A general framework for the design of efficient passive pitch systems

Abstract

Mitigating the impact of variable inflow conditions is critical for a wide range of engineering systems such as drones or wind and tidal turbines. Passive control systems are of increasing interest for their inherent reliability, but a mathematical framework to aid the design of such systems is currently lacking. To this end, in this paper a two-dimensional rigid foil that passively pitches in response to changes in the flow velocity is considered. Both an analytical quasi-steady model and a dynamic low-order model are developed to investigate the pivot point position that maximizes unsteady load mitigation. The paper focuses on streamwise gusts, but the proposed methodology would apply equally to any change in the inflow velocity (speed and/or direction). The quasi-steady model shows that the force component in any arbitrary direction can be kept constant if the pivot lies on a particular line, and that the line coordinates depend on the gust and the foil characteristics. The dynamic model reveals that the optimum distance of the pivot location from the foil increases with decreasing inertia. For a foil at small angles of incidence, the optimum pivot point is along the extended chord line. This knowledge provides a methodology to design optimum passively pitching systems for a plethora of applications, including flying and swimming robotic vehicles, and provides new insights into the underlying physics of gust mitigation.