Harmonic oscillations of a lamina in a viscous fluid near a solid surface: A lattice Boltzmann-immersed boundary approach

In this paper, a rigid thickless lamina is immersed in a quiescent viscous fluid and it undergoes transverse finite amplitude harmonic oscillations near a solid surface. The surrounding flow physics is computed through the lattice Boltzmann method. In order to account for the presence of the lamina in the lattice fluid background, the Immersed Boundary method is adopted. Several scenarios are investigated by varying the distance between the initial position of the lamina and the solid wall. For a given lamina-solid surface distance, the effect of the Reynolds number is investigated, together with the influence of the Keulegan-Carpenter number. Findings in terms of drag coefficient show that the force exerted by the encompassing fluid upon the lamina is remarkably influenced by the distance from the solid surface, especially for low values of the Reynolds number. Moreover, such results are confirmed by the computation of the hydrodynamic function. In fact, it highlights that the added mass effect and the non-linear damping experienced by the oscillating lamina grow as the above mentioned distance and the Reynolds number reduce.