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Hydrodynamic performance of slender swimmer: effect of travelling wavelength

Published online by Cambridge University Press:  17 August 2022

Li-Ming Chao Open the ORCID record for Li-Ming Chao [Opens in a new window] ,
Md. Mahbub Alam Open the ORCID record for Md. Mahbub Alam [Opens in a new window]  and
Liang Cheng
Li-Ming Chao
Affiliation:
Center for Turbulence Control, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, PR China
Md. Mahbub Alam*
Affiliation:
Center for Turbulence Control, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, PR China
Liang Cheng
Affiliation:
Faculty of Infrastructure Engineering, Dalian University of Technology, Dalian, Liaoning, 116024,PR China School of Civil Engineering, University of Western Australia, Perth, WA 6009, Australia
*
†Email address for correspondence: alam@hit.edu.cn, alamm28@yahoo.com
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Abstract

The impact of Strouhal number St (= 0.1–1.0), Reynolds number Re (= 50–2000) and dimensionless wavelength λ (= 0.5–2.0) on the hydrodynamic performance of a travelling wavy foil of a constant length is extensively investigated. The relationship of time-mean thrust with St, Re and λ is presented, suggesting that the propulsive force increases with increasing St, Re and λ. As such, the drag–thrust boundary advances as these parameters increase. A shorter λ makes the thrust steadier while a longer λ enhances the maximum instantaneous thrust. The latter is beneficial for prey to escape from a predator. The fluid added mass caused by the foil oscillation increases with St and λ but declines with Re (<500). Seven types of wake structures produced by the foil are identified, discussed and connected to thrust generation, showing how St, Re and λ affect the fluid dynamics, wake transition, vortex strength, wake jet, velocity, added mass, added damping, power input, efficiency and pressure profiles. The outcome of this work renders a physical basis for understanding the swimming of aquatic animals.

JFM classification

Biological Fluid Dynamics: Swimming/flying Aerodynamics: Flow-structure interactions

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Type
JFM Papers
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Journal of Fluid Mechanics , Volume 947 , 25 September 2022 , A8
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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Footnotes

The online version of this article has been updated since original publication. A notice detailing the change has also been published.

References

Alam, M.M. 2022 A note on flow-induced force measurement of oscillating cylinder by loadcell. Ocean Engng 245, 110538.CrossRefGoogle Scholar
Alam, M.M. & Muhammad, Z. 2020 Dynamics of flow around a pitching hydrofoil. J. Fluids Struct. 99, 103151.CrossRefGoogle Scholar
Andersen, A., Bohr, T., Schnipper, T. & Walther, J.H. 2017 Wake structure and thrust generation of a flapping foil in two-dimensional flow. J. Fluid Mech. 812, R4.CrossRefGoogle Scholar
Anderson, E.J., Mcgillis, W.R. & Grosenbaugh, M.A. 2001 The boundary layer of swimming fish. J. Exp. Biol. 204, 81–102.CrossRefGoogle ScholarPubMed
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
Bhatt, R. & Alam, M.M. 2018 Vibration of a square cylinder submerged in a wake. J. Fluid Mech. 853, 301–332.CrossRefGoogle Scholar
Bos, F.M., Lentink, D., van Oudheusden, B. & Bijl, H. 2008 Influence of wing kinematics on aerodynamic performance in hovering insect flight. J. Fluid Mech. 594, 341–368.CrossRefGoogle Scholar
Breder, C.M. 1926 The locomotion of fish. Zoologica 4, 159–256.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.CrossRefGoogle Scholar
Carling, J., Williams, T.L. & Bowtell, G. 1998 Self-propelled anguilliform swimming: simultaneous solution of the two-dimensional Navier-Stokes equations and Newton's laws of motion. J. Expl Biol. 201, 3143–3166.CrossRefGoogle ScholarPubMed
Chao, L.-M., Alam, M.M. & Ji, C. 2021 a Drag-thrust transition and wake structures of a pitching foil undergoing asymmetric oscillation. J. Fluids Struct. 103, 103289.CrossRefGoogle Scholar
Chao, L.-M., Alam, M.M., Ji, C. & Wang, H. 2021 b Flow map of foil undergoing fast and slow pitching. Phy. Fluids 33, 101902.CrossRefGoogle Scholar
Chao, L.-M., Cao, Y.-H. & Pan, G. 2017 A review of underwater bio-mimetic propulsion: cruise and fast-start. Fluid Dyn. Res. 49, 044501.CrossRefGoogle Scholar
Chao, L.-M., Pan, G., Zhang, D. & Yan, G.-X. 2019 Numerical investigations on the force generation and wake structures of a nonsinusoidal pitching foil. J. Fluids Struct. 85, 27–39.CrossRefGoogle Scholar
Dabiri, J.O. 2009 Optimal vortex formation as a unifying principle in biological propulsion. Annu. Rev. Fluid Mech. 41, 17–33.CrossRefGoogle 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
Deng, J., Shao, X.M. & Ren, A.L. 2006 Numerical Study on propulsive performance of fish-like swimming foils. J. Hydrodyn. 18, 681–687.CrossRefGoogle Scholar
Deng, J., Sun, L.P. & Shao, X.M. 2015 Dynamical features of the wake behind a pitching foil. Phys. Rev E 92, 063013.CrossRefGoogle ScholarPubMed
Deng, J., Sun, L.P., Teng, L.B., Pan, D.Y. & Shao, X.M. 2016 The correction between wake transition and propulsive efficiency of a flapping foil: a numerical study. Phys. Fluids 28, 094101.CrossRefGoogle Scholar
Dong, G.J. & Lu, X.Y. 2005 Numerical analysis on the propulsive performance and vortex shedding of fish-like travelling wavy plate. Intl J. Numer. Methods Fluids 48, 1351–1373.CrossRefGoogle Scholar
Eloy, C. 2012 Optimal Strouhal number for swimming animals. J. Fluids Struct. 30, 191–202.CrossRefGoogle Scholar
Facchinetti, M.L., de Langre, E. & Biolley, F. 2004 Coupling of structure and wake oscillators in vortex-induced vibrations. J. Fluids Struct. 19, 123–140.CrossRefGoogle 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
Flanagan, P.J. 2004 Unsteady Navier–stokes simulation of rainbow trout swimming hydrodynamics. MSc thesis, Washington State University, Department of Civil and Environmental Engineering.Google Scholar
Floryan, D., van Buren, T., Rowley, C.W. & Smits, A.J. 2017 Scaling the propulsive performance of heaving and pitching foil. J. Fluid Mech. 822, 386–397.CrossRefGoogle Scholar
Floryan, D., van Buren, T. & Smits, A.J. 2019 Large-amplitude oscillations of foils for efficient propulsion. Phys. Rev. Fluids 4, 093102.CrossRefGoogle Scholar
Floryan, D., van Buren, T. & Smits, A.J. 2020 Swimmer's wake structures are not reliable indicators of swimming performance. Bioinspir. Biomim. 15, 024001.CrossRefGoogle Scholar
Gazzola, M., Argentina, M. & Mahadevan, L. 2014 Scaling macroscopic aquatic locomotion. Nat. Phys. 10, 758–761.CrossRefGoogle Scholar
Gazzola, M., van Rees, M. & Koumoutsakos, P. 2012 C-start: optimal start of larval fish. J. Fluid Mech. 698, 5–18.CrossRefGoogle Scholar
Godoy-Diana, R., Aider, J.-L. & Wesfreid, J.E. 2008 Transitions in the wake of a flapping foil. Phys. Rev. E 77, 016308.CrossRefGoogle ScholarPubMed
Godoy-Diana, R., Marais, C., Aider, J.-L. & Wesfreid, J.E. 2009 A model for the symmetry breaking of the reverse Bénard-Von Kármán vortex street produced by a flapping foil. J. Fluid Mech. 622, 23–32.CrossRefGoogle Scholar
Gray, J. 1933 Studies in animal locomotion: I, the movement of fish with special reference to the eel. J. Expl Biol. 10, 88–104.CrossRefGoogle Scholar
Gupta, S., Sharma, A., Agrawal, A., Thompson, M.C. & Hourigan, K. 2021 Hydrodynamics of a fish-like body undulation mechanism: scaling laws and regimes for vortex wake modes. Phys. Fluids 33, 101904.CrossRefGoogle Scholar
Han, P. & de Langre, E. 2022 There is no critical mass ratio for galloping of a square cylinder under flow. J. Fluid Mech. 931, A45.CrossRefGoogle Scholar
Kern, S. & Koumoutsakos, P. 2006 Simulations of optimized anguilliform swimming. J. Expl Biol. 209, 4841–4857.CrossRefGoogle ScholarPubMed
Kinsey, T. & Dumas, G. 2008 Parametric study of an oscillating airfoil in a power-extraction regime. AIAA J. 46, 1318–1330.CrossRefGoogle Scholar
Konstantinidis, E., Dorogi, D. & Baranyi, L. 2021 Resonance in flow-induced in-line vibrations at low Reynolds number. J. Fluid Mech. 907, A34.CrossRefGoogle Scholar
Koochesfahani, M.M. 1989 Vortical patterns in the wake of an oscillating airfoil. AIAA J. 27, 1200–1205.CrossRefGoogle Scholar
Lauder, G.V. 2009 Swimming hydrodynamics: ten questions and the technical approaches needed to resolve them. Exp Fluids 51, 23–35.CrossRefGoogle Scholar
Lauder, G.V. 2015 Fish locomotion: advances and new directions. Annu. Rev. Mar. Sci. 7, 521–545.CrossRefGoogle ScholarPubMed
Liao, J.C., Beal, D.N., Lauder, G.V. & Triantafyllou, M.S. 2003 Fish exploiting vortices decrease muscle activity. Science 302, 1566–1569.CrossRefGoogle ScholarPubMed
Lighthill, M.J. 1969 Hydromechanics of aquatic animal propulsion. Annu. Rev. Fluid Mech. 1, 413–446.CrossRefGoogle Scholar
Lighthill, M.J. 1970 Aquatic animal propulsion of high hydromechanical efficiency. J. Fluid Mech. 44, 265–301.CrossRefGoogle Scholar
Lindsey, C.C. 1978 Form, function and locomotory habits in fish. In Fish Physiology Locomotion, (ed. W. Hoar & D. Randall). Academic Press.CrossRefGoogle Scholar
Lu, X.Y. & Yin, X.Z. 2005 Propulsive performance of a fish-like travelling. Acta Mech. 175, 197–215.CrossRefGoogle 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. Commun. 5, 3293.CrossRefGoogle ScholarPubMed
Lucas, K.N., Lauder, G.V. & Tytell, E.D. 2020 Airfoil-like mechanics generate thrust on the anterior body of swimming fish. Proc. Natl Acad. Sci. USA 117 (19), 10585–10592.CrossRefGoogle Scholar
Marais, C., Thiria, J.E., Wesfreid, J.E. & Godoy-Diana, R. 2012 Stabilizing effect of flexibility in the wake of a flapping foil. J. Fluid Mech. 710, 659–669.CrossRefGoogle Scholar
Muhammad, Z., Alam, M.M. & Noack, B.R. 2022 Efficient thrust enhancement by modified pitching motion. J. Fluid Mech. 933, A13.CrossRefGoogle Scholar
Paniccia, D., Graziani, G., Lugni, C. & Piva, R. 2021 On the role of added mass and vorticity release for self-propelled aquatic locomotion. J. Fluid Mech. 918, A45.CrossRefGoogle 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).CrossRefGoogle ScholarPubMed
Qin, B., Alam, M.M. & Zhou, Y. 2017 Two tandem cylinders of different diameters in cross-flow: flow-induced vibration. J. Fluid Mech. 829, 621–658.CrossRefGoogle Scholar
Rohr, J.J. & Fish, F.E. 2004 Strouhal numbers and optimization of swimming by odontocete cetaceans. J. Expl Biol. 207, 1633–1642.CrossRefGoogle ScholarPubMed
Sapède, D., Gompel, N., Dambly-Chaudière, C. & Ghysen, A. 2002 Cell migration in the postembryonic development of the fish lateral line. Development 129 (3), 605–615.CrossRefGoogle ScholarPubMed
Shelley, M.J. & Zhang, J. 2011 Flapping and bending bodies interacting with fluid flows. Annu. Rev. Fluid Mech. 43, 449–465.CrossRefGoogle Scholar
Shen, L., Zhang, X., Yue, D.K.P. & Triantafyllou, M.S. 2003 Turbulent flow over a flexible wall undergoing a streamwise travelling wave motion. J. Fluid Mech. 484, 197–221.CrossRefGoogle Scholar
Shi, X.Y., Alam, M.M. & Bai, H.L. 2020 a Wakes of elliptical cylinders at low Reynolds number. Wind. Struct. 30, 525–532.Google Scholar
Shi, X.Y., Alam, M.M., Bai, H.L. & Wang, H.F. 2020 b The effect of Reynolds number on the elliptical cylinder wake. Intl J. Heat Fluid Flow 82, 108553.CrossRefGoogle Scholar
Shu, D.-G., Luo, H.-L., Morris, S.C., Zhang, X.L., Hu, S.-X., Chen, L., Han, J., Zhu, M., Li, Y. & Chen, L.Z. 1999 Lower Cambrian vertebrates from South China. Nature 402, 42–46.CrossRefGoogle Scholar
Smits, A.J. 2019 Undulatory and oscillating swimming. J. Fluid Mech. 874, P1.CrossRefGoogle Scholar
Spalart, P. & Allmaras, S. 1992 A one-equation turbulence model for aerodynamic flows. AIAA Paper 92-0439.CrossRefGoogle Scholar
Taylor, G.K., Nudds, R.L. & Thomas, A. 2003 Flying and swimming animals cruise at a Strouhal number tuned for high power efficiency. Nature 425, 707–711.CrossRefGoogle Scholar
Triantafyllou, M.S., Triantafyllou, G.S. & Yue, D.K.P. 2000 Hydrodynamic of fishlike swimming. Annu. Rev. Fluid Mech. 32, 33–53.CrossRefGoogle Scholar
Triantafyllou, M.S., Weymouth, G.D. & Miao, J.M. 2015 Biomimetic survival hydrodynamics and flow sensing. Annu. Rev. Fluid Mech. 48, 1–24.CrossRefGoogle Scholar
Van Buren, T., Floryan, D., Quinn, D. & Smits, A.J. 2017 Nonsinusoidal gaits for unsteady propulsion. Phys. Rev. Fluids 2, 053101.CrossRefGoogle Scholar
Verma, S., Papadimitriou, C., Lüthen, N., Arampatzis, G. & Koumoutsakos, P. 2020 Optimal sensor placement for artificial swimmers. J. Fluid Mech. 884, A24.CrossRefGoogle Scholar
Videler, J.J. 1993 Fish Swimming. Chapman & Hall.CrossRefGoogle Scholar
Von Kármán, T. & Burgers, J.M. 1934 General aerodynamic theory-perfect fluids. In Aerodynamic Theory (ed. Durand). Stanford University.Google Scholar
Webb, P.W. 1984 Forms and functions in fish swimming. Sci. Am. 251, 72–82.CrossRefGoogle Scholar
Wilcox, D.C. 1998 Turbulence Modeling for CFD. DCW Industries, Inc, LaCanada.Google Scholar
Williamson, C.H.K. & Govardhan, R. 2004 Vortex-induced vibrations. Annu. Rev. Fluid Mech. 36, 413–455.CrossRefGoogle Scholar
Wu, T.Y. 2011 Fish swimming and bird/insect flight. Annu. Rev. Fluid Mech. 43, 25–58.CrossRefGoogle Scholar
Xiao, Q., Sun, K., Liu, H. & Hu, J. 2011 Computational study on near wake interaction between undulation body and a D-section cylinder. Ocean Engng 38, 673–683.CrossRefGoogle Scholar
Zhang, J. 2017 Footprints of a flapping wing. J. Fluid Mech. 818, 1–4.CrossRefGoogle Scholar
Zhang, D., Pan, G., Chao, L.-M. & Zhang, Y. 2018 Effects of Reynolds number and thickness on an undulatory self-propelled foil. Phys. Fluids 30, 071902.CrossRefGoogle Scholar
Zheng, Z.C. & Wei, Z. 2012 Study of mechanisms and factors that influence the formation of vortical wake of a heaving airfoil. Phys. Fluids 24, 103601.CrossRefGoogle Scholar