‐0.020‐0.0100.0000.0100.0200.0300.0400.0500.060‐40 ‐20 0 20 40X´Rudder angle [deg]CFD, Fr=0.260EFD, Fr=0.260CFD, Fr=0.201EFD, Fr=0.201CFD, Fr=0.156EFD, Fr=0.156Figure 8. Computed and measured non-dim X force for “static rudder”. ‐0.080‐0.060‐0.040‐0.0200.0000.0200.0400.0600.080‐40 ‐20 0 20 40Y´Rudder angle [deg]CFD, Fr=0.260EFD, Fr=0.260CFD, Fr=0.201EFD, Fr=0.201CFD, Fr=0.156EFD, Fr=0.156Figure 9. Computed and measured non-dim Y force for “static rudder”. For Y´ good agreement between EFD and CFD is also observed. Increased  rudder angle leads to increased Y-force which makes sense since the rudder lifts more at higher rudder angles. It is seen that the slope of the curves increases as the speed is reduced and the weak non-linearity occurs at the larger rudder angles.   N´ also shows increased slope of the curves as the speed is reduced and the weak non-linearity at the larger rudder angles. This behavior is expected as the yaw moment for the static rudder case to a large degree is caused by the rudder lift force. Again good agreement between EFD and CFD is observed.   Figure 11 to Figure 13 show the computed and measured non-dimensionalized forces and moments, X´,  Y´and  N´ as function of the drift angle for three different speeds. Again  X´ shows the effect of the constant RPM approach discussed above. Further, it can be noticed that the largest deviations occur at the lowest speed, which presumably is caused by the body-force propeller not being able to model the propeller flow in the case where the propeller loading is increasing. However, in spite of the difference, the CFD code generally predicts the force fairly well compared to the measurement, plus it is able to capture variation in X´ with the drift angle.    Figure 12 and Figure 13 show  Y´  and N´ for the three speeds. Compared to  the static rudder case it is here seen that the non-dimensionalization basically collapses the force and moment curves into one curve, which is often seen for the static drift force and moment. It is also seen that as the drift angle is increased the Y-force becomes non-linear. The yaw moment also shows non-linearity, but not as pronounced as the Y-force.  Further, it seems that the non-linearity in  N´ is more pronounced for lower speeds. Concerning the comparison between model test and CFD results, it appears the computation agrees well with the measurement.         The final set of results to be shown covers the static drift and rudder results. Figure 14 to Figure 16 show the forces and moments as function of the rudder angle for the two negative drift angles  β=-4° and  β=-12°, while Figure 17 to Figure 19 show the forces and moments as function of the rudder angle for two corresponding positive drift angles β=4° and β=12°.     Only the two lower speeds are covered in this case. The reason is that the test program reflects the conditions the ship will experience during maneuvering and typically the combined drift and rudder angle condition occurs later in the maneuver, where the ship is experiencing a speed loss.  For all the forces and moments the overall agreement between the measured and computed PMM results is fairly good. Though, it generally seems that it is most difficult to capture the measured data at the lowest speed. One of the main reasons for this is believed to be the propeller model. The rudder load is strongly dependent of the flow over the propeller since it is located in the propeller slip stream. On the other hand the propeller flow is strongly dependent of the wake field behind the ship as this generates the propeller inflow field. The simplified propeller does not really reflect the difference in propeller load distribution over the disk occurring from the change in the wake field that occurs during drift conditions and reduced speed due to the  prescribed body-force approach. If the load distribution over the propeller disk is not correct, the distribution of the propeller slipstream velocity that hits the rudder will not be correct, which again means that the rudder performance will be influenced. This again will influence X´, Y´and N´ and probably lead to larger deviations between EFD and CFD, particularly for lower speeds and large drift angles, which also change the wake flow significantly.      angles. Based on the above comparison the idea of generating PMM data on the basis of CFD looks promising. However, the question is if the small differences between EFD and CFD will influence the final maneuvers after applying the data as input to the maneuvering simulator. This is investigated in the following sections where simulations with both EFD and CFD data will be compared.   Mathematical model applied for the manoeuvring simulations   A mathematical model was generated to determine a specific set of X, Y and N derivative with the most optimal fit to the measured forces of the KCS.  The analysis was performed in a classic way where initially the linear Y  and N coefficients,  Y’v and  N’v were determined from the pure drift test at nominal speed with drift angle in the linear range between +/-4 degrees. These two coefficients were then fixed and included in the following general static analysis where the total matrix of static test data is applied to solve the total matrix of static coefficients, i.e. the remaining static derivatives are determined in a single combined analysis. The two added mass coefficients, v Y '   and v N '  was determined based on a special pure sway analysis which comprised the time series from all the dynamic pure sway tests.    The general dynamic analysis was performed similar to the static analysis with a combined analysis for all of the dynamic test types. In the dynamic analysis all the static coefficients were fixed to the values adopted from the static analysis.  The final coefficient formulation applied for the simulation of manoeuvres were output from the dynamic analysis (including the static analysis) supplemented with the two added mass coefficients from the pure sway analysis and an empirical value for the added mass coefficient ܺԢ௨, which was calculated as 6 percent of the non-dimensional mass of the vessel. I.e. based on the model tests the final coefficient formulation becomes:  ' u X'   r' X'    r' X'     r' X'   v' X'   v' X'      v' X'     u' X'   u' X' X'    X'     X'     X'     r' v' X'     r' X    r' X'   v' X'     v' X'     u' X'     u' X'     X'X'' u2r'2r' r' r'2v'2v' v'v'2u' u'42 2r' v'2r' r'r'2v' v' v'2u' u' u' o'                                   (28)  ' r Y'     ' v Y'  r' v' Y'     r' Y'   | r' | Y'     r' Y'    r' Y'     v' Y'   | v' | Y'     v' Y'  v' Y'   u' Y'     u' Y'     u' Y'  Y'     Y'     Y'     r' v' Y'     | r' | v' Y'     r' v' Y'   r' | v' | Y'     r' Y'| r' | r' Y'     r' Y'     r' Y'     v' u' Y v' Y'    | v' | v' Y'     v' Y'     v' Y'     u' Y'     Y'Y'' r ' vr' v'2r' | r' |2r' r'r'2v' | v' |2v' v'v'3u'2u' u'3 2 2r' r' v'| r' | v'2r' v' v' r' | v' |3r' r' r'| r' | r'2r' r' r' v' u'3v' v' v'| v' | v'2v' v' v' u' o                                                 (29)  ' r N'     ' v N'  r' v' N'     r' N'   | r' | N'     r' N'    r' N'     v' N'   | v' | N'     v' N'  v' N'   u' N'     u' N'     u' N'  N'     N'     N'     r' v' N'     | r' | v' N'     r' v' N'   r' | v' | N'     r' N'| r' | r' N'     r' N'     r' N'     v' u' N v' N'    | v' | v' N'     v' N'     v' N'     u' N'     N'N'' r ' vr' v'2r' | r' |2r' r'r'2v' | v' |2v' v'v'3u'2u' u'3 2 2r' r' v'| r' | v'2r' v' v' r' | v' |3r' r' r'| r' | r'2r' r' r' v' u'3v' v' v'| v' | v'2v' v' v' u' o                                                 (30)  In case of a 4DOF model  a corresponding set of derivatives for the roll (K) moment would have been generated. However, this has been omitted due to the focus on 3DOF.    Since the vessel is a single screw ship it possesses inherent asymmetry regarding port starboard manoeuvring ability. This asymmetry is reflected in a number of X, Y and N coefficients. The asymmetry is partly due to the propeller side force and partly due to unavoidable asymmetry in the physical model used for the model tests. To account for the scewness of the model, the Y and N forces acting on the model in a bare hull resistance test at drift angle zero is subtracted from  Gothenburg, Sweden, 26-31 August 2012  those measured in the PMM series with the propeller working.  The generated model is strictly speaking only applicable for the given approach speed. In case of different approach speeds the model ought to be re-evaluated to find the corresponding coefficients.  Test matrix reduction and simulation results based on EFD   For standard PMM tests a full standard test program (STP) similar to the programme presented in  Table 2 is usually applied. When running just tank tests there has been no significant motivation for minimizing the test programme since the main costs are associated with the initial setup of the model and there has rather been a tendency to utilize the length of the entire towing tank to pick up as many points as possible. This approach is suitable for tank tests, but in connection with numerical model tests where the calculation time is the most expensive “cost”, there is a need to minimize the number of points/calculations. To evaluate a minimum test programme (MTP), a set of simulated manoeuvres based on MTP were compared to similar manoeuvres based on the STP. To establish whether the MTP was acceptable or not a set of criteria or tolerances were defined. If the initially tested MTP did not meet the defined tolerances the number of measuring points was to be increased until the limits were fulfilled.  The predefined acceptable tolerances between STP and MTP are presented in Table 10.    FD生成的PMM数据在初步设计阶段进行评估英文文献和中文翻译(6):http://www.youerw.com/fanyi/lunwen_63925.html