Flapping dynamics of a flexible flag in a uniform flow

Abstract

Numerical simulations using the immersed boundary method were performed to investigate the flapping dynamics of a flexible flag in a uniform flow. The relevant parameters related to the problem are the mass ratio (rho = rho(1)/rho L-f), the bending rigidity of the flag(K-B = EI/rho(fU infinity L3)-L-2) and the Reynolds number (Re = U infinity L/nu), where rho(1) denotes the line density difference between the flag and the surrounding fluid. By varying the parameters over the ranges 0 <=rho <= 10 and 10(-4)<= K-B <= 10(-1) for Re = 200, we identified three dynamical states: the stretched-straight state (I), the regular flapping state (II), and the irregular flapping state (III) with a region in which violent snapping events occurred, characterized by rapid changes in velocity, tension and drag. The description of the flapping dynamics at each dynamic state was provided through a sequence of time-evolving instantaneous fields, and was examined in detail with respect to the frequency and the energy rank based on the dynamic mode decomposition technique. Furthermore, the hysteresis phenomena with varying the mass ratio and the Reynolds number was examined, and the results showed that the hysteresis loop width was varied for approximately 20-65%, depending on the values of the relevant parameters employed.