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Connections between resonance and nonlinearity in swimming performance of a flexible heaving plate

Published online by Cambridge University Press:  11 February 2020

Andres Goza Open the ORCID record for Andres Goza [Opens in a new window] ,
Daniel Floryan Open the ORCID record for Daniel Floryan [Opens in a new window]  and
Clarence Rowley
Andres Goza*
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08540, USA
Daniel Floryan
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08540, USA
Clarence Rowley
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08540, USA
*
†Present address: Department of Aerospace Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA. Email address for correspondence: ajgoza@gmail.com
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Abstract

We investigate the role of resonance in finite-amplitude swimming of a flexible flat plate in a viscous fluid. The role of resonance in performance remains unclear for two reasons: (i) a lack of definition of resonance for the fully coupled fluid–structure interaction system in a viscous flow, and (ii) the presence of nonlinear effects, which makes it difficult to disentangle resonant and non-resonant mechanisms in finite-amplitude swimming. We address point (i) and provide an unambiguous definition for system resonance by computing global linear stability modes of the fully coupled fluid–structure interaction system that account for the viscous fluid, the plate and the coupling between them. We resolve point (ii) by considering high-fidelity nonlinear simulations of systematically increased amplitude. By comparing the results for different amplitudes with one another and with the linear stability modes, we separate linear and/or resonant effects from nonlinear and/or non-resonant effects. Resonant behaviour is observed over a wide range of plate stiffnesses, with peaks in trailing-edge motion and thrust occurring near the resonant frequency defined by the global linear analysis. The peaks broaden and weaken with increasing heave amplitude, consistent with an increased damping effect from the fluid. At the same time, non-resonant mechanisms are present at large heave amplitudes. The input power exhibits qualitatively different dynamics at large heave amplitudes compared to smaller heave amplitudes, where resonance dominates. Moreover, leading-edge separation is present for stiff plates at large heave amplitudes, which can drastically alter the performance characteristics from what one would expect through linear predictions.

JFM classification

Biological Fluid Dynamics: Propulsion Biological Fluid Dynamics: Swimming/flying
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 888 , 10 April 2020 , A30
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

Alben, S. 2008 Optimal flexibility of a flapping appendage in an inviscid fluid. J. Fluid Mech. 614, 355–380.CrossRefGoogle Scholar
Alben, S., Witt, C., Baker, T. V., Anderson, E. & Lauder, G. V. 2012 Dynamics of freely swimming flexible foils. Phys. Fluids 24 (5), 051901.CrossRefGoogle Scholar
Barrett, D. S., Triantafyllou, M. S., Yue, D. K. P., Grosenbaugh, M. A. & Wolfgang, M. J. 1999 Drag reduction in fish-like locomotion. J. Fluid Mech. 392, 183–212.CrossRefGoogle Scholar
Colonius, T. & Taira, K. 2008 A fast immersed boundary method using a nullspace approach and multi-domain far-field boundary conditions. Comput. Meth. Appl. Mech. Engng 197 (25), 2131–2146.CrossRefGoogle Scholar
Criesfield, M. A. 1991 Non-Linear Finite Element Analysis of Solids and Structures, vol. 1. Wiley.Google Scholar
Das, A., Shukla, R. K. & Govardhan, R. N. 2016 Existence of a sharp transition in the peak propulsive efficiency of a low-Re pitching foil. J. Fluid Mech. 800, 307–326.CrossRefGoogle 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.CrossRefGoogle Scholar
Ebert, D. S., Musgrave, F. K., Peachey, D., Perlin, K. & Worley, S. 2003 Texturing and Modeling: A Procedural Approach. Morgan Kaufmann.Google Scholar
Fish, F. E. & Lauder, G. V. 2006 Passive and active flow control by swimming fishes and mammals. Annu. Rev. Fluid Mech. 38, 193–224.CrossRefGoogle Scholar
Floryan, D. & Rowley, C. W. 2018 Clarifying the relationship between efficiency and resonance for flexible inertial swimmers. J. Fluid Mech. 853, 271–300.CrossRefGoogle Scholar
Floryan, D., Van Buren, T., Rowley, C. W. & Smits, A. J. 2017 Scaling the propulsive performance of heaving and pitching foils. J. Fluid Mech. 822, 386–397.CrossRefGoogle Scholar
Goza, A. & Colonius, T. 2017 A strongly-coupled immersed-boundary formulation for thin elastic structures. J. Comput. Phys. 336, 401–411.CrossRefGoogle Scholar
Goza, A., Colonius, T. & Sader, J. E. 2018 Global modes and nonlinear analysis of inverted-flag flapping. J. Fluid Mech. 857, 312–344.CrossRefGoogle Scholar
Goza, A., Liska, S., Morley, B. & Colonius, T. 2016 Accurate computation of surface stresses and forces with immersed boundary methods. J. Comput. Phys. 321, 860–873.CrossRefGoogle Scholar
Hua, R.-N., Zhu, L. & Lu, X.-Y. 2013 Locomotion of a flapping flexible plate. Phys. Fluids 25 (12), 121901.CrossRefGoogle Scholar
Kang, C.-K., Aono, H., Cesnik, C. ES. & Shyy, W. 2011 Effects of flexibility on the aerodynamic performance of flapping wings. J. Fluid Mech. 689, 32–74.CrossRefGoogle Scholar
Lehoucq, R. B., Sorensen, D. C. & Yang, C. 1998 ARPACK Users’ Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods. SIAM.CrossRefGoogle Scholar
Liu, G., Ren, Y., Dong, H., Akanyeti, O., Liao, J. C. & Lauder, G. V. 2017 Computational analysis of vortex dynamics and performance enhancement due to body-fin and fin-fin interactions in fish-like locomotion. J. Fluid Mech. 829, 65–88.CrossRefGoogle Scholar
Mackowski, A. W. & Williamson, C. H. K. 2015 Direct measurement of thrust and efficiency of an airfoil undergoing pure pitching. J. Fluid Mech. 765, 524–543.CrossRefGoogle Scholar
Maertens, A. P., Triantafyllou, M. S. & Yue, D. K. P. 2015 Efficiency of fish propulsion. Bioinspir. Biomim. 10 (4), 046013.CrossRefGoogle ScholarPubMed
Michelin, S. & Llewellyn Smith, S. G. 2009 Resonance and propulsion performance of a heaving flexible wing. Phys. Fluids 21 (7), 071902.CrossRefGoogle Scholar
Moored, K. W., Dewey, P. A., Boschitsch, B. M., Smits, A. J. & Haj-Hariri, H. 2014 Linear instability mechanisms leading to optimally efficient locomotion with flexible propulsors. Phys. Fluids 26 (4), 041905.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle ScholarPubMed
Senturk, U. & Smits, A. J. 2019 Reynolds number scaling of the propulsive performance of a pitching airfoil. AIAA J. 57 (7), 2663–2669.CrossRefGoogle Scholar
Smits, A. J. 2019 Undulatory and oscillatory swimming. J. Fluid Mech. 874, P1.CrossRefGoogle Scholar
Triantafyllou, M. S., Triantafyllou, G. S. & Yue, D. K. P. 2000 Hydrodynamics of fishlike swimming. Annu. Rev. Fluid Mech. 32 (1), 33–53.CrossRefGoogle Scholar
Vanella, M., Fitzgerald, T., Preidikman, S., Balaras, E. & Balachandran, B. 2009 Influence of flexibility on the aerodynamic performance of a hovering wing. J. Expl Biol. 212 (1), 95–105.CrossRefGoogle ScholarPubMed
Webb, P. W. 1988 Simple physical principles and vertebrate aquatic locomotion. Am. Zool. 23 (2), 709–725.CrossRefGoogle Scholar
Wu, T. Y. 2011 Fish swimming and bird/insect flight. Annu. Rev. Fluid Mech. 43, 25–58.CrossRefGoogle Scholar
Wu, T. Y.-T. 1961 Swimming of a waving plate. J. Fluid Mech. 10 (3), 321–344.CrossRefGoogle Scholar
Young, J. & Lai, J. C. S. 2007 Mechanisms influencing the efficiency of oscillating airfoil propulsion. AIAA J. 45 (7), 1695–1702.CrossRefGoogle Scholar
Zhang, Y., Zhou, C. & Luo, H. 2017 Effect of mass ratio on thrust production of an elastic panel pitching or heaving near resonance. J. Fluids Struct. 74, 385–400.CrossRefGoogle Scholar
Zhou, Z. & Mittal, R. 2018 Swimming performance and unique wake topology of the sea hare (aplysia). Phys. Rev. Fluids 3 (3), 033102.CrossRefGoogle Scholar
Zhu, X., He, G. & Zhang, X. 2014 How flexibility affects the wake symmetry properties of a self-propelled plunging foil. J. Fluid Mech. 751, 164–183.CrossRefGoogle Scholar