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Description of the transitional wake behind a strongly streamwise rotating sphere

Published online by Cambridge University Press:  01 June 2020

M. Lorite-Díez Open the ORCID record for M. Lorite-Díez [Opens in a new window]  and
J. I. Jiménez-González Open the ORCID record for J. I. Jiménez-González [Opens in a new window]
M. Lorite-Díez
Affiliation:
Departamento de Ingeniería Mecánica y Minera, Universidad de Jaén, Campus de las Lagunillas, 23071, Jaén, Spain
J. I. Jiménez-González*
Affiliation:
Departamento de Ingeniería Mecánica y Minera, Universidad de Jaén, Campus de las Lagunillas, 23071, Jaén, Spain
*
†Email address for correspondence: jignacio@ujaen.es
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Abstract

Direct numerical simulations are performed to study the flow regimes at the wake behind a strongly streamwise rotating sphere, covering the range of rotation parameters $0\leqslant \unicode[STIX]{x1D6FA}\leqslant 3$ and laminar and transitional Reynolds numbers $Re=250$, 500 and 1000. The wake dynamics is investigated in terms of flow topology, dominant modes and force coefficients. A higher wake complexity is found for growing values of the rotation parameter $\unicode[STIX]{x1D6FA}$ for all the Reynolds numbers investigated. In particular, at low and intermediate $Re$, successive bifurcations entail the development of periodic, quasi-periodic and irregular regimes, constituting a classical scenario of route to chaos, through the destabilization of different structures associated to incommensurate frequencies, which have been analysed by means of flow decomposition techniques. At low $Re$ and high rotation rates, the flow is governed by double-threaded structures due to the destabilization of helical symmetries of azimuthal wavenumber $m=2$, which are not dominant at larger $Re$. Interestingly, at intermediate values of $\unicode[STIX]{x1D6FA}$ and $Re=500$, a bistable dynamics is observed whereby the wake undergoes a random switching between a modulated quasi-periodic regime and an irregular regime, which is associated to a sudden increase of the drag coefficient, on account of the development of a double-celled recirculating bubble. Finally, for $Re=1000$, the flow is already chaotic at $\unicode[STIX]{x1D6FA}=0$, and the evolution with the rotation rate of the flow dynamics is simpler, with wake regimes being characterized by the rotation and massive shedding of vortex loops, that are a continuous deformation through axial rotation of the irregular wake behind the static sphere.

JFM classification

Wakes/Jets: Wakes
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 896 , 10 August 2020 , A18
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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Lorite-Díez and Jiménez-González supplementary movie 1

Wake behind a streamwise rotating sphere (Re=250, Ω=0.4)

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Lorite-Díez and Jiménez-González supplementary movie 2

Wake behind a streamwise rotating sphere (Re=250, Ω=1.2)

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Lorite-Díez and Jiménez-González supplementary movie 3

Wake behind a streamwise rotating sphere (Re=250, Ω=1.6)

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Video 667.5 KB

Lorite-Díez and Jiménez-González supplementary movie 4

Wake behind a streamwise rotating sphere (Re=250, Ω=2.2)

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Video 602.5 KB

Lorite-Díez and Jiménez-González supplementary movie 5

Wake behind a streamwise rotating sphere (Re=250, Ω=3.0)

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Video 652.7 KB

Lorite-Díez and Jiménez-González supplementary movie 6

Wake behind a streamwise rotating sphere (Re=500, Ω=0.0)

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Video 173.6 KB

Lorite-Díez and Jiménez-González supplementary movie 7

Wake behind a streamwise rotating sphere (Re=500, Ω=0.4)

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Lorite-Díez and Jiménez-González supplementary movie 8

Wake behind a streamwise rotating sphere (Re=500, Ω=0.6)

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Video 357.9 KB

Lorite-Díez and Jiménez-González supplementary movie 9

Wake behind a streamwise rotating sphere (Re=500, Ω=1.1)

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Lorite-Díez and Jiménez-González supplementary movie 10

Wake behind a streamwise rotating sphere (Re=500, Ω=1.2)

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Lorite-Díez and Jiménez-González supplementary movie 11

Wake behind a streamwise rotating sphere (Re=500, Ω=3.0)

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Lorite-Díez and Jiménez-González supplementary movie 12

Wake behind a streamwise rotating sphere (Re=1000, Ω=1)

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