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Wake of a bio-inspired flapping wing with morphing wingspan

变翼展的仿生扑翼尾迹特征

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Abstract

This work uses a bio-inspired flapping wing model to numerically investigate the effect of morphing wingspan on wake structures. The model consists of a rectangular flat-plate wing heaving harmonically in a uniform incoming flow at the Reynolds number of 300 and Strouhal number of 0.3. The wingspan changes during heaving, with a maximum wingspan at the middle of downstroke and minimum wingspan at the middle of upstroke. The wake is characterized by two oblique chains of interconnected vortex loops. Although the morphing wingspan has little effect on the wake topology, it significantly affects the magnitude and size of the vortices near the wing surface, which leads to an asymmetric distribution of vortex loop chains in the wake. The shrinking of leading-edge vortex under the lower surface of the wing in downstroke and the destructive interaction of tip vortices in upstroke are identified as the two vortex dynamics corresponding to the asymmetric wake structures. The analysis on the lift coefficients shows that the above vortex interactions are mainly caused by the change of span length instead of spanwise velocity.

摘要

本文基于仿生扑翼流动的数值模拟研究变形翼展对尾迹结构的影响. 所采用的扑翼模型为一个在均匀来流中上下扑动的平 板. 翼展随着扑动而变化, 最大翼展在下扑行程的中间, 最小翼展在上挥行程的中间. 其尾迹的特征表现为两条相互连接的倾斜涡链. 虽然变形翼展对尾流拓扑结构的影响不大, 但它显著影响了扑翼附近涡结构, 导致尾流中涡环链的分布不对称. 下扑过程中, 位于扑翼 下表面的前缘涡收缩, 与上挥中翼尖涡相互作用, 通过分析升力系数, 发现上述涡的相互作用是由翼展长度的变化引起的.

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References

  1. G. R. Spedding, and A. Hedenström, PIV-based investigations of animal flight, Exp. Fluids 46, 749 (2009).

    Article  Google Scholar 

  2. J. O. Dabiri, Optimal vortex formation as a unifying principle in biological propulsion, Annu. Rev. Fluid Mech. 41, 17 (2009).

    Article  MathSciNet  MATH  Google Scholar 

  3. J. D. Zhang, Q. H. Zuo, M. D. Lin, W. X. Huang, W. J. Pan, and G. X. Cui, Evolution of vortices in the wake of an ARJ21 airplane: Application of the lift-drag model, Theor. Appl. Mech. Lett. 10, 419 (2020).

    Article  Google Scholar 

  4. X. Meng, and M. Sun, Wing kinematics, aerodynamic forces and vortex-wake structures in fruit-flies in forward flight, J. Bionic Eng. 13, 478 (2016).

    Article  Google Scholar 

  5. Y. Wang, X. He, G. He, Q. Wang, L. Chen, and X. Liu, Aerodynamic performance of the flexibility of corrugated dragonfly wings in flapping flight, Acta Mech. Sin. 38, 322038 (2022).

    Article  Google Scholar 

  6. D. Zhang, J. D. Zhang, and W. X. Huang, Physical models and vortex dynamics of swimming and flying: A review, Acta Mech. 233, 1249 (2022).

    Article  MathSciNet  MATH  Google Scholar 

  7. X. T. Huang, P. N. Sun, H. G. Lyu, and S. Y. Zhong, Study of 3D self-propulsive fish swimming using the δ+-SPH model, Acta Mech. Sin. 39, 722053 (2023).

    Article  Google Scholar 

  8. G. He, G. Jin, and Y. Yang, Space-time correlations and dynamic coupling in turbulent flows, Annu. Rev. Fluid Mech. 49, 51 (2017).

    Article  MATH  Google Scholar 

  9. Z. Jane Wang, Two dimensional mechanism for insect hovering, Phys. Rev. Lett. 85, 2216 (2000).

    Article  Google Scholar 

  10. M. A. Ashraf, J. Young, and J. C. S. Lai, Reynolds number, thickness and camber effects on flapping airfoil propulsion, J. Fluids Struct. 27, 145 (2011).

    Article  Google Scholar 

  11. D. Majumdar, S. Ravi, and S. Sarkar, Passive dynamics regulates aperiodic transitions in flapping wing systems, PNAS Nexus, 2023, doi: https://doi.org/10.1093/pnasnexus/pgad086.

  12. Y. Xiang, H. Hang, S. Qin, and H. Liu, Scaling analysis of the circulation growth of leading-edge vortex in flapping flight, Acta Mech. Sin. 37, 1530 (2021).

    Article  MathSciNet  Google Scholar 

  13. M. Zhang, Q. Wu, B. Huang, and G. Wang, Lagrangian-based numerical investigation of aerodynamic performance of an oscillating foil, Acta Mech. Sin. 34, 839 (2018).

    Article  Google Scholar 

  14. J. M. Anderson, K. Streitlien, D. S. Barrett, and M. S. Triantafyllou, Oscillating foils of high propulsive efficiency, J. Fluid Mech. 360, 41 (1998).

    Article  MathSciNet  MATH  Google Scholar 

  15. X. Lin, J. Wu, and T. Zhang, Performance investigation of a self-propelled foil with combined oscillating motion in stationary fluid, Ocean Eng. 175, 33 (2019).

    Article  Google Scholar 

  16. G. Y. Dynnikova, Y. A. Dynnikov, S. V. Guvernyuk, and T. V. Malakhova, Stability of a reverse Karman vortex street, Phys. Fluids 33, 024102 (2021).

    Article  Google Scholar 

  17. B. Turhan, Z. Wang, and I. Gursul, Interaction of vortex streets with a downstream wing, Phys. Rev. Fluids 7, 094701 (2022).

    Article  Google Scholar 

  18. L. Schouveiler, F. S. Hover, and M. S. Triantafyllou, Performance of flapping foil propulsion, J. Fluids Struct. 20, 949 (2005).

    Article  Google Scholar 

  19. L. Tian, Z. Zhao, W. Wang, and N. Liu, Length and stiffness effects of the attached flexible plate on the flow over a traveling wavy foil, Acta Mech. Sin. 37, 1404 (2021).

    Article  MathSciNet  Google Scholar 

  20. Y. W. Jung, and S. O. Park, Vortex-shedding characteristics in the wake of an oscillating airfoil at low Reynolds number, J. Fluids Struct. 20, 451 (2005).

    Article  Google Scholar 

  21. X. Lin, J. Wu, T. Zhang, and L. Yang, Phase difference effect on collective locomotion of two tandem autopropelled flapping foils, Phys. Rev. Fluids 4, 054101 (2019).

    Article  Google Scholar 

  22. X. Lin, G. He, X. He, and Q. Wang, Dynamic response of a semi-free flexible filament in the wake of a flapping foil, J. Fluids Struct. 83, 40 (2018).

    Article  Google Scholar 

  23. Z. C. Zheng, and Z. Wei, Study of mechanisms and factors that influence the formation of vortical wake of a heaving airfoil, Phys. Fluids 24, 103601 (2012).

    Article  Google Scholar 

  24. Z. Wei, and Z. C. Zheng, Mechanisms of wake deflection angle change behind a heaving airfoil, J. Fluids Struct. 48, 1 (2014).

    Article  Google Scholar 

  25. B. Li, X. Zhang, and X. Zhang, Classifying wakes produced by self-propelled fish-like swimmers using neural networks, Theor. Appl. Mech. Lett. 10, 149 (2020).

    Article  Google Scholar 

  26. I. Fenercioglu, and O. Cetiner, Categorization of flow structures around a pitching and plunging airfoil, J. Fluids Struct. 31, 92 (2012).

    Article  Google Scholar 

  27. G. R. Abdizadeh, M. Farokhinejad, and S. Ghasemloo, Numerical investigation on the aerodynamic efficiency of bio-inspired corrugated and cambered airfoils in ground effect, Sci. Rep. 12, 19117 (2022).

    Article  Google Scholar 

  28. L. Liu, G. He, X. He, Q. Wang, and L. Chen, Numerical study on the effects of a semi-free and non-uniform flexible filament in different vortex streets, Acta Mech. Sin. 37, 929 (2021).

    Article  MathSciNet  Google Scholar 

  29. X. Zhu, G. He, and X. Zhang, How flexibility affects the wake symmetry properties of a self-propelled plunging foil, J. Fluid Mech. 751, 164 (2014).

    Article  MathSciNet  Google Scholar 

  30. C. Koehler, P. Beran, M. Vanella, and E. Balaras, Flows produced by the combined oscillatory rotation and translation of a circular cylinder in a quiescent fluid, J. Fluid Mech. 764, 148 (2015).

    Article  Google Scholar 

  31. K. D. von Ellenrieder, K. Parker, and J. Soria, Flow structures behind a heaving and pitching finite-span wing, J. Fluid Mech. 490, 129 (2003).

    Article  MATH  Google Scholar 

  32. P. Blondeaux, F. Fornarelli, L. Guglielmini, M. S. Triantafyllou, and R. Verzicco, Numerical experiments on flapping foils mimicking fish-like locomotion, Phys. Fluids 17, 113601 (2005).

    Article  MATH  Google Scholar 

  33. H. Dong, R. Mittal, and F. M. Najjar, Wake topology and hydrodynamic performance of low-aspect-ratio flapping foils, J. Fluid Mech. 566, 309 (2006).

    Article  MathSciNet  MATH  Google Scholar 

  34. J. H. J. Buchholz, and A. J. Smits, On the evolution of the wake structure produced by a low-aspect-ratio pitching panel, J. Fluid Mech. 546, 433 (2006).

    Article  MATH  Google Scholar 

  35. J. H. J. Buchholz, and A. J. Smits, The wake structure and thrust performance of a rigid low-aspect-ratio pitching panel, J. Fluid Mech. 603, 331 (2008).

    Article  MATH  Google Scholar 

  36. T. O. Yilmaz, and D. Rockwell, Three-dimensional flow structure on a maneuvering wing, Exp. Fluids 48, 539 (2010).

    Article  Google Scholar 

  37. M. A. Green, C. W. Rowley, and A. J. Smits, The unsteady three-dimensional wake produced by a trapezoidal pitching panel, J. Fluid Mech. 685, 117 (2011).

    Article  MATH  Google Scholar 

  38. O. Barannyk, B. J. Buckham, and P. Oshkai, On performance of an oscillating plate underwater propulsion system with variable chordwise flexibility at different depths of submergence, J. Fluids Struct. 28, 152 (2012).

    Article  Google Scholar 

  39. H. Dai, H. Luo, P. J. S. A. F. de Sousa, and J. F. Doyle, Thrust performance of a flexible low-aspect-ratio pitching plate, Phys. Fluids 24, 101903 (2012).

    Article  Google Scholar 

  40. L. Yan, J. Pan, and C. Shao, Modes of vortex shedding from a rotary oscillating plate, Acta Mech. Sin. 38, 321481 (2022).

    Article  Google Scholar 

  41. T. Liu, S. Jones, K. Kuykendoll, and R. Rhew, Avian wing geometry and kinematics, AIAA J. 44, 954 (2006).

    Article  Google Scholar 

  42. J. A. Cheney, J. P. J. Stevenson, N. E. Durston, M. Maeda, J. Song, D. A. Megson-Smith, S. P. Windsor, J. R. Usherwood, and R. J. Bomphrey, Raptor wing morphing with flight speed, J. R. Soc. Interface. 18, 20210349 (2021).

    Article  Google Scholar 

  43. C. Harvey, V. B. Baliga, J. C. M. Wong, D. L. Altshuler, and D. J. Inman, Birds can transition between stable and unstable states via wing morphing, Nature 603, 648 (2022).

    Article  Google Scholar 

  44. C. Harvey, L. L. Gamble, C. R. Bolander, D. F. Hunsaker, J. J. Joo, and D. J. Inman, A review of avian-inspired morphing for UAV flight control, Prog. Aerosp. Sci. 132, 100825 (2022).

    Article  Google Scholar 

  45. M. Wolf, L. C. Johansson, R. von Busse, Y. Winter, and A. Hedenström, Kinematics of flight and the relationship to the vortex wake of a Pallas’ long tongued bat (Glossophaga soricina), J. Exp. Biol. 213, 2142 (2010).

    Article  Google Scholar 

  46. A. Hedenström, L. C. Johansson, M. Wolf, R. von Busse, Y. Winter, and G. R. Spedding, Bat flight generates complex aerodynamic tracks, Science 316, 894 (2007).

    Article  Google Scholar 

  47. S. Wang, X. Zhang, G. He, and T. Liu, Lift enhancement by dynamically changing wingspan in forward flapping flight, Phys. Fluids 26, 061903 (2014), arXiv: 1309.2726.

    Article  Google Scholar 

  48. S. Wang, and X. Zhang, An immersed boundary method based on discrete stream function formulation for two- and three-dimensional incompressible flows, J. Comput. Phys. 230, 3479 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  49. X. Yang, X. Zhang, Z. Li, and G. W. He, A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations, J. Comput. Phys. 228, 7821 (2009).

    Article  MathSciNet  MATH  Google Scholar 

  50. S. Wang, G. He, and X. Zhang, Parallel computing strategy for a flow solver based on immersed boundary method and discrete stream-function formulation, Comput. Fluids 88, 210 (2013).

    Article  MathSciNet  MATH  Google Scholar 

  51. S. Wang, X. Zhang, G. He, and T. Liu, A lift formula applied to low-Reynolds-number unsteady flows, Phys. Fluids 25, 093605 (2013).

    Article  Google Scholar 

  52. J. Jeong, and F. Hussain, On the identification of a vortex, J. Fluid. Mech. 285, 69 (1995).

    Article  MathSciNet  MATH  Google Scholar 

  53. A. K. De, and S. Sarkar, Spatial wake transition past a thin pitching plate, Phys. Rev. E 104, 025106 (2021).

    Article  Google Scholar 

  54. A. K. De, and S. Sarkar, Dependence of wake structure on pitching frequency behind a thin panel at Re = 1000, J. Fluid Mech. 924, A33 (2021).

    Article  MathSciNet  MATH  Google Scholar 

  55. M. Visbal, T. O. Yilmaz, and D. Rockwell, Three-dimensional vortex formation on a heaving low-aspect-ratio wing: Computations and experiments, J. Fluids Struct. 38, 58 (2013).

    Article  Google Scholar 

  56. Z. C. Zheng, Betz invariants and generalization of vorticity moment invariants, AIAA J. 39, 431 (2001).

    Article  Google Scholar 

  57. K. Taira, and T. Colonius, Three-dimensional flows around low-aspect-ratio flat-plate wings at low Reynolds numbers, J. Fluid Mech. 623, 187 (2009).

    Article  MATH  Google Scholar 

  58. J. Anderson, and J. D. Anderson, Fundamentals of Aerodynamics, 5 ed. (McGraw-Hill, Columbus, 2010).

    Google Scholar 

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Acknowledgements

This work was supported by Basic Science Center Program of the National Natural Science Foundation of China for “Multiscale Problems in Nonlinear Mechanics” (Grant No. 11988102), the National Natural Science Foundation of China (Grant Nos. 12102439, 92252203, and 91952301), and the China Postdoctoral Science Foundation (Grant No. 2021M703290). The computations were conducted on Tianhe-3F at the National Supercomputer Center in Tianjin.

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Contributions

Xinyi He: Writing–original draft, Investigation, Validation. Yi Liu: Formal analysis, Software. Yixin Chen: Visualization, Data curation. Shizhao Wang: Conceptualization, Writing–review & editing, Supervision, Funding acquisition.

Corresponding author

Correspondence to Shizhao Wang  (王士召).

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He, X., Liu, Y., Chen, Y. et al. Wake of a bio-inspired flapping wing with morphing wingspan. Acta Mech. Sin. 39, 323061 (2023). https://doi.org/10.1007/s10409-023-23061-x

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