Aerodynamic force generation and power requirements in forward flight in a fruit fly with modeled wing motion

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Abstract
SUMMARY Aerodynamic force generation and power requirements in forward flight in a fruit fly with modeled wing motion were studied using the method of computational fluid dynamics. The Navier-Stokes equations were solved numerically. The solution provided the flow velocity and pressure fields, from which the vorticity wake structure and the unsteady aerodynamic forces and torques were obtained (the inertial torques due to the acceleration of the wing-mass were computed analytically). From the flow-structure and force information, insights were gained into the unsteady aerodynamic force generation. On the basis of the aerodynamic and inertial torques, the mechanical power was obtained, and its properties were investigated. The unsteady force mechanisms revealed previously for hovering (i.e. delayed stall, rapid acceleration at the beginning of the strokes and fast pitching-up rotation at the end of the strokes) apply to forward flight. Even at high advance ratios, e.g. J=0.53-0.66 (J is the advance ratio), the leading edge vortex does not shed (at such advance ratios, the wing travels approximately 6.5 chord lengths during the downstroke). At low speeds (J≈0.13), the lift (vertical force) for weight support is produced during both the down- and upstrokes (the downstroke producing approximately 80% and the upstroke producing approximately 20% of the mean lift), and the lift is contributed mainly by the wing lift; the thrust that overcomes the body drag is produced during the upstroke, and it is contributed mainly by the wing drag. At medium speeds (J≈0.27), the lift is mainly produced during the downstroke and the thrust mainly during the upstroke; both of them are contributed almost equally by the wing lift and wing drag. At high speeds (J≈0.53), the lift is mainly produced during the downstroke and is mainly contributed by the wing drag; the thrust is produced during both the down- and upstrokes, and in the downstroke, is contributed by the wing lift and in the upstroke, by the wing drag. In forward flight, especially at medium and high flight speeds, the work done during the downstroke is significantly greater than during the upstroke. At advance ratios J≈0.13, 0.27 and 0.53, the work done during the downstroke is approximately 1.6, 2.8 and 4.2 times as much as that during the upstroke, respectively. At J=0 (hovering), the body-mass-specific power is approximately 29 W kg-1; at J=0.13 and 0.27, the power is approximately 10% less than that of hovering; at J=0.40, the power is approximately the same as that of hovering; when J is further increased, the power increases sharply. The graph of power against flying speeds is approximately J-shaped. From the graph of power against flying speeds, it is predicted that the insect usually flies at advance ratios between zero and 0.4, and for fast flight, it would fly at an advance ratio between 0.4 and 0.53.

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