TY - RPRT

T1 - A Dynamic Model for Roll Motion of Ships Due to Flooding

T2 - Technical Report for the Damage Stability Modeling of the Safety of Passenger/RoRo Vessel Project

AU - Xia, Jinzhu

AU - Jensen, Jørgen Juncher

AU - Pedersen, Preben Terndrup

PY - 1997

Y1 - 1997

N2 - 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.

AB - 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.

M3 - Report

BT - A Dynamic Model for Roll Motion of Ships Due to Flooding

ER -