Skip to main content Accessibility help
×
Home

Revisiting the aerodynamics of hovering flight using simple models

  • CHENG-TA HSIEH (a1) (a2), CHIEN C. CHANG (a1) (a2) and CHIN-CHOU CHU (a1)

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.

Copyright

Corresponding author

Email address for correspondence: mechang@gate.sinica.edu.tw; chucc@iam.ntu.edu.tw

References

Hide All
Biesheuvel, A. & Hagmeijer, R. 2006 On the force on a body moving in a fluid. Fluid Dyn. Res. 38, 716742.
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, 341368.
Burgers, J. M. 1920 On the resistance of fluids and vortex motion. Proc. Kon. Akad. Westenschappen te Amsterdam 774–782.
Chang, C. C. 1992 Potential flow and forces for incompressible viscous flow. Proc. R. Soc. A 437, 517525.
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, 243263.
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, 23692395.
Chang, C. C. & Lei, S. Y. 1996 b An analysis of aerodynamic forces on a delta wing. J. Fluid. Mech. 316, 173196.
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, 95104.
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, 29953007.
Dickinson, M. H. 1994 The effects of wing rotation on unsteady aerodynamic performance at low Reynolds number. J. Exp. Biol. 192, 179206.
Dickinson, M. H. & Götz, K. G. 1993 Unsteady aerodynamic performance of model wings at low Reynolds numbers. J. Exp. Biol. 174, 4564.
Dickinson, M. H., Lehmann, F. O. & Sane, S. P. 1999 Wing rotation and the aerodynamic basis of insect flight. Science 284, 19541960.
Ellington, C. P. 1984 The aerodynamics of hovering insect flight. Phil. Trans. R. Soc. Lond. B 305, 1181.
Ellington, C. P., van den Berg, C., Willmott, A. P. & Thomas, A. L. R. 1996 Leading-edge vortices in insect flight. Nature 384, 626630.
Howarth, L. 1935 The theoretical determination of the lift coefficient for a thin elliptic cylinder. Proc. R. Soc. London. A 149, 558586.
Howe, M. S. 1989 On unsteady surface forces, and sound produced by the normal chopping of a rectilinear vortex. J. Fluid Mech. 206, 131153.
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, 401426.
Howe, M. S., Lauchle, G. C. & Wang, J. 2001 Aerodynamic lift and drag fluctuations of a sphere. J. Fluid Mech. 436, 4157.
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, 20532059.
Kambe, T. 1986 Acoustics emissions by vortex motions. J. Fluid Mech. 173, 643666.
Landau, L. D. & Lifshitz, E. M. 1987 Fluid Mechanics (2nd ed.) Pergamon.
Lehmann, F. O. 2008 When wings touch wakes: understanding locomotor force control by wake–wing interference in insect wings. J. Exp. Biol. 211, 224233.
Lighthill, M. J. 1973 On Weis-Fogh mechanism of lift generation. J. Fluid Mech. 60, 117.
Lighthill, M. J. 1979 Wave and hydrodynamic loading. Proc. Second Intl Conf. Behaviour Off-Shore Struct., BHRA Cranfield, 1, 140.
Lighthill, M. J. 1986 Fundamentals concerning wave loading on offshore structures. J. Fluid Mech. 173, 667681.
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, 4763.
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.
Ramamurti, R. & Sandberg, W. C. 2002 A three-dimensional computational study of the aerodynamic mechanisms of insect flight. J. Exp. Biol. 205, 15071518.
Rayner, J. M. V. 1979 A vortex theory of animal flight. Part 1. The vortex wake of a hovering animal. J. Fluid Mech. 91, 697730.
Sane, S. P. 2003 The aerodynamics of insect flight. J. Exp. Biol. 206, 41914208.
Sane, S. P. & Dickinson, M. H. 2001 The control of flight force by a flapping wing: lift and drag production. J. Exp. Biol. 204, 26072626.
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, 10871096.
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, 10731083.
Srygley, R. B. & Thomas, A. L. R. 2002 Unconventional lift-generating mechanisms in free-flying butterflies. Nature 420, 660664.
Sun, M. & Tang, J. 2002 Unsteady aerodynamic force generation by a model fruit fly wing in flapping motion. J. Exp. Biol. 205, 5570.
Thomas, P. D. & Lombard, C. K. 1979 Geometric conservation law and its application to flow computations on moving grids. AIAA J. 17, 10301037.
Wang, Z. J. 2000 a Two dimensional mechanism for insect hovering. Phys. Rev. Lett. 85, 22162219.
Wang, Z. J. 2000 b Vortex shedding and frequency selection in flapping flight. J. Fluid Mech. 410, 323341.
Wang, Z. J. 2005 Dissecting insect flight. Annu. Rev. Fluid. Mech. 37, 183210.
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, 461474.
Weis-Fogh, T. 1973 Quick estimates of flight fitness in hovering animals, including novel mechanisms for lift production. J. Exp. Biol. 59, 169230.
Wu, J. C. 1981 Theory for aerodynamic force and moment in viscous flows. AIAA J. 19, 432441.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Revisiting the aerodynamics of hovering flight using simple models

  • CHENG-TA HSIEH (a1) (a2), CHIEN C. CHANG (a1) (a2) and CHIN-CHOU CHU (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed