Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-27T06:06:46.300Z Has data issue: false hasContentIssue false
  • English
  • Français

Vortex dynamics and hydrodynamic performance enhancement mechanism in batoid fish oscillatory swimming

Published online by Cambridge University Press:  11 November 2021

Dong Zhang Open the ORCID record for Dong Zhang [Opens in a new window] ,
Qiao-Gao Huang ,
Guang Pan Open the ORCID record for Guang Pan [Opens in a new window] ,
Li-Ming Yang  and
Wei-Xi Huang Open the ORCID record for Wei-Xi Huang [Opens in a new window]
Dong Zhang
Affiliation:
School of Marine Science and Technology, Northwestern Polytechnical University, Xi'an 710072, PR China Key Laboratory for Unmanned Underwater Vehicle, Northwestern Polytechnical University, Xi'an 710072, PR China AML, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, PR China
Qiao-Gao Huang*
Affiliation:
School of Marine Science and Technology, Northwestern Polytechnical University, Xi'an 710072, PR China Key Laboratory for Unmanned Underwater Vehicle, Northwestern Polytechnical University, Xi'an 710072, PR China
Guang Pan
Affiliation:
School of Marine Science and Technology, Northwestern Polytechnical University, Xi'an 710072, PR China Key Laboratory for Unmanned Underwater Vehicle, Northwestern Polytechnical University, Xi'an 710072, PR China
Li-Ming Yang
Affiliation:
Department of Aerodynamics, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, PR China
Wei-Xi Huang*
Affiliation:
AML, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, PR China
*
†Email addresses for correspondence: [email protected]; [email protected]
†Email addresses for correspondence: [email protected]; [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The effects of chordwise deformation and the half-amplitude asymmetry on the hydrodynamic performance and vortex dynamics of batoid fish have been numerically investigated, in which the two parameters were represented by the wavenumber ($W$) and the ratio of the half-amplitude above the longitudinal axis to that below ($HAR$). Fin kinematics were prescribed based on biological data. Simulations were conducted using the immersed boundary method. It was found that moderate chordwise deformation enhances the thrust, saves the power and increases the efficiency. A large $HAR$ can also increase thrust performance. By using the derivative-moment transformation theory at several subdomains to capture the local vortical structures and a force decomposition, it was shown that, at high Strouhal numbers ($St$), the tip vortex is the main source of thrust, whereas the leading-edge vortex (LEV) and trailing-edge vortex weaken the thrust generation. However, at lower $St$, the LEV would enhance the thrust. The least deformation ($W=0$) leads to the largest effective angle of attack, and thus the strongest vortices. However, moderate deformation ($W=0.4$) has an optimal balance between the performance enhancement and the opposite effect of different local structures. The performance enhancement of $HAR$ was also due to the increase of the vortical contributions. This work provides a new insight into the role of vortices and the force enhancement mechanism in aquatic swimming.

JFM classification

Biological Fluid Dynamics: Propulsion Biological Fluid Dynamics: Swimming/flying Vortex Flows: Vortex dynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 930 , 10 January 2022 , A28
Check for updates
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

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
Birch, J.M. & Dickinson, M.H. 2001 Spanwise flow and the attachment of the leading-edge vortex on insect wings. Nature 412 (6848), 729–733.CrossRefGoogle Scholar
Birch, J.M., Dickson, W.B. & Dickinson, M.H. 2004 Force production and flow structure of the leading edge vortex on flapping wings at high and low Reynolds numbers. J. Expl Biol. 207 (7), 1063–1072.CrossRefGoogle Scholar
Bomphrey, R.J., Nakata, T., Phillips, N. & Walker, S.M. 2017 Smart wing rotation and trailing-edge vortices enable high frequency mosquito flight. Nature 544 (7648), 92–95.CrossRefGoogle ScholarPubMed
Borazjani, I. & Daghooghi, M. 2013 The fish tail motion forms an attached leading edge vortex. Proc. R. Soc. Lond. B 280 (1756), 20122071.Google ScholarPubMed
Borazjani, I., Sotiropoulos, F., Tytell, E.D. & Lauder, G.V. 2012 Hydrodynamics of the bluegill sunfish c-start escape response: three-dimensional simulations and comparison with experimental data. J. Expl Biol. 215 (4), 671–684.CrossRefGoogle ScholarPubMed
Bottom, 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
Breder, C.M. 1926 The locomotion of fishes. Zool. Sci. Contrib. N.Y. Zool. Soc. 4 (5), 159–297.Google 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
Dong, H., Mittal, R. & Najjar, F.M. 2006 Wake topology and hydrodynamic performance of low-aspect-ratio flapping foils. J. Fluid Mech. 566, 309–343.CrossRefGoogle Scholar
Ellington, C.P., Van Den Berg, C., Willmott, A.P. & Thomas, A.L.R. 1996 Leading-edge vortices in insect flight. Nature 384 (6610), 626–630.CrossRefGoogle Scholar
Eloy, C. 2012 Optimal Strouhal number for swimming animals. J. Fluids Struct. 30, 205–218.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), 1–24.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
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), 8116–8118.CrossRefGoogle ScholarPubMed
Garmann, D.J., Visbal, M.R. & Orkwis, P.D. 2013 Three-dimensional flow structure and aerodynamic loading on a revolving wing. Phys. Fluids 25, 034101.CrossRefGoogle Scholar
Gazzola, M., Argentina, M. & Mahadevan, L. 2014 Scaling macroscopic aquatic locomotion. Nat. Phys. 10 (10), 758–761.CrossRefGoogle Scholar
Gray, J. 1933 Studies in animal locomotion. J. Expl Biol. 10 (1), 88–104.CrossRefGoogle Scholar
Hamlett, W.C. 1999 Sharks, Skates, and Rays: The Biology of Elasmobranch Fishes, 398–443. JHU Press.Google Scholar
Han, J.S., Chang, J.W. & Cho, H.K. 2015 Vortices behavior depending on the aspect ratio of an insect-like flapping wing in hover. Exp. Fluids 56, 181.CrossRefGoogle Scholar
Han, P., Lauder, G.V. & Dong, H. 2020 Hydrodynamics of median-fin interactions in fish-like locomotion: effects of fin shape and movement. Phys. Fluids 32, 011902.Google Scholar
Heathcote, S., Wang, Z. & Gursul, I. 2008 Effect of spanwise flexibility on flapping wing propulsion. J. Fluids Struct. 24 (2), 183–199.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
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
Hunt, J.C.R., Wray, A.A. & Moin, P. 1988 Eddies, streams, and convergence zones in turbulent flows. Report No. CTR-S88. Center for Turbulence Research.Google Scholar
Kang, L.L., Liu, L.Q., Su, W.D. & Wu, J.Z. 2018 Minimum-domain impulse theory for unsteady aerodynamic force. Phys. Fluids 30 (1), 016107.CrossRefGoogle Scholar
Kim, M.J. & Lee, J.H. 2019 Wake transitions of flexible foils in a viscous uniform flow. Phys. Fluids 31, 111906.Google Scholar
Kriegseis, J. & Rival, D.E. 2014 Vortex force decomposition in the tip region of impulsively-started flat plates. J. Fluid Mech. 756, 758–770.CrossRefGoogle Scholar
Kruyt, J.W., van Heijst, G.J.F., Altshuler, D.L. & Lentink, D. 2015 Power reduction and the radial limit of stall delay in revolving wings of different aspect ratio. J. R. Soc. Interface 12 (105), 20150051.CrossRefGoogle ScholarPubMed
Lauder, G.V. 2015 Fish locomotion: recent advances and new directions. Ann. Rev. Mar. Sci. 7 (1), 521–545.CrossRefGoogle ScholarPubMed
Lauder, G.V. & Tytell, E.D. 2005 Hydrodynamics of undulatory propulsion. Fish Biol. 23, 425–468.Google Scholar
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
Li, G.J. & Lu, X.Y. 2012 Force and power of flapping plates in a fluid. J. Fluid Mech. 712, 598–613.CrossRefGoogle Scholar
Liao, J.C., Beal, D.N., Lauder, G.V. & Triantafyllou, M.S. 2003 Fish exploiting vortices decrease muscle activity. Science 302 (5650), 1566–1569.CrossRefGoogle ScholarPubMed
Lighthill, M.J. 1960 Note on the swimming of slender fish. J. Fluid Mech. 9 (2), 305–317.CrossRefGoogle Scholar
Lin, X., Wu, J. & Zhang, T. 2021 Self-directed propulsion of an unconstrained flapping swimmer at low Reynolds number: hydrodynamic behaviour and scaling laws. J. Fluid Mech. 907, R3.CrossRefGoogle Scholar
Lin, X., Wu, J., Zhang, T. & Yang, L. 2019 a Phase difference effect on collective locomotion of two tandem autopropelled flapping foils. Phys. Rev. Fluids 4, 054101.CrossRefGoogle Scholar
Lin, X., Wu, J., Zhang, T. & Yang, L. 2019 b Self-organization of multiple self-propelling flapping foils: energy saving and increased speed. J. Fluid Mech. 884, R1.CrossRefGoogle Scholar
Liu, G., Dong, H. & Li, C. 2016 Vortex dynamics and new lift enhancement mechanism of wing-body interaction in insect forward flight. J. Fluid Mech. 795, 634–651.CrossRefGoogle Scholar
Liu, L.-G., Du, G. & Sun, M. 2020 a Aerodynamic-force production mechanisms in hovering mosquitoes. J. Fluid Mech. 898, A19.CrossRefGoogle Scholar
Liu, Y., Pan, C. & Liu, Y. 2020 b Propulsive performance and flow-field characteristics of a jellyfish-like ornithopter with asymmetric pitching motion. Phys. Fluids 32, 071904.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
Lu, Y., Gong, X.S. & Guo, J.L. 2006 Dual leading-edge vortices on flapping wings. J. Expl Biol. 209 (24), 5005–5016.CrossRefGoogle ScholarPubMed
Maertens, A.P., Triantafyllou, M.S. & Yue, D.K.P. 2015 Efficiency of fish propulsion. Bioinspir. Biomim. 10, 046013.CrossRefGoogle ScholarPubMed
Marongiu, C. & Tognaccini, R. 2010 Far-field analysis of the aerodynamic force by Lamb vector integrals. AIAA J. 48 (11), 2543–2555.CrossRefGoogle Scholar
Muijres, F.T., Johansson, L.C., Barfield, R., Wolf, M., Spedding, G.R. & Hedenström, A. 2008 Leading-edge vortex improves lift in slow-flying bats. Science 319 (5867), 1250–1253.CrossRefGoogle ScholarPubMed
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
Ringuette, M.J., Milano, M. & Gharib, M. 2007 Role of the tip vortex in the force generation of low-aspect-ratio normal flat plates. J. Fluid Mech. 581, 453–468.CrossRefGoogle Scholar
Ristroph, L., Liao, J.C. & Zhang, J. 2015 Lateral line layout correlates with the differential hydrodynamic pressure on swimming fish. Phys. Rev. Lett. 114, 018102.CrossRefGoogle ScholarPubMed
Rosenberger, L.J. 2001 Pectoral fin locomotion in batoid fishes: undulation versus oscillation. J. Expl Biol. 204 (2), 379–394.CrossRefGoogle ScholarPubMed
Ryu, J., Byeon, H., Lee, S.J. & Sung, H.J. 2019 Flapping dynamics of a flexible plate with Navier slip. Phys. Fluids 31, 091901.Google Scholar
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, 083102.CrossRefGoogle Scholar
Sane, S.P. 2003 The aerodynamics of insect flight. J. Expl. Biol. 206 (23), 4191–4208.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
Schouveiler, L., Hover, F.S. & Triantafyllou, M.S. 2005 a Performance of flapping foil propulsion. J. Fluids Struct. 20 (7), 949–959.CrossRefGoogle Scholar
Schouveiler, L., Hover, F.S. & Triantafyllou, M.S. 2005 b Performance of flapping foil propulsion. J. Fluids Struct. 20 (7), 949–959.CrossRefGoogle Scholar
Schultz, W.W. & Webb, P.W. 2002 Power requirements of swimming: Do new methods resolve old questions? Integr. Compar. Biol. 42 (5), 1018–1025.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
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
Shoele, K. & Zhu, Q. 2013 Performance of a wing with nonuniform flexibility in hovering flight. Phys. Fluids 25, 041901.CrossRefGoogle Scholar
Shumway, N., Gabryszuk, M. & Laurence, S. 2020 The impact of dragonfly wing deformations on aerodynamic performance during forward flight. Bioinspir. Biomim. 15, 026005.CrossRefGoogle ScholarPubMed
Smits, A.J. 2019 Undulatory and oscillatory swimming. J. Fluid Mech. 874, P1.CrossRefGoogle Scholar
Suzuki, K. & Inamuro, T. 2011 Effect of internal mass in the simulation of a moving body by the immersed boundary method. Comput. Fluids 49 (1), 173–187.CrossRefGoogle Scholar
Ten Cate, A., Nieuwstad, C.H., Derksen, J.J. & Van den Akker, H.E.A. 2002 Particle imaging velocimetry experiments and lattice-Botlzmann simulations on a single sphere settling under gravity. Phys. Fluids 14 (11), 4012–4025.CrossRefGoogle Scholar
Thekkethil, N., Sharma, A. & Agrawal, A. 2020 a Self-propulsion of fishes-like undulating hydrofoil: a unified kinematics based unsteady hydrodynamics study. J. Fluids Struct. 93, 102875.CrossRefGoogle Scholar
Thekkethil, N., Sharma, A. & Agrawal, A. 2020 b Three-dimensional biological hydrodynamics study on various types of batoid fishlike locomotion. Phys. Rev. Fluids 5, 023101.CrossRefGoogle Scholar
Thielicke, W. & Stamhuis, E.J. 2018 The effects of wing twist in slow-speed flapping flight of birds: trading brute force against efficiency. Bioinspir. Biomim. 13, 056015.CrossRefGoogle ScholarPubMed
Tong, W., Yang, Y. & Wang, S. 2021 Estimating thrust from shedding vortex surfaces in the wake of a flapping plate. J. Fluid Mech. 920, A10.CrossRefGoogle Scholar
Triantafyllou, M.S., Triantafyllou, G.S. & Gopalkrishnan, R. 1991 Wake mechanics for thrust generation in oscillating foils. Phys. Fluids 3, 2835–2837.CrossRefGoogle Scholar
Uddin, E., Huang, W.-X. & Sung, H.J. 2015 Actively flapping tandem flexible flags in a viscous flow. J. Fluid Mech. 780, 120–142.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
Van Buren, T., Floryan, D. & Smits, A.J. 2019 Scaling and performance of simultaneously heaving and pitching foils. AIAA J. 57 (9), 3666–3677.CrossRefGoogle Scholar
Van Buren, T., Floryan, D., Wei, N. & Smits, A.J. 2018 Flow speed has little impact on propulsive characteristics of oscillating foils. Phys. Rev. Fluids 3, 013103.CrossRefGoogle Scholar
Videler, J.J., Stamhuis, E.J. & Povel, G.D.E. 2004 Leading-edge vortex lifts swifts. Science 306 (5703), 1960–1962.CrossRefGoogle ScholarPubMed
Wang, J., Ren, Y., Li, C. & Dong, H. 2019 Computational investigation of wing-body interaction and its lift enhancement effect in hummingbird forward flight. Bioinspir. Biomim. 14, 046010.CrossRefGoogle ScholarPubMed
Wang, S., Ryu, J., He, G.Q., Qin, F. & Sung, H.J. 2020 A self-propelled flexible plate with a Navier slip surface. Phys. Fluids 32, 021906.Google Scholar
Wen, L., Wang, T.M., Wu, G.H. & Liang, J.H. 2012 Hydrodynamic investigation of a self-propelled robotic fish based on a force-feedback control method. Bioinspir. Biomim. 7, 036012.CrossRefGoogle ScholarPubMed
Wu, J.-Z., Lu, X.-Y. & Zhuang, L.-X. 2007 Integral force acting on a body due to local flow structures. J. Fluid Mech. 576, 265–286.CrossRefGoogle Scholar
Yang, S.-B., Qiu, J. & Han, X.-Y. 2009 Kinematics modeling and experiments of pectoral oscillation propulsion robotic fish. J. Bionic. Engng 6 (2), 174–179.CrossRefGoogle Scholar
Yang, L.M., Shu, C., Wang, Y. & Sun, Y. 2016 Development of discrete gas kinetic scheme for simulation of 3D viscous incompressible and compressible flows. J. Comput. Phys. 319 (15), 129–144.CrossRefGoogle Scholar
Yang, L.M., Shu, C. & Wu, J. 2015 A three-dimensional explicit sphere function-based gas-kinetic flux solver for simulation of inviscid compressible flows. J. Comput. Phys. 295 (15), 322–339.CrossRefGoogle Scholar
Yang, L.M., Shu, C., Yang, W.M., Wang, Y. & Wu, J. 2017 An immersed boundary-simplified sphere function-based gas kinetic scheme for simulation of 3D incompressible flows. Phys. Fluids 29 (8), 083605.CrossRefGoogle Scholar
Yao, J. & Yeo, K.S. 2020 Forward flight and sideslip manoeuvre of a model hawkmoth. J. Fluid Mech. 896, A22.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, 051906.Google 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, 071902.CrossRefGoogle 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, 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