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The centrifugal instability of the boundary-layer flow over a slender rotating cone in an enforced axial free stream

Published online by Cambridge University Press:  22 December 2015

Z. Hussain ,
S. J. Garrett ,
S. O. Stephen  and
P. T. Griffiths
Z. Hussain*
Affiliation:
School of Computing, Mathematics and Digital Technology, Manchester Metropolitan University, Manchester M1 5GD, UK
S. J. Garrett
Affiliation:
Department of Engineering, University of Leicester, Leicester LE1 7RH, UK
S. O. Stephen
Affiliation:
School of Mathematics and Statistics, University of Sydney, Sydney, NSW 2006, Australia
P. T. Griffiths
Affiliation:
Department of Engineering, University of Leicester, Leicester LE1 7RH, UK
*
†Email address for correspondence: Z.Hussain@mmu.ac.uk
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Abstract

In this study, a new centrifugal instability mode, which dominates within the boundary-layer flow over a slender rotating cone in still fluid, is used for the first time to model the problem within an enforced oncoming axial flow. The resulting problem necessitates an updated similarity solution to represent the basic flow more accurately than previous studies in the literature. The new mean flow field is subsequently perturbed, leading to disturbance equations that are solved via numerical and short-wavelength asymptotic approaches, yielding favourable comparisons with existing experiments. Essentially, the boundary-layer flow undergoes competition between the streamwise flow component, due to the oncoming flow, and the rotational flow component, due to effect of the spinning cone surface, which can be described mathematically in terms of a control parameter, namely the ratio of streamwise to axial flow. For a slender cone rotating in a sufficiently strong axial flow, the instability mode breaks down into Görtler-type counter-rotating spiral vortices, governed by an underlying centrifugal mechanism, which is consistent with experimental and theoretical studies for a slender rotating cone in otherwise still fluid.

JFM classification

Boundary Layers: Boundary layer stability Geophysical and Geological Flows: Rotating flows Instability: Transition to turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 788 , 10 February 2016 , pp. 70 - 94
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Copyright
© 2016 Cambridge University Press 

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