SUMMARY: In this study, the passive pitching due to wing torsional flexibility and its lift generation in dipteran flight were investigated using (a) the non-linear finite element method for the fluid–structure interaction,which analyzes the precise motions of the passive pitching of the wing interacting with the surrounding fluid flow, (b) the fluid–structure interaction similarity law, which characterizes insect flight, (c) the lumped torsional flexibility model as a simplified dipteran wing, and (d) the analytical wing model, which explains the characteristics of the passive pitching motion in the simulation. Given sinusoidal flapping with a frequency below the natural frequency of the wing torsion, the resulting passive pitching in the steady state, under fluid damping, is approximately sinusoidal with the advanced phase shift. We demonstrate that the generated lift can support the weight of some Diptera.

SUMMARY: We have studied the passive maintenance of high angle of attack and its lift generation during the crane fly's flapping translation using a dynamically scaled model. Since the wing and the surrounding fluid interact with each other, the dynamic similarity between the model flight and actual insect flight was measured using not only the non-dimensional numbers for the fluid (the Reynolds and Strouhal numbers) but also those for the fluid—structure interaction (the mass and Cauchy numbers). A difference was observed between the mass number of the model and that of the actual insect because of the limitation of available solid materials. However, the dynamic similarity during the flapping translation was not much affected by the mass number since the inertial force during the flapping translation is not dominant because of the small acceleration. In our model flight, a high angle of attack of the wing was maintained passively during the flapping translation and the wing generated sufficient lift force to support the insect weight. The mechanism of the maintenance is the equilibrium between the elastic reaction force resulting from the wing torsion and the fluid dynamic pressure. Our model wing rotated quickly at the stroke reversal in spite of the reduced inertial effect of the wing mass compared with that of the actual insect. This result could be explained by the added mass from the surrounding fluid. Our results suggest that the pitching motion can be passive in the crane fly's flapping flight.

The relative importance of the wing's inertial and aerodynamic forces is the key to revealing how the kinematical characteristics of the passive pitching motion of insect flapping wings are generated, which is still unclear irrespective of its importance in the design of insect-like micro air vehicles. Therefore, we investigate three species of flies in order to reveal this, using a novel fluid-structure interaction analysis that consists of a dynamically scaled experiment and a three-dimensional finite element analysis. In the experiment, the dynamic similarity between the lumped torsional flexibility model as a first approximation of the dipteran wing and the actual insect is measured by the Reynolds number Re, the Strouhal number St, the mass ratio M, and the Cauchy number Ch. In the computation, the three-dimension is important in order to simulate the stable leading edge vortex and lift force in the present Re regime over 254. The drawback of the present experiment is the difficulty in satisfying the condition of M due to the limitation of available solid materials. The novelty of the present analysis is to complement this drawback using the computation. We analyze the following two cases: (a) The equilibrium between the wing's elastic and fluid forces is dynamically similar to that of the actual insect, while the wing's inertial force can be ignored. (b) All forces are dynamically similar to those of the actual insect. From the comparison between the results of cases (a) and (b), we evaluate the contributions of the equilibrium between the aerodynamic and the wing's elastic forces and the wing's inertial force to the passive pitching motion as 80-90% and 10-20%, respectively. It follows from these results that the dipteran passive pitching motion will be based on the equilibrium between the wing's elastic and aerodynamic forces, while it will be enhanced by the wing's inertial force.

The high torsional flexibility of insect wings allows for elastic recoil after the rotation of the wing during stroke reversal. However, the underlying mechanism of this recoil remains unclear because of the dynamic process of transitioning from the wing rotation during stroke reversal to the maintenance of a high angle of attack during the middle of each half-stroke, when the inertial, elastic, and aerodynamic effects all have a significant impact. Therefore, the interaction between the flapping wing and the surrounding air was directly simulated by simultaneously solving the incompressible Navier–Stokes equations, the equation of motion for an elastic body, and the fluid-structure interface conditions using the three-dimensional finite element method. This direct numerical simulation controlling the aerodynamic effect revealed that the recoil is the residual of the free pitch vibration induced by the flapping acceleration during stroke reversal in the transient response very close to critical damping due to the dynamic pressure resistance of the surrounding air. This understanding will enable the control of the leading-edge vortex and lift generation, the reduction of the work performed by flapping wings, and the interpretation of the underlying necessity for the kinematic characteristics of the flapping motion.

A flight device for insect-inspired flapping wing nano air vehicles (FWNAVs), which consists of the micro wings, the actuator, and the transmission, can use the fluid-structure interaction (FSI) to create the characteristic motions of the flapping wings. This design will be essential for further miniaturization of FWNAVs, since it will reduce the mechanical and electrical complexities of the flight device. Computational approaches will be necessary for this biomimetic concept because of the complexity of the FSI. Hence, in this study, a computational approach for the FSI design of insect-inspired micro flapping wings is proposed. This approach consists of a direct numerical modeling of the strongly coupled FSI, the dynamic similarity framework, and the design window (DW) search. The present numerical examples demonstrated that the dynamic similarity framework works well to make different two FSI systems with the strong coupling dynamically similar to each other, and this framework works as the guideline for the systematic investigation of the effect of characteristic parameters on the FSI system. Finally, an insect-inspired micro flapping wing with the 2.5-dimensional structure was designed using the proposed approach such that it can create the lift sufficient to support the weight of small insects. The existing area of satisfactory design solutions or the DW increases the fabricability of this wing using micromachining techniques based on the photolithography in the micro-electro-mechanical systems (MEMS) technology. Hence, the proposed approach will contribute to the further miniaturization of FWNAVs.