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Global vorticity shedding for a shrinking cylinder

Global vorticity shedding for a shrinking cylinder
Global vorticity shedding for a shrinking cylinder
We study numerically the viscous flow around a steadily moving two-dimensional cylinder undergoing a rapid reduction in its diameter as a model problem for force production through shape change which is encountered in the locomotion of certain animals. We consider first the case of a rapidly collapsing circular cylinder in steady translation, starting from an original diameter and reaching a final, smaller diameter under prescribed kinematics. We show that the difference in added mass energy is recovered by the body, and the boundary layer vorticity is reduced through annihilation with opposite-sign vorticity generated during the reduction phase. Next we consider a steadily moving circular cylinder which undergoes rapid but orderly melting, resulting in the same reduction of its diameter but which exhibits radically different flow patterns compared to the collapsing cylinder. The original vorticity in the boundary layer is shed instantaneously and globally in the fluid at the start of the melting phase, and then rapidly rolls up to form a pair of strong vortices, which contain the energy difference between the original and final cylinder states. The formation of the vortices in the melting cylinder takes less than a third of the time required by a rigid translating cylinder to form such vortices.
0022-1120
470-487
Weymouth, G.D.
b0c85fda-dfed-44da-8cc4-9e0cc88e2ca0
Triantafyllou, M.S.
8b2b42be-39f5-41ab-b9c8-5ba019b04b6d
Weymouth, G.D.
b0c85fda-dfed-44da-8cc4-9e0cc88e2ca0
Triantafyllou, M.S.
8b2b42be-39f5-41ab-b9c8-5ba019b04b6d

Weymouth, G.D. and Triantafyllou, M.S. (2012) Global vorticity shedding for a shrinking cylinder. Journal of Fluid Mechanics, 702, 470-487. (doi:10.1017/jfm.2012.200).

Record type: Article

Abstract

We study numerically the viscous flow around a steadily moving two-dimensional cylinder undergoing a rapid reduction in its diameter as a model problem for force production through shape change which is encountered in the locomotion of certain animals. We consider first the case of a rapidly collapsing circular cylinder in steady translation, starting from an original diameter and reaching a final, smaller diameter under prescribed kinematics. We show that the difference in added mass energy is recovered by the body, and the boundary layer vorticity is reduced through annihilation with opposite-sign vorticity generated during the reduction phase. Next we consider a steadily moving circular cylinder which undergoes rapid but orderly melting, resulting in the same reduction of its diameter but which exhibits radically different flow patterns compared to the collapsing cylinder. The original vorticity in the boundary layer is shed instantaneously and globally in the fluid at the start of the melting phase, and then rapidly rolls up to form a pair of strong vortices, which contain the energy difference between the original and final cylinder states. The formation of the vortices in the melting cylinder takes less than a third of the time required by a rigid translating cylinder to form such vortices.

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More information

e-pub ahead of print date: 7 June 2012
Published date: 10 July 2012
Organisations: Fluid Structure Interactions Group

Identifiers

Local EPrints ID: 349800
URI: http://eprints.soton.ac.uk/id/eprint/349800
ISSN: 0022-1120
PURE UUID: 3fee799e-aa6a-4327-a2c2-bc6be06fe645
ORCID for G.D. Weymouth: ORCID iD orcid.org/0000-0001-5080-5016

Catalogue record

Date deposited: 11 Mar 2013 13:50
Last modified: 28 Apr 2022 02:09

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Contributors

Author: G.D. Weymouth ORCID iD
Author: M.S. Triantafyllou

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