Technical Report for the Damage Stability Modeling of the Safety of Passenger/RoRo Vessel Project
A dynamic model is presented of the roll motion of damaged RoRo vessels which couples the internal cross-flooding flow and the air action in the equalizing compartment. The cross flooding flow and the air motion are modelled by a modified Bernoulli equation, where artificial damping is introduced to avoid modal instability based on the original Bernoulli equation. The fluid action of the flooded water on the ship is expressed by its influence on the moment of inertia of the ship and the heeling moment, which is a couple created by the gravitational force of the flooded water and the change of buoyancy of the ship.Two limiting flooding cases are examined in the present analysis: The sudden ingress of a certain amount of water to the damaged compartment with no further water exchange between the sea and the flooded compartment during the roll motion, and the continuous ingress of water through a very large damage hole, implying that the water surface in the flooded compartment is always at the same level as the mean water surface.Ignoring roll motion, asymptotic and numerical solutions for the cross-flooding process and the associated air flow through the air pipe are obtained. A simple approximation to the water flow process is derived on the basis of a numerical simulation which takes into account the influence of the air compression in the equalizing compartment and improves the formula given in the existing rules.The coupled air, water and roll motion are solved numerically and presented for a 133.5 m long Ro-Ro ship. The variations of peak values of the flooding-induced roll angle with non-dimensional tank size, cross-flow duct area, area of air escape pipe etc. are systematically investigated. Simple exponential series expressions are obtained for the approximation of the maximum flooding-induced roll angle as functions of important ship parameters and flooding tank dimensions.