Added-Mass and Viscous-Damping Forces Acting on Various Oscillating 3D Objects

In many fluid-structure-interaction problems, the “added mass”, “inertial mass”, “virtual mass”, “carried mass” or “induced mass” is one of important interests. In the present study, the authors propose a simple and efficient method to specify fluid-force coefficients of an oscillating object in stationary fluid. In this method, the authors consider incompressible-and-viscous fluid under the assumption of an infinitesimal oscillation amplitude of a three-dimensional object, and properly modify the Navier-Stokes equations into linear equations, namely, the Brinkman equations. The solving method is based on a discrete singularity method, one of the boundary methods. Furthermore, the authors conduct experiments, in addition to computations. In order to confirm the method’s effectivity and validity, the authors compute a sphere, comparing our computations to theories and experiments which show good agreement.