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Systematic investigation of a flapping wing in inclined stroke-plane hovering

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Abstract

The objective of the paper is to perform a systematic investigation of a flapping wing in inclined stroke-plane hovering which is observed in insects such as dragonflies, true hoverflies and Coleopteran. Numerical simulations are performed at pitch amplitudes (15° ≤ B ≤ 75°) in conjunction with other kinematic parameters such as stroke-plane inclination (10° ≤ β ≤ 80°), stroke amplitude (0.5 ≤ Ao/c ≤ 5), heave-pitch phase difference (− 45° ≤ φ ≤ 90°) and Reynolds number (15.7 ≤ Re ≤ 10,000). Moving mesh strategy implemented in finite volume code is used to simulate the flapping motion. The aerodynamic performance and vortex structures are obtained for each parametric space. Results indicate that the maximum time-averaged vertical force coefficient \(\overline{{C_{\text{v}} }}\) is obtained at B ≈ 30°–40°, β ≈ 52°–60°, Ao/c ≈ 2–4 and φ ≈ + 27°–+ 60°. On the other hand, the maximum lifting efficiency ηl is obtained at B ≈ 42°–57°, β ≈ 50°–70°, Ao/c ≈ 1–2 and φ ≈ 0°–+ 15°. Vortex structures show that the strength, growth and position of LEV and TEV play a significant role in the vertical force generation. To the best of author’s knowledge, this is the first work which has discussed the significance of pitch amplitude in inclined hovering insects. In addition, the best operating conditions are determined by mapping \(\overline{{C_{\text{v}} }}\) and ηl over a wide parametric space. The optimal parameters are then compared with the existing experimental results that show a good match.

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References

  1. Weis-Fogh T (1973) Quick estimates of flight fitness in hovering animals, including novel mechanisms for lift production. J Exp Biol 59(1):169–230

    Google Scholar 

  2. Norberg RÅ (1975) Hovering flight of the dragonfly Aeschna juncea L., kinematics and aerodynamics. In: Swimming and flying in nature, Springer, Boston, MA, pp 763–781

    Chapter  Google Scholar 

  3. Wang ZJ (2000) Two dimensional mechanism for insect hovering. Phys Rev Lett 85(10):2216

    Article  Google Scholar 

  4. Wang ZJ (2004) The role of drag in insect hovering. J Exp Biol 207(23):4147–4155

    Article  Google Scholar 

  5. Hsieh CT, Chang CC, Chu CC (2009) Revisiting the aerodynamics of hovering flight using simple models. J Fluid Mech 623:121–148

    Article  MathSciNet  Google Scholar 

  6. Sudhakar Y, Vengadesan S (2010) Flight force production by flapping insect wings in inclined stroke plane kinematics. Comput Fluids 39(4):683–695

    Article  Google Scholar 

  7. Jones SK, Laurenza R, Hedrick TL, Griffith BE, Miller LA (2015) Lift vs. drag based mechanisms for vertical force production in the smallest flying insects. J Theor Biol 384:105–120

    Article  Google Scholar 

  8. Kim D, Choi H (2007) Two-dimensional mechanism of hovering flight by single flapping wing. J Mech Sci Technol 21(1):207–221

    Article  Google Scholar 

  9. Ellington C (1995) Unsteady aerodynamics of insect flight. In: Symposia of the society for experimental biology, pp 109–129

  10. Dickinson MH, Lehmann FO, Sane SP (1999) Wing rotation and the aerodynamic basis of insect flight. Science 284(5422):1954–1960

    Article  Google Scholar 

  11. Le TQ, Byun D, Ko JH, Park HC, Kim M (2010) Numerical investigation of the aerodynamic characteristics of a hovering Coleopteran insect. J Theor Biol 266(4):485–495

    Article  MathSciNet  Google Scholar 

  12. Mou XL, Liu YP, Sun M (2011) Wing motion measurement and aerodynamics of hovering true hoverflies. J Exp Biol 214(17):2832–2844

    Article  Google Scholar 

  13. Birch JM, Dickson WB, Dickinson MH (2004) Force production and flow structure of the leading edge vortex on flapping wings at high and low Reynolds numbers. J Exp Biol 207(7):1063–1072

    Article  Google Scholar 

  14. Ansari SA, Żbikowski R, Knowles K (2006) Non-linear unsteady aerodynamic model for insect-like flapping wings in the hover. Part 2: implementation and validation. P I Mech Eng G-J Aer 220(3):169–186

    Article  Google Scholar 

  15. Wang ZJ, Birch JM, Dickinson MH (2004) Unsteady forces and flows in low Reynolds number hovering flight: two-dimensional computations vs robotic wing experiments. J Exp Biol 207(3):449–460

    Article  Google Scholar 

  16. Li Q, Zheng M, Pan T, Su G (2018) Experimental and numerical investigation on dragonfly wing and body motion during voluntary take-off. Sci Rep 8(1):1011

    Article  Google Scholar 

  17. Eldredge JD, Jones AR (2019) Leading-edge vortices: mechanics and modeling. Annu Rev Fluid Mech 51(1):75–104

    Article  Google Scholar 

  18. Nabawy MR, Crowther WJ (2017) The role of the leading edge vortex in lift augmentation of steadily revolving wings: a change in perspective. J R Soc Interface 14(132):20170159

    Article  Google Scholar 

  19. Bhat SS, Zhao J, Sheridan J, Hourigan K, Thompson MC (2019) Uncoupling the effects of aspect ratio, Reynolds number and Rossby number on a rotating insect-wing planform. J Fluid Mech 859:921–948

    Article  MathSciNet  Google Scholar 

  20. Phillips N, Knowles K, Bomphrey RJ (2015) The effect of aspect ratio on the leading-edge vortex over an insect-like flapping wing. Bioinspir Biomim 10(5):056020

    Article  Google Scholar 

  21. Harbig RR, Sheridan J, Thompson MC (2014) The role of advance ratio and aspect ratio in determining leading-edge vortex stability for flapping flight. J Fluid Mech 751:71–105

    Article  MathSciNet  Google Scholar 

  22. Lee YJ, Lua KB, Lim TT (2016) Aspect ratio effects on revolving wings with Rossby number consideration. Bioinspir Biomim 11(5):056013

    Article  Google Scholar 

  23. Ellington C (2006) Insects versus birds: the great divide. In: 44th AIAA aerospace sciences meeting and exhibit. https://doi.org/10.2514/6.2006-35

  24. Ellington CP, Usherwood JR (2001) Lift and drag characteristics of rotary and flapping wings. In: Fixed and flapping wing aerodynamics for micro air vehicle applications, Progress in astronautics and aeronautics, AIAA, pp. 231–248. https://doi.org/10.2514/5.9781600866654.0231.0248

  25. Zhu J, Jiang L, Zhao H, Tao B, Lei B (2015) Numerical study of a variable camber plunge airfoil under wind gust condition. J Mech Sci Technol 29(11):4681–4690

    Article  Google Scholar 

  26. Zymaris AS, Papadimitriou DI, Giannakoglou KC, Othmer C (2009) Continuous adjoint approach to the Spalart-Allmaras turbulence model for incompressible flows. Comput Fluids 38(8):1528–1538

    Article  Google Scholar 

  27. Fluent ANSYS (2012) 14.5 theory guide. ansys Inc, Canonsburg, PA

  28. Gao T, Lu XY (2008) Insect normal hovering flight in ground effect. Phys Fluids 20(8):087101

    Article  Google Scholar 

  29. Alexander DE (1984) Unusual phase relationships between the forewings and hindwings in flying dragonflies. J Exp Biol 109(1):379–383

    Google Scholar 

  30. Rüppell G (1989) Kinematic analysis of symmetrical flight manoeuvres of Odonata. J Exp Biol 144(1):13–42

    Google Scholar 

  31. Ellington CP (1984) The aerodynamics of hovering insect flight. IV. Aerodynamic mechanisms. Phil Trans R Soc Lond B 305(1122):79–113

    Article  Google Scholar 

  32. Wakeling JM, Ellington CP (1997) Dragonfly flight. II. Velocities, accelerations and kinematics of flapping flight. J Exp Biol 200(3):557–582

    Google Scholar 

  33. Dickinson MH, Gotz KG (1993) Unsteady aerodynamic performance of model wings at low Reynolds numbers. J Exp Biol 174(1):45–64

    Google Scholar 

  34. Khan ZA, Agrawal SK (2011) Optimal hovering kinematics of flapping wings for micro air vehicles. AIAA J 49(2):257–268

    Article  Google Scholar 

  35. Wang Q, Goosen JF, Van Keulen A (2013) Optimal hovering kinematics with respect to various flapping-wing shapes. In: IMAV 2013, Proceedings of the international micro air vehicle conference and flight competition, Toulouse, France

  36. Lua KB, Zhang XH, Lim TT, Yeo KS (2015) Effects of pitching phase angle and amplitude on a two-dimensional flapping wing in hovering mode. Exp Fluids 56(2):35

    Article  Google Scholar 

  37. Chen Y, Gravish N, Desbiens AL, Malka R, Wood RJ (2016) Experimental and computational studies of the aerodynamic performance of a flapping and passively rotating insect wing. J Fluid Mech 791:1–33

    Article  MathSciNet  Google Scholar 

  38. Azuma A, Watanabe T (1988) Flight performance of a dragonfly. J Exp Biol 137(1):221–252

    Google Scholar 

  39. Wakeling JM (1993) Dragonfly aerodynamics and unsteady mechanisms: a review. Odonatologica 22(3):319–334

    Google Scholar 

  40. Ellington CP (1984) The aerodynamics of flapping animal flight. Am Zool 24(1):95–105

    Article  Google Scholar 

  41. Lua KB, Lim TT, Yeo KS (2011) Effect of wing–wake interaction on aerodynamic force generation on a 2D flapping wing. Exp Fluids 51(1):177–195

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education [NRF-2017R1D1A1B03032472].

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  1. School of Mechanical Engineering, Kyungpook National University, Daegu, 41566, South Korea

    A. R. Shanmugam & C. H. Sohn

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  1. A. R. Shanmugam
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  2. C. H. Sohn
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Correspondence to C. H. Sohn.

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Technical Editor: André Cavalieri.

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Shanmugam, A.R., Sohn, C.H. Systematic investigation of a flapping wing in inclined stroke-plane hovering. J Braz. Soc. Mech. Sci. Eng. 41, 347 (2019). https://doi.org/10.1007/s40430-019-1840-6

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  • DOI: https://doi.org/10.1007/s40430-019-1840-6

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