Port engine 1940 RPM, starboard 600RPM, no jet deflection.
Fig.11 Speed change at acceleration.
30° in the uniform current (velocity 1.5 m/s, direction 60°).
30° turning in waves (wave length 15 m, wave height 1 m, wave direction 90°).
5.2 Sea Trial Data
Table 2 Overshoot angles of 30° zig-zag test (engine RPM 1940 and 1000)
|Overshoot angle No.
||Engine RPM 1940/1940
||Engine RPM 1000/1000
Table 3 Turning
Table 4 Stopping Trial (engine RPM both at 1940, throttle back to idle and into reverse at 1600)
||Distance to Stop
5.3 Analyze and Discussion
1) Compared with the sea trial data, the accuracy of the simulation results are generally acceptable for engineering application, which indicates that it is successful to replace the waterjet propulsions by the rotatable propellers and to adjust some hydrodynamic derivatives at different speeds.
2) Fig.5 shows that in 30° zig-zag test with engine RPM at 1940 the first overshoot angle is larger than the later ones, which is conform with the sea trial data. The comparison between Fig.5 and Fig.6 indicates that the overshoot angles are usually larger at higher engine RPM.
3) From Fig.8 and Fig.9, it can be seen that the turning circle is smaller at higher RPM under the same deflection. The reason may lie in the fact that side thrust force is larger, although the ship is approaching at higher speed. As shown in Fig. 10, even without jet deflection, the differences between the thrust of two jets can provide considerable manoeuvring force as expected.
4) The decrease of ship speed is acute during the initial turning stage at full speed. This decrease reaches up to 40% of the approaching speed, while the lateral speed increase amounts to 25% of the speed, and the non-dimensional value of yaw rate 0.6 during stable turning stage. Compared with the experimental results presented in Reference , the changes in speed and yaw rate look quite similar in trend. On the other hand, traced back to the deviation of turning diameter between simulation result and the sea trial data shown in Fig.8 and Table 3, r = 6.0 may be a bit smaller than that should be.
5) As shown in Table 4, the stopping distances both simulated and measured are no more than 1.6L, and the time less than 15 seconds, which demonstrates that the reverse thrust plays the most important role in the braking. On the other hand, as shown in Fig. 11, the speed increase at acceleration only takes about 50 seconds to get full speed. Consequently, it is safe to say that waterjet propelled catamaran is excellent in the accelerating and braking.
6) Because the sea trial was conducted under the condition of calm water and no wind, the simulation results with environmental effects are partly given without comparison.
This paper presents a mathematical model of manoeuvring motion for waterjet propelled catamaran, where rotatable propellers are substituted for the waterjet and the hydrodynamic derivatives estimated and amended in term of the speed. In addition, environmental effects including wind, wave, current and water depth are taken into account and processed in the conventional way.
The simulation results of ship motion have been validated by a proper comparison with sea trial data and the following conclusion may be drawn.
1) From the viewpoint of engineering, the proposed mathematical model is satisfactory and practical.
2) The equivalence of propeller for waterjet propulsion is effective and practical.
3) The hydrodynamic derivatives amended according to speed are reasonable.
4) In order to get better simulation results, it is necessary to find better expressions for the hydrodynamic derivatives and the waterjet characteristics. In addition, a 4 DOF model is also requested.
The work presented in this paper is financially supported by the Ministry of Education of China and the National Natural Science Foundation of China under the Grant No.10272085.
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Junmin Mou: Ph.D. course student in Wuhan University of Technology, China. His previous research experience includes ship maneuvering simulation and the safety of navigation.
Zaojian Zou: Prof. Dr-Ing., is Head of the Institute of CFD in Ship and Ocean Engineering, Wuhan University of Technology, China. His research interest includes prediction of ship maneuverability, calculation of hydrodynamic forces on maneuvering ships and CFD in ship design.
Xiaotu Zhang: Postdoctor at State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, China. His previous research experience includes ship maneuvering simulation and CFD in ship and ocean engineering.