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Cylinders with square cross-section: wake instabilities with incidence angle variation

Published online by Cambridge University Press:  10 July 2009

GREGORY J. SHEARD ,
MATTHEW J. FITZGERALD  and
KRIS RYAN
GREGORY J. SHEARD*
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, Monash University, VIC 3800, Australia
MATTHEW J. FITZGERALD
Affiliation:
AMOG Consulting, Sea Technology House, 19 Business Park Drive, Monash Business Park, Notting Hill, VIC 3168, Australia
KRIS RYAN
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, Monash University, VIC 3800, Australia
*
†Email address for correspondence: [email protected]
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Abstract

The wakes behind square cylinders with variation in incidence angle are computed over a range of Reynolds numbers to elucidate the three-dimensional stability and dynamics up to a Reynolds number of Re = 300, based on the projected height of the inclined square cylinder. Three-dimensional instability modes are predicted and computed using a linear stability analysis technique and three-dimensional simulations, respectively. Depending on the incidence angle, the flow is found to transition to three-dimensional flow through either a mode A instability, or a subharmonic mode C instability. The mode A instability is predicted as the first-occurring instability at incidence angles smaller than 12° and greater than 26°, with the mode C instability predicted between these incidence angles. At a zero-degree angle of incidence, the wake instabilities closely match modes A, B and a quasi-periodic mode predicted in earlier studies behind square and circular cylinders. With increasing angle of incidence, the three-dimensional wake transition Reynolds number first increases from Re = 164 as the mode A instability weakens, before decreasing again beyond an incidence angle of 12° as the wake becomes increasingly unstable to the mode C instability, and then again to the mode A instability as the incidence angle approaches 45°. A spanwise autocorrelation analysis from computations over a cylinder span 20 times the square cross-section side length reveals that beyond the onset of three-dimensional instabilities, the vortex street breaks down with patterns consistent with spatio-temporal chaos. This effect was more pronounced at higher incidence angles.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 630 , 10 July 2009 , pp. 43 - 69
Copyright
Copyright © Cambridge University Press 2009

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