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

Anirudh Rao, Justin S. Leontini, Mark C. Thompson, Kerry Hourigan

Research output: Contribution to journalArticleResearchpeer-review

Abstract

The wake of an elliptical cylinder at low incident angles is investigated for different aspect 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 ; 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 and , become unstable; these modes have spatio-temporal symmetries similar to their circular cylinder wake counterparts, modes A and mode B, respectively. While mode persists for all incident angles investigated here, mode is found only to be unstable for incident angles up to . Surprisingly, for , 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.

Original languageEnglish
Pages (from-to)245-283
Number of pages39
JournalJournal of Fluid Mechanics
Volume825
DOIs
Publication statusPublished - 25 Aug 2017

Keywords

  • parametric instability
  • vortex shedding
  • wakes

Cite this

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title = "Three-dimensionality of elliptical cylinder wakes at low angles of incidence",
abstract = "The wake of an elliptical cylinder at low incident angles is investigated for different aspect 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 ; 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 and , become unstable; these modes have spatio-temporal symmetries similar to their circular cylinder wake counterparts, modes A and mode B, respectively. While mode persists for all incident angles investigated here, mode is found only to be unstable for incident angles up to . Surprisingly, for , 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.",
keywords = "parametric instability, vortex shedding, wakes",
author = "Anirudh Rao and Leontini, {Justin S.} and Thompson, {Mark C.} and Kerry Hourigan",
year = "2017",
month = "8",
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language = "English",
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pages = "245--283",
journal = "Journal of Fluid Mechanics",
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Three-dimensionality of elliptical cylinder wakes at low angles of incidence. / Rao, Anirudh; Leontini, Justin S.; Thompson, Mark C.; Hourigan, Kerry.

In: Journal of Fluid Mechanics, Vol. 825, 25.08.2017, p. 245-283.

Research output: Contribution to journalArticleResearchpeer-review

TY - JOUR

T1 - Three-dimensionality of elliptical cylinder wakes at low angles of incidence

AU - Rao, Anirudh

AU - Leontini, Justin S.

AU - Thompson, Mark C.

AU - Hourigan, Kerry

PY - 2017/8/25

Y1 - 2017/8/25

N2 - The wake of an elliptical cylinder at low incident angles is investigated for different aspect 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 ; 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 and , become unstable; these modes have spatio-temporal symmetries similar to their circular cylinder wake counterparts, modes A and mode B, respectively. While mode persists for all incident angles investigated here, mode is found only to be unstable for incident angles up to . Surprisingly, for , 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.

AB - The wake of an elliptical cylinder at low incident angles is investigated for different aspect 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 ; 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 and , become unstable; these modes have spatio-temporal symmetries similar to their circular cylinder wake counterparts, modes A and mode B, respectively. While mode persists for all incident angles investigated here, mode is found only to be unstable for incident angles up to . Surprisingly, for , 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.

KW - parametric instability

KW - vortex shedding

KW - wakes

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U2 - 10.1017/jfm.2017.366

DO - 10.1017/jfm.2017.366

M3 - Article

VL - 825

SP - 245

EP - 283

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -