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A direct numerical simulation of laminar and turbulent flow over riblet-mounted surfaces

Published online by Cambridge University Press:  26 April 2006

Douglas C. Chu  and
George Em Karniadakis
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Abstract

The flow in a channel with its lower wall mounted with streamwise riblets is simulated using a highly efficient spectral element-Fourier method. The range of Reynolds numbers investigated is 500 to 3500, which corresponds to laminar, transitional, and turbulent flow states. A complete study is presented for V-groove riblets; the effect of rounded riblets is also investigated. Our results suggest that in the laminar regime there is no drag reduction, while in the transitional and turbulent regimes drag reduction exists (approximately 6 % at Reynolds number 3500) for the riblet-mounted wall in comparison with the smooth wall of the channel. For the first time, we present detailed turbulent statistics (turbulence intensities, Reynolds shear stresses, skewness and flatness) as well as a temporal analysis using a numerical analog of the VITA technique. The flow structure over the riblet-mounted wall is also analysed in some detail and compared with the corresponding flow over the smooth wall in an attempt to identify the physical mechanisms that cause drag reduction. The accuracy of the computation is established by comparing flow quantities corresponding to the smooth wall with previous direct numerical simulation results as well as with experimental results; on the riblet-mounted wall comparison is made with available experimental results. The agreement is very good for both cases. The current computation is the first direct numerical simulation of turbulence in a complex geometry domain.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 250 , May 1993 , pp. 1 - 42
Copyright
© 1993 Cambridge University Press

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References

Antonia, R. A., Teitel, M., Kim, J. & Browne, L. W. B. 1992 Low-Reynolds-number effects in a fully developed turbulent channel flow. J. Fluid Mech. 236, 579–605.Google Scholar
Babuska, I. & Suri, M. 1987 The h-p version of the finite element method with quasi-uniform meshes. Mathematical Modelling and Numerical Analysis 21, 199.Google Scholar
Bacher, E. V. & Smith, C. R. 1985 A combined visualization–anemometry study of the turbulent drag reducing mechanisms of triangular micro-groove surface modifications. AIAA-85-0548.
Bechert, D. W. & Bartenwerfer, M. 1989 The viscous flow on surfaces with longitudinal ribs. J. Fluid Mech. 206, 105–129.Google Scholar
Bechert, D. W., Bartenwerfer, M. & Hoppe, G. 1986 Drag reduction mechanisms derived from shark skin. In 15th Congress, Intl Council for Aeronautical Sci., London, Paper 86-1.8.3, pp. 1044–1067.
Benhalilou, M., Anselmet, F., Liandrat, J. & Fulacher, L. 1991 Experimental and numerical investigation of a turbulent boundary layer over riblets. In Proc. 8th Symp. Turbulent Shear Flows, Munich, pp. 18–5.
Blackwelder, R. F. & Kaplan, R. E. 1976 On the wall structure of the turbulent boundary layer. J. Fluid Mech. 76, 89–112.Google Scholar
Bushnell, D. M. & Hefner, J. N. (ed.) 1990 Viscous drag reduction in Boundary Layers. Progress in Astronautics and Aeronautics, vol. 123.
Bushnell, D. M. & Moore, K. J. 1991 Drag reduction in nature. Ann. Rev. Fluid Mech. 23, 65–79.Google Scholar
Choi, H., Moin, P. & Kim, J. 1991 On the effect of riblets in fully developed laminar channel flows. Phys. Fluids A 3, 1892–1896.Google Scholar
Choi, K. S. 1989 Drag reduction mechanisms and near wall turbulence structure with riblets. In Proc. 2nd IUTAM Symp. on Structure of Turbulence and Drag Reduction, Zurich, Switzerland.
Chu, D. C., Henderson, R. D. & Karniadakis, G. E. 1992 Parallel spectral element–Fourier simulation of turbulent flow over riblet-mounted surfaces. Theoret. Comput. Fluid Dyn. 3, 219–229.Google Scholar
Chu, D. C. & Karniadakis, G. E. 1991 Numerical investigation of drag reduction in flow over surface with streamwise aligned riblets. AIAA-91-0518.
Coustols, E. & Cousteix, J. 1989 Experimental investigation of turbulent boundary layers manipulated with internal devices. Riblets. In Proc. 2nd IUTAM Symp. on Structure of Turbulence and Drag Reduction, Zurich, Switzerland.
Coustols, E. & Savill, A. M. 1992 Turbulent skin friction drag reduction by active and passive means. Tech. Rep. AGARD FDP/VKI. Von Karman Institute, Brussels.
Dean, R. B. 1978 Reynolds number dependence of skin friction and other bulk flow variables in two-dimensional rectangular duct flow. Trans. ASME I: Fluids Engng 100, 215–223.Google Scholar
Djenidi, L., Liandrat, J., Anselmet, F. & Fulachier, L. 1986 Viscous effects in drag reduction over riblets. In Drag Reduction in Fluid Flows: Techniques for Friction Control (ed. R. H. Sellin & R. T. Moses), pp. 35–41.
Falco, R. E., Klewicki, J. C. & Pan, K. 1989 Production of turbulence in boundary layers and potential for modification in the near wall region. In Proc. 2nd IUTAM Symp. on Structure of Turbulence and Drag Reduction, Zurich, Switzerland.
Gaudet, L. 1987 An assessment of the drag reduction properties of riblets and the penalties of offdesign conditions. Royal Aircraft Establishment Tech. Memo, Aero2113, pp. 363–376.Google Scholar
Gupta, A. K. & Kaplan, R. E. 1972 Statistical characteristics of Reynolds stress in a turbulent boundary layer. Phys. Fluids 15, 981–985.Google Scholar
Hooshmand, A. 1985 An experimental investigation of the influence of a drag reducing longitudinally aligned, triangular riblet surface on the velocity and streamwise vorticity fields of a zero-pressure gradient turbulent boundary layer. PhD thesis, University of Maryland.
Karniadakis, G. E. 1989 Spectral element simulations of laminar and turbulent flows in complex geometries. Appl. Numer. Maths 6, 85–105.Google Scholar
Karniadakis, G. E. 1990 Spectral element–Fourier methods for incompressible turbulent flows. Comput. Meth. Appl. Mech. Engng 80, 367–380.Google Scholar
Karniadakis, G. E., Israeli, M. & Orszag, S. A. 1991 High-order splitting methods for the incompressible Navier–Stokes equations. J. Comput. Phys. 97, 414–443.Google Scholar
Khan, M. S. 1986 A numerical investigation of the drag reduction by riblet surfaces. AIAA-86- 1127.
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low 19. J. Fluid Mech. 177, 133–166.Google Scholar
Kline, S. J. & Robinson, S. K. 1989 Turbulent boundary layer structure: Progress, status, and challenges. In Proc. 2nd IUTAM Symp. on Structure of Turbulence and Drag Reduction, Zurich, Switzerland.
Kreplin, H. & Eckelmann, H. 1979 Behavior of the three fluctuating velocity components in the wall region of a turbulent channel flow. Phys. Fluids 22, 1233–1239.Google Scholar
Launder, B. E. & Savill, A. M. 1988 Recent developments in the modeling of thin rectangular riblets and manipulators. In Proc. 3rd Turbulent Drag Reduction Working Party, ONERA-Chantillon, Paris.
Liu, K. N., Christodoulou, C., Riccius, O. & Joseph, D. D. 1989 Drag reduction in pipes lined with riblets. In Proc. 2nd IUTAM Symp. on Structure of Turbulence and Drag Reduction, Zurich, Switzerland.
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
Lynch, F. T. & Klinge, M. D. 1991 Some practical aspects of viscous drag reduction concepts. Proc. Aerospace Tech. Conf., Long Beach, CA, (SAE Tech. Paper 912129).
Moin, P. & Kim, J. 1982 Numerical investigation of turbulent channel flow. J. Fluid Mech. 118, 341–377.Google Scholar
Orszag, S. A. & Patera, A. T. 1983 Secondary instability of wall-bounded shear flows. J. Fluid Mech. 128, 347–385.Google Scholar
Patera, A. T. 1984 A spectral element method for fluid dynamics: laminar flow in a channel expansion. J. Comput. Phys. 54, 468–488.Google Scholar
Robert, J. P. 1992 Drag reduction: an industrial challenge. Technical report, Airbus Industries, preprint.
Robinson, S. K. 1988 Effects of riblets on turbulence in a supersonic boundary layer. AIAA-88- 2526.
Robinson, S. K. 1989 A review of vortex structures and associated coherent motions in turbulent boundary layers. In Proc. 2nd IUTAM Symp. on Structure of Turbulence and Drag Reduction, Zurich, Switzerland.
Roon, J. B. & Blackwelder, R. F. 1989 The effects of longitudinal roughness elements and local suction upon the turbulent boundary layer. In Proc. 2nd IUTAM Symp. on Structure of Turbulence and Drag Reduction, Zurich, Switzerland.
Smith, C. R. & Metzler, S. P. 1983 The characteristics of low-speed streaks in the near-wall region of a turbulent boundary layer. J. Fluid Mech. 129, 27–54.Google Scholar
Smith, C. R., Walker, J. D. A., Haidari, A. H. & Taylor, B. K. 1989 Hairpin vortices in turbulent boundary layers: the implications for reducing surface drag. In Proc. 2nd IUTAM Symp. on Structure of Turbulence and Drag Reduction, Zurich, Switzerland.
Squire, L. C. & Savill, A. M. 1986 High-speed riblets. In Proc. European Meeting on Turbulent Drag Reduction, Lausanne, Switzerland.
Tani, I. 1988 Drag reduction by riblet viewed as roughness problem. Proc. Japan Acad. 64B, 21–24.Google Scholar
Tomboulides, A. G., Israeli, M. & Karniadakis, G. E. 1989 Efficient removal of boundary-divergence errors in time-splitting methods. J. Sci. Comput. 4, 291–308.Google Scholar
Tsinober, A. 1989 Turbulent drag reduction versus structure of turbulence. In Proc. 2nd IUTAM Symp. on Structure of Turbulence and Drag Reduction, Zurich, Switzerland.
Vukoslavcević, P., Wallace, J. M. & Balint, J. L. 1987 On the mechanism of viscous drag reduction using streamwise aligned riblets: a review with new results. In Turbulent Drag Reduction by Passive Means.
Vukoslavcević, P., Wallace, J. M. & Balint, J. L. 1991 The velocity and vorticity vector fields of a turbulent boundary layer. Part 1. Simultaneous measurement by hot-wire anemometry. J. Fluid Mech. 228, 25–51.Google Scholar
Walker, J. D. A., Smith, C. R., Cerra, A. W. & Doligalski, T. L. 1987 The impact of a vortex ring on a wall. J. Fluid Mech. 181, 99–140.Google Scholar
Wallace, J. M. 1982 On the structure of bounded turbulent shear flow: a personal view. In Developments in Theoretical and Applied Mechanics, vol. XI, p. 509.Google Scholar
Wallace, J. M. & Balint, J. L. 1987 Viscous drag reduction using streamwise aligned riblets: survey and new results. In Turbulence Management and Relaminarisation (ed. H. W. Liepmann & R. Narasimha), pp. 133–147.
Walsh, M. J. 1980 Drag characteristics of V-groove and transverse curvature riblets. Prog. Astronaut. Aeronaut. 72, 168.Google Scholar
Walsh, M. J. 1990a Effect of detailed surface geometry on riblet drag reduction performance. J. Aircraft 27, 572–573.Google Scholar
Walsh, M. J. 1990b In Viscous Drag Reduction in Boundary Layers (ed. D. Bushnell & J. Hefner), vol. 123, pp. 204–261.
Walsh, M. J. & Anders, J. B. 1989 Riblet/LEBU research at NASA Langley. Appl. Sci. Res. 46, 255–262.Google Scholar
Walsh, M. J. & Lindermann, A. M. 1984 Optimization and application of riblets for turbulent drag reduction. AIAA-84-0347.
Willmarth, W. W. & Lu, S. S. 1972 Structure of the Reynolds stress near the wall. J. Fluid Mech. 55, 65–92.Google Scholar
Zores, R. 1989 Numerische untersuchungen mit einem grobauflosenden simulationsmodell fur die turbulente kanalstromung. Tech. Rep. IB 221-89 A 24, Institut fur Theoretische Stromungsmechanik, DLR Göttingen.