Optimal propulsive flapping in Stokes flows.

Abstract:

:Swimming fish and flying insects use the flapping of fins and wings to generate thrust. In contrast, microscopic organisms typically deform their appendages in a wavelike fashion. Since a flapping motion with two degrees of freedom is able, in theory, to produce net forces from a time-periodic actuation at all Reynolds numbers, we compute in this paper the optimal flapping kinematics of a rigid spheroid in a Stokes flow. The hydrodynamics for the force generation and energetics of the flapping motion is solved exactly. We then compute analytically the gradient of a flapping efficiency in the space of all flapping gaits and employ it to derive numerically the optimal flapping kinematics as a function of the shape of the flapper and the amplitude of the motion. The kinematics of optimal flapping are observed to depend weakly on the flapper shape and are very similar to the figure-eight motion observed in the motion of insect wings. Our results suggest that flapping could be a exploited experimentally as a propulsion mechanism valid across the whole range of Reynolds numbers.

journal_name

Bioinspir Biomim

authors

Was L,Lauga E

doi

10.1088/1748-3182/9/1/016001

subject

Has Abstract

pub_date

2014-03-01 00:00:00

pages

016001

issue

1

eissn

1748-3182

issn

1748-3190

journal_volume

9

pub_type

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