Practical Ship Hydrodynamics

196 Practical Ship Hydrodynamics
d = P − PV r . V2 / 2
8
7
6
5
4
3
2
1
0
h = 6 m
5 m
4 m
3 m
h = 2 m
1m
h = 8 m
10 m
12 m
14 m
16 m
18 m
20 m
h = 0 m
16 20 24 28 32 36
V (kn)
Figure 5.21 Cavitation numbers as a function of the ship speed V with the submersion h
(depth below water surface) as parameter
causes a complete separation of flow from the suction side. Otherwise its
influence on rudder forces is small (Kracht (1987)). Cavitation erosion is of
interest only if it occurs within the range of rudder angles υ Dš5° used for
course keeping. Evaluation of model experiments shows that the onset of
cavitation is indeed observed if the pressure determined by potential-flow
theory is smaller than the water vaporization pressure pv. pv lies typically
between 1% and 3% of the atmospheric pressure. It may therefore (not in
model tests, but for full-scale ships) simply be taken as zero. Thus, to test
for blade side cavitation in the design stage of ships, one may proceed as
follows:
– Determine the slipstream radius r C 1r and the inflow speed to the rudder
Vcorr from Fig. 5.19 or the corresponding formulae at about 80% of the
propeller tip radius above and below the propeller axis.
– Correct these values to obtain Vx and rx by (see above):
Vx D ⊲V 2 corr C t Ð V2 ⊳/Vcorr
rx D ⊲r C 1r⊳ Ð � Vcorr/Vx
– Because of non-uniform distribution of the slipstream velocity, add 12%
of V to obtain the maximum axial speed at the rudder:
Vmax D Vx C 0.12 Ð ⊲Vcorr VA⊳