Numerical analysis for the added mass of oscillating body in viscous fluid

Abstract

In many fluid-structure interaction problems, the virtual mass, namely, the added mass is one of important interests. In the present study, the authors investigate the validity of a numerical method previously proposed by them in order to specify the added mass coefficient of arbitrary two-dimensional solid bodies efficiently and conveniently. In this method, we consider a two-dimensional incompressible viscous fluid under the assumption of an infinitesimal oscillation amplitude of the body, and properly modify the Navier-Stokes equations into linear equations the Brinkman equations. The solving method is based on a discrete singularity method. In order to show the method's effectivity and validity, the authors compute some flows around the bodies with fundamental cross sections with/without sharp edges, which oscillate in infinite flow fields. In addition, the authors solve the full Navier-Stokes equations by a finite difference method, and compare with each other to specify the valid range for the method. Then, the authors confirm the nonlinear amplitude effect and specify the valid range for the method.

Keywords

• fluid force
• numerical analysis
• added mass
• virtual mass
• discrete singularity method