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Boundary-layer transition on a rotating cone in still fluid

Published online by Cambridge University Press:  20 April 2006

R. Kobayashi  and
H. Izumi
R. Kobayashi
Affiliation:
Institute of High Speed Mechanics, Tohoku University, Sendai, Japan
H. Izumi
Affiliation:
Asahi Glass Co. Ltd, Yokohama, Japan
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Abstract

A linear stability analysis and experiments were carried out for the laminar–turbulent transition of three-dimensional incompressible boundary layers induced on the surface of a cone rotating around the axis of symmetry with constant angular speed in still fluid. Five cones having total angle of 30°–150° were tested. The results show that the critical and transition Reynolds numbers, the direction of spiral vortices appearing in the transition region and their number on a cone increase as the cone angle is increased, and they tend to the values for the case of a rotating disk. Flow visualizations were made for the transitional process and also for cross-sectional flows of spiral vortices.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 127 , February 1983 , pp. 353 - 364
Copyright
© 1983 Cambridge University Press

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References

Chen, C. F. & Christensen, D. K. 1967 Stability of flow induced by an impulsively started rotating cylinder Phys. Fluids 10, 1845–1846.Google Scholar
Chin, D.-T. & Litt, M. 1972 An electrochemical study of flow instability on a rotating disk J. Fluid Mech. 54, 613–625.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. R. Soc. Lond. A248, 155–199.
Kappesser, R., Greif, R. & Cornet, I. 1973 Mass transfer to rotating cones Appl. Sci. Res. 28, 442–452.Google Scholar
Kármán, T. Von 1921 Über laminare and turbulente Reibung Z. angew. Math. Mech. 1, 233–252.Google Scholar
Kirchner, R. P. & Chen, C. F. 1970 Stability of time-dependent rotational Couette flow. Part 1. Experimental investigation J. Fluid Mech. 40, 39–47.Google Scholar
Kobayashi, R., Kohama, Y. & Takamadate, CH. 1980 Spiral vortices in boundary layer transition regime on a rotating disk Acta Mech. 35, 71–81.Google Scholar
Kobayashi, R. 1981 Linear stability theory of boundary layer along a cone rotating in axial flow Bull. Japan Soc. Mech. Engrs 24, 934–940.Google Scholar
Kobayashi, R., Kohama, Y. & Kurosawa, M. 1983 Boundary-layer transition on a rotating cone in axial flow J. Fluid Mech. 127, 341–352.Google Scholar
Kreith, F., Ellis, D. & Giesing, J. 1962 An experimental investigation of the flow engendered by a rotating cone Appl. Sci. Res. All, 430–440.Google Scholar
Malik, M. R., Wilkinson, S. P. & Orszag, S. A. 1981 Instability and transition in rotating disk flow A.I.A.A. J. 19, 1131–1138.Google Scholar
Theodorsen, Th. & Regier, A. 1944 Experiments on drag of revolving disks, cylinders, and streamline rods at high speeds. NACA Rep. 793, pp. 367–384.
Tien, C. L. 1960 Heat transfer by laminar flow from a rotating cone. Trans. A.S.M.E. C: J. Heat Transfer 82, 252–253.
Tien, C. L. & Campbell, D. T. 1963 Heat and mass transfer from rotating cones J. Fluid Mech. 17, 105–112.Google Scholar
Walowit, J., Tsao, S. & Diprima, R. C. 1964 Stability of flow between arbitrarily spaced concentric cylindrical surfaces including the effect of a radial temperature gradient. Trans. A.S.M.E. E: J. Appl. Mech., 31, 585–593.Google Scholar
Wu, C. S. 1959 The three dimensional incompressible laminar boundary layer on a spinning cone Appl. Sci. Res. A8, 140–146.Google Scholar