Introduction

The method used for the calculation simplifies the flow as one-dimensional along the mean tank axis and assumes the incompressibility of the fluid [1, 2]. In general a transient flow is considered. The air flow above the fluid is important and is treated as well.

Due to these simplifications, no flow details such as breaking waves or flow separation can be considered. To capture these effects, much more time consuming methods would be needed (approximately more than 1000 times slower). The large amount of computing time makes these methods unattractive for the combination with seakeeping codes. The selected method uses a simple approach and saves computational time. Empirical stationary pressure drop factors describe the viscous effects. The fluid surface is assumed to be nearly perpendicular to the mean tank axis. The conservation equations are applied in integral form resulting in a finite volume method. The tank domain is subdivided with finite control volumes and the complete tank up to its top is modelled. The time is subdivided in time steps.

At both tank tops (tank ends) the pressure is given as boundary condition. This can be e.g. the ambient pressure if free flow through these ends is assumed. It is assumed that valves are fitted to the tank tops, which can be opened and closed by a control mechanism to regulate the air flow. Two types of valve control modes are considered: passive and active control.

The passive valve control mode avoids the sloshing of the fluid against the tank tops. For this purpose, the valve of the non-endangered tank side is closed. The air volume of the most empty tank side then acts as a gas spring and, therefore, the theory of an ideal gas is applied assuming isentropic behaviour. In this case the fluid flow is nearly suppressed. According to the pressure in the ”air buffer”, the pressure boundary condition at this tank end is set. At the endangered tank end, the pressure is set to ambient pressure. Even if the fluid in the tank is idealised as incompressible, the application of the pressure condition in the simulation results in a behaviour in which the air compressibility is taken into account. The valve closes if the fluid level is higher than a certain value below tank top.

The active valve control under certain flow conditions, close the valves, preventing the fluid flow and keeping it on the advantageous side. This can increase the damping at frequencies lower than the resonance frequency, see [1].