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

Z. Hussain, S. J. Garrett, S. O. Stephen, P. T. Griffiths

Research output: Contribution to journalArticle

8 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)70-94
Number of pages25
JournalJournal of Fluid Mechanics
Volume788
Early online date22 Dec 2015
DOIs
Publication statusPublished - 10 Feb 2016
Externally publishedYes

Keywords

  • boundary layer stability
  • rotating flows
  • transition to turbulence

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

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