In this study, the limiting maximum drag reduction asymptote for the moment coefficient of an enclosed rotating disk with fine spiral grooves in turbulent flow region were obtained analytically. Analysis which were based on an assumption for a simple parabolic velocity distribution of turbulent pipe flow to represent relative tangential velocity, was carried out using momentum integral equations of the boundary layer. For a certain K- parameter the moment coefficient results agree well with experimental results for maximum drag reduction in an enclosed rotating disk with fine spiral grooves and drag reduction ratio approximately was 15 %. Additionally, the experimental results for drag reduction on a rotating disk can be explained well with the analytical results.


Toms, B.A., 1948, “Some Observations on the Flow of Linear Polymer Solutions Through Straight Tubes at Large Reynolds Numbers”, Proc. Int.

Congress of Rheologie. Scheveningen, Holland.

Watanabe K & Ogata S.,1997, “Drag reduction for a rotating disk with highly water-repellent wall”, ASME Fluids Engineering Division Summer Meeting FEDSM.

Watanabe K & Ogata S., 1999), “Flow characteristics of a drag reducing rotating disk with highly water-repellent wall”, Proc.of Symposium on Flow Control of Wall-Boundary and Free shear Flows Joint . ASME/JSME Fluids Eng.Conf. San Francisco.

Young, A.D., 1989, “Boundary Layers”, AIAA Ed. Series, Black Wall Sci. Publ. Ltd., p. 256, London.

Walsh, M.J., 1982, “Turbulent Boundary Layer Drag Reduction Using Riblets “, AIAA paper 82-0169.

Watanabe, K., Budiarso, and Ogata, S., 2005, “Drag Reduction of a Rotating Disk with Spiral Grooves”, Annual Meeting of JSME Symposium, Cyuugoku-Shikoku, Branch, Japan.

Ogata, S., and Watanabe, K., 2002, “Limiting Max. Drag Reduction Asymtote for the Moment Coeff. of a Rot. Disk in Drag Reduction Surfactant Solution”, J. Fluid Mech. Vol. 457, pp. 325-337.

Schlichting,H., 1979, “Boundary Layer Theory”, 7 th edn. McGraw-Hill.

Kurokawa, J., and Sakuma, M.,1987, “Flow in a Narrow Gap along an Enclosed Rotating Disk with Through-Flow”, Trans, Jpn. Soc. Mech. Eng.,B, 53-492, p.2468-2476 (in Japanese).

Goldstein, S., 1935, “On the Resistance to the Rotation of a Disk Immersed in a Fluid”, Proceedings, Cambridge Philosophical Society, Vol.31, part 2, p. 232.

Blasius H.,1913,“Das Ahnlichkeitsgesetz be Reibungsvorgangen in Flussigkeiten”, Forschg.Ing.—Wes.No. 134, Berlin.

Weiegardt, K.,1946,“Turbulente Grenzchichten, Gottinger Monographie, Part B 5.



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