Numerical simulation of bending and length-varying flapping wing using discrete vortex method

Abstract

The paper aims to perform numerical simulations of flapping flight using Discrete Vortex Method (DVM) scheme. The scheme is suitable for moderately low Reynolds number [Formula: see text] and computationally less expensive as the flow domain doesn’t need to be discretized at each time step. Flapping of a one-dimensional (1D) flexible filament in a two-dimensional (2D) inviscid flow is simulated. The effect of bending by varying the wing shape along the spanwise length on aerodynamic performance was studied. It is observed that compared to rigid wings, bending wings are found to be better in generating lift. The effect of various bending wing configurations ([Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]) and different methods of imposing the bending ([Formula: see text], [Formula: see text] and [Formula: see text]) is studied. It was demonstrated that applying wing bending only during the downstroke phase ([Formula: see text]) is more effective than imposing bending throughout the flapping cycle ([Formula: see text]). Moreover, an effort is made to replicate the bending configuration observed in manta ray fish ([Formula: see text]) to investigate its impact on flow domain characteristics, lift, and thrust forces. Furthermore, the inclusion of a winglet is found to significantly enhance lift generation. In addition to the study of bending effects on aerodynamic performance, the study also seeks to emulate a unique aspect of bat flight kinematics, specifically the dynamic variation in wing span length during flapping. In a comparative analysis of two span length variation strategies, it is discerned that exclusively varying span length during the upstroke phase is the optimal approach for achieving increased lift generation. The study highlights the crucial role of wing bending and span length modulation in achieving elevated lift forces while simultaneously reducing drag. These findings are seen as holding significant promise for the design and optimization of Micro Air Vehicles (MAVs) utilizing flapping-based lift generation mechanisms, contributing substantially to the identification of optimal parameters for enhancing MAVs’ aerodynamic performance and operational efficiency.