Study on flapping modes of a flexible filament in the wake of an upstream rotating cylinder

Flapping mode of a flexible filament in wake flow behind a rotating circular cylinder has been studied numerically by using of an immersed-boundary-based lattice Boltzmann method. In a parameter space of α =0.1–3.0 and G /D=0.05–3.5, where α is the cylinder rotation rate and G / D is the distance ratio between the filament and cylinder which has a diameter of D , flapping modes of the filament are analyzed in the phase diagram to examine the mode transition features and the mechanism of formation for different modes. Specifically, three kinds of flapping modes have been found which are labelled as reversed, coiled, and normal flapping modes; six sub-modes: reversed one-side, two-side and steady modes, and normal one-side, two-side and steady modes have been identified. Based on the phase diagram in the ( α , G /D) plane, the transition pathways from the reversed to normal modes have been revealed as a consequence of increasing G / D . The critical value of G / D for transitions to the normal flapping modes demonstrates a decreasing trend for a small rotation rate, then becomes unaltered for a large α . The forming mechanism of different modes has been explored by analyzing the vortical wake behind the rotating cylinder and flexible filament. Moreover, great feedback effect of filament flapping on the cylinder wake flow has been revealed. Specifically, at specific parameters, the interaction between the flapping filament and the cylinder wake flow acts to totally suppress or trigger on the unsteady vortex shedding behind the cylinder, which correspondingly leads to great drag reduction even generation of thrust for the rotating cylinder, or significant drag enhancement.