Passive control of a single flexible flag using two side-by-side flags

Numerical simulations using an improved version of the immersed boundary method are performed to explore a passive control concept for a single flexible flag in a viscous uniform flow. In order to control a single flag passively, we utilize the distinct dynamics of two side-by-side flags, characterized by in-phase and out-of-phase flapping modes depending on their spanwise gap distance. When the two side-by-side flags are in an in-phase flapping mode with a small spanwise gap distance, the flapping amplitude of a single downstream flag is highly enhanced due to synchronization between the vortices shed from the upstream and downstream flags. However, when the two upstream flags flap in an out-of-phase flapping mode with a large spanwise gap distance, the flapping of the single flag is significantly weakened with a reduction of the dominant flapping frequency. Because the upstream flags induce consecutive counter-rotating vortex pairs with a high frequency due to their flapping mode (out-of-phase state), relatively strong interaction with an upcoming vortex of the opposite rotational direction leads to flapping inhibition of the single flag. For an intermediate spanwise gap distance, the vortex-to-vortex interaction between the flags becomes more complicated, and a change of the flapping phases of the two side-by-side flags depending on streamwise gap distance between the upstream and downstream flags occurs. The interactions between coupled flags are documented through the root-mean-square cross-stream tail positions, frequency, drag coefficient, vorticity and pressure contours of the flags with varying non-dimensional parameters relevant to the problem. The proposed passive control concept of a single flag using two side-by-side flags is applicable to the development of energy harvesting systems to extract more energy and flapping control systems to suppress vibration.