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Modelling of an actuated elastic swimmer

  • M. Piñeirua (a1) (a2), B. Thiria (a1) and R. Godoy-Diana (a1)
Abstract

We study the force production dynamics of undulating elastic plates as a model for fish-like inertial swimmers. Using a beam model coupled with Lighthill’s large-amplitude elongated-body theory, we explore different localised actuations at one extremity of the plate (heaving, pitching and a combination of both) in order to quantify the reactive and resistive contributions to the thrust. The latter has the form of a quadratic drag in large Reynolds number swimmers and has recently been pointed out as a crucial element in the thrust force balance. We validate the output of a weakly nonlinear solution to the fluid–structure model using thrust force measurements from an experiment with flexible plates subjected to the three different actuation types. The model is subsequently used in a self-propelled configuration – with a skin friction model that balances thrust to produce a constant cruising speed – to map the reactive versus resistive thrust production in a parameter space defined by the aspect ratio and the actuation frequency. We show that this balance is modified as the frequency of excitation changes and the response of the elastic plate shifts between different resonant modes, the pure heaving case being the most sensitive to the modal response with drastic changes in the reactive/resistive contribution ratio along the frequency axis. We analyse also the role of the phase lag between the heaving and pitching components in the case of combined actuation, showing in particular a non-trivial effect on the propulsive efficiency.

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Corresponding author
Email address for correspondence: ramiro@pmmh.espci.fr
References
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AlbenS. 2008 Optimal flexibility of a flapping appendage in an inviscid fluid. J. Fluid Mech. 614, 355380.
AlbenS. 2009 Simulating the dynamics of flexible bodies and vortex sheets. J. Comput. Phys. 228 (7), 25872603.
AlbenS., WittC., BakerT. V., AndersonE. & LauderG. 2012 Dynamics of freely swimming flexible foils. Phys. Fluids 24, 051901.
ArgentinaM. & MahadevanL. 2005 Fluid-flow-induced flutter of a flag. Proc. Natl Acad. Sci. USA 102 (6), 18291834.
BlakeR. W. 2004 Fish functional design and swimming performance. J. Fish Biol. 65 (5), 11931222.
BorazjaniI. & SotiropoulosF. 2010 On the role of form and kinematics on the hydrodynamics of self-propelled body/caudal fin swimming. J. Exp. Biol. 213 (1), 89107.
CandelierF., BoyerF. & LeroyerA. 2011 Three-dimensional extension of lighthill’s large-amplitude elongated-body theory of fish locomotion. J. Fluid Mech. 674, 196226.
ChildressS. 1981 Mechanics of Swimming and Flying. Cambridge Studies in Mathematical Biology.
CrosA. & Arellano CastroR. F. 2016 Experimental study on the resonance frequencies of a cantilevered plate in air flow. J. Sound Vib. 363, 240246.
DeweyP. A., BoschitschB. M., MooredK. W., StoneH. A. & SmitsA. J. 2013 Scaling laws for the thrust production of flexible pitching panels. J. Fluid Mech. 732, 2946.
EhrensteinU. & EloyC. 2013 Skin friction on a moving wall and its implications for swimming animals. J. Fluid Mech. 718, 321346.
EhrensteinU., MarquillieM. & EloyC. 2014 Skin friction on a flapping plate in uniform flow. Phil. Trans. R. Soc. Lond. A 372 (2020), 20130345.
EloyC. 2013 On the best design for undulatory swimming. J. Fluid Mech. 717, 4889.
EloyC., KofmanN. & SchouveilerL. 2012 The origin of hysteresis in the flag instability. J. Fluid Mech. 691, 583593.
FeilichK. L. & LauderG. V. 2015 Passive mechanical models of fish caudal fins: effects of shape and stiffness on self-propulsion. Bioinspir. Biomim. 10 (3), 036002.
Fernández-PratsR., RaspaV., ThiriaB., Huera-HuarteF. & Godoy-DianaR. 2015 Large-amplitude undulatory swimming near a wall. Bioinspir. Biomim. 10, 016003.
GazzolaM., ArgentinaM. & MahadevanL. 2015 Gait and speed selection in slender inertial swimmers. Proc. Natl Acad. Sci. USA 112 (13), 38743879.
KangC. & ShyyW. 2013 Scaling law and enhancement of lift generation of an insect-size hovering flexible wing. J. R. Soc. Interface 10, 20130361.
LaugaE. & PowersT. 2009 The hydrodynamics of swimming microorganisms. Rep. Prog. Phys. 72, 096601.
LeftwichM. C., TytellE. D., CohenA. H. & SmitsA. J. 2012 Wake structures behind a swimming robotic lamprey with a passively flexible tail. J. Exp. Biol. 215 (3), 416425.
LiG., MüllerU. K., van LeeuwenJ. L. & LiuH. 2016 Fish larvae exploit edge vortices along their dorsal and ventral fin folds to propel themselves. J. R. Soc. Interface 13 (116), 20160068.
LighthillM. J. 1960 Note on the swimming of slender fish. J. Fluid Mech. 9 (02), 305317.
LighthillM. J. 1970 Aquatic animal propulsion of high hydromechanical efficiency. J. Fluid Mech. 44 (02), 265301.
LighthillM. J. 1971 Large amplitude elongated-body theory of fish locomotion. Proc. R. Soc. Lond. B 179, 125138.
LucasK. N., JohnsonN., BeaulieuW. T., CathcartE., TirrellG., ColinS. P., GemmellB. J., DabiriJ. O. & CostelloJ. H. 2014 Bending rules for animal propulsion. Nat. Comms. 5, 3293.
MichelinS. & Llewellyn SmithS. G. 2009 Resonance and propulsion performance of a heaving flexible wing. Phys. Fluids 21 (7), 071902.
MichelinS., Llewellyn SmithS. G. & GloverB. J. 2008 Vortex shedding model of a flapping flag. J. Fluid Mech. 617, 110.
ParazF., EloyC. & SchouveilerL. 2014 Experimental study of the response of a flexible plate to a harmonic forcing in a flow. C. R. Méc. 342, 532538.
ParazF., SchouveilerL. & EloyC. 2016 Thrust generation by a heaving flexible foil: Resonance, nonlinearities, and optimality. Phys. Fluids 28, 011903.
PiñeiruaM., Godoy-DianaR. & ThiriaB. 2015 Resistive thrust production can be as crucial as added mass mechanisms for inertial undulatory swimmers. Phys. Rev. E 92, 021001(R).
PiñeiruaM., DoaréO. & MichelinS. 2015 Influence and optimization of the electrodes position in a piezoelectric energy harvesting flag. J. Sound Vib. 346, 200215.
PorezM., BoyerF. & IjspeertA. J. 2014 Improved Lighthill fish swimming model for bio-inspired robots: Modeling, computational aspects and experimental comparisons. Intl J. Robot. Res. 33 (10), 13221341.
QuinnD. B., LauderG. V. & SmitsA. J. 2014 Scaling the propulsive performance of heaving flexible panels. J. Fluid Mech. 738, 250267.
QuinnD. B., LauderG. V. & SmitsA. J. 2015 Maximizing the efficiency of a flexible propulsor using experimental optimization. J. Fluid Mech. 767, 430448.
RamananarivoS., Godoy-DianaR. & ThiriaB. 2011 Rather than resonance, flapping wing flyers may play on aerodynamics to improve performance. Proc. Natl Acad. Sci. USA 108 (15), 59645969.
RamananarivoS., Godoy-DianaR. & ThiriaB. 2013 Passive elastic mechanism to mimic fish-muscle action in anguilliform swimming. J. R. Soc. Interface 10 (88), 2013066720130667.
RamananarivoS., Godoy-DianaR. & ThiriaB. 2014a Propagating waves in bounded elastic media: transition from standing waves to anguilliform kinematics. Europhys. Lett. 105, 15.
RamananarivoS., ThiriaB. & Godoy-DianaR. 2014b Elastic swimmer on a free surface. Phys. Fluids 26 (9), 091112.
RaspaV., RamananarivoS., ThiriaB. & Godoy-DianaR. 2014 Vortex-induced drag and the role of aspect ratio in undulatory swimmers. Phys. Fluids 26, 041701.
van ReesW. M., GazzolaM. & KoumoutsakosP. 2013 Optimal shapes for anguilliform swimmers at intermediate Reynolds numbers. J. Fluid Mech. 722, R3.
van ReesW. M., GazzolaM. & KoumoutsakosP. 2015 Optimal morphokinematics for undulatory swimmers at intermediate Reynolds numbers. J. Fluid Mech. 775, 178188.
ShengJ. X., YsasiA., KolomenskiyD., KansoE., NitscheM. & SchneiderK. 2012 Simulating vortex wakes of flapping plates. In Natural Locomotion in Fluids and on Surfaces (ed. Childress S., Hosoi A., Schultz W. W. & Wang Z. J.), pp. 255262. Springer.
SinghK., MichelinS. & de LangreE. 2012 The effect of non-uniform damping on flutter in axial flow and energy-harvesting strategies. Proc. R. Soc. Lond. A 468 (2147), 36203635.
TaylorG. I. 1952 Analysis of the swimming of long and narrow animals. Proc. R. Soc. Lond. A 214 (1117), 158183.
TytellE. D., HsuC. Y. & FauciL. J. 2014 The role of mechanical resonance in the neural control of swimming in fishes. Zoology 117, 4856.
van WeerdenJ. F., ReidD. A. P. & HemelrijkC. K. 2014 A meta-analysis of steady undulatory swimming. Fish Fisheries 15 (3), 397409.
WuT. Y. 1961 Swimming of a waving plate. J. Fluid Mech. 10, 321344.
YehP. D. & AlexeevA. 2014 Free swimming of an elastic plate plunging at low Reynolds number. Phys. Fluids 26 (5), 053604.
YehP. D. & AlexeevA. 2016 Effect of aspect ratio in free-swimming plunging flexible plates. Comput. Fluids 124, 220225.
ZhangJ., LiuN. S. & LuX. Y. 2010 Locomotion of a passively flapping flat plate. J. Fluid Mech. 659, 4368.
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Journal of Fluid Mechanics
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