Large amplitude flow-induced oscillations and energy harvesting using a cyber-physical pitching plate

Abstract

The dynamics of an elastically mounted flat plate in a uniform stream undergoing flow-induced pitching oscillations is studied with the aid of a cyber-physical system which is capable of simulating arbitrary structural dynamics. The system measures the angular position and velocity, and combines them with appropriate gains to provide a torque to a computer-controlled servomotor that emulates arbitrary torsional stiffness and damping. A series of experiments were carried out over a wide range of parameter space and the results demonstrate that inertial scaling of the stiffness and damping effectively captures the system behavior. As the torsional stiffness decreases, the system exhibits several bifurcations in its dynamical behavior. Firstly, a subcritical transition through a saddle-node bifurcation results in small-amplitude asymmetric limit-cycle oscillations and later, a subcritical transition through a Hopf bifurcation gives rise to large-amplitude symmetric limit-cycle oscillations. At very low stiffness the plate does not oscillate. Energy harvesting from the flow is only ~1% efficient, but is found to be optimized at a non-dimensional stiffness close to unity while increasing the Reynolds number is found to extend the range of damping over which large scale oscillations and energy harvesting can be sustained. Although velocity measurements are not made, the details of torque-position phase plane are used to infer the details of the formation time and stability of the leading-edge vortex associated with the rapidly pitching plate.