Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-28T05:24:39.289Z Has data issue: false hasContentIssue false
  • English
  • Français

Hydrodynamic stability and breakdown of the viscous regime over riblets

Published online by Cambridge University Press:  19 April 2011

RICARDO GARCÍA-MAYORAL  and
JAVIER JIMÉNEZ
RICARDO GARCÍA-MAYORAL*
Affiliation:
School of Aeronautics, Universidad Politécnica de Madrid, 28040 Madrid, Spain
JAVIER JIMÉNEZ
Affiliation:
School of Aeronautics, Universidad Politécnica de Madrid, 28040 Madrid, Spain
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The interaction of the overlying turbulent flow with a riblet surface and its impact on drag reduction are analysed. The ‘viscous regime’ of vanishing riblet spacing, in which the drag reduction produced by the riblets is proportional to their size, is reasonably well understood, but this paper focuses on the behaviour for spacings s+ ≃ 10–20, expressed in wall units, where the viscous regime breaks down and the reduction eventually becomes an increase. Experimental evidence suggests that the two regimes are largely independent, and, based on a re-evaluation of existing data, it is shown that the optimal rib size is collapsed best by the square root of the groove cross-section, ℓg+=Ag+1/2. The mechanism of the breakdown is investigated by systematic DNSs with increasing riblet sizes. It is found that the breakdown is caused by the appearance of long spanwise rollers below y+ ≈ 20, with typical streamwise wavelengths λx+ ≈ 150, that develop from a two-dimensional Kelvin–Helmholtz-like instability of the mean streamwise flow, similar to those over plant canopies and porous surfaces. They account for the drag breakdown, both qualitatively and quantitatively. It is shown that a simplified linear instability model explains the scaling of the breakdown spacing with ℓg+.

JFM classification

Flow Control: Drag reduction Turbulent Flows: Turbulent boundary layers Turbulent Flows: Turbulence control
Type
Papers
Information
Journal of Fluid Mechanics , Volume 678 , 10 July 2011 , pp. 317 - 347
Copyright
Copyright © Cambridge University Press 2011

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

del Álamo, J. C. & Jiménez, J. 2009 Estimation of turbulent convection velocities and corrections to Taylor's approximation. J. Fluid Mech. 640, 5–26.CrossRefGoogle Scholar
Bechert, D. W. & Bartenwerfer, M. 1989 The viscous flow on surfaces with longitudinal ribs. J. Fluid Mech. 206, 105–129.CrossRefGoogle Scholar
Bechert, D. W., Bruse, M., Hage, W., van der Hoeven, J. G. T. & Hoppe, G. 1997 Experiments on drag-reducing surfaces and their optimization with adjustable geometry. J. Fluid Mech. 338, 59–87.CrossRefGoogle Scholar
Breugem, W. P., Boersma, B. J. & Uittenbogaard, R. E. 2006 The influence of wall permeability on turbulent channel flow. J. Fluid Mech. 562, 35–72.Google Scholar
Bruse, M., Bechert, D. W., van der Hoeven, J. G. T., Hage, W. & Hoppe, G. 1993 Experiments with conventional and with novel adjustable drag-reducing surfaces. In Near-Wall Turbulent Flows (ed. So, R. M. C., Speziale, C. G. & Launder, B. E.), pp. 719–738. Elsevier.Google Scholar
Cess, R. D. 1958 A survey of the literature on heat transfer in turbulent tube flow. Report 8-0529-R24. Westinghouse Research.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
Chu, D. C. & Karniadakis, G. E. M. 1993 A direct numerical simulation of laminar and turbulent flow over riblet-mounted surfaces. J. Fluid Mech. 250, 1–42.CrossRefGoogle Scholar
Clauser, F. H. 1956 The turbulent boundary layer. Adv. Appl. Mech. 4, 1–51.CrossRefGoogle Scholar
Drazin, P. G. & Reid, W. H. 1981 Hydrodynamic Stability. Cambridge University Press.Google Scholar
El-Samni, O. A., Chun, H. H. & Yoon, H. S. 2007 Drag reduction of turbulent flow over thin rectangular riblets. Intl J. Engng Sci. 45, 436–454.CrossRefGoogle Scholar
Fadlun, E. A., Verzicco, R., Orlandi, P. & Mohd-Yusof, J. 2000 Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations. J. Comput. Phys. 161, 35–60.CrossRefGoogle Scholar
Ferziger, J. H. & Perić, M. 1996 Computational Methods for Fluid Dynamics. Springer.CrossRefGoogle Scholar
Finnigan, J. 2000 Turbulence in plant canopies. Annu. Rev. Fluid Mech. 32, 519–571.CrossRefGoogle Scholar
García-Mayoral, R. & Jiménez, J. 2007 On the effect of riblet geometry on drag reduction. Tech. Rep. ETSIA/MF-072. School of Aeronautics, Universidad Politécnica de Madrid.Google Scholar
García-Mayoral, R. & Jiménez, J. 2011 Drag reduction by riblets. Phil. Trans. R. Soc. A 369, 1412–1427.CrossRefGoogle Scholar
Goldstein, D. B., Handler, R. & Sirovich, L. 1995 Direct numerical simulation of turbulent flow over a modeled riblet covered surface. J. Fluid Mech. 302, 333–376.Google Scholar
Goldstein, D. B. & Tuan, T. C. 1998 Secondary flow induced by riblets. J. Fluid Mech. 363, 115–151.CrossRefGoogle Scholar
Hoyas, S. & Jiménez, J. 2008 Reynolds number effects on the Reynolds-stress budgets in turbulent channels. Phys. Fluids 20, 101511.CrossRefGoogle Scholar
Iaccarino, G. & Verzicco, R. 2003 Immersed boundary technique for turbulent flow simulations. Appl. Mech. Rev. 56 (3), 331–347.Google Scholar
Itoh, M., Tamano, S., Iguchi, R., Yokota, K., Akino, N., Hino, R. & Kubo, S. 2006 Turbulent drag reduction by the seal fur surface. Phys. Fluids 18 (6), 065102.CrossRefGoogle Scholar
Jiménez, J. 1992 Wall friction and the structure of near-wall turbulence. In 11th Australasian Fluid Mech. Conf. (ed. Davis, M. R. & Walker, G. J.), pp. 813–816. Hobart, Australia.Google Scholar
Jiménez, J. 1994 On the structure and control of near wall turbulence. Phys. Fluids 6 (2), 944–953.CrossRefGoogle Scholar
Jiménez, J. 2004 Turbulent flows over rough walls. Annu. Rev. Fluid Mech. 36, 173–196.CrossRefGoogle Scholar
Jiménez, J. & Pinelli, A. 1999 The autonomous cycle of near wall turbulence. J. Fluid Mech. 389, 335–359.CrossRefGoogle Scholar
Jiménez, J., Uhlman, M., Pinelli, A. & Kawahara, G. 2001 Turbulent shear flow over active and passive porous surfaces. J. Fluid Mech. 442, 89–117.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, 1605–1607.CrossRefGoogle Scholar
Kim, J., Moin, P. & Moser, R. D. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166.CrossRefGoogle Scholar
Le, H. & Moin, P. 1991 An improvement of fractional step methods for the incompressible Navier–Stokes equations. J. Comput. Phys. 92 (2), 369–379.CrossRefGoogle Scholar
Lee, S.-J. & Lee, S.-H. 2001 Flow field analysis of a turbulent boundary layer over a riblet surface. Exp. Fluids 30, 153–166.CrossRefGoogle Scholar
Linnick, M. N. & Fasel, H. F. 2005 A high-order immersed interface method for simulating unsteady incompressible flows on irregular domains. J. Comput. Phys. 204 (1), 157–192.CrossRefGoogle Scholar
Luchini, P. 1995 Asymptotic analysis of laminar boundary-layer flow over finely grooved surfaces. Eur. J. Mech. B/Fluids 14, 169–195.Google Scholar
Luchini, P., Manzo, F. & Pozzi, A. 1991 Resistance of a grooved surface to parallel flow and cross-flow. J. Fluid Mech. 228, 87–109.Google Scholar
Nördstrom, J., Mattsson, K. & Swanson, C. 2007 Boundary conditions for a divergence free velocity-pressure formulation of the Navier–Stokes equations. J. Comput. Phys. 225, 874–890.CrossRefGoogle Scholar
Orlandi, P. & Jiménez, J. 1994 On the generation of turbulent wall friction. Phys. Fluids 6, 634–641.CrossRefGoogle Scholar
Orlandi, P., Leonardi, S. & Antonia, R. A. 2006 Turbulent channel flow with either transverse or longitudinal roughness elements on one wall. J. Fluid Mech. 561, 279–305.CrossRefGoogle Scholar
Py, C., de Langre, E. & Moulia, B. 2006 A frequency lock-in mechanism in the interaction between wind and crop canopies. J. Fluid Mech. 568, 425–449.Google Scholar
Raupach, M. R., Finnigan, J. & Brunet, Y. 1996 Coherent eddies and turbulence in vegetation canopies: the mixing-layer analogy. Boundary-Layer Meteorol. 78, 351–382.CrossRefGoogle Scholar
Reynolds, W. C. & Hussain, A. K. M. F. 1972 The mechanics of an organized wave in turbulent shear flow. Part 3. Theoretical models and comparisons with experiments. J. Fluid Mech. 54, 263–288.CrossRefGoogle Scholar
Roshko, A. 1953 On the development of turbulent wakes from vortex streets. NACA Tech. Note 2913.Google Scholar
Simens, M. P., Jiménez, J., Hoyas, S. & Mizuno, Y. 2009 A high-resolution code for turbulent boundary layers. J. Comput. Phys. 228, 4218–4231.CrossRefGoogle Scholar
Stalio, E. & Nobile, E. 2003 Direct numerical simulation of heat transfer over riblets. Intl J. Heat Fluid Flow 24, 356–371.CrossRefGoogle Scholar
Suzuki, Y. & Kasagi, N. 1994 Turbulent drag reduction mechanism above a riblet surface. AIAA J. 32 (9), 1781–1790.CrossRefGoogle Scholar
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT Press.CrossRefGoogle Scholar
Walsh, M. J. 1990 a Effect of detailed surface geometry on riblet drag reduction performance. J. Aircraft 27 (6), 572–573.CrossRefGoogle Scholar
Walsh, M. J. 1990 b Riblets. In Viscous Drag Reduction in Boundary Layers (ed. Bushnell, D. M. & Hefner, J. N.), pp. 203–261. AIAA.Google Scholar
Walsh, M. J. & Lindemann, A. M. 1984 Optimization and application of riblets for turbulent drag reduction. AIAA Paper 84-0347.CrossRefGoogle Scholar
Williamson, C. H. K. 1989 Oblique and parallel modes of vortex shedding in the wake of a circular cylinder at low Reynolds numbers. J. Fluid Mech. 206, 579–627.CrossRefGoogle Scholar