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Self-propelled swimming of a flexible filament driven by coupled plunging and pitching motions

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Abstract

This paper numerically investigates the self-propelled swimming of a flexible filament driven by coupled pitching and plunging motions at the leading edge. The influences of bending rigidity and some actuation parameters (including the phase offset between pitching and plunging, and the amplitudes of pitching and plunging motions) on the swimming performance are explored. It is found that with increasing rigidity, the swimming style gradually transits from the undulatory mode to the oscillatory mode. The plunging-pitching actuation is found to be superior to the plunging-only actuation, in the sense that it prevents the decrease of speed at high rigidity and achieves a higher efficiency across a wide range of rigidity. The comparison of the body kinematics with those of animal swimmers, and the classification of the wake structures are discussed. The results of this study provide some novel insights for the bio-inspired design of autonomous underwater vehicles.

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References

  1. Lauder G. V., Anderson E. J., Tangorra J. et al. Fish biorobotics: Kinematics and hydrodynamics of self-propulsion [J]. Journal of Experimental Biology, 2007, 210(16): 2767–2780.

    Article  Google Scholar 

  2. Wang S. Z., He G. W., Zhang X. Self-propulsion of flapping bodies in viscous fluids: Recent advances and perspectives [J]. Acta Mechanica Sinica, 2016, 32(6): 980–990.

    Article  MathSciNet  MATH  Google Scholar 

  3. Liu C., Hu C. An efficient immersed boundary treatment for complex moving object [J]. Journal of Computational Physics, 2014, 274: 654–680.

    Article  MATH  Google Scholar 

  4. Gronskis A., Artana G. A simple and efficient direct forcing immersed boundary method combined with a high order compact scheme for simulating flows with moving rigid boundaries [J]. Computers and Fluids, 2016, 124: 86–104.

    Article  MathSciNet  MATH  Google Scholar 

  5. Hua R. N., Zhu L., Lu X. Y. Locomotion of a flapping flexible plate [J]. Physics of Fluids, 2013, 25(12): 121901.

    Article  Google Scholar 

  6. Zhu X., He G., Zhang X. Numerical study on hydrodynamic effect of flexibility in a self-propelled plunging foil [J]. Computers and Fluids, 2014, 97: 1–20.

    Article  MathSciNet  MATH  Google Scholar 

  7. Olivier M., Dumas G. Effects of mass and chordwise flexibility on 2D self-propelled flapping wings [J]. Journal of Fluids and Structures, 2016, 64: 46–66.

    Article  Google Scholar 

  8. Zhang D., Pan G., Chao L. et al. Effects of Reynolds number and thickness on an undulatory self-propelled foil [J]. Physics of Fluids, 2018, 30(7): 071902.

    Article  Google Scholar 

  9. Hoover A. P., Cortez R., Tytell E. D. et al. Swimming performance, resonance and shape evolution in heaving flexible panels [J]. Journal of Fluid Mechanics, 2018, 847: 386–416.

    Article  MathSciNet  MATH  Google Scholar 

  10. Ryu J., Park S. G., Huang W. X. et al. Hydrodynamics of a three-dimensional self-propelled flexible plate [J]. Physics of Fluids, 2019, 31(2): 021902.

    Article  Google Scholar 

  11. Zhu X., He G., Zhang X. How flexibility affects the wake symmetry properties of a self-propelled plunging foil [J]. Journal of Fluid Mechanics, 2014, 751: 164–183.

    Article  MathSciNet  Google Scholar 

  12. Lauder G. V., Madden P. G. A., Tangorra J. L. Bioinspiration from fish for smart material design and function [J]. Smart Materials and Structures, 2011, 20(9): 094014.

    Article  Google Scholar 

  13. Lauder G. V., Lim J., Shelton R. et al. Robotic models for studying undulatory locomotion in fishes [J]. Marine Technology Society Journal, 2011, 45(4): 41–55.

    Article  Google Scholar 

  14. Lauder G. V., Flammang B., Alben S. Passive robotic models of propulsion by the bodies and caudal fins of fish [J]. Integrative and Comparative Biology, 2012, 52(5): 576–587.

    Article  Google Scholar 

  15. Shelton R. M., Thornycroft P. J. M., Lauder G. V. Undulatory locomotion of flexible foils as biomimetic models for understanding fish propulsion [J]. Journal of Experimental Biology, 2014, 217(12): 2110–2120.

    Google Scholar 

  16. Feilich K. L., Lauder G. V. Passive mechanical models of fish caudal fins: Effects of shape and stiffness on self-propulsion [J]. Bioinspiration and Biomimetics, 2015, 10(3): 036002.

    Article  Google Scholar 

  17. Lucas K. N., Thornycroft P. J. M., Gemmell B. J. et al. Effects of non-uniform stiffness on the swimming performance of a passively-flexing, fish-like foil model [J]. Bioinspiration and Biomimetics, 2015, 10(5): 056019.

    Article  Google Scholar 

  18. Ramananarivo S., Godoy-Diana R., Thiria B. Passive elastic mechanism to mimic fish-muscle action in anguilliform swimming [J]. Journal of the Royal Society Interface, 2013, 10 (88): 20130667.

    Article  Google Scholar 

  19. Dai L., He G., Zhang X. et al. Stable formations of self-propelled fish-like swimmers induced by hydrodynamic interactions [J]. Journal of Royal Society Interface, 2018, 15(147): 20180490.

    Article  Google Scholar 

  20. Dai L., He G., Zhang X. et al. Intermittent loco-motion of a fish-like swimmer driven by passive elastic mechanism [J]. Bioinspiration and Biomimetics, 2018, 13(5): 056011.

    Article  Google Scholar 

  21. Kim B., Park S. G., Huang W. et al. Self-propelled heaving and pitching flexible fin in a quiescent flow [J]. International Journal of Heat and Fluid Flow, 2016, 62: 273–281.

    Article  Google Scholar 

  22. Piñeirua M., Thiria B., Godoy-Diana R. Modelling of an actuated elastic swimmer [J]. Journal of Fluid Mechanics, 2017, 829: 731–750.

    Article  MathSciNet  MATH  Google Scholar 

  23. Huang W. X., Shin S. J., Sung H. J. Simulation of flexible filaments in a uniform flow by the immersed boundary method [J]. Journal of Computational Physics, 2007, 226(2): 2206–2228.

    Article  MathSciNet  MATH  Google Scholar 

  24. Wang S. Z., Zhang X. An immersed boundary method based on discrete stream function formulation for two- and three-dimensional incompressible flows [J]. Journal of Computational Physics, 2011, 230(9): 3479–3499.

    Article  MathSciNet  MATH  Google Scholar 

  25. Wang S., He G., Zhang X. Parallel computing strategy for a flow solver based on immersed boundary method and discrete stream-function formulation [J]. Computers and Fluids, 2013, 88: 210–224.

    Article  MathSciNet  MATH  Google Scholar 

  26. Dai L., He G., Zhang X. Self-propelled swimming of a flexible plunging foil near a solid wall [J]. Bioinsipration and Biomimetics, 2016, 11(4): 046005.

    Article  Google Scholar 

  27. Yang X., Zhang X., Li Z. et al. A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations [J]. Journal of Computational Physics, 228(20): 7821–7836.

  28. Kern S., Koumoutsakos P. Simulations of optimized anguilliform swimming [J]. Journal of Experimental Biology, 2006, 209(24): 4841–4857.

    Article  Google Scholar 

  29. Videler J. J. Fish swimming [M]. Berlin, Germany: Springer, 1993.

    Book  Google Scholar 

  30. Piñeirua M., Thiria B., Godoy-Diana R. Resistive thrust production can be as crucial as added mass mechanisms for inertial undulatory swimmers [J]. Physical Review E, 2015, 92(2): 021001.

    Article  Google Scholar 

  31. Cui Z., Yang Z. X., Shen L. et al. Complex modal analysis of the movements of swimming fish propelled by body and/or caudal fin [J]. Wave Motion, 2018, 78: 83–97.

    Article  MathSciNet  MATH  Google Scholar 

  32. Taylor G. K., Nudds R. L., Thomas A. L. R. Flying and swimming animals cruise at a Strouhal number tuned for high power efficiency [J]. Nature, 2003, 425(6959): 707–711.

    Article  Google Scholar 

  33. Triantafyllou M., Triantafyllou G., Gopalkrishnan R. Wake mechanics for thrust generation in oscillating foils [J]. Physics of Fluids A: Fluid Dynamics, 1991, 3(12): 2835–2837.

    Article  Google Scholar 

  34. Borazjani I., Sotiropoulos F. Numerical investigation of the hydrodynamics of carangiform swimming in the transitional and inertial flow regimes [J]. Journal of Experimental Biology, 2008, 211(10): 1541–1558.

    Article  Google Scholar 

  35. Borazjani I., Sotiropoulos F. Numerical investigation of the hydrodynamics of anguilliform swimming in the transitional and inertial flow regimes [J]. Journal of Experimental Biology, 2009, 212(4): 576–592.

    Article  Google Scholar 

  36. Nangia N., Bale R., Chen N. et al. Optimal specific wavelength for maximum thrust production in undulatory propulsion [J]. PLoS One, 2017, 12(6): e0179727.

    Article  Google Scholar 

  37. Reid D. A. P., Hildenbrandt H., Padding J. T. et al. Fluid dynamics of moving fish in a two-dimensional multiparticle collision dynamics model [J]. Physical Review E, 2012, 85(2): 021901.

    Article  Google Scholar 

  38. Weerden J. F., Reid D. A. P., Hemelrijk C. K. A meta-analysis of steady undulatory swimming [J]. Fish and Fisheries, 2014, 15(3): 397–409.

    Article  Google Scholar 

  39. Lin X., Wu J., Zhang T. Performance investigation of a self-propelled foil with combined oscillating motion in stationary fluid [J]. Ocean Engineering, 2019, 175: 33–49.

    Article  Google Scholar 

  40. Quinn D. B., Lauder G. V., Smits A. J. Maximizing the efficiency of a flexible propulsor using experimental optimization [J]. Journal of Fluid Mechanics, 2015, 767: 430–448.

    Article  Google Scholar 

  41. Isogai K., Shinmoto Y., Watanabe Y. Effects of dynamic stall on propulsive efficiency and thrust of flapping airfoil [J]. AIAA Journal, 1993, 37(10): 1145–1151.

    Article  Google Scholar 

  42. Ramamurti R., Sandberg W. Simulation of flow about flapping airfoils using finite element incompressible flow solver [J]. AIAA Journal, 2001, 39(2): 253–260.

    Article  Google Scholar 

  43. Guglielmini L., Blondeaux P. Propulsive efficiency of oscillating foils [J]. European Journal of Mechanics, B/Fluids, 2004, 23(2): 255–278.

    Article  MATH  Google Scholar 

  44. Schnipper T., Andersen A., Bohr T. Vortex wakes of a flapping foil [J]. Journal of Fluid Mechanics, 2009, 633: 411–423.

    Article  MATH  Google Scholar 

  45. Marais C., Thiria B., Wesfreid J. E. et al. Stabilizing effect of flexibility in the wake of a flapping foil [J]. Journal of Fluid Mechanics, 2012, 710: 659–669.

    Article  MATH  Google Scholar 

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Acknowledgements

This work was supported by the Chinese Academy of Sciences (Grant Nos. XDB22040104, XDA22040203). We would like to thank Dr. Long-zhen Dai for the development of the FSI code, and the National Supercomputing Center in Tianjin (NSCC-TJ) for the allocation of computing time.

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Correspondence to Xing Zhang.

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Project supported by the National Natural Science Foundation of China (Grant Nos. 11772338, 11372331).

Biography

Bing-lin Li (1993-), Male, Master, E-mail: binglinli106@126.com

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Li, Bl., Wang, Yw., Yin, B. et al. Self-propelled swimming of a flexible filament driven by coupled plunging and pitching motions. J Hydrodyn 33, 157–169 (2021). https://doi.org/10.1007/s42241-021-0018-8

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  • DOI: https://doi.org/10.1007/s42241-021-0018-8

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