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The viscous flow on surfaces with longitudinal ribs

Published online by Cambridge University Press:  26 April 2006

D. W. Bechert  and
M. Bartenwerfer
D. W. Bechert
Affiliation:
DLR, Abteilung Turbulenzforschung, Müller-Breslau-Straße 8, 1000 Berlin-West 12, West Germany
M. Bartenwerfer
Affiliation:
DLR, Abteilung Turbulenzforschung, Müller-Breslau-Straße 8, 1000 Berlin-West 12, West Germany
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Abstract

The viscous sublayer of a turbulent boundary layer on a surface with fine longitudinal ribs (riblets) is investigated theoretically. The mean flow constituent of this viscous flow is considered. Using conformal mapping, the velocity distributions on various surface configurations are calculated. The geometries that were investigated include sawtooth profiles with triangular and trapezoidal grooves as well as profiles with thin blade-shaped ribs, ribs with rounded edges and ribs having sharp ridges and U-shaped grooves. (This latter riblet configuration is also found on the tiny scales of fast sharks.) Our calculations enable us to determine the location of the origin of the velocity profile that lies somewhat below the tips of the ridges. The distance between this origin and the tip of the ridge we call ‘protrusion height’. The upper limit for the protrusion height is found to be 22% of the lateral rib spacing; the coefficient 0.22 being the value of the expression π−1 In 2. This limit is valid for two-dimensional riblet geometries. Analogous experiments with an electrolytic tank are carried out as an additional check on the theoretical calculations. This is also an easy way to determine experimentally the location of the origin of the velocity profile for arbitrary new riblet geometries. A possible connection between protrusion height and drag reduction in a turbulent boundary layer flow is discussed. Finally, the present theory also produces an orthogonal grid pattern above riblet surfaces which may be utilized in future numerical calculations of the whole turbulent boundary layer.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 206 , September 1989 , pp. 105 - 129
Copyright
© 1989 Cambridge University Press

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References

Abramovitz, M. & Stegun, I. A. 1972 Handbook of Mathematical Functions. Dover.
Acarlar, M. S. & Smith, C. R. 1987 A study of hairpin vortices in a laminar boundary layer. Part 1. Hairpin vortices generated by a hemisphere protuberance. J. Fluid Mech. 175, 1–41.Google Scholar
Bartenwerfer, M. & Bechert, D. W. 1987 Die viskose Strömung über Oberflächen mit Längsrippen. DFVLR-FB 87-21. (English transl. The viscous flow on surfaces with streamwise aligned riblets. ESA-TT-1091 1988.)
Bechert, D. W., Bartenwerfer, M., Hoppe, G. & Reif, W.-E. 1986 Drag reduction mechanisms derived from shark skin. 15th Congr. of the Int. Counc. of the Aeronautical Sciences, Sept. 7-12, 1986, London, Paper ICAS-86-1.8.3. AIAA.
Bechert, D. W., Hoppe, G. & Reif, W.-E. 1985 On the drag reduction of the shark skin. AIAA-Paper 85-0546.Google Scholar
Betz, A. 1964 Konforme Abbildung. Springer.
Burdak, V. D. 1969 Function of the ctenoid apparatus of fish in the presence of a turbulent boundary layer. Zoologichevskiy Zhurnal 48, 1053–1055 (in Russian).Google Scholar
Chernyshov, O. B. & Zayets, V. A. 1970 Some peculiarities of the structure of the skin of sharks. In Hydrodynamic Problems of Bionics. Bionica Nr. 4, pp. 77–83 (in Russian).
Choi, K. S. 1987 Test of drag reducing riblets on a one-third scale racing yacht. Proc. Turbulent Drag Reduction by Passive Means, Royal Aeronautical Society, 15-17 Sept., London.
Coles, D. 1978 A model for flow in the viscous sublayer. Proc. Coherent Struciures of Turbulent Boundary Layers. AFOSR/Lehigh Workshop 1978, pp. 462–475.
Corrsin, S. 1956 Some current problems in turbulent shear flows. Symp. on Naval Hydrodynamics, Washington, DC, 24-28 Sept., 1956. Publ. 515, National Academy of Sciences-National Research Council, 1957.
Dinkelacker, A., Nitschke-Kowsky, P. & Reif, W.-E. 1988 On the possibility of drag reduction with the help of longitudinal ridges in the walls. IUTAM Symp. on Turbulence Management and Relaminarization, Bangalore, India, Jan. 1987 (ed. H. W. Liepmann & R. Narasimha). Springer.
Gradstein, I. S. & Ryshik, I. M. 1981 Tables of Series, Products, and Integrals. (Transl. from Russian.) Frankfurt: Harri Deutsch.
Hooshmand, D., Youngs, R. & Wallace, J. M. 1983 An experimental study of changes in the structure of a turbulent layer due to surface geometry changes. AIAA-paper 83-0230.Google Scholar
Jang, P. S., Benney, D. J. & Gran, R. L. 1986 On the origin of streamwise vortices in a turbulent boundary layer. J. Fluid Mech. 169, 109–123.Google Scholar
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.Google Scholar
Kober, H. 1957 Dictionary of Conformal Representations. Dover.
Kramer, M. 1939 Einrichtung zur Verminderung des Reibungswiderstandes. Reichspatentamt, Patentschrift Nr. 669897, Klasse 62b, Gruppe 408. Patentiert vom 17.März 1937 an.
Liu, C. K., Kline, S. J. & Johnston, J. P. 1966 An experimental study of turbulent boundary layer on rough walls. Stanford University, Dep. Mech. Eng., Rep. MD-15, July 1966.Google Scholar
McLean, J. D., George-Falvy, D. N. & Sullivan, P. P. 1987 Flight-test of turbulent skin-friction reduction by riblets. Proc. Turbulent Drag Reduction by Passive Means, the Royal Aeronautical Society, 16-17 Sept., London.
Nitschke, P. 1983 Experimentelle Untersuchung der turbulenten Strömung in glatten und längsgerillten Rohren. Max-Planck-Institut für Strömungsforschung, Göttingen, Bericht 3/1983. (Trans.: Experimental investigation of the turbulent flow in smooth and longitudinally grooved tubes. NASA TM 77 480, 1984.)
Pearson, C. F. 1988 Interaction of streamwise vorticity with a grooved boundary. Bull. Am. Phys. Soc., 33, 2233.Google Scholar
Raschi, W. G. & Musick, J. A. 1984 Hydrodynamic aspects of shark scales. Virginia Institute of Marine Science, Gloucester Point, Va. 22062, Rep. 272, Jan. 1984.Google Scholar
Reif, W.-E. 1982 Morphogenesis and function of the squamation in sharks. Neues Jahrbuch für Geologie und Palaentologie, Abhandlungen Band 164, pp. 172–183. Stuttgart: E. Schweizerbart'sche Verlagsbuchhandlung.
Reif, W.-E. 1985 Squamation and ecology of sharks. Courier Forschungsinstitut Senckenberg, Frankfurt/M., Nr. 78, 255 p.Google Scholar
Reif, W.-E. & Dinkelacker, A. 1982 Hydrodynamics of the squamation in fast swimming sharks. Neues Jahrbuch für Geologie und Palaentologie, Abhandlungen Band 164, pp. 184–187. Stuttgart: E. Schweizerbart'sche Verlagsbuchhandlung.
Sawyer, W. G. & Winter, K. G. 1987 An investigation of the effect on turbulent skin friction of surfaces with streamwise grooves. Proc. Turbulent Drag Reduction by Passive Means, Royal Aeronautical Society, London 15-17 Sept.
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
Steuben, K. S. & Kreeft, G. 1978 Die Haie der Sieben Meere (The sharks of the seven seas). Hamburg: Verlag Paul Parey.
Van Dam, W. P. 1986 Weerstandsvermindering en een turbulente grenslag als gevolg van microgroeven. Technische Hogeschool Delft, Vakgroep Stromingsleer, Rep. June 1986.Google Scholar
Van Dyke, M. 1982 An Album of Fluid Motion. Stanford: Parabolic.
Wallace, J. M. 1987 On the mechanism of viscous drag reduction using streamwise aligned riblets: a review with some new results. Proc. Turbulent Drag Reduction by Passive Means, Royal Aeronautical Society, 15-17 Sept., London.
Walsh, M. J. 1980 Drag characteristics of V-groove and transverse curvature riblets. In : Viscous Flow Drag Reduction (ed. G. R. Hough), Progress in Astronautics and Aeronautics, vol. 72. AIAA.
Walsh, M. J. 1982 Turbulent boundary layer drag reduction using riblets. AIAA-paper 82-0169.Google Scholar
Walsh, M. J. 1983 Riblets as a viscous drag reduction technique. AIAA J. 21, 485–486.Google Scholar
Walsh, M. J. 1984 Optimization and application of riblets for turbulent drag reduction. AIAA Paper 84-0347.Google Scholar
Wilkinson, S. P. & Lazos, B. S. 1987 Direct drag and hot-wire measurements on thin-element riblet arrays. IUTAM Symp. on Turbulence Management and Relaminarization. Bangalore, India, Jan. 1987 (ed. H. W. Liepmann & R. Narasimha). Springer.