Practical Ship Hydrodynamics

136 Practical Ship Hydrodynamics
in the determination of the constants Ai and Bi resulting, e.g., in numerically
triggered oscillations. Pereira (1988) gives details of such a simulation method.
The simulation method has been extended considerably in the mean time and
can also consider simultaneously the flow of water through a damaged hull,
sloshing of water in the hull, or water on deck.
A far simpler and far faster approach is described, e.g., in Söding (1987).
Here only the strongly non-linear surge and roll motions are determined by a
direct solution of the equations of motion in the time-domain simulation. The
other four degrees of freedom are linearized and then treated similarly as the
incident waves, i.e. they are computed from RAOs in the time domain. This
is necessary to couple the four linear motions to the two non-linear motions.
(Roll motions are often simulated as independent from the other motions,
but this yields totally unrealistic results.) The restriction to surge and roll
much simplifies the computation, because the history effect for these degrees
of freedom is negligible. Extensive validation studies for this approach with
model tests gave excellent agreement for capsizing of damaged roro vessels
drifting without forward speed in transverse waves (Chang and Blume (1998)).
Simulations often aim to predict the average occurrence z⊲rA⊳ of incidents
where in a given period T a seakeeping response r⊲t⊳ exceeds a limit rA. Anew
incident is then counted when after a previous incident another zero crossing
of r occurred. The average occurrence is computed by multiple simulations
with the characteristic data, but other random phases jl for the superposition
of the seaway. Alternatively, the simulation time can be chosen as nT and the
number of occurrences can be divided by n. Both alternatives yield the same
results except for random fluctuations.
Often seldom (extremely unlikely) incidents are of interest which would
require simulation times of weeks to years to determine z⊲rA⊳ directly if the
occurrences are determined as described above. However, these incidents are
expected predominantly in the presence of one or several particularly high
waves. One can then reduce the required simulation time drastically by substituting
the real seaway of significant wave height Hreal by a seaway with larger
significant wave height Hsim. The periods of both seaways shall be the same.
The following relation between the incidents in the real seaway and in the
simulated seaway exists (Söding (1987)):
H 2 sim
H 2 real
D ln[zreal⊲rA⊳/z⊲0⊳] C 1.25
ln[zsim⊲rA⊳/z⊲0⊳] C 1.25
This equation is sufficiently accurate for zsim/z⊲0⊳