Practical Ship Hydrodynamics

166 Practical Ship Hydrodynamics
of the ship. Installed power P, cross-section area of the pipe A, andflow
velocity v in the jet thruster are related by:
T D Ð A Ð v 2
P D 1 Ð 1
2 Av2
is here the efficiency of the thruster propeller. These equations yield:
P v
D
T 2
T
D v2
A
D 0.8andv D 11 m/s yield typical relations: approximately 120 kN/m 2 thrust
per thruster cross-section area and 7 kW power per kN thrust.
With increasing speed, jet thrusters become less effective and rudders
become more effective. The reason is that the jet is bent backwards and may
reattach to the ship hull. The thrust is then partially compensated by an opposite
suction force. This effect may be reduced by installing a second (passive) pipe
without a propeller downstream of the thruster (Brix (1993)).
5.2.8 CFD for ship manoeuvring
For most ships, the linear system of equations determining the drift and yaw
velocity in steady turning motion is nearly singular. This produces large relative
errors in the predicted steady turning rate especially for small rudder angles
and turning rates. For large rudder angle and turning rate, non-linear forces
alleviate these problems somewhat. But non-linear hull forces depend crucially
on the cross-flow resistance or the direction of the longitudinal vortices, i.e.
on quantities which are determined empirically and which vary widely. In
addition, extreme rudder forces depend strongly on the rudder stall angle
which – for a rudder behind the hull and propeller – requires at least twodimensional
RANSE simulations. Thus large errors are frequently made in
predicting both the ship’s path in hard manoeuvres and the course-keeping
qualities. (The prediction of the full ship is fortunately easier as at the higher
Reynolds numbers stall rarely occurs). In spite of that, published comparisons
between predictions and measurements almost always indicate excellent accuracy.
A notable exception is Söding (1993a). The difference is that Söding
avoids all information which would not be available had the respective model
not been tested previously. The typical very good agreement published by
others is then suspected to be either chosen as best results from a larger set of
predictions or due to empirical corrections of the calculation method based on
experiments which include the ship used for demonstrating the attained accuracy.
Naturally, these tricks are not possible for a practical prediction where
no previous test results for the ship design can be used. Thus the accuracy of
manoeuvring predictions is still unsatisfactory, but differences between alternative
designs and totally unacceptable designs may be easily detected using
the available methods for manoeuvring prediction. With appropriate validation,
it may also be possible to predict full-scale ship motions with sufficient