The Mechanics Of Flexibility Effects Of Insect Wing In Flapping

Among natural creatures, insects have a small average scale, i.e., fly at a low Re (Reynolds number). By quickly flapping wings in the air, they are capable of performing flight with highly maneuverability and stability though with low energy cost, which cannot be explained by the conventional aerodynamic theory. Therefore, the insect flight mechanisms and its biomimetic applications have attracted more and more attention of researchers. Thomas Mueller has noticed that the reason of insects overcoming the aerodynamic limitations brought by low Re, relies on two specific mechanisms: (1) flapping, and (2) flexibility. On the first problem, wing flapping, much progress has been made, including studies on high lift, thrust and power requirements in hovering and forward flight, using various approaches such as free-flight investigations, intelligent model experiments, numerical simulations and theoretical modeling. Whereas, on the second problem, flexibility effects, such topics are unknown: whether these effects may lead to aerodynamic force increment, energy saving or flight stability enhancement. And these issues are involved: constitutive relation and mechanical property of the insect wing material, the aerodynamic force response generated by dynamic deformation, and fluid-structure interaction, etc. With respect of above issues, either a few available works have no consistent opinion, or no related publication has appeared.Aiming at above issues, this thesis studies on three aspects as follows:1. For the first time, a viscoelastic constitutive relation model related to the deformation of the dragonfly wing was established, that is, the standard linear solid model. Firstly, based on the stress relaxation experiment of a realistic dragonfly wing (in vitro), it was found that such biological material behaves with visible viscoelasticity, and further analysis suggests that the constitutive relation of the material agrees well with the standard linear solid model in viscoelastic theory. Secondly, the viscoelastic model was examined by the finite element analysis of the dynamic deformation response for a model dragonfly wing under the action of the periodical inertial force in flapping motion, compared with the elastic constitutive relation model at the same time. Results show that the elastic model is not consistent with reality, as the resultant amplitude of elastic deformation is too large, furthermore, considerable higher-frequency components is produced. However, the viscoelastic deformation agrees well with the experiment, where these higher-frequency components have been damped remarkably by viscosity, and the amplitude of the deformation decreases and approaches to be steadily periodic. As a result, the viscoelastic constitutive relation model is confirmed to be the proper description of the insect wing material.2. According to measured data of the dynamic deformation of insect wing, numerical simulation of flows around simplified flexible wing with flapping motion, base on unsteady Navier-Stokes equations, has been made. It was revealed that the dynamic deformation produces more notable aerodynamic force response than static deformation does. Firstly, numerical simulation was performed with two kinds of element motions of the wing, i.e., the accelerating translation and the rotation with non-uniform angular velocity; it was discovered that the accelerating rate of the dynamic deformation is the key factor to determine the value of instantaneous aerodynamic force response, which is an unsteadiness effect helping insects to get over aerodynamic limitations caused by low Re. Secondly, the same simulation was performed with the whole cyclic flapping motion; results also indicate that the dynamic deformation considerably influence instantaneous aerodynamic force response, and enhances the time-averaged lift and thrust.3. Considering that during the flapping motion of insect wing, its deformation takes place with the action of both inertial and aerodynamic forces, this thesis made a primary exploration on the complicated FSI (Fluid-Structure Interaction) problem, implementing a process consisted of a simplified estimation method for the acted unsteady aerodynamic forces, a simplified structure model of insect wing and a simplified flapping mode. First of all, necessity of resolving the coupled FSI problem was proved out, through comparing values of inertial and aerodynamic forces. Second, utilizing the finite element analysis of the structure and estimation formula on unsteady aerodynamic force, an iterative method was developed to simulate the FSI problem, that is, the process of interaction between the deformation response of viscoelastic dragonfly wing in flapping motion and the action of both inertial and aerodynamic forces. Results lead to that, both the amplitude and the phase of the total deformation changes a lot, comparing with that under the action of only inertial force; in this process, the dynamic deformation also approaches quickly to be steadily periodic. Finally, we investigated the power cost due to the dynamic deformations of the viscoelastic wing in comparison with that in the rigid wing case.