Trans RINA, Vol 157, Part A3, Intl J Maritime Eng, Jul-Sep 2015
length. The amplitude is a = 0.5 m, the propagation direction is β=180° (head sea).
In Figure 11 is given a sample of the intact ship motions (heave and pitch) in time domain, obtained from the simulation model, for the chosen wave. The wave profile is observed at the CG. The ship behavior in this condition shows a mean heave value above the initial draft, and a negative mean pitch, very close to zero; all this means that the ship is slightly over-immersed in the bow part and it could be mainly justified by considering the slender volume that characterizes this zone. Moreover from Figure 11 it can be noticed that the ship experiences the maximum over-immersion when the crest is located above the CG. At the same instant, instead, the pitch is presented close to zero.
Figure 10. Heave response comparison.
In both Figures 10 and 11 the continuous line represents the response amplitude operator (RAO) for heave and pitch motions, obtained by a linear potential code, while the discrete points represent the amplitude, of the respective motion responses, from the simulation model. They are made non-dimensional using the correspondent wave amplitudes used in running the computations. The wave amplitudes were chosen in order to obtain significant motions, avoiding the weather-tight deck of the ship to be underwater.
The differences between the linear and the non-linear
approach are more pronounced at lower frequencies, especially for the pitch (Figure 11). This is in accordance with the knowledge that at lower frequencies the non-linear Froude-Krylov forces prevail on the linear diffraction forces.
Assuming the same grounding scenario reported in the next section, the damaged ship behavior was simulated both in presence and in absence of wave. The time history of the flooding with no wave actions (see Table 4 for the final equilibrium) is compared to the
ship
flooding behavior in head seas: the developed method, discussed in section 2.1, was applied.
Figure 12. Ship grounding simulations. Figure 11. Pitch response comparison. 6. DAMAGED SHIP DYNAMIC BEHAVIOUR
The main results obtained from the numerical simulation for the ship in damaged scenarios, in longitudinal regular seas, are presented in this section. The wave chosen for the application is characterized by a frequency ɷ= 0.975 rad/s that leads to a wave length ʎ equal to the ship
A-158
In Figure 12 the results obtained by the numerical simulation, performed on this scenario, are presented. The dashed line represents the response for the transient stage of flooding in still water; as could be noticed from the details of Figure 13, the equilibrium condition is reached after around 95s. In introducing the wave effects on the flooding numerical simulation, it is possible to observe that the mean heave of the damaged ship seems to be above the draft time history with
©2015: The Royal Institution of Naval Architects
Page 1 |
Page 2 |
Page 3 |
Page 4 |
Page 5 |
Page 6 |
Page 7 |
Page 8 |
Page 9 |
Page 10 |
Page 11 |
Page 12 |
Page 13 |
Page 14 |
Page 15 |
Page 16 |
Page 17 |
Page 18 |
Page 19 |
Page 20 |
Page 21 |
Page 22 |
Page 23 |
Page 24 |
Page 25 |
Page 26 |
Page 27 |
Page 28 |
Page 29 |
Page 30 |
Page 31 |
Page 32 |
Page 33 |
Page 34 |
Page 35 |
Page 36 |
Page 37 |
Page 38 |
Page 39 |
Page 40 |
Page 41 |
Page 42 |
Page 43 |
Page 44 |
Page 45 |
Page 46 |
Page 47 |
Page 48 |
Page 49 |
Page 50 |
Page 51 |
Page 52 |
Page 53 |
Page 54 |
Page 55 |
Page 56 |
Page 57 |
Page 58 |
Page 59 |
Page 60 |
Page 61 |
Page 62 |
Page 63 |
Page 64 |
Page 65 |
Page 66 |
Page 67 |
Page 68 |
Page 69 |
Page 70 |
Page 71 |
Page 72 |
Page 73 |
Page 74 |
Page 75 |
Page 76