Hostname: page-component-669899f699-vbsjw Total loading time: 0 Render date: 2025-04-27T20:34:11.126Z Has data issue: false hasContentIssue false
  • English
  • Français

Hydrodynamics of a swimming batoid fish at Reynolds numbers up to 148 000

Published online by Cambridge University Press:  16 May 2023

Dong Zhang Open the ORCID record for Dong Zhang [Opens in a new window]  and
Wei-Xi Huang Open the ORCID record for Wei-Xi Huang [Opens in a new window]
Dong Zhang
Affiliation:
AML, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, PR China Qingdao Innovation and Development Base, Harbin Engineering University, Qingdao 266000, PR China
Wei-Xi Huang*
Affiliation:
AML, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, PR China
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Flow around a tethered model of a swimming batoid fish is studied by using the wall-modelled large-eddy simulation in conjunction with the immersed boundary method. A Reynolds number ($Re$) up to 148 000 is chosen, and it is comparable to that of a medium-sized aquatic animal in cruising swimming state. At such a high $Re$, we provide, to the best of our knowledge, the first evidence of hairpin vortical (HV) structures near the body surface using three-dimensional high-fidelity flow field data. It is observed that such small-scale vortical structures are mainly formed through two mechanisms: the leading-edge vortex (LEV)–secondary filament–HV and LEV–HV transformations in different regions. The HVs create strong fluctuations in the pressure distribution and frequency spectrum. Simulations are also conducted at $Re=1480$ and 14 800 to reveal the effect of Reynolds number. Variations of the flow separation behaviour and local pressure with $Re$ are presented. Our results indicate that low-$Re$ simulations are meaningful when the focus is on the force variation tendency, whereas high-$Re$ simulations are needed when concerning flow fluctuations and turbulence mechanisms.

JFM classification

Biological Fluid Dynamics: Swimming/flying Biological Fluid Dynamics: Propulsion Vortex Flows: Vortex dynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 963 , 25 May 2023 , A16
Check for updates
Copyright
© The Author(s), 2023. 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.)

Article purchase

Temporarily unavailable

References

Acarlar, M.S. & Smith, C.R. 1987 A study of hairpin vortices in a laminar boundary layer. Part 1. Hairpin vortices generated by a hemisphere protuberance. J. Fluid Mech. 175, 1–41.CrossRefGoogle Scholar
Adrian, R.J. 2007 Hairpin vortex organization in wall turbulence. Phys. Fluids 19 (4), 041301.CrossRefGoogle Scholar
Adrian, R.J., Meinhart, C.D. & Tomkins, C.D. 2000 Vortex organization in the outer region of the turbulent boundary layer. J. Fluid Mech. 422, 1–54.CrossRefGoogle Scholar
Alam, M. & Sandham, N.D. 2000 Direct numerical simulation of ‘short’ laminar separation bubbles with turbulent reattachment. J. Fluid Mech. 410, 1–28.CrossRefGoogle Scholar
Borazjani, I. & Daghooghi, M. 2013 The fish tail motion forms an attached leading edge vortex. Proc. R. Soc. B 280 (1756), 20122071.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
Borazjani, I. & Sotiropoulos, F. 2009 Numerical investigation of the hydrodynamics of anguilliform swimming in the transitional and inertial flow regimes. J. Expl Biol. 212 (4), 576–592.CrossRefGoogle ScholarPubMed
Borazjani, I. & Sotiropoulos, F. 2010 On the role of form and kinematics on the hydrodynamics of self-propelled body/caudal fin swimming. J. Expl Biol. 213 (1), 89–107.CrossRefGoogle ScholarPubMed
Bottom II, R.G., Borazjani, I., Blevins, E.L. & Lauder, G.V. 2016 Hydrodynamics of swimming in stingrays: numerical simulations and the role of the leading-edge vortex. J. Fluid Mech. 788, 407–443.CrossRefGoogle Scholar
Bozkurttas, M., Mittal, R., Dong, H., Lauder, G.V. & Madden, P. 2009 Low-dimensional models and performance scaling of a highly deformable fish pectoral fin. J. Fluid Mech. 631, 311–342.CrossRefGoogle Scholar
Chen, D., Kolomenskiy, D., Nakata, T. & Liu, H. 2017 Forewings match the formation of leading-edge vortices and dominate aerodynamic force production in revolving insect wings. Bioinspir. Biomim. 13 (1), 016009.CrossRefGoogle ScholarPubMed
Combes, S.A. & Dudley, R. 2009 Turbulence-driven instabilities limit insect flight performance. Proc. Natl Acad. Sci. USA 106 (22), 9105–9108.CrossRefGoogle ScholarPubMed
Daghooghi, M. & Borazjani, I. 2015 The hydrodynamic advantages of synchronized swimming in a rectangular pattern. Bioinspir. Biomim. 10 (5), 056018.CrossRefGoogle Scholar
Délery, J.M. 2001 Robert Legendre and Henri Werlé: toward the elucidation of three-dimensional separation. Annu. Rev. Fluid Mech. 33 (1), 129–154.CrossRefGoogle Scholar
Dong, H., Bozkurttas, M., Mittal, R., Madden, P. & Lauder, G.V. 2010 Computational modelling and analysis of the hydrodynamics of a highly deformable fish pectoral fin. J. Fluid Mech. 645, 345–373.CrossRefGoogle Scholar
Drucker, E.G. & Lauder, G.V. 2000 A hydrodynamic analysis of fish swimming speed: wake structure and locomotor force in slow and fast labriform swimmers. J. Expl Biol. 203 (16), 2379–2393.CrossRefGoogle ScholarPubMed
Eldredge, J.D. & Jones, A.R. 2019 Leading-edge vortices: mechanics and modeling. Annu. Rev. Fluid Mech. 51, 75–104.CrossRefGoogle Scholar
Enders, E.C., Boisclair, D. & Roy, A.G. 2003 The effect of turbulence on the cost of swimming for Juvenile Atlantic Salmon (Salmo Salar). Can. J. Fish. Aquat. Sci. 60 (9), 1149–1160.CrossRefGoogle Scholar
Fish, F.E., Schreiber, C.M., Moored, K.W., Liu, G., Dong, H. & Bart-Smith, H. 2016 Hydrodynamic performance of aquatic flapping: efficiency of underwater flight in the manta. Aerospace 3 (3), 20.CrossRefGoogle Scholar
Gazzola, M., Argentina, M. & Mahadevan, L. 2014 Scaling macroscopic aquatic locomotion. Nat. Phys. 10 (10), 758–761.CrossRefGoogle Scholar
Guo, C.-Y., Kuai, Y.-F., Han, Y., Xu, P., Fan, Y.-W. & Yu, C.-D. 2022 Hydrodynamic analysis of propulsion process of zebrafish. Phys. Fluids 34 (2), 021910.CrossRefGoogle Scholar
Han, J.-S., Chang, J.-W. & Kim, S.-T. 2014 Reynolds number dependency of an insect-based flapping wing. Bioinspir. Biomim. 9 (4), 046012.CrossRefGoogle ScholarPubMed
Harbig, R.R., Sheridan, J. & Thompson, M.C. 2013 Reynolds number and aspect ratio effects on the leading-edge vortex for rotating insect wing planforms. J. Fluid Mech. 717, 166–192.CrossRefGoogle Scholar
Horton, H.P. 1968 Laminar separation bubbles in two and three dimensional incompressible flow. PhD thesis, Queen Mary University of London.Google Scholar
Huang, Q., Zhang, D. & Pan, G. 2020 Computational model construction and analysis of the hydrodynamics of a Rhinoptera Javanica. IEEE Access 8, 30410–30420.CrossRefGoogle Scholar
Huang, W.-X., Chang, C.B. & Sung, H.J. 2011 An improved penalty immersed boundary method for fluid–flexible body interaction. J. Comput. Phys. 230 (12), 5061–5079.CrossRefGoogle Scholar
Khosronejad, A., Mendelson, L., Techet, A.H., Kang, S., Angelidis, D. & Sotiropoulos, F. 2020 Water exit dynamics of jumping archer fish: integrating two-phase flow large-eddy simulation with experimental measurements. Phys. Fluids 32 (1), 011904.CrossRefGoogle Scholar
Kim, D. & Gharib, M. 2010 Experimental study of three-dimensional vortex structures in translating and rotating plates. Exp. Fluids 49 (1), 329–339.CrossRefGoogle Scholar
Laporte, F. & Corjon, A. 2000 Direct numerical simulations of the elliptic instability of a vortex pair. Phys. Fluids 12 (5), 1016–1031.CrossRefGoogle Scholar
Lauder, G.V. 2015 Fish locomotion: recent advances and new directions. Annu. Rev. Mar. Sci. 7 (1), 521–545.CrossRefGoogle ScholarPubMed
Lentink, D. & Dickinson, M.H. 2009 Rotational accelerations stabilize leading edge vortices on revolving fly wings. J. Expl Biol. 212 (16), 2705–2719.CrossRefGoogle ScholarPubMed
Leweke, T., Le Dizes, S. & Williamson, C.H.K. 2016 Dynamics and instabilities of vortex pairs. Annu. Rev. Fluid Mech. 48, 507–541.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
Liu, L.-G., Du, G. & Sun, M. 2020 Aerodynamic-force production mechanisms in hovering mosquitoes. J. Fluid Mech. 898, A19.CrossRefGoogle Scholar
Lu, Y., Shen, G.X. & Lai, G.J. 2006 Dual leading-edge vortices on flapping wings. J. Expl Biol. 209 (24), 5005–5016.CrossRefGoogle ScholarPubMed
Ma, M., Huang, W.-X. & Xu, C.-X. 2019 A dynamic wall model for large eddy simulation of turbulent flow over complex/moving boundaries based on the immersed boundary method. Phys. Fluids 31 (11), 115101.Google Scholar
Ma, M., Huang, W.-X., Xu, C.-X. & Cui, G.-X. 2021 A hybrid immersed boundary/wall-model approach for large-eddy simulation of high-Reynolds-number turbulent flows. Intl J. Heat Fluid Flow 88, 108769.CrossRefGoogle Scholar
Maertens, A.P., Triantafyllou, M.S. & Yue, D.K.P. 2015 Efficiency of fish propulsion. Bioinspir. Biomim. 10 (4), 046013.CrossRefGoogle ScholarPubMed
Marusic, I. & Adrian, R.J. 2012 The eddies and scales of wall turbulence. In Ten Chapters in Turbulence (ed. P. Davidson, Y. Kaneda, & K. Sreenivasan), chap. 5, pp. 176–220. Cambridge University Press.CrossRefGoogle Scholar
McKeown, R., Ostilla-Mónico, R., Pumir, A., Brenner, M.P. & Rubinstein, S.M. 2020 Turbulence generation through an iterative cascade of the elliptical instability. Sci. Adv. 6 (9), eaaz2717.CrossRefGoogle ScholarPubMed
Menzer, A., Gong, Y., Fish, F.E. & Dong, H. 2022 Bio-inspired propulsion: towards understanding the role of pectoral fin kinematics in manta-like swimming. Biomimetics 7 (2), 45.CrossRefGoogle ScholarPubMed
Motoori, Y. & Goto, S. 2019 Generation mechanism of a hierarchy of vortices in a turbulent boundary layer. J. Fluid Mech. 865, 1085–1109.CrossRefGoogle Scholar
Oh, S., Lee, B., Park, H., Choi, H. & Kim, S.-T. 2020 A numerical and theoretical study of the aerodynamic performance of a hovering rhinoceros beetle (trypoxylus dichotomus). J. Fluid Mech. 885, A18.CrossRefGoogle Scholar
Park, S.-J. et al. 2016 Phototactic guidance of a tissue-engineered soft-robotic ray. Science 353 (6295), 158–162.CrossRefGoogle ScholarPubMed
Peskin, C.S. 2002 The immersed boundary method. Acta Numerica 11, 479–517.CrossRefGoogle Scholar
Pournazeri, S., Segre, P.S., Princevac, M. & Altshuler, D.L. 2013 Hummingbirds generate bilateral vortex loops during hovering: evidence from flow visualization. Exp. Fluids 54 (1), 1–11.CrossRefGoogle Scholar
Rosenberger, L.J. 2001 Pectoral fin locomotion in batoid fishes: undulation versus oscillation. J. Expl Biol. 204 (2), 379–394.CrossRefGoogle ScholarPubMed
Saadat, M., Fish, F.E., Domel, A.G., Di Santo, V., Lauder, G.V. & Haj-Hariri, H. 2017 On the rules for aquatic locomotion. Phys. Rev. Fluids 2 (8), 083102.CrossRefGoogle Scholar
Salazar, R., Fuentes, V. & Abdelkefi, A. 2018 Classification of biological and bioinspired aquatic systems: a review. Ocean Engng 148, 75–114.CrossRefGoogle Scholar
Sato, M., Asada, K., Nonomura, T., Kawai, S. & Fujii, K. 2017 Large-eddy simulation of NACA 0015 airfoil flow at Reynolds number of $1.6\times 10^6$. AIAA J. 55 (2), 673–679.CrossRefGoogle Scholar
Sayadi, T., Hamman, C.W. & Moin, P. 2013 Direct numerical simulation of complete h-type and k-type transitions with implications for the dynamics of turbulent boundary layers. J. Fluid Mech. 724, 480–509.CrossRefGoogle Scholar
Schlatter, P., Brandt, L., De Lange, H.C. & Henningson, D.S. 2008 On streak breakdown in bypass transition. Phys. Fluids 20 (10), 101505.CrossRefGoogle Scholar
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
Shyy, W. & Liu, H. 2007 Flapping wings and aerodynamic lift: the role of leading-edge vortices. AIAA J. 45 (12), 2817–2819.CrossRefGoogle Scholar
Smith, C.R., Walker, J.D.A., Haidari, A.H. & Sobrun, U. 1991 On the dynamics of near-wall turbulence. Phil. Trans. R. Soc. Lond. A 336 (1641), 131–175.Google Scholar
Smits, A.J. 2019 Undulatory and oscillatory swimming. J. Fluid Mech. 874, P1.CrossRefGoogle Scholar
Sotiropoulos, F. & Yang, X. 2014 Immersed boundary methods for simulating fluid–structure interaction. Prog. Aerosp. Sci. 65, 1–21.CrossRefGoogle Scholar
Srygley, R.B. & Thomas, A.L.R. 2002 Unconventional lift-generating mechanisms in free-flying butterflies. Nature 420 (6916), 660–664.CrossRefGoogle ScholarPubMed
Tani, I. 1964 Low-speed flows involving bubble separations. Prog. Aeronaut. Sci. 5, 70–103.CrossRefGoogle Scholar
Taylor, G.K., Nudds, R.L. & Thomas, A.L.R. 2003 Flying and swimming animals cruise at a Strouhal number tuned for high power efficiency. Nature 425 (6959), 707–711.CrossRefGoogle Scholar
Thomas, A.L.R., Taylor, G.K., Srygley, R.B., Nudds, R.L. & Bomphrey, R.J. 2004 Dragonfly flight: free-flight and tethered flow visualizations reveal a diverse array of unsteady lift-generating mechanisms, controlled primarily via angle of attack. J. Expl Biol. 207 (24), 4299–4323.CrossRefGoogle ScholarPubMed
Toppings, C.E. & Yarusevych, S. 2021 Structure and dynamics of a laminar separation bubble near a wingtip. J. Fluid Mech. 929, A39.CrossRefGoogle Scholar
Triantafyllou, M.S., Triantafyllou, G.S. & Gopalkrishnan, R. 1991 Wake mechanics for thrust generation in oscillating foils. Phys. Fluids A 3 (12), 2835–2837.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
Tytell, E.D. 2004 The hydrodynamics of eel swimming. II. Effect of swimming speed. J. Expl Biol. 207 (19), 3265–3279.CrossRefGoogle ScholarPubMed
Tytell, E.D. & Lauder, G.V. 2004 The hydrodynamics of eel swimming. 1. Wake structure. J. Expl Biol. 207 (11), 1825–1841.CrossRefGoogle ScholarPubMed
Verma, S. & Hemmati, A. 2021 Evolution of wake structures behind oscillating hydrofoils with combined heaving and pitching motion. J. Fluid Mech. 927, A23.CrossRefGoogle Scholar
Wang, S., Zhang, X., He, G. & Liu, T. 2015 a Lift enhancement by bats’ dynamically changing wingspan. J. R. Soc. Interface 12 (113), 20150821.CrossRefGoogle ScholarPubMed
Wang, Y., Huang, W. & Xu, C. 2015 b On hairpin vortex generation from near-wall streamwise vortices. Acta Mechanica Sin. 31 (2), 139–152.CrossRefGoogle Scholar
Welch, P. 1967 The use of fast fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms. IEEE Trans. Audio Electroacoust. 15 (2), 70–73.CrossRefGoogle Scholar
Zhang, D., Huang, Q., Pan, G., Yang, L. & Huang, W.X. 2022 a Vortex dynamics and hydrodynamic performance enhancement mechanism in batoid fish oscillatory swimming. J. Fluid Mech. 930, A28.CrossRefGoogle Scholar
Zhang, D., Pan, G., Chao, L. & Zhang, Y. 2018 Effects of Reynolds number and thickness on an undulatory self-propelled foil. Phys. Fluids 30 (7), 071902.CrossRefGoogle Scholar
Zhang, D., Zhang, J.-D. & Huang, W.-X. 2022 b Physical models and vortex dynamics of swimming and flying: a review. Acta Mechanica 233 (4), 1249–1288.CrossRefGoogle Scholar
Zhang, J.-D. & Huang, W.-X. 2019 On the role of vortical structures in aerodynamic performance of a hovering mosquito. Phys. Fluids 31 (5), 051906.Google Scholar
Zhang, J.-D., Sung, H.J. & Huang, W.-X. 2020 Specialization of tuna: a numerical study on the function of caudal keels. Phys. Fluids 32 (11), 111902.CrossRefGoogle Scholar
Zhong, Q., Dong, H. & Quinn, D.B. 2019 How dorsal fin sharpness affects swimming speed and economy. J. Fluid Mech. 878, 370–385.CrossRefGoogle Scholar
Zhong, Q., Zhu, J., Fish, F.E., Kerr, S.J., Downs, A.M., Bart-Smith, H. & Quinn, D.B. 2021 Tunable stiffness enables fast and efficient swimming in fish-like robots. Sci. Robot. 6 (57), eabe4088.CrossRefGoogle ScholarPubMed
Zhu, L., He, G., Wang, S., Miller, L., Zhang, X., You, Q. & Fang, S. 2011 An immersed boundary method based on the Lattice Boltzmann approach in three dimensions, with application. Comput. Maths Applics. 61 (12), 3506–3518.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