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Stability and transition of three-dimensional rotating boundary layers

Hussain, Zahir (2010)
Ph.D. thesis, University of Birmingham.

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Abstract

The flow over a rotating cone in still fluid is susceptible to crossflow and centrifugal instability modes of spiral nature, depending on the cone half-angle. For parameters ranging from propeller nose cones to rotating disks, the instability triggers co-rotating vortices, whereas for slender spinning missiles, counter-rotating vortices are observed. Upon introduction of an oncoming flow, the problem essentially becomes a battle between the streamwise and azimuthal shear flow, due to the rotating surface. The boundary layer instability is again visualized by the formation of spiral vortices, which wrap around the cone surface in a helical nature. For both crossflow and centrifugal instabilities, we derive the mean flow boundary layer equations and investigate the high Reynolds number asymptotic linear stability of the flow to inviscid crossflow modes (type I), type II modes, which arise from a viscous-Coriolis force balance, and neutral modes for a slender cone. The influence of the cone half-angle (ψ) and axial flow strength (s or Ts) on the number and orientation of the spiral vortices is examined, with comparisons made with previous experimental and numerical results.

Type of Work:Ph.D. thesis.
Supervisor(s):Stephens, Sharon
School/Faculty:Colleges (2008 onwards) > College of Engineering & Physical Sciences
Department:School of Mathematics
Subjects:QA Mathematics
Institution:University of Birmingham
ID Code:839
This unpublished thesis/dissertation is copyright of the author and/or third parties. The intellectual property rights of the author or third parties in respect of this work are as defined by The Copyright Designs and Patents Act 1988 or as modified by any successor legislation. Any use made of information contained in this thesis/dissertation must be in accordance with that legislation and must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the permission of the copyright holder.
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