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Effect of actuation method on hydrodynamics of elastic plates oscillating at resonance

Published online by Cambridge University Press:  08 January 2021

Ersan Demirer Open the ORCID record for Ersan Demirer [Opens in a new window] ,
Yu-Cheng Wang ,
Alper Erturk Open the ORCID record for Alper Erturk [Opens in a new window]  and
Alexander Alexeev Open the ORCID record for Alexander Alexeev [Opens in a new window]
Ersan Demirer
Affiliation:
George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA30332, USA
Yu-Cheng Wang
Affiliation:
George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA30332, USA
Alper Erturk
Affiliation:
George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA30332, USA
Alexander Alexeev*
Affiliation:
George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA30332, USA
*
†Email address for correspondence: alexander.alexeev@me.gatech.edu
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Abstract

In this work we investigate the effects of two distinct actuation methods on the hydrodynamics of elastic rectangular plates oscillating at resonance. Plates are driven by plunging motion at the root or actuated by a distributed internal bending moment at Reynolds numbers between 500 and 4000. The latter actuation method represents internally actuated smart materials and emulates the natural ability of swimming animals to continuously change their shapes with muscles. We conduct experiments with plunging elastic plates and piezoelectric plate actuators that are simulated using a fully coupled three-dimensional computational model based on the lattice Boltzmann method. After experimental validation the computational model is employed to probe plate hydrodynamics for a wide range of parameters, including large oscillation amplitudes which prompts nonlinear effects. The comparison between the two actuation methods reveals that, for the same level of tip deflection, externally actuated plates significantly outperform internally actuated plates in terms of thrust production and hydrodynamic efficiency. The reduced performance of internally actuated plates is associated with their suboptimal bending shapes which leads to a trailing edge geometry with enhanced vorticity generation and viscous dissipation. Furthermore, the difference in actuation methods impacts the inertia coefficient characterizing the plate oscillations, especially for large amplitudes. It is found that the inertia coefficient strongly depends on the tip deflection amplitude and the Reynolds number, and actuation method, especially for larger amplitudes.

JFM classification

Biological Fluid Dynamics: Swimming/flying Biological Fluid Dynamics: Propulsion
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 910 , 10 March 2021 , A4
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Alben, S. 2009 On the swimming of a flexible body in a vortex street. J. Fluid Mech. 635, 27–45.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), 051901.10.1063/1.4709477CrossRefGoogle Scholar
Alexeev, A. & Balazs, A. C. 2007 Designing smart systems to selectively entrap and burst microcapsules. Soft Matt. 3 (12), 1500–1505.10.1039/b711769hCrossRefGoogle ScholarPubMed
Alexeev, A., Verberg, R. & Balazs, A. C. 2005 Modeling the motion of microcapsules on compliant polymeric surfaces. Macromolecules 38 (24), 10244–10260.10.1021/ma0516135CrossRefGoogle Scholar
Alexeev, A., Verberg, R. & Balazs, A. C. 2006 Modeling the interactions between deformable capsules rolling on a compliant surface. Soft Matt. 2 (6), 499–509.10.1039/b602417cCrossRefGoogle ScholarPubMed
Amabili, M. & Paidoussis, M. P. 2003 Review of studies on geometrically nonlinear vibrations and dynamics of circular cylindrical shells and panels, with and without fluid-structure interaction. Appl. Mech. Rev. 56 (4), 349–381.10.1115/1.1565084CrossRefGoogle Scholar
Anderson, E. J., Mcgillis, W. R. & Grosenbaugh, M. A. 2001 The boundary layer of swimming fish. J. Expl Biol. 204 (1), 81–102.Google ScholarPubMed
Anderson, J. M., Streitlien, K., Barrett, D. S. & Triantafyllou, M. S. 1998 Oscillating foils of high propulsive efficiency. J. Fluid Mech. 360, 41–72.CrossRefGoogle Scholar
Aureli, M., Basaran, M. E. & Porfiri, M. 2012 Nonlinear finite amplitude vibrations of sharp-edged beams in viscous fluids. J. Sound Vib. 331 (7), 1624–1654.10.1016/j.jsv.2011.12.007CrossRefGoogle Scholar
Bhalla, A. P. S., Bale, R., Griffith, B. E. & Patankar, N. A. 2013 A unified mathematical framework and an adaptive numerical method for fluid–structure interaction with rigid, deforming, and elastic bodies. J. Comput. Phys. 250, 446–476.10.1016/j.jcp.2013.04.033CrossRefGoogle Scholar
Bidkar, R. A., Kimber, M., Raman, A., Bajaj, A. K. & Garimella, S. V. 2009 Nonlinear aerodynamic damping of sharp-edged flexible beams oscillating at low Keulegan–Carpenter numbers. J. Fluid Mech. 634, 269–289.10.1017/S0022112009007228CrossRefGoogle Scholar
Borazjani, I. & Sotiropoulos, F. 2008 Numerical investigation of the hydrodynamics of carangiform swimming in the transitional and inertial flow regimes. J. Expl Biol. 211 (10), 1541–1558.10.1242/jeb.015644CrossRefGoogle ScholarPubMed
Bouzidi, M., Firdaouss, M. & Lallemand, P. 2001 Momentum transfer of a Boltzmann-lattice fluid with boundaries. Phys. Fluids 13 (11), 3452–3459.10.1063/1.1399290CrossRefGoogle Scholar
Branscomb, J. & Alexeev, A. 2010 Designing ciliated surfaces that regulate deposition of solid particles. Soft Matt. 6 (17), 4066–4069.10.1039/c0sm00185fCrossRefGoogle Scholar
Cen, L. & Erturk, A. 2013 Bio-inspired aquatic robotics by untethered piezohydroelastic actuation. Bioinspir. Biomim. 8 (1), 016006.10.1088/1748-3182/8/1/016006CrossRefGoogle ScholarPubMed
Cha, Y., Kim, H. & Porfiri, M. 2013 Energy harvesting from underwater base excitation of a piezoelectric composite beam. Smart Mater. Struct. 22 (11), 115026.CrossRefGoogle Scholar
Chen, X.-J., Wu, Y.-S., Cui, W.-C. & Jensen, J. J. 2006 Review of hydroelasticity theories for global response of marine structures. Ocean Engng 33 (3–4), 439–457.CrossRefGoogle Scholar
Chen, Z., Shatara, S. & Tan, X. 2009 Modeling of biomimetic robotic fish propelled by an ionic polymer–metal composite caudal fin. IEEE ASME Trans. Mechatron. 15 (3), 448–459.CrossRefGoogle Scholar
Chen, Z., Um, T. I., Zhu, J. & Bart-Smith, H. 2011 Bio-inspired robotic cownose ray propelled by electroactive polymer pectoral fin. In ASME 2011 International Mechanical Engineering Congress and Exposition, pp. 817–824. American Society of Mechanical Engineers Digital Collection.CrossRefGoogle Scholar
Chun, B. & Ladd, A. J. C. 2007 Interpolated boundary condition for lattice Boltzmann simulations of flows in narrow gaps. Phys. Rev. E 75, 066705.CrossRefGoogle ScholarPubMed
Combes, S. A. & Daniel, T. L. 2001 Shape, flapping and flexion: wing and fin design for forward flight. J. Expl Biol. 204 (12), 2073–2085.Google ScholarPubMed
Dai, H., Luo, H., de Sousa, P. J. S. A. F. & Doyle, J. F. 2012 Thrust performance of a flexible low-aspect-ratio pitching plate. Phys. Fluids 24 (10), 101903.CrossRefGoogle Scholar
De Rosis, A. & Lévêque, E. 2016 Central-moment lattice Boltzmann schemes with fixed and moving immersed boundaries. Comput. Maths Applics. 72 (6), 1616–1628.10.1016/j.camwa.2016.07.025CrossRefGoogle Scholar
Dowell, E. H. & Hall, K. C. 2001 Modeling of fluid-structure interaction. Annu. Rev. Fluid Mech. 33 (1), 445–490.CrossRefGoogle Scholar
Elmer, F.-J. & Dreier, M. 1997 Eigenfrequencies of a rectangular atomic force microscope cantilever in a medium. J. Appl. Phys. 81 (12), 7709–7714.10.1063/1.365379CrossRefGoogle Scholar
Eloy, C. & Schouveiler, L. 2011 Optimisation of two-dimensional undulatory swimming at high reynolds number. Intl J. Non-Linear Mech. 46 (4), 568–576.10.1016/j.ijnonlinmec.2010.12.007CrossRefGoogle Scholar
Engels, T., Kolomenskiy, D., Schneider, K. & Sesterhenn, J. 2017 Numerical simulation of vortex-induced drag of elastic swimmer models. Theor. Appl. Mech. Lett. 7 (5), 280–285.CrossRefGoogle Scholar
Erturk, A. & Delporte, G. 2011 Underwater thrust and power generation using flexible piezoelectric composites: an experimental investigation toward self-powered swimmer-sensor platforms. Smart Mater. Struct. 20 (12), 125013.CrossRefGoogle Scholar
Erturk, A. & Inman, D. J. 2011 Piezoelectric Energy Harvesting. John Wiley & Sons.CrossRefGoogle Scholar
Esposito, C. J., Tangorra, J. L., Flammang, B. E. & Lauder, G. V. 2012 A robotic fish caudal fin: effects of stiffness and motor program on locomotor performance. J. Expl Biol. 215 (1), 56–67.10.1242/jeb.062711CrossRefGoogle ScholarPubMed
Facci, A. L. & Porfiri, M. 2013 Analysis of three-dimensional effects in oscillating cantilevers immersed in viscous fluids. J. Fluids Struct. 38, 205–222.CrossRefGoogle Scholar
Fish, F. & Lauder, G. V. 2006 Passive and active flow control by swimming fishes and mammals. Annu. Rev. Fluid Mech. 38, 193–224.CrossRefGoogle Scholar
Flammang, B. E. & Lauder, G. V. 2009 Caudal fin shape modulation and control during acceleration, braking and backing maneuvers in bluegill sunfish, lepomis macrochirus. J. Expl Biol. 212 (2), 277–286.CrossRefGoogle ScholarPubMed
Ghatkesar, M. K., Braun, T., Barwich, V., Ramseyer, J.-P., Gerber, C., Hegner, M. & Lang, H. P. 2008 Resonating modes of vibrating microcantilevers in liquid. Appl. Phys. Lett. 92 (4), 043106.CrossRefGoogle Scholar
Hoover, A. P., Cortez, R., Tytell, E. D. & Fauci, L. J. 2018 Swimming performance, resonance and shape evolution in heaving flexible panels. J. Fluid Mech. 847, 386–416.CrossRefGoogle Scholar
Hou, G., Wang, J. & Layton, A. 2012 Numerical methods for fluid-structure interaction – a review. Commun. Comput. Phys. 12 (2), 337–377.CrossRefGoogle Scholar
Hu, H., Liu, J., Dukes, I. & Francis, G. 2006 Design of 3d swim patterns for autonomous robotic fish. In 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 2406–2411. IEEE.10.1109/IROS.2006.281680CrossRefGoogle Scholar
Jayne, B. C. & Lauder, G. V. 1995 Speed effects on midline kinematics during steady undulatory swimming of largemouth bass, micropterus salmoides. J. Expl Biol. 198 (2), 585–602.Google Scholar
Keulegan, G. H. 1958 Forces on cylinders and plates in an oscillating fluid. J. Res. Natl Bur. Stand. 2857, 423–440.10.6028/jres.060.043CrossRefGoogle Scholar
Kirchhoff, G. 1850 Über das Gleichgewicht und die Bewegung einer elastischen Scheibe. J. Reine Angew. Math. 1850 (40), 51–88.Google Scholar
Kolomenskiy, D., Moffatt, H. K., Farge, M. & Schneider, K. 2011 The Lighthill–Weis-Fogh clap–fling–sweep mechanism revisited. J. Fluid Mech. 676, 572–606.10.1017/jfm.2011.83CrossRefGoogle Scholar
Kopman, V., Laut, J., Acquaviva, F., Rizzo, A. & Porfiri, M. 2015 Dynamic modeling of a robotic fish propelled by a compliant tail. IEEE J. Ocean. Engng 40 (1), 209–221.10.1109/JOE.2013.2294891CrossRefGoogle Scholar
Ladd, A. J. C. & Verberg, R. 2001 Lattice-Boltzmann simulations of particle-fluid suspensions. J. Stat. Phys. 104 (5–6), 1191–1251.CrossRefGoogle Scholar
Lauder, G. V. & Tangorra, J. L. 2015 Fish Locomotion: Biology and Robotics of Body and Fin-Based Movements, pp. 25–49. Springer.Google Scholar
Lauder, G. V. & Tytell, E. D. 2005 Hydrodynamics of undulatory propulsion. Fish Physiol. 23, 425–468.CrossRefGoogle Scholar
Li, G., Müller, U. K., van Leeuwen, J. L. & Liu, H. 2014 Escape trajectories are deflected when fish larvae intercept their own C-start wake. J. R. Soc. Interface 11 (101), 20140848.CrossRefGoogle ScholarPubMed
Lighthill, M. J. 1960 Note on the swimming of slender fish. J. Fluid Mech. 9 (2), 305–317.10.1017/S0022112060001110CrossRefGoogle Scholar
Lighthill, M. J. 1970 Aquatic animal propulsion of high hydromechanical efficiency. J. Fluid Mech. 44 (2), 265–301.CrossRefGoogle Scholar
Lighthill, M. J. 1971 Large-amplitude elongated-body theory of fish locomotion. Proc. R. Soc. Lond. B 179 (1055), 125–138.Google 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, 65–88.10.1017/jfm.2017.533CrossRefGoogle Scholar
Liu, H. & Aono, H. 2009 Size effects on insect hovering aerodynamics: an integrated computational study. Bioinspir. Biomim. 4 (1), 015002.CrossRefGoogle Scholar
Mao, W. & Alexeev, A. 2014 Motion of spheroid particles in shear flow with inertia. J. Fluid Mech. 749, 145–166.CrossRefGoogle Scholar
Masoud, H. & Alexeev, A. 2010 Resonance of flexible flapping wings at low Reynolds number. Phys. Rev. E 81, 056304.CrossRefGoogle ScholarPubMed
Masoud, H. & Alexeev, A. 2011 Harnessing synthetic cilia to regulate motion of microparticles. Soft Matt. 7 (19), 8702–8708.CrossRefGoogle Scholar
Masoud, H., Bingham, B. I. & Alexeev, A. 2012 Designing maneuverable micro-swimmers actuated by responsive gel. Soft Matt. 8 (34), 8944–8951.CrossRefGoogle Scholar
McHenry, M. J., Pell, C. A. & Long, J. H. 1995 Mechanical control of swimming speed: stiffness and axial wave form in undulating fish models. J. Expl Biol. 198 (11), 2293–2305.Google ScholarPubMed
Michelin, S. & Llewellyn Smith, S. G. 2009 Resonance and propulsion performance of a heaving flexible wing. Phys. Fluids 21 (7), 071902.CrossRefGoogle Scholar
Mittal, R., Dong, H., Bozkurttas, M., Najjar, F. M., Vargas, A. & Von Loebbecke, A. 2008 A versatile sharp interface immersed boundary method for incompressible flows with complex boundaries. J. Comput. Phys. 227 (10), 4825–4852.CrossRefGoogle ScholarPubMed
Morison, J. R., Johnson, J. W. & Schaaf, S. A. 1950 The force exerted by surface waves on piles. J. Petrol. Technol. 2 (5), 149–154.10.2118/950149-GCrossRefGoogle Scholar
Nauen, J. C. & Lauder, G. V. 2002 Hydrodynamics of caudal fin locomotion by chub mackerel, Scomber japonicus (scombridae). J. Expl Biol. 205 (12), 1709–1724.Google Scholar
Paraz, F., Schouveiler, L. & Eloy, C. 2016 Thrust generation by a heaving flexible foil: resonance, nonlinearities, and optimality. Phys. Fluids 28 (1), 011903.CrossRefGoogle Scholar
Philen, M. & Neu, W. 2011 Hydrodynamic analysis, performance assessment, and actuator design of a flexible tail propulsor in an artificial alligator. Smart Mater. Struct. 20 (9), 094015.10.1088/0964-1726/20/9/094015CrossRefGoogle 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
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 (4), 041701.CrossRefGoogle Scholar
Sader, J. E. 1998 Frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope. J. Appl. Phys. 84 (1), 64–76.CrossRefGoogle Scholar
Sader, J. E., Cossé, J., Kim, D., Fan, B. & Gharib, M. 2016 Large-amplitude flapping of an inverted flag in a uniform steady flow–a vortex-induced vibration. J. Fluid Mech. 793, 524–555.CrossRefGoogle Scholar
Sarpkaya, T. 1976 Vortex shedding and resistance in harmonic flow about smooth and rough circular cylinders at high Reynolds numbers. Tech. Rep. NPS-59SL76021. Naval Postgraduate School, Monterey, CA.Google Scholar
Sarpkaya, T. 1986 Force on a circular cylinder in viscous oscillatory flow at low Keulegan–Carpenter numbers. J. Fluid Mech. 165, 61–71.CrossRefGoogle Scholar
Sarpkaya, T. & Isaacson, M. 1981 Mechanics of Waves Forces on Offshore Structures. Van Nostrand.Google Scholar
Scaradozzi, D., Palmieri, G., Costa, D. & Pinelli, A. 2017 BCF swimming locomotion for autonomous underwater robots: a review and a novel solution to improve control and efficiency. Ocean Engng 130, 437–453.10.1016/j.oceaneng.2016.11.055CrossRefGoogle Scholar
Sfakiotakis, M., Lane, D. M. & Davies, J. B. C. 1999 Review of fish swimming modes for aquatic locomotion. IEEE J. Ocean. Engng 24 (2), 237–252.CrossRefGoogle Scholar
Shahab, S., Tan, D. & Erturk, A. 2015 Hydrodynamic thrust generation and power consumption investigations for piezoelectric fins with different aspect ratios. Eur. Phys. J. Spec. Top. 224 (17–18), 3419–3434.CrossRefGoogle Scholar
Shelley, M. J. & Zhang, J. 2011 Flapping and bending bodies interacting with fluid flows. Annu. Rev. Fluid Mech. 43, 449–465.CrossRefGoogle Scholar
Su, Z., Yu, J., Tan, M. & Zhang, J. 2014 Implementing flexible and fast turning maneuvers of a multijoint robotic fish. IEEE ASME Trans. Mechatron. 19 (1), 329–338.10.1109/TMECH.2012.2235853CrossRefGoogle Scholar
Tan, D. & Erturk, A. 2018 On the coupling of nonlinear macro-fiber composite piezoelectric cantilever dynamics with hydrodynamic loads. In Active and Passive Smart Structures and Integrated Systems XII, vol. 10595, p. 105950R. International Society for Optics and Photonics.CrossRefGoogle Scholar
Timoshenko, S. & Woinowsky-Krieger, S. 1959 Theory of Plates and Shells. McGraw-Hill.Google Scholar
Triantafyllou, M. S. & Triantafyllou, G. S. 1995 An efficient swimming machine. Sci. Am. 272 (3), 64–70.10.1038/scientificamerican0395-64CrossRefGoogle Scholar
Tuck, E. O. 1969 Calculation of unsteady flows due to small motions of cylinders in a viscous fluid. J. Engng Maths 3 (1), 29–44.CrossRefGoogle Scholar
Van Eysden, C. A. & Sader, J. E. 2006 Resonant frequencies of a rectangular cantilever beam immersed in a fluid. J. Appl. Phys. 100 (11), 114916.CrossRefGoogle Scholar
Van Eysden, C. A. & Sader, J. E. 2007 Frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope: arbitrary mode order. J. Appl. Phys. 101 (4), 044908.CrossRefGoogle Scholar
Weaver, W. Jr., Timoshenko, S. P. & Young, D. H. 1990 Vibration Problems in Engineering. John Wiley & Sons.Google Scholar
Weiss, J. 1991 The dynamics of enstrophy transfer in two-dimensional hydrodynamics. Physica D 48 (2–3), 273–294.CrossRefGoogle Scholar
Wu, T. Y.-T. 1961 Swimming of a waving plate. J. Fluid Mech. 10 (3), 321–344.CrossRefGoogle Scholar
Yeh, P. D. & Alexeev, A. 2014 Free swimming of an elastic plate plunging at low Reynolds number. Phys. Fluids 26 (5), 053604.CrossRefGoogle Scholar
Yeh, P. D. & Alexeev, A. 2016 a Biomimetic flexible plate actuators are faster and more efficient with a passive attachment. Acta Mechanica Sin. 32 (6), 1001–1011.10.1007/s10409-016-0592-0CrossRefGoogle Scholar
Yeh, P. D. & Alexeev, A. 2016 b Effect of aspect ratio in free-swimming plunging flexible plates. Comput. Fluids 124, 220–225.CrossRefGoogle Scholar
Yeh, P. D., Li, Y. & Alexeev, A. 2017 Efficient swimming using flexible fins with tapered thickness. Phys. Rev. Fluids 2, 102101.CrossRefGoogle Scholar
Yu, C.-L., Ting, S.-C., Yeh, M.-K. & Yang, J.-T. 2011 Three-dimensional numerical simulation of hydrodynamic interactions between pectoral-fin vortices and body undulation in a swimming fish. Phys. Fluids 23 (9), 091901.CrossRefGoogle Scholar
Zhang, J., Liu, N.-S. & Lu, X.-Y. 2010 Locomotion of a passively flapping flat plate. J. Fluid Mech. 659, 43–68.CrossRefGoogle Scholar
Zhu, Q., Wolfgang, M. J., Yue, D. K. P. & Triantafyllou, M. S. 2002 Three-dimensional flow structures and vorticity control in fish-like swimming. J. Fluid Mech. 468, 1–28.CrossRefGoogle Scholar

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