an investigation into the numerical simulation of green water

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dimensional flow onto a deck is studied, without ship motions. The present ... theoretical dam breaking problem, Stoker (1957), see Figure 1. Breaking wave type ...
AN INVESTIGATION INTO THE NUMERICAL SIMULATION OF GREEN WATER B. Buchner and J.L. Cozijn Maritime Research Institute Netherlands (MARÏN) Offshore Research Department P.O. Box 28 6700 AA Wageningen The Netherlands

ABSTRACT Naval ships as well as floating offshore units can suffer serious damage due to green water loading. In recent model test research at MARIN the physical behaviour of the shipping of green water has been studied. The non-linear relative wave motion, the complex flow onto the deck and the impact on deck structures were investigated. In the present pilot study an investigation is made into the numerical time domain simulation of the shipping of green water. A fully non-linear boundary integral method is used. As a fïrst step a two dimensional flow onto a deck is studied, without ship motions. The present numerical model is capable of simulating the shipping of green water on a two dimensional conflguration. Some results from calculations are presented. Results from two dimensional model tests justify the simplifïcations made in the present model. However, a number of numerical problems arise, which are also treated in this paper.

KEYWORDS rtoating Production Storage and Offloading units, green water loading, numerical time domain simulation, model testing, non-linear waves

INTRODUCTION Damage to superstructures, hatches and decks of ships due to green water loading is still a common occurrence. For naval vessels, such as frigates, green water affects their performance in terms of operability considerably, Buchner (September 1995). But also for turret moored Floating (Production) Storage and Offloading (FPSO) units, green water impact loading has become an important factor in the design, Buchner (May 1995). Due to the weathervaning character of turret moored systems the bow of an F(P)SO is always exposed to the waves. The green water can cause damage to the sensitive equipment at the bow, such as the fluid swivel, piping, turret structure and chemical stores. Recent experience with F(P)SOs at the North Sea confirmed that green water loading can cause serious damage in the bow region. This can result in repairs and downtime of the field. Although green water is an important design aspect, there is little known about its complex and non-linear phenomena. In recent years MARIN carried out extensive research on the subject of green water and F(P)SOs

based on model tests. The research focused on the observation and description of the occurring phenomena, resulting in the conclusion that green water occurrence and loading cannot be predicted with present day prediction methods. The related ship motions, relative wave motions and drift forces are considerable nonlinear in wave heights associated with the survival conditions of F(P)SOs in harsh environments, Buchner (May 1996). Also design aspects were investigated, such as the effect of the bow shape and the efficiency of protecting breakwaters, Buchner (May 1995). The present paper starts with an overview of the main physics of the green water problem, using the results of earlier research. Using the experience from a pilot study the paper then presents the modelling of the complex green water phenomena with a non-linear boundary integral method, Cozijn (November 1995), Cozijn (March 1996). Two dimensional simulations are presented and compared with model tests in similar conditions. The complexity of the use of this type of program for the green water problem is increased due to the fact that the non-linearities are very strong and due to large discontinuities at the boundary (such as the deck edge). Therefore numerical problems are idenüfied and discussed in the paper.

THE PHYSICS OF GREEN WATER Flow onto the Deck Uhe flow of the water onto the deck was studied in detail in earlier research, Buchner (May 1995), Buchner (September 1995). Figure 1 shows a typical contour of the wave with time steps of 0.3 seconds. The following behaviour can be observed: When the pitch angle is at its maximum an almost vertical wall of water is present in front of the bow. The horizontal velocity of this wall of water is almost zero. The vertical wall of water translates onto the deck and starts to be considerably curved. This gives the impression that it intends to break. However, due to the high quasi-static pressure at deck level the water close to the deck starts to accelerate and prevents actual breaking. Finally a high velocity jet shoots over the deck.

ater

surface

y=0

Figure 1 : Wave contour of water flowing onto deck of a FPSO (left) and the theoretical dam breaking problem (right) The best resemblance between the flow of green water onto the deck and another phenomenon is the theoretical dam breaking problem, Stoker (1957), see Figure 1. Breaking wave type behaviour onto the deck is not observed.

Water Behaviour on the Deck As soon as the water is on the deck, it behaves like a shallow water wave as a result of gravity, the pitch angle of the ship and the vertical acceleration of the deck. Figure 2 shows a typical contour of the water front over the deck with time steps of 0.3 seconds for two different wave lengths. In Figure 2 the following behaviour can be observed: At the most forward part of the bow the water has a velocity in the longitudinal direction. At the side of the bow a transverse component towards the middle of the deck plays a role. The combined flow results in a high water 'longue' which flows with a high velocity aft along the middle of the deck. Velocities of 15-30 m/s are observed. The high velocity flow along the middle of the deck results in a concentrated loading in the middle of the structure on the deck.

Figure 2 : Flow of the wave front over the deck of a FPSO for regular waves of 11.2 s (above) and 12.9 s (below) ) h e pressure of the green water on the deck can be significantly higher than the static water head. For a frigate with forward speed dynamic pressures are found of even 15 times the static water pressure. A correction for the vertical acceleration of the deck is not sufficiënt to explain the impulsive peak loads. It was found that this impulsive loading is due to the rate of change of water height on deck at the moment the deck has a vertical velocity, Buchner (September 1995). When the water height at a certain point increases rapidly at the moment that the deck has a vertical velocity, large pressure peaks can occur. Taking into account the acceleration of gravity with a pitch inclination angle 6, it was shown that the complete pressure on the deck can be expressed as:

P = P(—)w + p(g cosö + — )h ot ot

(1)

Impact at the Structure At the moment that the green water reaches a structure on the deck, the water flow changes its direction 90 degrees and the flow shoots high up in the air. Study of the impact in previous research showed that the load of the water at the structure is not due to a solid impact but due to a jet with a (rapidly) increasing height. The load may therefore be seen as a sequence of quasi-stationary loads due to the impinging jet of an increasing height h, see Buchner (September 1995). This is a case of classical fluid dynamics. For each time step in the initial stage of the impact the incoming momentum of the water flow is destroyed by the impulse of the structure on the fluid. Based upon the assumption of a constant velocity U of the incoming water flow in the initial stage of the impact and the shallow water assumption of a constant velocity over the full height h, it is assumed that the peak force per metre breadth can now be expressed as the rate of change of linear momentum at the moment the maximum water height h max at the deck reaches the structure with a horizontal velocity U. This can be expressed as:

* W = P * W U2

(2)

ÖBJECTIVES AND METHOD OF THE PRESENT STUDY Until now the research was focused on physical model tests and the description of the physics of green water. Based on the output of this research it was decided to investigate the possibilities for the numerical modelling of the green water problem. The objective of this study was to determine whether numerical simulation can be used as a tooi for the prediction of the shipping of green water. If this is the case, second aim of the study is tó identify problems which need to be solved before this type of methods can be used as a reliable tooi. This paper presents the results of a pilot study, which is reported in more detail in Cozijn (September 1995) and Cozijn (May 1996). In the presented study use was made of a non-linear boundary integral method, van Daalen (1993), Romate (1989). The green water problem was simplified to a two dimensional problem, representing the typical situation along the longitudinal axis of a full snip without ship motions or forward speed. Also the limited draft of the ship huil is neglected. The result, presented in Figure 3, is a numerical wave tank. On one side a flap type wave generator can be found and on the opposite side a fixed solid wall with a deck structure, representing the ship's huil and deck geometry. This configuration is typical for the calculations in the present paper. The justification of this simplification will be discussed in the section on the two-dimensional model ^>t$ performed at Delft University of Technology. Free Water Surface

7

I

Fixed Solid Boundary

S Wave Maker B Figure 3 : Two dimensional model for the shipping of green water

In the paper the following aspects will now be highlighted: - The numerical model of the shipping of green water - The two dimensional model tests - The first results of the numerical model - Possible future developments

NUMERICAL MODEL OF THE SHIPPING OF GREEN WATER Boundary Integral Equation For the present study the computer program TIPHYS-2D is used as a basis, see van Daalen (1993) and Romate (1989). Based on the assumption of an ideal fluid in a rotation-free flow field this program solves Laplace's equation for the velocity potential