Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-12-01T02:40:11.207Z Has data issue: false hasContentIssue false
  • English
  • Français

Changes in turbulent dissipation in a channel flow with oscillating walls

Published online by Cambridge University Press:  25 April 2012

Pierre Ricco ,
Claudio Ottonelli ,
Yosuke Hasegawa  and
Maurizio Quadrio
Pierre Ricco*
Affiliation:
Department of Mechanical Engineering, The University of Sheffield, Mappin Street, Sheffield S1 3JD, UK
Claudio Ottonelli
Affiliation:
Dipartimento di Ingegneria Aerospaziale del Politecnico di Milano, via La Masa 34, 20156 Milano, Italy
Yosuke Hasegawa
Affiliation:
Center of Smart Interfaces, TU Darmstadt, Petersenstrasse 32, 64287, Darmstadt, Germany Department of Mechanical Engineering, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-8656, Japan
Maurizio Quadrio
Affiliation:
Dipartimento di Ingegneria Aerospaziale del Politecnico di Milano, via La Masa 34, 20156 Milano, Italy
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Harmonic oscillations of the walls of a turbulent plane channel flow are studied by direct numerical simulations to improve our understanding of the physical mechanism for skin-friction drag reduction. The simulations are carried out at constant pressure gradient in order to define an unambiguous inner scaling: in this case, drag reduction manifests itself as an increase of mass flow rate. Energy and enstrophy balances, carried out to emphasize the role of the oscillating spanwise shear layer, show that the viscous dissipation of the mean flow and of the turbulent fluctuations increase with the mass flow rate, and the relative importance of the latter decreases. We then focus on the turbulent enstrophy: through an analysis of the temporal evolution from the beginning of the wall motion, the dominant, oscillation-related term in the turbulent enstrophy is shown to cause the turbulent dissipation to be enhanced in absolute terms, before the slow drift towards the new quasi-equilibrium condition. This mechanism is found to be responsible for the increase in mass flow rate. We finally show that the time-average volume integral of the dominant term is linearly related to the drag reduction.

JFM classification

Flow Control: Drag reduction Turbulent Flows: Turbulence control Turbulent Flows: Turbulent boundary layers
Type
Papers
Information
Journal of Fluid Mechanics , Volume 700 , 10 June 2012 , pp. 77 - 104
Copyright
Copyright © Cambridge University Press 2012

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.)

Footnotes

‡

Present address: ONERA, Département d’Aérodynamique Fondamentale et Expérimentale, 8, rue des Vertugadins, 92190 Meudon, France.

References

1. Abe, H., Antonia, R. A. & Kawamura, H. 2009 Correlation between small-scale velocity and scalar fluctuations in a turbulent channel flow. J. Fluid Mech. 627, 1–32.CrossRefGoogle Scholar
2. del Álamo, J. C. & Jiménez, J. 2003 Spectra of the very large anisotropic scales in turbulent channels. Phys. Fluids 15 (6), L41–L44.CrossRefGoogle Scholar
3. Antonia, R. A. & Kim, J. 1994 Low-Reynolds-number effects on near-wall turbulence. J. Fluid Mech. 276, 61–80.CrossRefGoogle Scholar
4. Bandyopadhyay, P. R. 2006 Stokes mechanism of drag reduction. J. Appl. Mech. 73, 483–489.CrossRefGoogle Scholar
5. Baron, A. & Quadrio, M. 1996 Turbulent drag reduction by spanwise wall oscillations. Appl. Sci. Res. 55, 311–326.CrossRefGoogle Scholar
6. Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
7. 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
8. 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
9. 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
10. Davidson, P. A. 2004 Turbulence: An Introduction for Scientists and Engineers. Oxford University Press.Google Scholar
11. Fischer, M., Jovanović, J. & Durst, F. 2001 Reynolds number effect in the near-wall region of turbulent channel flow. Phys. Fluids 13 (6), 1755–1767.CrossRefGoogle Scholar
12. Fukagata, K., Iwamoto, K. & Kasagi, N. 2002 Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows. Phys. Fluids 14 (11), L73–L76.CrossRefGoogle Scholar
13. Fukagata, K., Sugiyama, K. & Kasagi, N. 2009 On the lower bound of net driving power in controlled duct flows. Physica D 238, 1082–1086.CrossRefGoogle Scholar
14. Garabedian, P. R. 1964 Partial Differential Equations. John Wiley and Sons.Google Scholar
15. Gorski, J. J., Wallace, J. M. & Bernard, P. S. 1994 The enstrophy equation budget of bounded turbulent shear flows. Phys. Fluids 6 (9), 3197–3199.CrossRefGoogle Scholar
16. Hinze, J. O. 1975 Turbulence, 2nd edn. McGraw Hill.Google Scholar
17. 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
18. Kasagi, N., Hasegawa, Y. & Fukagata, K. 2009a Towards cost-effective control of wall turbulence for skin-friction drag reduction. In Advances in Turbulence XII, vol. 132, pp. 189–200. Springer.CrossRefGoogle Scholar
19. Kasagi, N., Suzuki, Y. & Fukagata, K. 2009b MEMS-based feedback control of turbulence for drag reduction. Annu. Rev. Fluid Mech. 41, 231–251.CrossRefGoogle Scholar
20. Kim, J. & Bewley, T. R. 2007 A linear systems approach to flow control. Annu. Rev. Fluid Mech. 39, 383–417.CrossRefGoogle Scholar
21. Kline, S. J., Reynolds, W. C., Schraub, F. A. & Runstadler, P. W. 1967 The structure of turbulent boundary layers. J. Fluid Mech. 30, 741–773.CrossRefGoogle Scholar
22. Laadhari, F. 2007 Reynolds number effect on the dissipation function in wall-bounded flows. Phys. Fluids 19, 038101.CrossRefGoogle Scholar
23. Lee, C., Kim, J. & Choi, H. 1998 Suboptimal control of turbulent channel flow for drag reduction. J. Fluid Mech. 358, 245–258.CrossRefGoogle Scholar
24. Leib, S. J., Wundrow, D. W. & Goldstein, M. E. 1999 Effect of free-stream turbulence and other vortical disturbances on a laminar boundary layer. J. Fluid Mech. 380, 169–203.CrossRefGoogle Scholar
25. Leschziner, M., Choi, H. & Choi, K.-S. 2011 Flow control approaches in aerodynamics: progress and prospects. Phil. Trans. R. Soc. Lond. A 369 (1940), 1349–1351.Google ScholarPubMed
26. Luchini, P. & Quadrio, M. 2006 A low-cost parallel implementation of direct numerical simulation of wall turbulence. J. Comput. Phys. 211 (2), 551–571.CrossRefGoogle Scholar
27. Mansour, N. N., Kim, J. & Moin, P. 1989 Near-wall turbulence modelling. AIAA J. 27 (8), 1068–1073.CrossRefGoogle Scholar
28. 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
29. Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
30. Quadrio, M. & Ricco, P. 2003 Initial response of a turbulent channel flow to spanwise oscillation of the walls. J. Turbul. 4 (7), 1–23.CrossRefGoogle Scholar
31. Quadrio, M. & Ricco, P. 2004 Critical assessment of turbulent drag reduction through spanwise wall oscillation. J. Fluid Mech. 521, 251–271.CrossRefGoogle Scholar
32. Quadrio, M. & Ricco, P. 2011 The laminar generalized Stokes layer and turbulent drag reduction. J. Fluid Mech. 667, 135–157.CrossRefGoogle Scholar
33. 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
34. Ricco, P. 2004 Modification of near-wall turbulence due to spanwise wall oscillations. J. Turbul. 5 (24), 1–18.CrossRefGoogle Scholar
35. 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
36. Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT Press.CrossRefGoogle Scholar
37. Xu, C.-X. & Huang, W.-X. 2005 Transient response of Reynolds stress transport to spanwise wall oscillation in a turbulent channel flow. Phys. Fluids 17, 018101.CrossRefGoogle Scholar