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Non-invasive determination of external forces in vortex-pair-cylinder interactions

Hartmann, D. and Schröder, W. and Shashikanth, B. N. (2012) Non-invasive determination of external forces in vortex-pair-cylinder interactions. Physics of Fluids, 24 (6). Art. No. 061903. ISSN 1070-6631. https://resolver.caltech.edu/CaltechAUTHORS:20121029-095211424

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Abstract

Expressions for the conserved linear and angular momenta of a dynamically coupled fluid + solid system are derived. Based on the knowledge of the flow velocity field, these expressions allow the determination of the external forces exerted on a body moving in the fluid such as, e.g., swimming fish. The verification of the derived conserved quantities is done numerically. The interaction of a vortex pair with a circular cylinder in various configurations of motions representing a generic test case for a dynamically coupled fluid + solid system is investigated in a weakly compressible Navier-Stokes setting using a Cartesian cut-cell method, i.e., the moving circular cylinder is represented by cut cells on a moving mesh. The objectives of this study are twofold. The first objective is to show the robustness of the derived expressions for the conserved linear and angular momenta with respect to bounded and discrete data sets. The second objective is to study the coupled dynamics of the vortex pair and a neutrally buoyant cylinder free to move in response to the fluid stresses exerted on its surface. A comparison of the vortex-body interaction with the case of a fixed circular cylinder evidences significant differences in the vortex dynamics. When the cylinder is fixed strong secondary vorticity is generated resulting in a repeating process between the primary vortex pair and the cylinder. In the neutrally buoyant cylinder case, a stable structure consisting of the primary vortex pair and secondary vorticity shear layers stays attached to the moving cylinder. In addition to these fundamental cases, the vortex-pair-cylinder interaction is studied for locomotion at constant speed and locomotion at constant thrust. It is shown that a similar vortex structure like in the neutrally buoyant cylinder case is obtained when the cylinder moves away from the approaching vortex pair at a constant speed smaller than the vortex pair translational velocity. Finally, the idealized symmetric settings are complemented by an asymmetric interaction of a vortex pair and a cylinder. This case is discussed for a fixed and a neutrally buoyant cylinder to show the validity of the derived relations for multi-dimensional body dynamics.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1063/1.4729613 DOIUNSPECIFIED
http://pof.aip.org/resource/1/phfle6/v24/i6/p061903_s1PublisherUNSPECIFIED
Additional Information:© 2012 American Institute of Physics. Received 21 September 2011; accepted 24 April 2012; published online 25 June 2012. This research was performed as part of the collaborative research center SFB 686, which is funded by the German Research Association (Deutsche Forschungsgemeinschaft (DFG)). The support is gratefully acknowledged. Banavara Shashikanth would like to acknowledge financial support in the form of a summer research fellowship from the Alexander von Humboldt Foundation. Daniel Hartmann is currently sponsored by the German Research Association (Deutsche Forschungsgemeinschaft (DFG)) under Grant No. HA 5535/2-1. The support is gratefully acknowledged.
Funders:
Funding AgencyGrant Number
Deutsche Forschungsgemeinschaft (DFG)SFB 686
Alexander von Humboldt FoundationUNSPECIFIED
Deutsche Forschungsgemeinschaft (DFG)HA 5535/2-1
Subject Keywords:biological fluid dynamics, compressible flow, flow instability, Navier-Stokes equations, shear flow, vortices
Issue or Number:6
Classification Code:PACS: 47.32.cb; 47.40.-x; 47.63.Gd; 47.10.ad; 47.20.Bp
Record Number:CaltechAUTHORS:20121029-095211424
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20121029-095211424
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:35145
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:29 Oct 2012 21:28
Last Modified:03 Oct 2019 04:25

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