Large aerodynamic forces on a sweeping wing at low Reynolds number
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The aerodynamic forces and flow structure of a model insect wing is studied by solving the Navier-Stokes equations numerically. After an initial start from rest, the wing is made to execute an azimuthal rotation (sweeping) at a large angle of attack and constant angular velocity. The Reynolds number (Re) considered in the present note is 480 (Re is based on the mean chord length of the wing and the speed at 60% wing length from the wing root). During the constant-speed sweeping motion, the stall is absent and large and approximately constant lift and drag coefficients can be maintained. The mechanism for the absence of the stall or the maintenance of large aerodynamic force coefficients is as follows. Soon after the initial start, a vortex ring, which consists of the leading-edge vortex (LEV), the starting vortex, and the two wing-tip vortices, is formed in the wake of the wing. During the subsequent motion of the wing, a base-to-tip spanwise flow converts the vorticity in the LEV to the wing tip and the LEV keeps an approximately constant strength. This prevents the LEV from shedding. As a result, the size of the vortex ring increases approximately linearly with time, resulting in an approximately constant time rate of the first moment of vorticity, or approximately constant lift and drag coefficients. The variation of the relative velocity along the wing span causes a pressure gradient along the wingspan. The base-to-tip spanwise flow is mainly maintained by the pressure-gradient force.
Key Wordsmodel insect wing sweeping motion high lift leading-edge-vortex
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- 1.Weis-Fogh T. Quick estimates of flight fitness in hovering animals, including novel mechanisms for lift production.J Exp Biol, 1973, 59: 169–230Google Scholar
- 2.Vogel S. Flight in drosophila. III. aerodynamic characteristics of fly wings and wing models.J Exp Biol, 1967, 44: 431–443Google Scholar
- 3.Willmott AP, Ellington, CP The mechanics of flight in the hawkmoth Manduca sexta. II. aerodynamic consequences of kinematic and morphological variation.J Exp Biol, 1997, 200: 2723–2745Google Scholar
- 4.Dickinson MH, Götz KG. Unsteady aerodynamic performance of model wings at low Reynolds numbers.J Exp Biol, 1993, 174: 45–64Google Scholar
- 7.Usherwood JR, Ellington CP. The aerodynamics of revolving wings. I. model hawkmoth wings.J Exp Biol, 2002, 205: 1547–1564Google Scholar
- 8.Usherwood JR, Ellington CP. The aerodynamics of revolving wings. II. propeller force coefficients from mayfly to quail.J Exp Biol, 2002, 205: 1565–1576Google Scholar
- 9.Sun M, Tang J. Unsteady aerodynamic force generation by a model fruit fly wing in flapping motion.J Exp Biol, 2002, 205: 55–70Google Scholar
- 10.Rogers SE, Kwak D, Kiris C. Steady and unsteady solutions of the incompressible Navier-Stokes equations.AIAA J, 1991, 29: 603–610Google Scholar
- 11.Hilgenstock A. A fast method for the elliptic generation of three dimensional grids with full boundary control. In: Sengupta S, Hauser J, et al. eds. Num Grid Generation in CFM'88, Swansea UK: Pineridge Press Ltd, 1988, 137–146Google Scholar
- 14.Ellington CP. The aerodynamics of hovering insect flight. III. kinematics.Phil Trans R Soc Lond, B, 1984, 305: 41–78Google Scholar
- 15.Wakeling JM, Ellington CP. Dragonfly flight I gliding flight and steady-state aerodynamic forces.J Exp Biol, 1997, 200: 543–556Google Scholar