The mechanics of variable mass systems applied to the added mass concept of a moving cylinder in water

Abstract

This paper constructs a physics-based surrogate mathematical model for the motion of a cylinder surrounded by a fluid under a distinct point of view: the mechanics of variable mass systems. Particularly, the concept of added mass is addressed. First, we introduce a 1 DoF problem, consisting of an equivalent virtual particle, free to oscillate in one direction, whose mass is let to depend on its position and velocity. The resulting kinetic energy models that of the whole system, solid and surrounding fluid. A general formulation for the equation of motion is then proposed, by applying the Extended Lagrange Equations for variable mass systems, from which the surrogate model is derived. We take as first case study the classic vortex-induced vibration (VIV) phenomenon of a cylinder mounted on an elastic base. Then, we assume the added mass as a polynomial function on position and velocity. The coefficients of this polynomial expansion are estimated by regression, where we minimize the residual between the model’s response and external data, herein coming from computational fluid dynamics (CFD) simulations. The results are rewarding and the well-known behavior of the added mass as a function of the reduced velocity observed in the technical literature, from experiments and from CFD simulations, is consistently recovered.