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Phase dynamics of freely swimming foils

Published online by Cambridge University Press:  02 July 2014

Cyndee L. Finkel  and
Karl D. von Ellenrieder
Cyndee L. Finkel
Affiliation:
Department of Physics, Florida Atlantic University, Boca Raton, FL 33431, USA
Karl D. von Ellenrieder*
Affiliation:
Department of Ocean and Mechanical Engineering, Florida Atlantic University, Dania Beach, FL 33004, USA
*
†Email address for correspondence: ellenrie@fau.edu
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Abstract

A two-dimensional D-shaped cylinder and heaving foil were mounted in tandem and used to simulate the main body and tail, respectively, of a natural swimmer. Thrust/drag measurements of the force on the foil and particle image velocimetry measurements of the flow downstream of the swimming system were conducted at a Reynolds number of about $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}10^4$ in a water channel with a constant free stream current speed. Two main sets of measurements were conducted: one set with the swimming system locked at a fixed streamwise location in the water channel as the heave frequency of the foil was varied; the other set with the system freely swimming to a desired set-point position from different upstream and downstream locations. When the freely swimming system reached and maintained its set-point position, so that its swimming speed matched that of the current, the oscillation frequency of the heaving foil corresponded to a Strouhal number of 0.36. Phase portraits of the measured thrust/drag forces reveal limit cycle oscillations for all swimming cases studied, which suggests that self-regulation drives the selection of this Strouhal number. No coupling was observed between the vortices shed by the D-shaped cylinder and the self-selected frequency of the heaving foil during free swimming. An examination of the ratio of the phase-locking indices for the input heaving motion of the foil and the coupled fluidic thrust/drag response reveals that it approaches a value of 0.5 over time when the freely swimming system is released from rest and allowed to achieve steady-state cruising. The jet produced by the freely swimming foil was inclined at an angle of approximately $4^\circ $ with respect to the direction of the mean flow.

JFM classification

Biological Fluid Dynamics: Biological Fluid Dynamics Biological Fluid Dynamics: Swimming/flying
Type
Papers
Information
Journal of Fluid Mechanics , Volume 752 , 10 August 2014 , pp. 5 - 21
Copyright
© 2014 Cambridge University Press 

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