Mathematical modeling of free-flooding anti-roll tanks

Abstract

One way of stabilizing a ship is by anti-roll tanks. There are three kinds of anti-roll tanks: the free-surface, U-tube and free-flooding tanks. Of these the free-flooding anti-roll tank is the least known and applied. The reason is that the performance of these tanks is reduced due to a momentum drag penalty incurred at forward speeds. This performance penalty does not occur for offshore installation vessels in operation, which remain stationary or sail at very low forward speeds. An advantage of free-flooding tanks over U-tube and free-surface tanks is that they are easy to retrofit, because they do not require a considerable amount of space in the center part of the vessel, but can be built into the sides where, generally, plenty of space is available due to the broad beam of such vessels. Also, they can be closed off and emptied for transits. Free-flooding tanks are thus a viable option for the stabilization of offshore installation vessels. How effective are free-flooding tanks? The modeling of this kind of tanks is complex, because of the interaction of the tank fluid with the environment. The amount of water in the tanks varies continuously due to the inflow and outflow of water through the flooding ports. In the 80s of the last century the US Navy were looking to improve the motions of their aircraft carriers, whose roll motion behavior had deteriorated as a result of upgrades over the years of service. They developed a prediction model in the frequency domain based on linearized ship motion theory and a regular wave input, which includes several non-linear effects to closer approximate the actual behavior of the water in the free-flooding tanks. In this study, this prediction model is programmed into SCILAB (a numerical solution program) and the model is evaluated for a pipelaying vessel. The input for the model is the hydrodynamic database from a 3D diffraction program, in this case AQWA. The results show that free-flooding tanks are effective at reducing the roll motions of the ship for lift operations. Tuned tanks, where the tank transfer period is tuned to the ship natural frequency, perform better than untuned tanks, because for tuned tanks the tank moment lags the ship motion 90° at resonance frequency. To support the design of free-flooding tanks the influences of different parameters in the tank model are quantified. Also, an attempt is made to transform this model to time domain simulation in AQWA. The coupling of the tank, the ship motions and the fluid pressures is of high importance for the tank moment. Due to limitations in AQWA it is impossible to integrate the tank equation directly and fully with the ship motions and the fluid domain. To check the results from the AQWA simulation a simple time domain simulation was programmed in SCILAB based on the same assumptions as for frequency domain. The results from this simulation match the results from the frequency domain, because based on the same assumptions. It is questionable whether these assumptions still hold in time domain. Also, the motions during a time interval are not influenced by the motions before this interval in this simple time domain simulation. Consequently, the results of the time domain simulation have been found to be unreliable and time domain simulation must be addressed in a different way.