Study of flapping filaments using the immersed boundary-lattice Boltzmann method

Abstract

In this study, flow over a flexible filament under a wide range of parameters is simulated using the immersed boundary-lattice Boltzmann method (IB-LBM). The leading end of the filament is fixed in the flow field and the trailing end is free to flap. To execute the simulation, we combine the IB-LBM and a semi-implicit discrete equation of force on the filament to better satisfy the boundary condition. After some numerical simulations validating the modified method, the motion of flexible filaments is examined with different dimensionless bending coefficients ( ${\kappa }^{*}$ ) and Reynolds numbers ( $\text{Re}$ ). From the trajectory of the flapping filament, different flapping modes are found. When the parameter is between that of two modes, the anti-resonance phenomenon is observed. Numerical results show that the dimensionless bending coefficient and Reynolds number both affect the flapping motion, but in different ways. The dimensionless bending coefficient mainly affects the mode of the flapping, while the Reynolds number mainly affects the perturbation to the filament motion, which is related to the motivation of this system. Some other motion characteristics, for example, the function of amplitude and perturbation propagation, are also discussed in this work.