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Turbulent flow on a planar moving belt and a rotating disk: modelling and comparisons

Published online by Cambridge University Press:  31 August 2007

JOHN M. McDARBY  and
FRANK T. SMITH
JOHN M. McDARBY
Affiliation:
Dept. of Mathematics, University College London, Gower Street, London, WC1E 6BT, UK
FRANK T. SMITH
Affiliation:
Dept. of Mathematics, University College London, Gower Street, London, WC1E 6BT, UK
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Abstract

Modelling of the fully turbulent flow produced on a moving belt and of that induced ona rotating disk is described, for each of which a more analytical approach is adopted than previously seen. The analysis for the two-dimensional moving belt indicates novel structures and these are found to carry over directly to the rotating disk flow which, ignoring the transitional regime, is three-componential but two-dimensional due to axisymmetry. This is based on addressing the Reynolds-averaged Navier–Stokes equations together with an eddy viscosity model, with the flow structure being analysed for high Reynolds numbers. A classical (von Kármán) constant within the model plays an important and surprising role, indicating that each of the belt and the disk flows has quite a massive thickness. Comparisons made with previous work show varying degrees of agreement. The approach, including the new prediction of massive thicknesses independent of the Reynoldsnumber, is expected to extend to flows induced by rotary blades, by related rotary devices and by other configurations of industrial interest.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 587 , 25 September 2007 , pp. 255 - 270
Copyright
Copyright © Cambridge University Press 2007

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