Simulations of a passively actuated oscillating airfoil using a Discontinuous Galerkin method

Natural flappers, such as birds and bats, effectively maneuver in transitional, low Reynolds number flow, outperforming any current small engineered flapping vehicle. Thus, engineers are inspired to investigate the flapping dynamics present in nature to further understand the non-tradional flow aerodynamics in which they operate. Undeniably the success of biological flapping flight is the exploitation of fluid structure interaction response i.e. wing mechanics, deformation, and morphing. Even though all these features are encountered in nature, it is important to note that natural flappers have not just adapted to optimize their aerodynamic behavior, they also have evolved due to biological constraints. Therefore, in bio-inspired design one carefully uses the insight gained from understanding natural flappers. Here, a 2-D simulation of a pitching and heaving foil attempts to indicate flapping parameter specifics that generate an efficient, thrust producing flapper. The simulations are performed using a high-order Discontinuous Galerkin finite element solver for the compressible Navier Stokes equations. A brief investigation of a simple problem in which pitch and heave of a foil are prescribed highlights the necessity to use an inexpensive lower fidelity model to narrow down the large design space to a manageable region of interest. A torsional spring is placed at the foil’s leading edge to passively modulate the pitch while the foil is harmonically heaved. This model gives the foil passive structural compliance that automatically determines the pitch. The two-way fluid structure interaction thus results from the simultaneous resolution of the fluid and moment equations. This thesis explores the pitch profile and force generation characteristics of the spring-driven, oscillating foil. The passive strategy is found to enhance the propulsive efficiency and thrust production of the flappers specifically in cases where separation is encountered. Furthermore, the passive spring system performs like an ideal actuator that enables the oscillating foil to extract energy from the fluid motion without additional power input. Thus, this is the optimal mechanism to drive the foil dynamics for efficient flight with kinematic flexibility. Thesis Supervisor: Prof. Jaime Peraire Title: Professor 3