Effect of wing inertia on hovering performance of flexible flapping wings

Abstract

Insect wings in flight typically deform under the combined aerodynamic force and wing inertia; whichever is dominant depends on the mass ratio defined as m ‫ء‬ = s h / ͑ f c͒, where s h is the surface density of the wing, f is the density of the air, and c is the characteristic length of the wing. To study the differences that the wing inertia makes in the aerodynamic performance of the deformable wing, a two-dimensional numerical study is applied to simulate the flow-structure interaction of a flapping wing during hovering flight. The wing section is modeled as an elastic plate, which may experience nonlinear deformations while flapping. The effect of the wing inertia on lift production, drag resistance, and power consumption is studied for a range of wing rigidity. It is found that both inertia-induced deformation and flow-induced deformation can enhance lift of the wing. However, the flow-induced deformation, which corresponds to the low-mass wing, produces less drag and leads to higher aerodynamic power efficiency. In addition, the wing deformation has a significant effect on the unsteady vortices around the wing. The implication of the findings on insect flight is discussed.

Numerical study on hydrodynamic effect of flexibility in a self-propelled plunging foil

“…It is interesting to note that a similar trend has also been reported in some studies of the flexibility effect on hovering performance of flapping foils or wings [19,52]. In these works, the maximum lift production was achieved at a moderate flexibility.…”

“…For example, Katz and Weihs [9] and Michelin and Llewellyn Smith [10] have used the potential flow theory to describe the interaction between an inviscid flow and a flexible flapping wing; whereas a reduced-order model has been used for the structures in other works [11][12][13]. With the availability of better computing power and more sophisticated numerical methods, simulations which include the interaction of viscous fluid and solid continuum were performed in some more recent studies [14][15][16][17][18][19][20][21][22]. One point has to be underlined here: in most studies concerning flapping foils, the interaction between a flapping body held static and an oncoming flow driven independently is considered.…”

Aerodynamics, sensing and control of insect-scale flapping-wing flight

“…Wing flexibility can enhance propulsive force generation, while reducing the power consumption (e.g. [9,[123][124][125][126]). Also, optimal efficiency are observed for an effective Strouhal number based on the deformed wing motion between 0.25 and 0.35 [127], similar to pitching and plunging rigid wings [15].…”

Propulsion for Biological Inspired Micro-Air Vehicles (MAVs)

“…The architecture of the wing and the material properties of its element determine how the wing changes their shape in response momentarily to external forces changing, since the wing movement is very complex. It is nowadays a great challenge to researchers, how to build a model with similar properties; of course, another challenge is how to incorporate the wing flexibility into the theoretical model predicting the aerodynamic force during insect flight-both, remains an ongoing challenge to the researchers [32]. As previously referred, leading-edge vortex is the main flight mechanism that allows insects to be able to fly; studies on the unsteady aerodynamics on the flapping wing of a Manduca sexta hawkmoth robotic model (while hovering) were made by the use of computational fluid dynamic (CFD) modelling [33]; CFD computations revealed a large leading-edge vortex (LEV1) presence during most of the downstroke movement (from the base at ~60/75% of the wing length); as the wing moves towards horizontal position, this structure becomes larger spiralling vortex with strong axial flow at the core, towards the wing tip.…”