Mechanics of flow-induced pitching of an inverted foil undergoing cross-flow

Abstract

This study investigates the fundamental mechanics of flow-induced pitching of an inverted foil undergoing cross-flow for reduced velocity U_r = 25 − 47 and damping ratio ζ = 0 − 0.325. The Reynolds number (Re), based on the foil chord length, is fixed at Re = 900. The foil oscillation amplitude, pitching frequency, hydrodynamic stiffness, hydrodynamic damping, and energy harvesting efficiency are presented and analyzed. The inverted foil system exhibits three distinct response modes: stationary, deflected pitching, and symmetric pitching. Symmetric pitching, occurring for a range of U_r centered around U_r = 37, involves a large amplitude oscillation about the equilibrium position of the foil. The hydrodynamic stiffness plays a crucial role in determining the three response modes and the pitching frequency. While hydrodynamic damping is negative during the forward stroke and positive during the return stroke, the hydrodynamic stiffness remains negative during both strokes, making the pitching frequency consistently lower than the natural frequency. The timing between forward and return strokes varies with U_r and ζ. The forward stroke is shorter than the return stroke for small ζ values while the pattern reverses for larger ζ values. Equal timing between the two strokes occurs at intermediate ζ values. The symmetric pitching in both space and time domains makes the efficiency as high as 16 % at U_r = 37 and ζ = 0.130. A deep understanding of the underlying mechanism of flow-induced vibration provides guidance for improving the energy efficiency of fully passive flapping-foil generators.