Skip to main content Accessibility help
×
Home
Hostname: page-component-768ffcd9cc-b9rrs Total loading time: 0.567 Render date: 2022-12-01T14:53:34.090Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "displayNetworkTab": true, "displayNetworkMapGraph": false, "useSa": true } hasContentIssue true

Effect of leading-edge curvature actuation on flapping fin performance

Published online by Cambridge University Press:  01 July 2021

David Fernández-Gutiérrez
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA02139, USA
Wim M. van Rees*
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA02139, USA
*
Email address for correspondence: wvanrees@mit.edu

Abstract

Ray-finned fish are able to adapt the curvature of their fins through musculature at the base of the fin. In this work we numerically investigate the effects of such leading-edge curvature actuation on the hydrodynamic performance of a heaving and pitching fin. We present a geometric and numerical framework for constructing the shape of ray-membrane-type fins with imposed leading-edge curvatures, under the constraint of membrane inextensibility. This algorithm is coupled with a three-dimensional Navier–Stokes solver, enabling us to assess the hydrodynamic performance of such fins. To determine the space of possible shapes, we present a simple model for leading-edge curvature actuation through two coefficients that determine chordwise and spanwise curvature, respectively. We systematically vary these two parameters through regimes that mimic both passive elastic deformations and active actuation against the hydrodynamic loading, and compute thrust and power coefficients, as well as hydrodynamic efficiency. Our results demonstrate that both thrust and efficiency are predominantly affected by chordwise curvature, with some small additional benefits of spanwise curvature on efficiency. The main improvements in performance are explained by the altered trailing-edge kinematics arising from leading-edge curvature actuation, which can largely be reproduced by a rigid fin whose trailing-edge kinematics follow that of the curving fin. Changes in fin camber, for fixed trailing-edge kinematics, mostly benefit efficiency. Based on our results, we discuss the use of leading-edge curvature actuation as a robust and versatile way to improve flapping fin performance.

Type
JFM Papers
Copyright
© The Author(s), 2021. Published by 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

REFERENCES

Alben, S., Madden, P.G. & Lauder, G.V. 2007 The mechanics of active fin-shape control in ray-finned fishes. J. R. Soc. Interface 4 (13), 243256.CrossRefGoogle ScholarPubMed
Bainbridge, R. 1963 Caudal fin and body movement in the propulsion of some fish. J. Expl Biol. 40 (1), 2356.CrossRefGoogle Scholar
Bernier, C., Gazzola, M., Ronsse, R. & Chatelain, P. 2019 Simulations of propelling and energy harvesting articulated bodies via vortex particle-mesh methods. J. Comput. Phys. 392, 3455.CrossRefGoogle Scholar
Boley, J.W., van Rees, W.M., Lissandrello, C., Horenstein, M.N., Truby, R.L., Kotikian, A., Lewis, J.A. & Mahadevan, L. 2019 Shape-shifting structured lattices via multimaterial 4D printing. Proc. Natl Acad. Sci. USA 116 (42), 2085620862.CrossRefGoogle ScholarPubMed
Bozkurttas, M., Tangorra, J., Lauder, G. & Mittal, R. 2009 Understanding the hydrodynamics of swimming: from fish fins to flexible propulsors for autonomous underwater vehicles. In Mining Smartness from Nature (CIMTEC 2008), Advances in Science and Technology (ed. P. Vincenzini & S. Graziani), vol. 58, pp. 193–202. Trans Tech Publications Ltd.CrossRefGoogle Scholar
Christianson, C., Goldberg, N.N., Deheyn, D.D., Cai, S. & Tolley, M.T. 2018 Translucent soft robots driven by frameless fluid electrode dielectric elastomer actuators. Sci. Robot. 3 (17), eaat1893.CrossRefGoogle ScholarPubMed
Chu, W.-S., Lee, K.-T., Song, S.-H., Han, M.-W., Lee, J.-Y., Kim, H.-S., Kim, M.-S., Park, Y.-J., Cho, K.-J. & Ahn, S.-H. 2012 Review of biomimetic underwater robots using smart actuators. Intl J. Precis. Engng Manuf. 13 (9), 17211721.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, 2946.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), 5667.CrossRefGoogle ScholarPubMed
Fernández-Gutiérrez, D. & van Rees, W.M. 2020 Effect of active and passive curvature on the hydrodynamic performance of flapping fins. In Proceedings of the ASME 2020 Fluids Engineering Division Summer Meeting (FEDSM), Fluid Mechanics; Multiphase Flows, vol. 2. ASME.CrossRefGoogle Scholar
Fish, F.E. & Lauder, G.V. 2006 Passive and active flow control by swimming fishes and mammals. Annu. Rev. Fluid Mech. 38 (1), 193224.CrossRefGoogle Scholar
Flammang, B.E. & Lauder, G.V. 2008 Speed-dependent intrinsic caudal fin muscle recruitment during steady swimming in bluegill sunfish, lepomis macrochirus. J. Expl Biol. 211 (4), 587598.CrossRefGoogle ScholarPubMed
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), 277286.CrossRefGoogle ScholarPubMed
Floryan, D., Van Buren, T. & Smits, A.J. 2018 Efficient cruising for swimming and flying animals is dictated by fluid drag. Proc. Natl Acad. Sci. USA 115 (32), 81168118.CrossRefGoogle ScholarPubMed
Garrick, I.E. 1936 Propulsion of a flapping and oscillating airfoil. NACA Tech. Rep. 567. National Advisory Committee for Aeronautics.Google Scholar
Gazzola, M., Argentina, M. & Mahadevan, L. 2014 a Scaling macroscopic aquatic locomotion. Nat. Phys. 10, 758761.CrossRefGoogle Scholar
Gazzola, M., Argentina, M. & Mahadevan, L. 2014 b Scaling macroscopic aquatic locomotion. Nat. Phys. 10 (10), 758761.CrossRefGoogle Scholar
Gazzola, M., Chatelain, P., van Rees, W.M. & Koumoutsakos, P. 2011 Simulations of single and multiple swimmers with non-divergence free deforming geometries. J. Comput. Phys. 230 (19), 70937114.CrossRefGoogle Scholar
Gazzola, M., Van Rees, W.M. & Koumoutsakos, P. 2012 C-start: optimal start of larval fish. J. Fluid Mech. 698, 518.CrossRefGoogle Scholar
Hu, K., Ren, Z., Wang, Y., Wang, T. & Wen, L. 2016 Quantitative hydrodynamic investigation of fish caudal fin cupping motion using a bio-robotic model. In 2016 IEEE International Conference on Robotics and Biomimetics (ROBIO), pp. 295–300. IEEE.CrossRefGoogle Scholar
Katz, J. & Weihs, D. 1978 Hydrodynamic propulsion by large amplitude oscillation of an airfoil with chordwise flexibility. J. Fluid Mech. 88 (3), 485497.CrossRefGoogle Scholar
Katzschmann, R.K., DelPreto, J., MacCurdy, R. & Rus, D. 2018 Exploration of underwater life with an acoustically controlled soft robotic fish. Sci. Robot. 3 (16), eaar3449.CrossRefGoogle ScholarPubMed
Lauder, G.V. 2015 Function of the caudal fin during locomotion in fishes: kinematics, flow visualization, and evolutionary patterns. Am. Zool. 40 (1), 101122.Google Scholar
Lauder, G.V., Anderson, E.J., Tangorra, J. & Madden, P.G.A. 2007 Fish biorobotics: kinematics and hydrodynamics of self-propulsion. J. Expl Biol. 210 (16), 27672780.CrossRefGoogle ScholarPubMed
Lauder, G.V. & Drucker, E.G. 2004 Morphology and experimental hydrodynamics of fish fin control surfaces. IEEE J. Ocean. Engng 29 (3), 556571.CrossRefGoogle Scholar
Lauder, G.V., Madden, P., Hunter, I., Tangorra, J., Davidson, N., Proctor, L., Mittal, R., Dong, H. & Bozkurttas, M. 2005 Design and performance of a fish fin-like propulsor for AUVs. In Proceedings of 14th International Symposium on Unmanned Untethered Submersible Technology, Durham, NH. AUSI.Google Scholar
Lauder, G.V. & Madden, P.G.A. 2007 Fish locomotion: kinematics and hydrodynamics of flexible foil-like fins. Exp. Fluids 43 (5), 641653.CrossRefGoogle Scholar
Liu, P. & Bose, N. 1997 Propulsive performance from oscillating propulsors with spanwise flexibility. Proc. R. Soc. Lond. A 453 (1963), 17631770.CrossRefGoogle Scholar
Nguyen, K., Yu, N., Bandi, M.M., Venkadesan, M. & Mandre, S. 2017 Curvature-induced stiffening of a fish fin. J. R. Soc. Interface 14 (130), 20170247.CrossRefGoogle ScholarPubMed
Prempraneerach, P., Hover, F.S. & Triantafyllou, M.S. 2003 The effect of chordwise flexibility on the thrust and efficiency of a flapping foil. In Proceedings of the 13th International Symposium on Unmanned Untethered Submersible Technology: Special Session on Bioengineering Research Related to Autonomous Underwater Vehicles, New Hampshire, vol. 152, pp. 152–170. AUSI.Google Scholar
Quinn, D.B., Lauder, G.V. & Smits, A.J. 2014 Scaling the propulsive performance of heaving flexible panels. J. Fluid Mech. 738, 250267.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, 430448.CrossRefGoogle Scholar
Read, D.A., Hover, F.S. & Triantafyllou, M.S. 2003 Forces on oscillating foils for propulsion and maneuvering. J. Fluids Struct. 17 (1), 163183.CrossRefGoogle Scholar
van Rees, W.M., Gazzola, M. & Koumoutsakos, P. 2013 Optimal shapes for anguilliform swimmers at intermediate Reynolds numbers. J. Fluid Mech. 722, R3.CrossRefGoogle Scholar
van Rees, W.M., Gazzola, M. & Koumoutsakos, P. 2015 Optimal morphokinematics for undulatory swimmers at intermediate Reynolds numbers. J. Fluid Mech. 775, 178188.CrossRefGoogle Scholar
van Rees, W.M., Leonard, A., Pullin, D.I. & Koumoutsakos, P. 2011 A comparison of vortex and pseudo-spectral methods for the simulation of periodic vortical flows at high Reynolds numbers. J. Comput. Phys. 230 (8), 27942805.CrossRefGoogle Scholar
Smits, A.J. 2019 Undulatory and oscillatory swimming. J. Fluid Mech. 874, P1.CrossRefGoogle Scholar
Tangorra, J.L., Esposito, C.J. & Lauder, G.V. 2009 Biorobotic fins for investigations of fish locomotion. In 2009 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 2120–2125. IEEE.CrossRefGoogle Scholar
Triantafyllou, M.S., Triantafyllou, G.S. & Yue, D.K.P. 2000 Hydrodynamics of fishlike swimming. Annu. Rev. Fluid Mech. 32 (1), 3353.CrossRefGoogle Scholar
Tytell, E.D., Leftwich, M.C., Hsu, C.-Y., Griffith, B.E., Cohen, A.H., Smits, A.J., Hamlet, C. & Fauci, L.J. 2016 Role of body stiffness in undulatory swimming: insights from robotic and computational models. Phys. Rev. Fluids 1, 073202.CrossRefGoogle Scholar
Winter, H.H. 1987 Viscous dissipation term in energy equations. In Modular Instruction Series C: Calculation and Measurement Techniques for Momentum, Energy and Mass Transfer, vol. 7, pp. 27–34. American Institute of Chemical Engineers.Google Scholar
Wu, X., Zhang, X., Tian, X., Li, X. & Lu, W. 2020 A review on fluid dynamics of flapping foils. Ocean Engng 195, 106712.CrossRefGoogle Scholar
Zhu, Q. 2007 Numerical simulation of a flapping foil with chordwise or spanwise flexibility. AIAA J. 45 (10), 24482457.CrossRefGoogle Scholar
Zhu, Q. & Shoele, K. 2008 Propulsion performance of a skeleton-strengthened fin. J. Expl Biol. 211 (13), 20872100.CrossRefGoogle ScholarPubMed

Fernández-Gutiérrez et al Supplementary Movie 1

Perspective views of the fin geometry during a flapping cycle for different combinations of chordwise and spanwise curvature parameters.

Download Fernández-Gutiérrez et al Supplementary Movie 1(Video)
Video 2 MB

Fernández-Gutiérrez et al Supplementary Movie 2

Vorticity field generated by the reference rigid fin during the first two cycles, viewed from different perspectives

Download Fernández-Gutiérrez et al Supplementary Movie 2(Video)
Video 2 MB

Fernández-Gutiérrez et al Supplementary Movie 3

Vorticity field generated by the curving fin in the maximum thrust configuration during the first two cycles, viewed from different perspectives.

Download Fernández-Gutiérrez et al Supplementary Movie 3(Video)
Video 2 MB

Fernández-Gutiérrez et al Supplementary Movie 4

Vorticity field generated by the curving fin in the maximum efficiency configuration during the first two cycles, viewed from different perspectives.

Download Fernández-Gutiérrez et al Supplementary Movie 4(Video)
Video 1 MB
Supplementary material: PDF

Fernández-Gutiérrez et al Supplementary Material

Fernández-Gutiérrez et al Supplementary Material

Download Fernández-Gutiérrez et al Supplementary Material(PDF)
PDF 4 MB
2
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Effect of leading-edge curvature actuation on flapping fin performance
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

Effect of leading-edge curvature actuation on flapping fin performance
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

Effect of leading-edge curvature actuation on flapping fin performance
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *