Two implementations of simplified methods used in the motion analysis of floating bodies that account for the presence of internal partially filled tanks are discussed here-in. These simplified methods do not explicitly model the internal tanks. These two methods are based on either a virtual rise of the center of gravity or by the inclusion of an additional stiffness matrix used in the solution of the equations of motion.
This paper presents the implementations of the two simplified methods and compares the evaluated motion responses to a method whereby the internal tanks are modelled using Boundary Element Method (BEM), and also compares against model test results.
A fundamental input in hydrodynamic loads and ship motions evaluation is the accurate definition of the loading condition of the ship. For ships with large, partially filled tanks, the effects of the sloshing of the fluid contents of tanks can be included in the motion analysis via explicit modelling of the tanks, and extension of the diffraction problem to these tanks. In this case the problem becomes a seakeeping-sloshing coupled analysis. This approach is more accurate than the simplified methods for modelling the internal tank effects upon ship motions analysis, however it requires additional modelling effort and greater complexity.
Alternatively, if internal tanks are not explicitly modelled, two simplified methods can be used to account for the effect of internal tanks in a more approximate manner. The two motion analysis methods consist of:
i. Either applying a destabilizing stiffness matrix to account for the free surface effects but consider the Vertical Centre of Gravity (VCG) of the loaded condition as if the cargo were frozen, or "solid" position. This method is here-in called the Stiffness Correction method.
ii. Or modelling a virtual rise of the VCG of the loaded vessel equivalent to the free-surface correction; effectively modelling the VCG in its "fluid" position. This method is here-in called the VCG Fluid method.
The difference between the two methods is further explained in the following sections. In the Stiffness Correction method, the inertia mass matrix of the loaded condition is assumed with its principal reference frame to pass through the solid VCG, but a correction term is applied to the hydrostatic stiffness matrix to account for the free-surface effects of the tanks
