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Secondary flow and turbulence in a cone-and-plate device

Published online by Cambridge University Press:  20 April 2006

H. P. Sdougos ,
S. R. Bussolari  and
C. F. Dewey
H. P. Sdougos
Affiliation:
Fluid Mechanics Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts
S. R. Bussolari
Affiliation:
Fluid Mechanics Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts
C. F. Dewey
Affiliation:
Fluid Mechanics Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts
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Abstract

The flow between a shallow rotating cone and a stationary plate has been investigated using flow visualization, hot-film heat-transfer probes, and measurements of the torque required to rotate the cone against the retardation of the viscous fluid that fills the device. Theory appropriate to these experiments is also presented.

An expansion of the Navier–Stokes equations is performed for small values of the single parameter $\tilde{R} = r^2\omega\alpha^2/12\nu $. (Here r is the local radius, ω the angular velocity of the cone, α([Lt ] 1) is the angle between the cone and plate, and v is the fluid kinematic viscosity.) The measurements at low rotational speeds describe a simple linear velocity profile as predicted for the laminar flow of a Newtonian fluid. At larger rotational speeds, strong secondary flows are observed. There is agreement between the laminar theory and the measured streamline angles and shear stresses for values of $\tilde{R} < 0.5$. Turbulence is observed for $\tilde{R} \gtrsim 4$.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 138 , January 1984 , pp. 379 - 404
Copyright
© 1984 Cambridge University Press

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