Numerical analysis of flow-induced rotation of an S-shaped rotor

Abstract

Flow-induced rotation of an S-shaped rotor is investigated using an adaptive numerical scheme based on a vortex particle method. The boundary integral equation with respect to Bernoulli’s function is solved using a panel method for obtaining the pressure distribution on the rotor surface which applies the torque to the rotor. The present work first addresses the validation of the scheme against the previous studies of a rotating circular cylinder. Then, we compute the automatic rotation start of an S-shaped rotor from a quiescent state for various values of the moment of inertia. The computed flow patterns where the rotor supplies (or is supplied with) the torque to (or from) the fluid are shown during one cycle of rotation. The vortex shedding from the tip of the advancing bucket is found to play a key role in generating positive torque on the rotor. A remarkable finding is the fact that, after the rotor reaches a stable rotation, the trajectory of the limit cycle in the present autonomous system accounts for the stable rotating movement of the rotor. Furthermore, the hydrodynamic scenario of the rotor automatically starting up from a quiescent state and entering the limit cycle is elucidated for various values of the moment of inertia and the initial angle of the rotor.