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Three-dimensionality of elliptical cylinder wakes at low angles of incidence

Published online by Cambridge University Press:  20 July 2017

Anirudh Rao Open the ORCID record for Anirudh Rao [Opens in a new window] ,
Justin S. Leontini ,
Mark C. Thompson  and
Kerry Hourigan
Anirudh Rao
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, 17 College Walk, Monash University, Clayton, Victoria 3800, Australia
Justin S. Leontini
Affiliation:
Department of Mechanical and Product Design Engineering, Swinburne University of Technology, John Street, Hawthorn, Victoria 3122, Australia
Mark C. Thompson*
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, 17 College Walk, Monash University, Clayton, Victoria 3800, Australia
Kerry Hourigan
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, 17 College Walk, Monash University, Clayton, Victoria 3800, Australia
*
†Email address for correspondence: [email protected]
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Abstract

The wake of an elliptical cylinder at low incident angles is investigated for different aspect ratio ($\unicode[STIX]{x1D6E4}=\text{major:minor axis ratio}$) cylinders using stability analysis and direct simulations. In particular, two- and three-dimensional transitions are mapped for cylinders of aspect ratios between 1 and 4 using Floquet stability analysis. The transition scenario for near-unity aspect ratio cylinders resembles that for a circular cylinder wake as Reynolds number is increased to $Re\lesssim 400$; first, with the transition from steady two-dimensional flow to unsteady two-dimensional flow, followed by the onset of three-dimensional flow via a long-wavelength instability (mode A), then, a short-wavelength instability (mode B) and, finally, an intermediary wavelength instability which is quasi-periodic in nature (mode QP). The effect of the incident angle on this transition scenario for the low-aspect-ratio cylinders is minimal. As the aspect ratio is increased towards 2, two synchronous modes, modes $\widehat{\text{A}}$ and $\widehat{\text{B}}$, become unstable; these modes have spatio-temporal symmetries similar to their circular cylinder wake counterparts, modes A and mode B, respectively. While mode $\widehat{\text{A}}$ persists for all incident angles investigated here, mode $\widehat{\text{B}}$ is found only to be unstable for incident angles up to $10^{\circ }$. Surprisingly, for $1.8\lesssim \unicode[STIX]{x1D6E4}\lesssim 2.9$, the mode A instability observed at zero incident angle emerges as a quasi-periodic mode as the incident angle is increased even slightly. At higher incident angles, this quasi-periodic mode once again transforms to a real mode on increasing the Reynolds number. The parameter space maps for the various aspect ratios are presented in the Reynolds number–incident angle plane, and the three-dimensional modes are discussed in terms of similarities to and differences from existing modes. A key aim of the work is to map the different modes and various transition sequences as a simple body geometry is systematically changed and as the flow symmetry is systematically broken; thus, insight is provided on the overall path towards fully turbulent flow.

JFM classification

Instability: Parametric instability Vortex Flows: Vortex shedding Wakes/Jets: Wakes
Type
Papers
Information
Journal of Fluid Mechanics , Volume 825 , 25 August 2017 , pp. 245 - 283
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© 2017 Cambridge University Press 

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