Can the water on deck influence the parametric roll of a FPSO? A numerical and experimental investigation

Abstract

Parametric roll and water on deck are investigated numerically and experimentally for a FPSO ship in head-sea regular waves in the zone of the first fundamental resonance. On the numerical side, a weakly-nonlinear potential seakeeping solver based on the weak-scatterer theory is coupled within a Domain-Decomposition (DD) strategy with a shallow-water approximation for water-shipping events and with a local analytical solution for bottom-slamming prediction. The comparison against the model tests confirmed the capability of the numerical method in predicting occurrence and features of parametric roll and water-on-deck phenomena. The solver has then been used to complement the physical analysis by examining the roll instability occurrence with a refined step of the calm-water roll natural frequency-to-excitation frequency ratio, ω4n0/ω, around to 0.5. It is confirmed that the water shipping features are qualitatively and quantitatively affected by the parametric roll: the flow onto the deck becomes asymmetric and the water-on-deck occurrence becomes periodic with the roll-natural period, the level of green-water induced pressures increases. In some cases water shipping is even directly induced by large roll. In return the green-water loads affect the parametric instability by changing (both increasing and decreasing) the duration of the transient phase. This has been measured in terms of the variation of the time, tmax, required to reach the largest peak in the roll envelope before occurrence of steady-state conditions. The water on deck mostly increases the steady-state roll amplitude, ξ4a, with an amount up to about seven degrees for the examined cases. Two scaling laws have been proposed for the variations of tmax and ξ4a involving a modified steepness ϵ=(2A−f)/λ, with A and λ the incident-wave amplitude and wavelength, respectively, and with f the ship mean freeboard. The scaling laws α1(δ1) and γ1(δ1), with α1=−(Δtmax/T)⋅ϵ, γ1=−10Δξ4a⋅ϵ, δ1=100(ω4n0/ω)2⋅ϵ and T the incident-wave period, appeared to be more suitable in the region where water shipping is more relevant for parametric roll. They are well approximated by polynomial curves which could be useful to estimate the variations of tmax and ξ4a due to water shipping for incident-wave parameters different from those examined here.