WAMIT-MOSES Hydrodynamic Analysis Comparison Study. JRME, July 2000

Transcription

1 - Hydrodynamic Analysis Comparison Study - Hydrodynamic Analysis Comparison Study JRME, Prepared by Hull Engineering Department J. Ray McDermott Engineering, LLC 1

2 - Hydrodynamic Analysis Comparison Study Summary Table of Contents 1. Introduction Test Models Results and Discussion References...3 List of Tables TABLE 2.1 GEOMETRY AND NUMBER OF PANELS... 5 TABLE 3.1 NORMALIZATION... 8 List of Figures FIGURE 2.1 SIMPLE BOX... 5 FIGURE 2.3 GENERAL SHIP FORM... 6 FIGURE 2.4 TLP... 7 FIGURE 2.5 SEMI-SUBMERSIBLE (MOB)... 7 FIGURE 3.1 ADDED MASS COEFFICIENTS FOR BOX... 1 FIGURE 3.2 DAMPING COEFFICIENTS FOR BOX FIGURE 3.3 WAVE EXCITING FORCES AND MOMENTS FOR BOX FIGURE 3.4 MOTION FOR BOX FIGURE 3.5 ADDED MASS COEFFICIENTS FOR CYLINDER FIGURE 3.6 DAMPING COEFFICIENTS FOR CYLINDER FIGURE 3.7 WAVE EXCITING FORCES AND MOMENTS FOR CYLINDER FIGURE 3.8 MOTION FOR CYLINDER FIGURE 3.9 ADDED MASS COEFFICIENTS FOR SHIP FIGURE 3.1 DAMPING COEFFICIENTS FOR SHIP FIGURE 3.11 WAVE EXCITING FORCES AND MOMENTS FOR SHIP... 2 FIGURE 3.12 MOTION FOR SHIP FIGURE 3.13 ADDED MASS COEFFICIENTS FOR TLP FIGURE 3.14 DAMPING COEFFICIENTS FOR TLP FIGURE 3.15 WAVE EXCITING FORCES AND MOMENTS FOR TLP FIGURE 3.16 MOTION FOR TLP FIGURE 3.17 ADDED MASS COEFFICIENTS FOR MOB FIGURE 3.18 DAMPING COEFFICIENTS FOR MOB FIGURE 3.19 WAVE EXCITING FORCES AND MOMENTS FOR MOB FIGURE 3.2 MOTION FOR MOB J. Ray McDermott Engineering, LLC 2

3 - Hydrodynamic Analysis Comparison Study Summary The global motion analysis and related installation procedures are very important tasks for floating offshore platforms. As new deep-water oil and gas production systems such as a SPAR, FPSO and TLP are introduced these tasks have become more important since the performance of these floating platforms might be decided by them. For the global motion analysis is the most widely used and well-proven 3-D diffraction and radiation computer program in the frequency domain. For the combined work such as a global motion analysis, installation simulation and fatigue analysis may be the most popular computer program in this area. Since has the same 3-D diffraction and radiation computer module one may use it as the tool for the global motion analysis. However, it may be necessary to examine the software performance before applying it to the floating production platforms. In this study the hydrodynamic analysis using and were carried out to investigate the performance of the two computer programs. Five models which can represent most of the floating platforms currently installed or under development were selected and the results were compared for a wide range of wave periods and wave heading angles. The mathematical formulation and theoretical background for the two computer programs can be found in Ref [1] and Ref [2] or and J. Ray McDermott Engineering, LLC 3

4 - Hydrodynamic Analysis Comparison Study 1. Introduction The use of to analyze the global motion and related installation procedures for floating platforms has increased since installation engineering and related work has become more complicated as new hull forms are introduced. The object of this study is to compare the hydrodynamic analysis results from and. is the most widely used 3-D computer program for the diffraction and radiation problem and is a well-proven computer program. also has the same capability and since both programs use conventional 3-D constant panel method and mathematical formulation one should have the same results. However, results have never been systematically compared with results. In order to compare the results one must choose various offshore floating structures and a wide range of wave periods. Different wave heading angles should also be considered to investigate the performance of both programs. In this study two simple geometries (rectangular box and vertical cylinder) and three offshore floating structures (ship, TLP, semi-submersible) are chosen with the proper number of panels. These five models can represent or simulate most offshore floating structures currently installed or under development such as a FPSO, SPAR, TLP and Semi-submersible. Using and, added mass and damping coefficients, wave exciting forces and moments and motions were calculated for the wide range of wave periods and heading angles. The version of each program used in this study was 5.4PC and J. Ray McDermott Engineering, LLC 4

5 - Hydrodynamic Analysis Comparison Study 2. Test Models In order to compare the effectiveness of the programs, five models were selected to cover most of the floating structures used for oil and gas production. By selecting the rectangular box, vertical cylinder, general ship form, TLP and semi-submersible type of structures one can examine the performance of the two computer programs for most floating structures currently installed or under development. For example, the box can represent a FPSO or Tanker that has a large block coefficient and the vertical cylinder can be regarded as a simplified SPAR platform. The TLP and MOB can represent a typical semi-submersible. The following table shows the basic dimension and characteristics of the five selected models, which were used in the numerical calculations. TYPE Length (meter) Beam or Diameter (meter) Draft (meter) Displacement (Metric- Tons) Center of Gravity (KG) Number of Panels Box , Cylinder , Ship , TLP , MOB , Table 2.1 Geometry and number of panels The three-dimensional mesh for each model used for both methods is shown in Figures Figure 2.1 Simple box J. Ray McDermott Engineering, LLC 5

6 - Hydrodynamic Analysis Comparison Study Figure 2.2 Simple Vertical cylinder Figure 2.2 General ship form J. Ray McDermott Engineering, LLC 6

7 - Hydrodynamic Analysis Comparison Study Figure 2.3 TLP Figure 2.4 Semi-Submersible (MOB) J. Ray McDermott Engineering, LLC 7

8 - Hydrodynamic Analysis Comparison Study The nodal and panel input data used for both programs ( and ) is actually the same since all geometry files were directly converted from s geometry input files. Since definition of the normal vector on the panel for the two programs is different, care must be taken when converting the geometry file to. By using the same number of panels and geometry more consistent comparison between the two programs is achieved. The wave periods used in the numerical calculation were selected from 4 seconds to 42 seconds (total 2 periods by increments of 2 seconds) which covers a wide range of waves. Three waveheading angles (head, quartering, and beam) were also studied. 3. Results and Discussion Hydrodynamic coefficients (added mass and damping coefficients), wave exciting forces and all motion response amplitude () were extracted and compared from both numerical outputs. All outputs are normalized by mass, frequency and wave amplitude. Table 3.1 shows the normalization of each parameter. All units are based on the metric system. Resulting components Units Normalized variable Added mass coefficient Mass A ij /Mass Damping coefficient Mass/Time SQRT(B ij /Mass) Wave exciting forces Tons Tons/A Wave exciting moments Tons*Meter Tons*Meter/A Linear motion Meter Meter/A Angular motion Degree Degree/A * A : Wave amplitude Table 3.1 Normalization Hydrodynamic coefficients, wave exciting forces and motion s for 45 degree wave heading are plotted in Figures Although the other two wave direction computations were completed, the results are not presented here. For all five models, results show very good agreement between two programss. This was expected since both programs use the same constant panel method. From this study the following statements can be made. 1. Results show very good agreement between the two computer programs. 2. For the magnitude near the resonance period, there are some differences. These differences near the resonance wave period are known to be normal for the different numerical methods. Near the resonance period the calculation is very sensitive so that the small numerical difference can cause relatively large differences. According to the results from this study the J. Ray McDermott Engineering, LLC 8

9 - Hydrodynamic Analysis Comparison Study differences are not that significant for the simple geometry like box, cylinder, ship and TLP. But complicate geometry like MOB has more pronounced difference than the simple geometry. 3. Both programs give very effective computing time when a moderate number of panels are used. But is more effective in the computing time when one uses the symmetry option. From this study we can conclude that the 3-D diffraction code can be used as a hydrodynamic analysis tool. The comparison with, which is a widely used and wellproven code, shows good agreement. As a further study, it is suggested to use larger number of panels for both programs to get more accurate results. J. Ray McDermott Engineering, LLC 9

10 - Hydrodynamic Analysis Comparison Study Added Mass Coefficient(Surge,A11) Added Mass Coefficient(Sway,A22) 2.5E-1 2.5E+ 2.E+ 1.5E-1 1.E-1 1.5E+ 1.E+ 5.E-2 5.E-1 Added Mass Coefficient(Heave,A33) Added Mass Coefficient(Roll,A44) 1.4E+ 1.8E+1 1.2E+ 1.6E+1 1.E+ 1.4E+1 1.2E+1 8.E-1 6.E-1 1.E+1 8.E+ 4.E-1 6.E+ 4.E+ 2.E+ Added Mass Coefficient(Pitch,A55) Added Mass Coefficient(Yaw,A66) 6.E+1 8.E+1 5.5E+1 7.E+1 5.E+1 4.5E+1 4.E+1 6.E+1 5.E+1 4.E+1 3.E+1 3.5E+1 2.E+1 1.E+1 3.E+1 Figure 3.1 Added Mass Coefficients for BOX J. Ray McDermott Engineering, LLC 1

11 - Hydrodynamic Analysis Comparison Study Damping Coefficient(Surge,B11) Damping Coefficient(Sway,B22) 1.E-1 9.E-1 9.E-2 8.E-1 8.E-2 7.E-2 6.E-2 5.E-2 4.E-2 3.E-2 7.E-1 6.E-1 5.E-1 4.E-1 3.E-1 2.E-2 1.E-2 1.E-1 Damping Coefficient(Heave,B33) Damping Coefficient(Roll,B44) 1.4E-1 1.E+1 1.2E-1 9.E+ 8.E+ 1.E-1 7.E+ 8.E-2 6.E-2 4.E-2 6.E+ 5.E+ 4.E+ 3.E+ 2.E-2 2.E+ 1.E+ Damping Coefficient(Pitch,B55) Damping Coefficient(Yaw,B66) 1.4E+1 5.E+1 1.2E+1 4.5E+1 4.E+1 1.E+1 3.5E+1 8.E+ 6.E+ 4.E+ 3.E+1 2.5E+1 2.E+1 1.5E+1 2.E+ 1.E+1 5.E+ Figure 3.2 Damping Coefficients for BOX J. Ray McDermott Engineering, LLC 11

12 - Hydrodynamic Analysis Comparison Study Surge Wave Exciting Force Sway Wave Exciting Force 2.E+3 6.E+3 1.8E+3 1.6E+3 5.E+3 F/A 1.4E+3 1.2E+3 1.E+3 8.E+2 6.E+2 F/A 4.E+3 3.E+3 2.E+3 4.E+2 2.E+2 1.E+3 Heave Wave Exciting Force Roll Wave Exciting Moment 8.E+3 6.E+4 7.E+3 5.E+4 6.E+3 5.E+3 4.E+4 F/A 4.E+3 M/A 3.E+4 3.E+3 2.E+4 2.E+3 1.E+3 1.E+4 Pitch Wave Exciting Moment Yaw Wave Exciting Moment 1.2E+5 4.E+5 1.E+5 3.5E+5 3.E+5 8.E+4 2.5E+5 M/A 6.E+4 4.E+4 M/A 2.E+5 1.5E+5 1.E+5 2.E+4 5.E+4 Figure 3.3 Wave exciting forces and moments for BOX J. Ray McDermott Engineering, LLC 12

13 - Hydrodynamic Analysis Comparison Study Surge Sway 8.E-1 8.E-1 7.E-1 7.E-1 6.E-1 6.E-1 5.E-1 4.E-1 3.E-1 5.E-1 4.E-1 3.E-1 1.E-1 1.E-1 Heave Roll 2.E+ 2.5E-1 1.8E+ 1.6E+ 1.4E+ 1.2E+ 1.E+ 8.E-1 6.E-1 1.5E-1 1.E-1 4.E-1 5.E-2 Pitch Yaw 2.5E+ 4.E-1 2.E+ 3.5E-1 3.E-1 1.5E+ 1.E+ 2.5E-1 1.5E-1 5.E-1 1.E-1 5.E-2 Figure 3.4 Motion for BOX J. Ray McDermott Engineering, LLC 13

14 - Hydrodynamic Analysis Comparison Study Added Mass Coefficient(Surge,A11) Added Mass Coefficient(Sway,A22) 1.2E+ 1.2E+ 1.E+ 1.E+ 8.E-1 8.E-1 6.E-1 6.E-1 4.E-1 4.E-1 Added Mass Coefficient(Heave,A33) Added Mass Coefficient(Roll,A44) 1.E-1 1.2E+2 9.E-2 8.E-2 1.E+2 7.E-2 6.E-2 5.E-2 4.E-2 8.E+1 6.E+1 3.E-2 4.E+1 2.E-2 1.E-2 2.E+1 Added Mass Coefficient(Pitch,A55) Added Mass Coefficient(Yaw,A66) 1.2E+2 7.E-3 1.E+2 6.E-3 8.E+1 5.E-3 6.E+1 4.E+1 4.E-3 3.E-3 2.E-3 2.E+1 1.E-3 Figure 3.5 Added Mass Coefficients for CYLINDER J. Ray McDermott Engineering, LLC 14

15 - Hydrodynamic Analysis Comparison Study Damping Coefficient(Surge,B11) Damping Coefficient(Sway,B22) 1.2E-1 1.2E-1 1.E-1 1.E-1 8.E-2 6.E-2 4.E-2 8.E-2 6.E-2 4.E-2 2.E-2 2.E-2 Damping Coefficient(Heave,B33) Damping Coefficient(Roll,B44) 7.E-4 1.2E+1 6.E-4 1.E+1 5.E-4 4.E-4 3.E-4 2.E-4 8.E+ 6.E+ 4.E+ 1.E-4 2.E+ Damping Coefficient(Pitch,B55) Damping Coefficient(Yaw,B66) 1.2E+1 5.E-4 4.5E-4 1.E+1 4.E-4 8.E+ 6.E+ 4.E+ 3.5E-4 3.E-4 2.5E-4 2.E-4 1.5E-4 2.E+ 1.E-4 5.E-5 Figure 3.6 Damping Coefficients for CYLINDER J. Ray McDermott Engineering, LLC 15

16 - Hydrodynamic Analysis Comparison Study Surge Wave Exciting Force Sway Wave Exciting Force F/A 2.E+3 1.8E+3 1.6E+3 1.4E+3 1.2E+3 1.E+3 8.E+2 6.E+2 4.E+2 2.E+2 F/A 2.E+3 1.8E+3 1.6E+3 1.4E+3 1.2E+3 1.E+3 8.E+2 6.E+2 4.E+2 2.E+2 Heave Wave Exciting Force Roll Wave Exciting Moment 9.E+2 1.2E+5 8.E+2 7.E+2 1.E+5 6.E+2 8.E+4 F/A 5.E+2 4.E+2 M/A 6.E+4 3.E+2 4.E+4 2.E+2 1.E+2 2.E+4 Pitch Wave Exciting Moment Yaw Wave Exciting Moment 1.2E+5 7.E-3 1.E+5 6.E-3 M/A 8.E+4 6.E+4 M/A 5.E-3 4.E-3 3.E-3 4.E+4 2.E-3 2.E+4 1.E-3 Figure 3.7 Wave exciting forces and moments for CYLINDER J. Ray McDermott Engineering, LLC 16

17 - Hydrodynamic Analysis Comparison Study Surge Sway 6.E-1 6.E-1 5.E-1 5.E-1 4.E-1 4.E-1 3.E-1 3.E-1 1.E-1 1.E-1 Heave Roll 1.8E+1 5.E-2 1.6E+1 1.4E+1 1.2E+1 1.E+1 8.E+ 6.E+ 4.5E-2 4.E-2 3.5E-2 3.E-2 2.5E-2 2.E-2 1.5E-2 4.E+ 1.E-2 2.E+ 5.E-3 Pitch Yaw 5.E-2 8.E-6 4.5E-2 4.E-2 3.5E-2 3.E-2 2.5E-2 2.E-2 1.5E-2 1.E-2 5.E-3 7.E-6 6.E-6 5.E-6 4.E-6 3.E-6 2.E-6 1.E-6 Figure 3.8 Motion for CYLINDER J. Ray McDermott Engineering, LLC 17

18 - Hydrodynamic Analysis Comparison Study Added Mass Coefficient(Surge,A11) Added Mass Coefficient(Sway,A22) 3.5E-2 1.2E+ 3.E-2 1.E+ 2.5E-2 8.E-1 2.E-2 1.5E-2 6.E-1 1.E-2 4.E-1 5.E-3 Added Mass Coefficient(Heave,A33) Added Mass Coefficient(Roll,A44) 5.E+ 7.E+ 4.5E+ 4.E+ 6.E+ 3.5E+ 5.E+ 3.E+ 2.5E+ 2.E+ 4.E+ 3.E+ 1.5E+ 2.E+ 1.E+ 5.E-1 1.E+ Added Mass Coefficient(Pitch,A55) Added Mass Coefficient(Yaw,A66) 1.2E+2 8.E+1 1.E+2 7.E+1 6.E+1 8.E+1 6.E+1 4.E+1 5.E+1 4.E+1 3.E+1 2.E+1 2.E+1 1.E+1 Figure 3.9 Added mass coefficients for SHIP J. Ray McDermott Engineering, LLC 18

19 - Hydrodynamic Analysis Comparison Study Damping Coefficient(Surge,B11) Damping Coefficient(Sway,B22) 1.E-2 6.E-1 9.E-3 8.E-3 5.E-1 7.E-3 6.E-3 5.E-3 4.E-3 3.E-3 4.E-1 3.E-1 2.E-3 1.E-3 1.E-1 Damping Coefficient(Heave,B33) Damping Coefficient(Roll,B44) 1.2E+ 3.5E+ 1.E+ 3.E+ 8.E-1 6.E-1 4.E-1 2.5E+ 2.E+ 1.5E+ 1.E+ 5.E-1-5.E-1 Damping Coefficient(Pitch,B55) Damping Coefficient(Yaw,B66) 6.E+1 6.E+1 5.E+1 5.E+1 4.E+1 3.E+1 2.E+1 4.E+1 3.E+1 2.E+1 1.E+1 1.E+1 Figure 3.1 Damping coefficients for SHIP J. Ray McDermott Engineering, LLC 19

20 - Hydrodynamic Analysis Comparison Study Surge Wave Exciting Force Sway Wave Exciting Force 3.5E+2 8.E+2 F/A 3.E+2 2.5E+2 2.E+2 1.5E+2 F/A 7.E+2 6.E+2 5.E+2 4.E+2 3.E+2 1.E+2 2.E+2 5.E+1 1.E+2 Heave Wave Exciting Force Roll Wave Exciting Moment 7.E+3 6.E+3 6.E+3 5.E+3 5.E+3 4.E+3 F/A 4.E+3 3.E+3 M/A 3.E+3 2.E+3 2.E+3 1.E+3 1.E+3 Pitch Wave Exciting Moment Yaw Wave Exciting Moment 2.E+5 6.E+4 1.8E+5 1.6E+5 5.E+4 M/A 1.4E+5 1.2E+5 1.E+5 8.E+4 6.E+4 M/A 4.E+4 3.E+4 2.E+4 4.E+4 2.E+4 1.E+4-2.E+4 Figure 3.11 Wave exciting forces and moments for SHIP J. Ray McDermott Engineering, LLC 2

21 - Hydrodynamic Analysis Comparison Study Surge Sway 8.E-1 8.E-1 7.E-1 7.E-1 6.E-1 6.E-1 5.E-1 4.E-1 3.E-1 5.E-1 4.E-1 3.E-1 1.E-1 1.E-1 Heave Roll 1.2E+ 1.4E+1 1.E+ 8.E-1 6.E-1 1.2E+1 1.E+1 8.E+ 6.E+ 4.E-1 4.E+ 2.E+ Pitch Yaw 8.E-1 4.5E-1 7.E-1 4.E-1 6.E-1 3.5E-1 5.E-1 4.E-1 3.E-1 1.E-1 3.E-1 2.5E-1 1.5E-1 1.E-1 5.E-2 Figure 3.12 Motion for SHIP J. Ray McDermott Engineering, LLC 21

22 - Hydrodynamic Analysis Comparison Study Added Mass Coefficient(Surge,A11) Added Mass Coefficient(Sway,A22) 1.2E+ 1.2E+ 1.E+ 1.E+ 8.E-1 8.E-1 6.E-1 6.E-1 4.E-1 4.E-1 Added Mass Coefficient(Heave,A33) Added Mass Coefficient(Roll,A44) 7.E-1 4.E+1 6.E-1 3.5E+1 5.E-1 3.E+1 4.E-1 3.E-1 2.5E+1 2.E+1 1.5E+1 1.E+1 1.E-1 5.E+ Added Mass Coefficient(Pitch,A55) Added Mass Coefficient(Yaw,A66) 4.E+1 6.E+1 3.5E+1 3.E+1 5.E+1 2.5E+1 2.E+1 1.5E+1 1.E+1 4.E+1 3.E+1 2.E+1 5.E+ 1.E+1 Figure 3.13 Added mass coefficients for TLP J. Ray McDermott Engineering, LLC 22

23 - Hydrodynamic Analysis Comparison Study Damping Coefficient(Surge,B11) Damping Coefficient(Sway,B22) 3.5E-1 3.5E-1 3.E-1 3.E-1 2.5E-1 2.5E-1 1.5E-1 1.E-1 1.5E-1 1.E-1 5.E-2 5.E-2 Damping Coefficient(Heave,B33) Damping Coefficient(Roll,B44) 1.4E-2 7.E+ 1.2E-2 6.E+ 1.E-2 8.E-3 6.E-3 4.E-3 5.E+ 4.E+ 3.E+ 2.E+ 2.E-3 1.E+ Damping Coefficient(Pitch,B55) Damping Coefficient(Yaw,B66) 7.E+ 3.5E+1 6.E+ 3.E+1 5.E+ 2.5E+1 4.E+ 3.E+ 2.E+ 2.E+1 1.5E+1 1.E+1 1.E+ 5.E+ Figure 3.14 Damping coefficients for TLP J. Ray McDermott Engineering, LLC 23

24 - Hydrodynamic Analysis Comparison Study Surge Wave Exciting Force Sway Wave Exciting Force 9.E+2 9.E+2 8.E+2 8.E+2 7.E+2 7.E+2 F/A 6.E+2 5.E+2 4.E+2 F/A 6.E+2 5.E+2 4.E+2 3.E+2 3.E+2 2.E+2 2.E+2 1.E+2 1.E+2 Heave Wave Exciting Force Roll Wave Exciting Moment 8.E+2 1.8E+4 F/A 7.E+2 6.E+2 5.E+2 4.E+2 M/A 1.6E+4 1.4E+4 1.2E+4 1.E+4 8.E+3 3.E+2 6.E+3 2.E+2 4.E+3 1.E+2 2.E+3 Pitch Wave Exciting Moment Yaw Wave Exciting Moment 1.8E+4 1.E+ 1.6E+4 9.E-1 1.4E+4 8.E-1 1.2E+4 7.E-1 M/A 1.E+4 8.E+3 6.E+3 4.E+3 M/A 6.E-1 5.E-1 4.E-1 3.E-1 2.E+3 1.E-1 Figure 3.15 Wave exciting forces and moments for TLP J. Ray McDermott Engineering, LLC 24

25 - Hydrodynamic Analysis Comparison Study Surge Sway 1.4E+ 1.4E+ 1.2E+ 1.2E+ 1.E+ 1.E+ 8.E-1 6.E-1 8.E-1 6.E-1 4.E-1 4.E-1 Heave Roll 1.E+1 9.E+ 8.E+ 7.E+ 6.E+ 5.E+ 4.E+ 3.E+ 3.E+ 2.5E+ 2.E+ 1.5E+ 1.E+ 2.E+ 1.E+ 5.E-1 Pitch Yaw 3.E+ 1.4E-5 2.5E+ 1.2E-5 2.E+ 1.E-5 1.5E+ 1.E+ 8.E-6 6.E-6 4.E-6 5.E-1 2.E-6 Figure 3.16 Motion for TLP J. Ray McDermott Engineering, LLC 25

26 - Hydrodynamic Analysis Comparison Study Added Mass Coefficient(Surge,A11) Added Mass Coefficient(Sway,A22) Added Mass Coefficient(Heave,A33) Added Mass Coefficient(Roll,A44) Added Mass Coefficient(Pitch,A55) Added Mass Coefficient(Yaw,A66) Figure 3.17 Added mass coefficients for MOB J. Ray McDermott Engineering, LLC 26

27 - Hydrodynamic Analysis Comparison Study Damping Coefficient(Surge,B11) Damping Coefficient(Sway,B22) Damping Coefficient(Heave,B33) Damping Coefficient(Roll,B44) Damping Coefficient(Pitch,B55) Damping Coefficient(Yaw,B66) Figure 3.18 Damping coefficients for MOB J. Ray McDermott Engineering, LLC 27

28 - Hydrodynamic Analysis Comparison Study Surge Wave Exciting Force Sway Wave Exciting Force F/A 15 1 F/A Heave Wave Exciting Force Roll Wave Exciting Moment F/A M/A Pitch Wave Exciting Moment Yaw Wave Exciting Moment M/A M/A Figure 3.19 Wave exciting forces and moments for MOB J. Ray McDermott Engineering, LLC 28

29 - Hydrodynamic Analysis Comparison Study Surge Sway Heave Roll Pitch Yaw Figure 3.2 Motion for MOB J. Ray McDermott Engineering, LLC 29

30 - Hydrodynamic Analysis Comparison Study 4. References 1. Version5.4 : A Radiation Diffraction Panel program for Wave-Body Interaction, MIT, Version Reference Manual, Ultra Marine, J. Ray McDermott Engineering, LLC 3