Viscous effects on the added mass and damping forces during free heave decay of a floating cylinder with a hemispherical bottom

Abstract

This paper presents an analysis of viscous effects on the added mass and damping forces during free heave decay of a cylinder with a hemispherical bottom. Results from unsteady Reynolds-averaged Navier–Stokes (URANS) simulations and linear potential-flow solutions are compared. Expressions for the cycle-averaged viscous added mass and damping coefficients are derived based on first-order Fourier analysis of the URANS results. Viscous effects are extracted by comparing the URANS results and linear potential-flow solutions, as nonlinear potential-flow effects in this case are demonstrated to be negligible. It is observed that viscous effects on the added mass coefficient are minor during heave decay, such that the linear potential-flow model can predict the value of the added mass coefficient to within 5% deviations. In contrast, the viscous damping coefficient exhibits strong cycle-dependent variations. A parametric study of the effects of initial displacement, cylinder diameter and draft shows that viscous damping forces can play an important role when the cylinder has a relatively small diameter and large draft. Further, the damping coefficient is transformed to the nondimensional drag force coefficient, and its dependence on the Reynolds number Re is investigated, for Keulegan–Carpenter numbers in the range KC= 1.5–2.5. It is found that the drag force coefficient is likely to be unrelated to Re and KC during the first cycle. From the second cycle to the fourth cycle, the drag force coefficient rapidly decreases with increasing Re, up to Re≈3×105.