High Fidelity Simulations of Flapping Wings Designed for Energetically Optimal Flight

A diversity of efficient solutions for flapping flight have evolved in nature; however, it is often difficult to isolate the key characteristics of efficient flapping flight from biological constraints. Rather than base micro aerial vehicle (MAV) design on natural flyers alone, we propose a multi-fidelity computational approach for analysis and design. At the lowest fidelity level, we use a wake-only energetics model that allows us to rapidly scan the global flapping kinematics for efficient kinematics and configurations. Following the wake-only design space characterization, we determine a series of candidate flapping wing geometries that can produce the desired wake characteristics. To do this, we have developed a quasiinverse wing design strategy that attempts to match the designed vehicle’s wake-circulation distribution with that predicted by the energetics model. Using our modified-doublet lattice method, we are able to determine how to modulate wing twist and camber to produce the desired wake vorticity. Because the method assumes inviscid flow, we are able to derive a large number of candidate designs to produce the target wake; however, as we show in this paper, only some of the designs perform adequately in physically relevant viscous fluids. As such, we use a high order, Discontinuous Galerkin, Navier-Stokes solver to simulate and assess the candidate designs, and examine which geometries minimize flow separation, improve performance and increase efficiency. The focus of this paper is on the design and analysis of efficient flapping wings. We present an application of our framework to a MAV design that has similar characteristics as medium sized fruit bat. We examine candidate wing designs to illustrate how adjusting wing section camber may be more favorable than adjusting wing twist alone. We find that the angle the leading edge of the wing presents to the flow is critical to minimizing flow separation.