Head Sea Waves Research Articles

Numerical prediction of green water incidents

Green water loads on moored or sailing ships occur when an incoming wave significantly exceeds the freeboard and water runs onto the deck. In this paper, a Navier–Stokes solver with a free surface capturing scheme (i.e. the VOF model; Hirt and Nichols, 1981) is used to numerically model green water loads on a moored FPSO exposed to head sea waves. Two cases are investigated: first, green water on a fixed vessel has been analysed, where resulting waterheight on deck, and impact pressure on a deck mounted structure have been computed. These results have been compared to experimental data obtained by Greco (2001) and show very favourable agreement. Second, a full green water incident, including vessel motions has been modelled. In these computations, the vertical motion has been modelled by the use of transfer functions for heave and pitch, but the rotational contribution from the pitch motion has been neglected. The computed water height on deck has been compared to the experimental data obtained by Buchner (1995a) and it also shows very good agreement. The modelling in the second case was performed in both 2-D and 3-D with very similar results, which indicates that 3-D effects are not dominant.

Green Water Loading on a FPSO

Abstract Green Water Loading in the bow region of a Floating Production Storage and Offloading unit (FPSO) in head sea waves is studied by numerical means. A 2-D method satisfying the exact nonlinear free-surface conditions within potential-flow theory has been developed as a step towards a fully 3-D method. The flow is assumed 2-D in a plane containing the ship’s centerplane. The method is partly validated by model tests. The importance of environmental conditions, 3-D flow effects, ship motions, and hull parameters are summarized. The wave steepness of the incident waves causes important nonlinear effects. The local flow at the bow is, in general, important to account for. It has become popular to use a dam-breaking model to study the propagation of water on the deck. However, the numerical studies show the importance of accounting for the coupled flow between the deck and outside the ship. When the water is propagating on the deck, a suitable distance from the bow can be found from where shallow-water equations can be used. Impact between green water on deck and a vertical deck-house side in the bow area is studied in details. A similarity solution for impact between a wedge-formed water front and a vertical rigid wall is used. Simplified solutions for an impacting fluid wedge with small and large interior angles are developed, both to support the numerical computations and to provide simpler formulas of practical use. It is demonstrated how the local design of the deck house can reduce the slamming loads. The importance of hydroelasticity during the impact is discussed by using realistic structural dimensions of a deck house. This indicates that hydroelasticity is insignificant. On the contrary, first results from an ongoing experimental investigation document blunt impacts against the deck during the initial stage of water shipping, which deserve a dedicated hydroelastic analysis.

Bow Flow and Added Resistance of Slender Ships at High Froude Number and Low Wave Lengths

Flow around a slender ship bow at high Froude number and regular incident head sea waves is analyzed by matched asymptotic expansions. The near-field solution implies solving a two-dimensional Laplace equation with complete linear free-surface conditions. A solution technique with fundamental sources and dipoles is used. The solution technique is tested with good results for transient forced heave oscillation of a circular cylinder and for steady flow around a wedge. Comparisons with other numerical and experimental results for steady bow flow around a Wigley hull and a Series 60, Cb = 0.6 model show partly satisfactory results. The theoretical model for unsteady flow around a ship bow is used to calculate added resistance on a slender ship in high Froude number and incident regular head sea waves of low wave lengths. Experimental results for added resistance at low wave length for a cargo ship with Cb = 0.61 are not in complete agreement with the theoretical predictions.

On the Calculation of Wave Exciting Forces on Ship Translating in Head Sea Waves

The diffraction problem appeared in the ship-wave interaction problem is treated by making use of the slender body theory under the short wave assumption. A solution which is valid in the bow near field as well as in the midship near field is derived and it turns out to be able to descrive the 3-D effect of the interaction of incident waves with a ship hull. This solution is thougth to be the extention of Faltinsen's3) in the meaning that it is valid at the vicinity of bow and also the extention of Maruo's4) in the meaning that it can treat not only zero forward speed case but also forward speed case.The wave load distribution calculated by the present method shows strong x-dependance, which can easily be attributed to the cumulative effect of the slowly varying source density function which is a representation of the effect of the interaction between incident waves and ship hull.By use of Green's theorem, the wave load can be calculated by the asymptotic behavior of the solution for the generalized radiation problem in which the 2-D Helmholtz equation is the governing field equation.Some heuristic numerical results are presented for a ship with circular cross section.

Calculation of Added Resistance in Head Sea Waves by Means of a Simplified Formula

The formula for the theoretical prediction of the added resistance in head sea waves is simplified by the assumption that the frequency of encounter is not small.Computations of the added resistance for the Series 60 models by means of the simplified formula are compared with computation by the original formula and results of experiments.The results of the new formula show a considerable improvement in the agreement with the measured results.

On the Wave Pressure Acting on the Surface of an Elongated Body Fixed in Head Seas

A method of calculating the wave induced pressure on the surface of an elongated body fixed horizontally in head sea waves is presented. Numerical results are given for the case of semicircular cross section and compared with measured results. Comparison is made also with the calculations by other theories such as the strip method and Faltinsen's theory. A consistent agreement with the experiment is obtained by the present method.