Thrust, drag and wake structure in flapping compliant membrane wings*

We present results from a theoretical framework developed to characterize the steady and unsteady aeroelastic behavior of compliant membrane wings, relevant to several applications including biological fliers such as bats and colugos, and engineered micro air vehicles (MAVs). The linearized model uses unsteady potential flow coupled to an elastic membrane equation. We use the model to explore the effects of wing compliance, inertia and flapping kinematics on aerodynamic performance. The effects of added mass and fluid damping are quantified using a simple damped oscillator model. We present results showing the optimal conditions for maximum lift and thrust. As the flapping frequency is increased, membranes go through a transition from thrust to drag at a frequency close to the membrane's resonant frequency. This transition is accompanied by a change in the character of the wake from a "reverse von Kármán" to a "von Kármán" vortex wake. The wake transition and the thrust/drag transition do not occur at the same frequency, resulting in some counter-intuitive flows for which thrust is accompanied by a "drag wake", and vice-versa.