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Fluid–solid Floquet stability analysis of self-propelled heaving foils

Published online by Cambridge University Press:  13 January 2021

Luis Benetti Ramos Open the ORCID record for Luis Benetti Ramos [Opens in a new window] ,
Olivier Marquet Open the ORCID record for Olivier Marquet [Opens in a new window] ,
Michel Bergmann  and
Angelo Iollo
Luis Benetti Ramos*
Affiliation:
ONERA – The French Aerospace Lab, F-92190Meudon, France
Olivier Marquet
Affiliation:
ONERA – The French Aerospace Lab, F-92190Meudon, France
Michel Bergmann
Affiliation:
Université de Bordeaux, IMB, UMR 5251, F-33400Talence, France Equipe-projet Memphis, Inria Bordeaux-Sud Ouest, F-33400Talence, France
Angelo Iollo
Affiliation:
Université de Bordeaux, IMB, UMR 5251, F-33400Talence, France Equipe-projet Memphis, Inria Bordeaux-Sud Ouest, F-33400Talence, France
*
†Email address for correspondence: [email protected]
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Abstract

We investigate the role of linear mechanisms in the emergence of nonlinear horizontal self-propelled states of a heaving foil in a quiescent fluid. Two states are analysed: a periodic state of unidirectional motion and a quasi-periodic state of slow back and forth motion around a mean horizontal position. The states emergence is explained through a fluid–solid Floquet stability analysis of the non-propulsive symmetric base solution. Unlike a purely hydrodynamic analysis, our analysis accurately determines the locomotion states onset. An unstable synchronous mode is found when the unidirectional propulsive solution is observed. The obtained mode has a propulsive character, featuring a mean horizontal velocity and an asymmetric flow that generates a horizontal force accelerating the foil. An unstable asynchronous mode, also featuring flow asymmetry and a non-zero velocity, is found when the back and forth state is observed. Its associated complex multiplier introduces a slow modulation of the flapping period, agreeing with the quasi-periodic nature of the back and forth regime. The temporal evolution of this perturbation shows how the horizontal force exerted by the flow is alternatively propulsive or resistive over a slow period. For both modes, an analysis of the velocity and force perturbation time-averaged over the flapping period is used to establish physical instability criteria. The behaviour for a large solid-to-fluid density ratio of the modes is thus analysed. The asynchronous fluid–solid mode converges towards the purely hydrodynamic one, whereas the synchronous mode becomes marginally unstable in our analysis not converging to the purely hydrodynamic analysis where it is never destabilised.

JFM classification

Biological Fluid Dynamics: Propulsion
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 910 , 10 March 2021 , A28
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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