Numerical study of sound generation by three-dimensional flexible flapping wings during hovering flight

Abstract

In this paper, the sound generated by three-dimensional flexible flapping wings during hovering flight is numerically studied by using an immersed boundary method. The wing shape, prescribed motion of the wing leading edge, Reynolds number, wing-to-fluid mass ratio and wing flexibility are systematically examined. The numerical results show that these governing parameters have a significant influence on the aerodynamic performances and consequently the acoustic outputs. The comparisons among four wing shapes indicate that the wing shape does not influence the sound directivity. The wing with larger area close to the wing-tip generates more lift associated with a larger acoustic output. The systematic examinations of four pitching amplitudes suggest that the optimal one is π∕2, which provides the highest efficiency with the lowest acoustic output. The effects of the flexibility are examined at two wing-to-fluid mass ratios (i.e., m∗=1.0 and 5.0) with the dimensionless flapping frequency ω∗ ranging from 0 to 0.5. The results show that an appropriate flexibility enhances the aerodynamic performance and reduces the acoustic outputs. The optimal choice is to use a flexible wing whose inertia is comparable to its aerodynamics, i.e., m∗=1.0 and ω∗=0.3, by which the highest efficiency is achieved with a relatively low acoustic outputs (30.5% lower than that of a rigid wing) and high lift generation. By collecting all the numerical data together, a linear relationship of the sound power and the root-mean-square of the power coefficient is observed. By using the fitted equation, the acoustic outputs of a flapping wing can be directly obtained from its aerodynamics, which can be used to simplify the engineering design and optimization process considering acoustic outputs.