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Turbulent boundary-layer flow on a rotating disk

Published online by Cambridge University Press:  29 March 2006

T-S. Cham  and
M. R. Head
T-S. Cham
Affiliation:
Cambridge University Engineering Department
M. R. Head
Affiliation:
Cambridge University Engineering Department
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Abstract

Calculations have been made of the development of the turbulent boundary layer on a disk rotating in free air, using circumferential and radial momentum-integral equations and an auxiliary equation of entrainment. In the calculations, circumferential velocity profiles are represented by Thompson's (1965) two-parameter family, while radial profiles are given by Mager's (1952) quadratic expression. The circumferential component of skin friction follows from the use of Thompson's profile family for the circumferential velocity. The entrainment, in dimensionless form, is assumed to be determined uniquely by the circumferential velocity profile in the same way as was proposed by Head (1958) for a two-dimensional turbulent boundary layer.

Detailed measurements have been made of the development of the turbulent boundary layer on the rotating disk, and the calculations are found to be in excellent agreement with the results when a suitable adjustment is made to Head's two-dimensional entrainment curve.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 37 , Issue 1 , 5 June 1969 , pp. 129 - 147
Copyright
© 1969 Cambridge University Press

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References

Banks, W. H. & GADD, G. E. 1962 A preliminary report on boundary layers on screw propellers and simpler rotating bodies. Nat. Phys. Lab. Ship Div. Rep. no. 27.Google Scholar
Case, P. 1966 Measurements of entrainment by a free rotating disc. J. Roy. Aero Soc. 71, 124.Google Scholar
Cham, T-S. 1968 Turbulent boundary layers in rotating flows. Ph.D. thesis, Cambridge University.
Clauser, F. H. 1954 Turbulent boundary layers in adverse pressure gradients. J. Aero. Sci. 21, 91–108.Google Scholar
Cochran, W. G. 1934 The flow due to a rotating disk. Proc. Camb. Phil. Soc. 30, 365–75.Google Scholar
Cumpsty, N. A. & HEAD, M. R. 1967 The calculation of three-dimensional turbulent boundary layers, pts 1 and 2. Aero. Quart. 18, 55–84, 150–164.Google Scholar
Dorfman, L. A. 1963 Hydrodynamic Resistance and the Heat Loss of Rotating Solids. Oliver and Boyd.
Goldstein, S. 1935 On the resistance to the rotation of a disk immersed in a fluid. Proc. Camb. Phil. Soc. 31, 232.Google Scholar
Gregory, N., STUART, J. T. & WALKER, W. S. 1955 On the stability of three-dimensional boundary layers with application to the flow due to a rotating disk. Phil. Trans. A 248, 155–99.Google Scholar
Head, M. R. 1958 Entrainment in the turbulent boundary layer. Aero. Res. Coun. R & M. no. 3152.Google Scholar
Johnston, J. P. 1960 On the three-dimensional turbulent boundary layer generated by secondary flow. ASME, J. Basic Engng 82, 233–248.Google Scholar
Kármán, TH. VON 1921 Über laminare und turbulente Reibung. ZAMM, 1, 233.Google Scholar
Kempf, G. VON 1922 Über Reibungswiderstand rotierender Scheiben. Vortrage aus dem Gebiete der Hydro und Aerodynamik, Innsbruck.
Mager, A. 1952 Generalisation of boundary layer momentum-integral equations to three-dimensional flows including those of rotating system. NACA Rep. no. 1067.Google Scholar
Rosenhead, L. 1963 Laminar Boundary Layers. Oxford University Press.
Schmidt, W. 1921 Ein einfaches Messverfahren für Drehmomente. ZVDI, 65, 441.Google Scholar
Stain, W. C. 1961 The three-dimensional turbulent boundary layer on a rotating disk. Aerophysics Department, Mississippi State University, Res. Rep. no. 35.Google Scholar
Theodorsen, T. & REGIER, A. 1944 Experiments on drag of revolving disks, eylinders and streamline rods at high speeds. NACA Rep. no. 793.Google Scholar
Thompson, B. G. J. 1965 A new two-parameter family of mean velocity profiles for incompressible turbulent boundary layers on smooth walls. Aero. Res. Coun. R & M no. 3463.Google Scholar