Hostname: page-component-745bb68f8f-kw2vx Total loading time: 0 Render date: 2025-01-10T05:39:02.164Z Has data issue: false hasContentIssue false
  • English
  • Français

Modelling of an actuated elastic swimmer

Published online by Cambridge University Press:  26 September 2017

M. Piñeirua ,
B. Thiria  and
R. Godoy-Diana Open the ORCID record for R. Godoy-Diana [Opens in a new window]
M. Piñeirua
Affiliation:
Laboratoire de Physique et Mécanique des Milieux Hétérogènes (PMMH), CNRS UMR 7636, ESPCI Paris – PSL Research University, Sorbonne Universités – Université Pierre et Marie Curie – Paris 6, Université Paris Diderot – Paris 7, 10 rue Vauquelin, 75005 Paris, France Institut de Recherche sur la Biologie de l’Insecte (IRBI), CNRS UMR 7261, UFR Sciences et Techniques, Université François Rabelais, 37200 Tours, France
B. Thiria
Affiliation:
Laboratoire de Physique et Mécanique des Milieux Hétérogènes (PMMH), CNRS UMR 7636, ESPCI Paris – PSL Research University, Sorbonne Universités – Université Pierre et Marie Curie – Paris 6, Université Paris Diderot – Paris 7, 10 rue Vauquelin, 75005 Paris, France
R. Godoy-Diana*
Affiliation:
Laboratoire de Physique et Mécanique des Milieux Hétérogènes (PMMH), CNRS UMR 7636, ESPCI Paris – PSL Research University, Sorbonne Universités – Université Pierre et Marie Curie – Paris 6, Université Paris Diderot – Paris 7, 10 rue Vauquelin, 75005 Paris, France
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

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.

JFM classification

Biological Fluid Dynamics: Biological Fluid Dynamics Biological Fluid Dynamics: Swimming/flying
Type
Papers
Information
Journal of Fluid Mechanics , Volume 829 , 25 October 2017 , pp. 731 - 750
Check for updates
Copyright
© 2017 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Alben, S. 2008 Optimal flexibility of a flapping appendage in an inviscid fluid. J. Fluid Mech. 614, 355–380.Google Scholar
Alben, S. 2009 Simulating the dynamics of flexible bodies and vortex sheets. J. Comput. Phys. 228 (7), 2587–2603.Google Scholar
Alben, S., Witt, C., Baker, T. V., Anderson, E. & Lauder, G. 2012 Dynamics of freely swimming flexible foils. Phys. Fluids 24, 051901.Google Scholar
Argentina, M. & Mahadevan, L. 2005 Fluid-flow-induced flutter of a flag. Proc. Natl Acad. Sci. USA 102 (6), 1829–1834.Google Scholar
Blake, R. W. 2004 Fish functional design and swimming performance. J. Fish Biol. 65 (5), 1193–1222.Google Scholar
Borazjani, I. & Sotiropoulos, F. 2010 On the role of form and kinematics on the hydrodynamics of self-propelled body/caudal fin swimming. J. Exp. Biol. 213 (1), 89–107.Google Scholar
Candelier, F., Boyer, F. & Leroyer, A. 2011 Three-dimensional extension of lighthill’s large-amplitude elongated-body theory of fish locomotion. J. Fluid Mech. 674, 196–226.Google Scholar
Childress, S. 1981 Mechanics of Swimming and Flying. Cambridge Studies in Mathematical Biology.Google Scholar
Cros, A. & Arellano Castro, R. F. 2016 Experimental study on the resonance frequencies of a cantilevered plate in air flow. J. Sound Vib. 363, 240–246.Google Scholar
Dewey, P. A., Boschitsch, B. M., Moored, K. W., Stone, H. A. & Smits, A. J. 2013 Scaling laws for the thrust production of flexible pitching panels. J. Fluid Mech. 732, 29–46.Google Scholar
Ehrenstein, U. & Eloy, C. 2013 Skin friction on a moving wall and its implications for swimming animals. J. Fluid Mech. 718, 321–346.Google Scholar
Ehrenstein, U., Marquillie, M. & Eloy, C. 2014 Skin friction on a flapping plate in uniform flow. Phil. Trans. R. Soc. Lond. A 372 (2020), 20130345.Google Scholar
Eloy, C. 2013 On the best design for undulatory swimming. J. Fluid Mech. 717, 48–89.Google Scholar
Eloy, C., Kofman, N. & Schouveiler, L. 2012 The origin of hysteresis in the flag instability. J. Fluid Mech. 691, 583–593.CrossRefGoogle Scholar
Feilich, K. L. & Lauder, G. V. 2015 Passive mechanical models of fish caudal fins: effects of shape and stiffness on self-propulsion. Bioinspir. Biomim. 10 (3), 036002.Google Scholar
Fernández-Prats, R., Raspa, V., Thiria, B., Huera-Huarte, F. & Godoy-Diana, R. 2015 Large-amplitude undulatory swimming near a wall. Bioinspir. Biomim. 10, 016003.Google Scholar
Gazzola, M., Argentina, M. & Mahadevan, L. 2015 Gait and speed selection in slender inertial swimmers. Proc. Natl Acad. Sci. USA 112 (13), 3874–3879.Google Scholar
Kang, C. & Shyy, W. 2013 Scaling law and enhancement of lift generation of an insect-size hovering flexible wing. J. R. Soc. Interface 10, 20130361.CrossRefGoogle ScholarPubMed
Lauga, E. & Powers, T. 2009 The hydrodynamics of swimming microorganisms. Rep. Prog. Phys. 72, 096601.Google Scholar
Leftwich, M. C., Tytell, E. D., Cohen, A. H. & Smits, A. J. 2012 Wake structures behind a swimming robotic lamprey with a passively flexible tail. J. Exp. Biol. 215 (3), 416–425.Google Scholar
Li, G., Müller, U. K., van Leeuwen, J. L. & Liu, H. 2016 Fish larvae exploit edge vortices along their dorsal and ventral fin folds to propel themselves. J. R. Soc. Interface 13 (116), 20160068.Google Scholar
Lighthill, M. J. 1960 Note on the swimming of slender fish. J. Fluid Mech. 9 (02), 305–317.Google Scholar
Lighthill, M. J. 1970 Aquatic animal propulsion of high hydromechanical efficiency. J. Fluid Mech. 44 (02), 265–301.Google Scholar
Lighthill, M. J. 1971 Large amplitude elongated-body theory of fish locomotion. Proc. R. Soc. Lond. B 179, 125–138.Google Scholar
Lucas, K. N., Johnson, N., Beaulieu, W. T., Cathcart, E., Tirrell, G., Colin, S. P., Gemmell, B. J., Dabiri, J. O. & Costello, J. H. 2014 Bending rules for animal propulsion. Nat. Comms. 5, 3293.Google Scholar
Michelin, S. & Llewellyn Smith, S. G. 2009 Resonance and propulsion performance of a heaving flexible wing. Phys. Fluids 21 (7), 071902.Google Scholar
Michelin, S., Llewellyn Smith, S. G. & Glover, B. J. 2008 Vortex shedding model of a flapping flag. J. Fluid Mech. 617, 1–10.Google Scholar
Paraz, F., Eloy, C. & Schouveiler, L. 2014 Experimental study of the response of a flexible plate to a harmonic forcing in a flow. C. R. Méc. 342, 532–538.Google Scholar
Paraz, F., Schouveiler, L. & Eloy, C. 2016 Thrust generation by a heaving flexible foil: Resonance, nonlinearities, and optimality. Phys. Fluids 28, 011903.Google Scholar
Piñeirua, M., Godoy-Diana, R. & Thiria, B. 2015 Resistive thrust production can be as crucial as added mass mechanisms for inertial undulatory swimmers. Phys. Rev. E 92, 021001(R).Google Scholar
Piñeirua, M., Doaré, O. & Michelin, S. 2015 Influence and optimization of the electrodes position in a piezoelectric energy harvesting flag. J. Sound Vib. 346, 200–215.Google Scholar
Porez, M., Boyer, F. & Ijspeert, A. J. 2014 Improved Lighthill fish swimming model for bio-inspired robots: Modeling, computational aspects and experimental comparisons. Intl J. Robot. Res. 33 (10), 1322–1341.Google Scholar
Quinn, D. B., Lauder, G. V. & Smits, A. J. 2014 Scaling the propulsive performance of heaving flexible panels. J. Fluid Mech. 738, 250–267.Google Scholar
Quinn, D. B., Lauder, G. V. & Smits, A. J. 2015 Maximizing the efficiency of a flexible propulsor using experimental optimization. J. Fluid Mech. 767, 430–448.Google Scholar
Ramananarivo, S., Godoy-Diana, R. & Thiria, B. 2011 Rather than resonance, flapping wing flyers may play on aerodynamics to improve performance. Proc. Natl Acad. Sci. USA 108 (15), 5964–5969.Google Scholar
Ramananarivo, S., Godoy-Diana, R. & Thiria, B. 2013 Passive elastic mechanism to mimic fish-muscle action in anguilliform swimming. J. R. Soc. Interface 10 (88), 20130667–20130667.Google Scholar
Ramananarivo, S., Godoy-Diana, R. & Thiria, B. 2014a Propagating waves in bounded elastic media: transition from standing waves to anguilliform kinematics. Europhys. Lett. 105, 1–5.Google Scholar
Ramananarivo, S., Thiria, B. & Godoy-Diana, R. 2014b Elastic swimmer on a free surface. Phys. Fluids 26 (9), 091112.Google Scholar
Raspa, V., Ramananarivo, S., Thiria, B. & Godoy-Diana, R. 2014 Vortex-induced drag and the role of aspect ratio in undulatory swimmers. Phys. Fluids 26, 041701.Google Scholar
van Rees, W. M., Gazzola, M. & Koumoutsakos, P. 2013 Optimal shapes for anguilliform swimmers at intermediate Reynolds numbers. J. Fluid Mech. 722, R3.Google Scholar
van Rees, W. M., Gazzola, M. & Koumoutsakos, P. 2015 Optimal morphokinematics for undulatory swimmers at intermediate Reynolds numbers. J. Fluid Mech. 775, 178–188.Google Scholar
Sheng, J. X., Ysasi, A., Kolomenskiy, D., Kanso, E., Nitsche, M. & Schneider, K. 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. 255–262. Springer.Google Scholar
Singh, K., Michelin, S. & de Langre, E. 2012 The effect of non-uniform damping on flutter in axial flow and energy-harvesting strategies. Proc. R. Soc. Lond. A 468 (2147), 3620–3635.Google Scholar
Taylor, G. I. 1952 Analysis of the swimming of long and narrow animals. Proc. R. Soc. Lond. A 214 (1117), 158–183.Google Scholar
Tytell, E. D., Hsu, C. Y. & Fauci, L. J. 2014 The role of mechanical resonance in the neural control of swimming in fishes. Zoology 117, 48–56.CrossRefGoogle ScholarPubMed
van Weerden, J. F., Reid, D. A. P. & Hemelrijk, C. K. 2014 A meta-analysis of steady undulatory swimming. Fish Fisheries 15 (3), 397–409.CrossRefGoogle Scholar
Wu, T. Y. 1961 Swimming of a waving plate. J. Fluid Mech. 10, 321–344.Google Scholar
Yeh, P. D. & Alexeev, A. 2014 Free swimming of an elastic plate plunging at low Reynolds number. Phys. Fluids 26 (5), 053604.Google Scholar
Yeh, P. D. & Alexeev, A. 2016 Effect of aspect ratio in free-swimming plunging flexible plates. Comput. Fluids 124, 220–225.Google Scholar
Zhang, J., Liu, N. S. & Lu, X. Y. 2010 Locomotion of a passively flapping flat plate. J. Fluid Mech. 659, 43–68.Google Scholar