Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-19T16:08:13.808Z Has data issue: false hasContentIssue false
  • English
  • Français

Revisiting the aerodynamics of hovering flight using simple models

Published online by Cambridge University Press:  06 March 2009

CHENG-TA HSIEH ,
CHIEN C. CHANG  and
CHIN-CHOU CHU
CHENG-TA HSIEH
Affiliation:
Institute of Applied Mechanics and Taida Institute of Mathematical Sciences, National Taiwan University, Taipei 106, Taiwan, ROC Division of Mechanics, Research Center for Applied Sciences, Academia Sinica, Taipei 115, Taiwan, ROC
CHIEN C. CHANG*
Affiliation:
Institute of Applied Mechanics and Taida Institute of Mathematical Sciences, National Taiwan University, Taipei 106, Taiwan, ROC Division of Mechanics, Research Center for Applied Sciences, Academia Sinica, Taipei 115, Taiwan, ROC
CHIN-CHOU CHU*
Affiliation:
Institute of Applied Mechanics and Taida Institute of Mathematical Sciences, National Taiwan University, Taipei 106, Taiwan, ROC
*
†Email address for correspondence: [email protected]; [email protected]
†Email address for correspondence: [email protected]; [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

In this study, we revisit two simplified models of hovering motion for fruit fly and dragonfly from the perspective of force decomposition. The unsteady aerodynamics are analysed by examining the lift force and its four constituent components, each of which is directly related to a physical effect. These force components include one from the vorticity within the flow, one from the surface vorticity and two contributions credited to the motion of the insect wing. According to the phase difference in the models, a hovering motion can be classified into one of three types: symmetric, advanced and delayed rotations. The relative importance of the force components under various flow conditions are carefully analysed. It is shown that the symmetric rotation has the maximum vorticity lift (from volume and surface vorticity), but the optimal average lift is attained for an advanced rotation, which, compared to the symmetric rotation, increases the force contribution due to the unsteady surface motion at the expense of sacrificing contribution from the vorticity. By identifying the variations of the vorticity lift with flow characteristics, we may further explore the detailed mechanisms associated with the unsteady aerodynamics at different phases of hovering motion. For the different types of rotation, the insect wing shares the same mechanism of gaining lift when in the phase of driving with a fuller speed but exhibits different mechanisms at turning from one phase of motion to another. Moreover, we also examine the effects of the Reynolds number in an appropriate range and evaluate the performance of different wing profiles from symmetric to largely cambered.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 623 , 25 March 2009 , pp. 121 - 148
Copyright
Copyright © Cambridge University Press 2009

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

Biesheuvel, A. & Hagmeijer, R. 2006 On the force on a body moving in a fluid. Fluid Dyn. Res. 38, 716–742.CrossRefGoogle Scholar
Bos, F. M., Lentink, D., Oudheusden, B. W. Van & Bijl, H. 2008 Influence of wing kinematics on aerodynamic performance in hovering insect flight. J. Fluid Mech. 594, 341–368.CrossRefGoogle Scholar
Burgers, J. M. 1920 On the resistance of fluids and vortex motion. Proc. Kon. Akad. Westenschappen te Amsterdam 774–782.Google Scholar
Chang, C. C. 1992 Potential flow and forces for incompressible viscous flow. Proc. R. Soc. A 437, 517–525.Google Scholar
Chang, C. C. & Chern, R. L. 1991 A numerical study of flow around an impulsively started circular cylinder by a deterministic vortex method. J. Fluid Mech. 233, 243–263.CrossRefGoogle Scholar
Chang, C. C. & Lei, S. Y. 1996 a On the sources of aerodynamic forces: steady flow around a sphere or a cylinder. Proc. R. Soc. A 452, 2369–2395.Google Scholar
Chang, C. C. & Lei, S. Y. 1996 b An analysis of aerodynamic forces on a delta wing. J. Fluid. Mech. 316, 173–196.CrossRefGoogle Scholar
Chang, C. C., Yang, S. H. & Chu, C. C. 2008 A many-body force decomposition with applications to flow about bluff bodies. J. Fluid Mech. 600, 95–104.CrossRefGoogle Scholar
Chu, C. C., Chang, C. C., Liu, C. C. & Chong, R. L. 1996 Suction effect on an impulsively started circular cylinder: vortex structure and drag reduction. Phys. Fluids 8, 2995–3007.CrossRefGoogle Scholar
Dickinson, M. H. 1994 The effects of wing rotation on unsteady aerodynamic performance at low Reynolds number. J. Exp. Biol. 192, 179–206.CrossRefGoogle Scholar
Dickinson, M. H. & Götz, K. G. 1993 Unsteady aerodynamic performance of model wings at low Reynolds numbers. J. Exp. Biol. 174, 45–64.CrossRefGoogle Scholar
Dickinson, M. H., Lehmann, F. O. & Sane, S. P. 1999 Wing rotation and the aerodynamic basis of insect flight. Science 284, 1954–1960.CrossRefGoogle ScholarPubMed
Ellington, C. P. 1984 The aerodynamics of hovering insect flight. Phil. Trans. R. Soc. Lond. B 305, 1–181.Google Scholar
Ellington, C. P., van den Berg, C., Willmott, A. P. & Thomas, A. L. R. 1996 Leading-edge vortices in insect flight. Nature 384, 626–630.CrossRefGoogle Scholar
Howarth, L. 1935 The theoretical determination of the lift coefficient for a thin elliptic cylinder. Proc. R. Soc. London. A 149, 558–586.Google Scholar
Howe, M. S. 1989 On unsteady surface forces, and sound produced by the normal chopping of a rectilinear vortex. J. Fluid Mech. 206, 131–153.CrossRefGoogle Scholar
Howe, M. S. 1995 On the force and moment on a body in an incompressible fluid, with application to rigid bodies and bubbles at high and low Reynolds numbers. Quart. J. Mech. Appl. Math. 48, 401–426.CrossRefGoogle Scholar
Howe, M. S., Lauchle, G. C. & Wang, J. 2001 Aerodynamic lift and drag fluctuations of a sphere. J. Fluid Mech. 436, 41–57.CrossRefGoogle Scholar
Isogai, K., Fujishiro Saitoh, T., Yamamoto, M., Yamasaki, M. & Matsubara, M. 2004 Unsteady three-dimensional viscous flow simulation of a dragonfly hovering. AIAA J. 42, 2053–2059.CrossRefGoogle Scholar
Kambe, T. 1986 Acoustics emissions by vortex motions. J. Fluid Mech. 173, 643–666.CrossRefGoogle Scholar
Landau, L. D. & Lifshitz, E. M. 1987 Fluid Mechanics (2nd ed.) Pergamon.Google Scholar
Lehmann, F. O. 2008 When wings touch wakes: understanding locomotor force control by wake–wing interference in insect wings. J. Exp. Biol. 211, 224–233.CrossRefGoogle ScholarPubMed
Lighthill, M. J. 1973 On Weis-Fogh mechanism of lift generation. J. Fluid Mech. 60, 1–17.CrossRefGoogle Scholar
Lighthill, M. J. 1979 Wave and hydrodynamic loading. Proc. Second Intl Conf. Behaviour Off-Shore Struct., BHRA Cranfield, 1, 1–40.Google Scholar
Lighthill, M. J. 1986 Fundamentals concerning wave loading on offshore structures. J. Fluid Mech. 173, 667–681.CrossRefGoogle Scholar
Maxworthy, T. 1979 Experiments on the Weis-Fogh mechanism of lift generation by insects in hovering flight. Part 1. Dynamics of the fling. J. Fluid Mech. 93, 47–63.CrossRefGoogle Scholar
Ragazzo, C. G. & Tabak, E. G. 2007 On the force and torque on systems of rigid bodies: a remark on an integral formula due to Howe. Phys. Fluids, 19, 057108.CrossRefGoogle Scholar
Ramamurti, R. & Sandberg, W. C. 2002 A three-dimensional computational study of the aerodynamic mechanisms of insect flight. J. Exp. Biol. 205, 1507–1518.CrossRefGoogle ScholarPubMed
Rayner, J. M. V. 1979 A vortex theory of animal flight. Part 1. The vortex wake of a hovering animal. J. Fluid Mech. 91, 697–730.CrossRefGoogle Scholar
Sane, S. P. 2003 The aerodynamics of insect flight. J. Exp. Biol. 206, 4191–4208.CrossRefGoogle ScholarPubMed
Sane, S. P. & Dickinson, M. H. 2001 The control of flight force by a flapping wing: lift and drag production. J. Exp. Biol. 204, 2607–2626.CrossRefGoogle ScholarPubMed
Sane, S. P. & Dickinson, M. H. 2002 The aerodynamic effects of wing rotation and a revised quasi-steady model of flapping flight. J. Exp. Biol. 205, 1087–1096.CrossRefGoogle Scholar
Smith, M., Wilkin, P. & Williams, M. 1996 The advantages of an unsteady panel method in modeling the aerodynamic forces on rigid flapping wings. J. Exp. Biol. 199, 1073–1083.CrossRefGoogle ScholarPubMed
Srygley, R. B. & Thomas, A. L. R. 2002 Unconventional lift-generating mechanisms in free-flying butterflies. Nature 420, 660–664.CrossRefGoogle ScholarPubMed
Sun, M. & Tang, J. 2002 Unsteady aerodynamic force generation by a model fruit fly wing in flapping motion. J. Exp. Biol. 205, 55–70.CrossRefGoogle Scholar
Thomas, P. D. & Lombard, C. K. 1979 Geometric conservation law and its application to flow computations on moving grids. AIAA J. 17, 1030–1037.CrossRefGoogle Scholar
Wang, Z. J. 2000 a Two dimensional mechanism for insect hovering. Phys. Rev. Lett. 85, 2216–2219.CrossRefGoogle Scholar
Wang, Z. J. 2000 b Vortex shedding and frequency selection in flapping flight. J. Fluid Mech. 410, 323–341.CrossRefGoogle Scholar
Wang, Z. J. 2005 Dissecting insect flight. Annu. Rev. Fluid. Mech. 37, 183–210.CrossRefGoogle Scholar
Wang, Z. J., Birch, J. M. & Dickinson, M. H. 2004 Unsteady forces and flows in low Reynolds number hovering flight: two-dimensional computations vs robotic wing experiments. J. Expl Biol. 207, 461–474.CrossRefGoogle ScholarPubMed
Weis-Fogh, T. 1973 Quick estimates of flight fitness in hovering animals, including novel mechanisms for lift production. J. Exp. Biol. 59, 169–230.CrossRefGoogle Scholar
Wu, J. C. 1981 Theory for aerodynamic force and moment in viscous flows. AIAA J. 19, 432–441.CrossRefGoogle Scholar