Applied Mathematics and Mechanics

, Volume 40, Issue 11, pp 1625–1646 | Cite as

Numerical investigation on aerodynamic performance of a bionic flapping wing

  • Xinghua Chang
  • Laiping ZhangEmail author
  • Rong Ma
  • Nianhua Wang


This paper numerically studies the aerodynamic performance of a bird-like bionic flapping wing. The geometry and kinematics are designed based on a seagull wing, in which flapping, folding, swaying, and twisting are considered. An in-house unsteady flow solver based on hybrid moving grids is adopted for unsteady flow simulations. We focus on two main issues in this study, i.e., the influence of the proportion of down-stroke and the effect of span-wise twisting. Numerical results show that the proportion of down-stroke is closely related to the efficiency of the flapping process. The preferable proportion is about 0.7 by using the present geometry and kinematic model, which is very close to the observed data. Another finding is that the drag and the power consumption can be greatly reduced by the proper span-wise twisting. Two cases with different reduced frequencies are simulated and compared with each other. The numerical results show that the power consumption reduces by more than 20%, and the drag coefficient reduces by more than 60% through a proper twisting motion for both cases. The flow mechanism is mainly due to controlling of unsteady flow separation by adjusting the local effective angle of attack. These conclusions will be helpful for the high-performance micro air vehicle (MAV) design.

Key words

flapping wing bird-like flapping unsteady flow radial basis function (RBF) hybrid dynamic mesh span-wise twisting mechanism 

Chinese Library Classification

O355 O357.1 

2010 Mathematics Subject Classification

76Dxx 76Gxx 76M12 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    GREENEWALT, C. H. Dimensional relationships for flying animals. Smithsonian Miscellaneous Collections Needs Pagination, 144, 1–46 (1962)Google Scholar
  2. [2]
    PENNYCUICK, C. J. Power requirements for horizontal flight in the pigeon columba livia. Journal of Experimental Biology, 49, 527–555 (1968)Google Scholar
  3. [3]
    PENNYCUICK, C. J. Speeds and wing-beat frequencies of migration birds compared with calculated benchmarks. Journal of Experimental Biology, 204, 3283–3294 (2001)Google Scholar
  4. [4]
    SHYY, W., BERG, M., and LJUNGQVIST, D. Flapping and flexible wings for biological and micro air vehicles. Progress in Aerospace Sciences, 35, 455–505 (1999)Google Scholar
  5. [5]
    SHYY, W., AONO, H., CHIMAKURTHI, S. K., TRIZILA, P., KANG, C. K., CESNIK, C. E. S., and LIU, H. Recent progress in flapping wing aerodynamics and aeroelasticity. Progress in Aerospace Sciences, 46(7), 284–327 (2010)Google Scholar
  6. [6]
    ELLINGTON, C. P., VANDENBERG, C., WILLMOTT, A. P., and THOMAS, A. L. R. Leading-edge vortices in insect flight. nature, 384, 626–630 (1996)Google Scholar
  7. [7]
    CHEN, Y. F., WANG, H. Q., HELBLING, E. F., JAFFERIS, N. T., ZUFFEREY, R., ONG, A., MA, K., GRAVISH, N., CHIRARATTANANON, P., KOVAC, M., and WOOD, R. J. A biologically inspired, flapping-wing, hybrid aerial-aquatic micro robot. Science Robotics, 2, eaao5619 (2017)Google Scholar
  8. [8]
    KEENNON, M., KLINGEBIEL, K., and WON, H. Development of the nano hummingbird: a tailless flapping wing micro air vehicle. 50th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, American Institute of Aeronautics and Astronautics, Nashville, Tennessee (2012)Google Scholar
  9. [9]
    SEND, W., FISCHER, M., JEBENS, K., MUGRAUER, R., NAGARATHINAM, A., and SCHARSTEIN, F. Artificial hinged-wing bird with active torsion and partially linear kinematics. 28th International Congress of the Aeronautical Sciences, Brisbane, Australia, 1148–1157 (2012)Google Scholar
  10. [10]
    ANDERSON, J. M., STREITLIEN, K., BARRETT, D. S., and TRIANTAFYLLOU, M. S. Oscillating foils of high propulsive efficiency. Journal of Fluid Mechanics, 360, 41–72 (1998)MathSciNetzbMATHGoogle Scholar
  11. [11]
    PLATZER, M., JONES, K. D., YOUNG, J., and LAI, J. C. S. Flapping-wing aerodynamics: progress and challenges. AIAA Journal, 46, 2136–2149 (2008)Google Scholar
  12. [12]
    NUDDS, R. L., TAYLOR, G. K., and THOMAS, A. L. R. Tuning of Strouhal number for high propulsive efficiency accurately predicts how wing beat frequency and stroke amplitude relate and scale with size and flight speed in birds. Proceedings of the Royal Society B: Biological Sciences, 271, 2071–2076 (2004)Google Scholar
  13. [13]
    SCHOUVEILER, L., HOVER, F., and TRIANTAFYLLOU, M. Performance of flapping foil propulsion. Journal of Fluid and Structures, 20, 949–959 (2005)Google Scholar
  14. [14]
    TIAN, F., LUO, H., SONG, J., and LU, X. Force production and asymmetric deformation of a flexible flapping wing in forward flight. Journal of Fluids and Structures, 36, 149–161 (2013)Google Scholar
  15. [15]
    UNGER, R., HAUPT, M. C., HORST, P., and RADESPIEL, R. Fluid-structure analysis of a flexible flapping airfoil at low Reynolds number flow. Journal of Fluids and Structures, 28, 72–88 (2012)Google Scholar
  16. [16]
    HEATHCOTE, S., WANG, Z., and GURSUL, I. Effect of spanwise flexibility on flapping wing propulsion. Journal of Fluids and Structures, 24, 183–199 (2008)Google Scholar
  17. [17]
    MAZAHERI, K. and EBRAHIMI, A. Experimental investigation on aerodynamic performance of a flapping wing vehicle in forward flight. Journal of Fluids and Structures, 27, 586–595 (2011)Google Scholar
  18. [18]
    ABDUL, N. and DIMITRIADIS, G. Experimental study of wings undergoing active root flapping and pitching. Journal of Fluids and Structures, 49, 687–704 (2014)Google Scholar
  19. [19]
    ITO, Y. and NAKAHASHI, K. Flow simulation of flapping wings of an insect using overset unstructured grid. 15th AIAA Computational Fluid Dynamics Conference, American Institute of Aeronautics and Astronautics, Anaheim, CA (2001)Google Scholar
  20. [20]
    LIANG, B. and SUN, M. Aerodynamic interactions between contralateral wings and between wings and body of a model insect at hovering and small speed motions. Chinese Journal of Aeronautics, 24(4), 396–409 (2011)Google Scholar
  21. [21]
    SUN, M. and WANG, J. K. Flight stabilization control of a hovering model insect. Journal of Experimental Biology, 210(15), 2714–2722 (2007)Google Scholar
  22. [22]
    DAI, H., LUO, H., and DOYLE, J. F. Dynamic pitching of an elastic rectangular wing in hovering motion. Journal of Fluid Mechanics, 693, 473–499 (2012)zbMATHGoogle Scholar
  23. [23]
    WANG, S., ZHANG, X., HE, G., and LIU, T. Lift enhancement by dynamically changing wingspan in forward flapping flight. Physical Fluids, 26(6), 169–230 (2013)Google Scholar
  24. [24]
    LIU, T. S., KUYKENDOLL, K., RHEW, R., and JONES, S. Avian wing geometry and kinematics. AIAA Journal, 44, 954–963 (2006)Google Scholar
  25. [25]
    CHANG, X. H., ZHANG, L. P., and HE, X. Numerical study of the plunging-pitching motion of S1223 airfoil (in Chinese). Acta Aerodynamic Sinica, 35(1), 62–70 (2017)Google Scholar
  26. [26]
    CHANG, X. H., MA, R., and ZHANG, L. P. Numerical study on the folding mechanism of seagull’s flapping wing (in Chinese). Acta Aerodynamic Sinica, 36(1), 135–143 (2018)Google Scholar
  27. [27]
    PHILIPS, P. J., EAST, R. A., and PRATT, N. H. An unsteady lifting line theory of flapping wings with application to the forward flight of birds. Journal of Fluid Mechanics, 112, 97–125 (1981)MathSciNetzbMATHGoogle Scholar
  28. [28]
    ZENG, R. Aerodynamic Characteristics of Flapping-wing MAV Simulating Bird Flight (in Chinese), Ph.D. dissertation, Nanjing University of Aeronautics and Astronautics (2004)Google Scholar
  29. [29]
    GUAN, Z. W. and YU, Y. L. Aerodynamics and mechanisms of elementary morphing models for flapping wing in forward flight of bat. Applied Mathematics and Mechanics (English Edition), 36(5), 669–680 (2015) MathSciNetGoogle Scholar
  30. [30]
    MILLER, L. A. and PESKIN, C. S. When vortices stick: an aerodynamic transition in tiny insect flight. Journal of Experimental Biology, 207, 3073–3088 (2004)Google Scholar
  31. [31]
    LIU, H. and ELLINGTON, C. P. Computational fluid dynamic study of hawkmoth hovering. Journal of Experimental Biology, 201, 461–477 (1998)Google Scholar
  32. [32]
    HE, X., ZHANG, L. P., ZHAO, Z., and CHANG, X. H. Research and development of structured/unstructured hybrid CFD software. Transactions of Nanjing University of Aeronautics & Astronautics, 30, 116–120 (2013)Google Scholar
  33. [33]
    HE, X., HE, X. Y., HE, L., ZHAO, Z., and ZHANG, L. P. HyperFLOW: a structured/unstructured hybrid integrated computational environment for multi-purpose fluid simulation. Procedia Engineering, 126, 645–649 (2015)Google Scholar
  34. [34]
    ZHANG, L. P., CHANG, X. H., DUAN, X. P., ZHAO, Z., and HE, X. Applications of dynamic hybrid grid method for three-dimensional moving/deforming boundary problems. Computers & Fluids, 62, 45–63 (2012)MathSciNetzbMATHGoogle Scholar
  35. [35]
    ZHANG, L. P. and WANG, Z. J. A block LU-SGS implicit dual time-stepping algorithm for hybrid dynamic meshes. Computers and Fluids, 33, 891–916 (2004)zbMATHGoogle Scholar
  36. [36]
    CHANG, X. H., MA, R., ZHANG, L. P., HE, X., and LI, M. Further study on the geometric conservation law for finite volume method on dynamic unstructured mesh. Computers and Fluids, 120, 98–110 (2015)MathSciNetzbMATHGoogle Scholar
  37. [37]
    RENDALL, T. C. S. and ALLEN, C. B. Reduced surface point selection options for efficient mesh deformation using radial basis functions. Journal of Computational Physics, 229, 2810–2820 (2010)MathSciNetzbMATHGoogle Scholar
  38. [38]
    WANG, N. H., LI, M., and ZHANG, L. P. Accuracy analysis and improvement of viscous flux schemes in unstructured second-order finite-volume discretization (in Chinese). Chinese Journal of Theoretical and Applied Mechanics, 50(3), 527–537 (2018)Google Scholar
  39. [39]
    ASHRAF, M. A., YOUNG, J., and LAI, J. C. S. Reynolds number, thickness and camber effects on flapping airfoil propulsion. Journal of Fluids and Structures, 27(2), 145–160 (2011)Google Scholar
  40. [40]
    TUNCER, I. H. and PLATZER, M. R. Thrust generation due to airfoil flapping. AIAA Journal, 34, 324–331 (1996)zbMATHGoogle Scholar
  41. [41]
    LIN, S. and HU, J. J. Aerodynamic performance study of flapping-wing flow fields. 23rd AIAA Applied Aerodynamics Conference, American Institute of Aeronautics and Astronautics, Toronto (2005)Google Scholar

Copyright information

© Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Xinghua Chang
    • 1
  • Laiping Zhang
    • 1
    Email author
  • Rong Ma
    • 2
  • Nianhua Wang
    • 2
  1. 1.China Aerodynamics Research and Development CenterState Key Laboratory of AerodynamicsMianyang, Sichuan ProvinceChina
  2. 2.China Aerodynamics Research and Development CenterComputational Aerodynamics InstituteMianyang, Sichuan ProvinceChina

Personalised recommendations