Added and coupling mass coefficients of a body oscillating in an unsteady flow

The evaluation of added mass holds practical significance in various engineering applications dealing with flow-induced vibration and fluid-structure interaction problems. A notable situation arises when bodies oscillate in an unsteady flow, leading to a coupling mass that deviates from the conventional added mass used for assessing inertial forces on a body oscillating in a steady fluid. In this paper, we revisit a comprehensive theoretical approach initially proposed by Batchelor in 1967 for quantifying the inertial force acting on a body in an accelerating fluid. To enhance this approach, we incorporate an exact and straightforward superposition of the acceleration fields along with numerical evaluation based on the kinetic energy of potential flow. Our refined approach encompasses a wide range of body shapes, ranging from simple two-dimensional primitive shapes to intricate three-dimensional bluff bodies. The paper presents a simplified concept to clarify the relationship between added mass for an accelerating body in a stationary fluid and the acceleration coefficient of a motionless object in an unsteady flow. This method benefits fluid-structure interaction studies, including seismic design, underwater systems, and multiphase flow modeling.