4.2 Case of Numerical Simulation

　

 The parameters selected in numerical simulation are shown in the Table 3. Considered parameters are the wave length, the wave height, the initial encounter angle of wave, the angle of rudder deflection, the rudder area and the relative position of the ship to a wave crest line at the time the rudder is steered. As described in section 2.3, relatively long wave length is considered.

 In this study, we investigate the rolling oscillation during a ship is turning to the right side (the starboard side) with the assumption that the rudder angle is kept constant after it is deflected and the propeller revolution is kept constant. The propeller thrust is estimated using the static curve expressing thrust versus advancing speed. In this estimation, instantaneous inflow velocity to the propeller is considered as advancing speed.

 In Table 3, ψini means the heading angle on Earth Fixed Axes at the time that the rudder starts to be steered. 'ψini =90 deg' means that a ship starts to turn in the beam sea toward the head sea, on the contrary 'ψini=270 deg' means it turns from the beam sea toward the following sea. The rudder rotates from neutral position to δmax in the velocity 10 deg/sec, and is kept as the constant angle during the ship is turning. All waves, which are employed in this study, are the regular high waves and the highest steepness is selected as the estimation accuracy is hold considering the validation results described in section 4.1. In this simulation it must be noticed that the wave height becomes high as the wave length becomes long.

　

4.3 Results and Evaluation

　

 At first, the numerical results of heading angle and rolling oscillation with ship's turning are shown in Fig.6 as time histories in actual ship scale. From the left side, three wave conditions of λ/L=1, λ/L=2 and λ/L=3 are arranged. The solid line indicates the heading angle. The 0 degree on vertical scale means the condition that the ship is located in following sea, and the normal distance between a broken curve and a solid line indicates the rolling amplitude.

 The natural rolling period of this ship is about 5.8 seconds, and this figure shows the transient oscillation, whose period corresponds roughly to the natural period of rolling, during the ship is turning. As we know generally, the wave encounter angle in which the rolling amplitude increasing varies with the condition of wave length. On condition of λ/L=1, the rolling amplitude tends to grow large in the range of the wave encounter angle from beam sea to head sea. On the other hand, in λ/L=2 or 3 conditions, it tends to grow large in the range from beam sea to following sea. As described later, in the case the ship turns from beam sea condition, there is a difference in the rolling oscillation between turning in following sea and in head sea, Fig.6 shows such the remarkable difference on condition of λ/L=3.

 To make clear description for such a complicated rolling motion, we investigated the significant correlations between the adopted parameters and the rolling oscillation on basis of numerical results. Some typical examples that express a remarkable tendency about the rolling motion with turning maneuver are shown below. Especially we pay attention to the motion during 180 degrees turning from the initial heading angle in this study.

　

　

　

　

　

- The effect of the wave condition;

 The upper figure of Fig.7 shows the track of ship's center of gravity with the rolling amplitude and the encounter wave amplitude during the ship is turning in waves. In addition, the ship locations at intervals of 10 seconds are drawn on it. The amplitude of the rolling and the encounter wave are expressed as the normal distance from the line of ship's track. The lower each four graphs show the time histories of, from the top, heading, rolling, encounter wave amplitude and period.

 The wave condition of case (7-a) is λ/L=1 and that of case (7-b) is λ/L=2. In both cases, the ship starts to steer in following waves whose H/λ is 1/20. The wave height of Case (7-a) is 1.15m that of Case (7-b) is 2.30m. As can be seen in the Fig.4, rolling motion is one kind of narrow-band-pass filter around natural period, so the rolling motion become large only when the encounter period become close to the natural frequency of roll. This characteristics can be clearly recognized in Case (7-a), and Case (7-b), whose λ/L is different. In Case (7-b), the drift force due to wave is greater than in Case (7-a), as a result the large difference in the track between these cases is shown.