hasegawa, Y. & Quadrio, M. 2012 Changes in turbulent dissipation in a channel flow with oscillating walls. J. Fluid Mech. 700, 77–104.Google Scholar
Robinson, S. K. 1991 Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23, 601–639.Google Scholar
Skote, M.2001 Studies of turbulent boundary layer flow through direct numerical simulation. PhD thesis, Royal Institute of Technology, Department of Mechanics, Stockholm, Sweden.Google Scholar
Strand, J. S. & Goldstein, D. B. 2011 Direct numerical simulations of riblets to constrain the growth of turbulent spots. J. Fluid Mech. 668, 267–292.Google Scholar
Touber, E. & Leschziner, M. A. 2012 Near-wall streak modification by spanwise osscilatory wall motion and drag-reduction mechanisms. J. Fluid Mech. 693, 150–200.Google Scholar
Tsukahara, T., Kawamura, H. & Shingai, K. 2006 DNS of turbulent Couette flow with emphasis on the large-scale structure in the core region. J. Turbul. 7 (19), 1–16.Google Scholar