Self-propulsion of an airfoil in combined heave-pitch motion*

In this work, we study the dynamics of flapping airfoils under the combined motion of heave and pitch. We impose such motions using our CPFD (Cyber-Physical Fluid Dynamics) facility, a closed-loop force-feedback control system. Steady state self-propulsion is achieved when the generated thrust becomes equal to the drag of the system. As we vary the airfoil motion in a heave-pitch diagram, we produce a set of contours of various parameters, for example a set of normalized velocity contours.  Along each contour, the self-propelled velocity is a constant, and we can find where the propulsive economy (a measure of efficiency) is maximized. In the heave-pitch plane, we can define a curve of maximum propulsive economy.  Measurements of vorticity are made using PIV, and enable us to observe the vortex dynamics corresponding with the optimal conditions.  By implementing this "virtual-physical" approach, we are able to complete around 400 equivalent purely-physical experiments. This capability is key in enabling us to define, with sufficient resolution, the contour plots within the heave-pitch diagrams.