SeaKeeping (SK) Validation Studies

Transcription

1 SeaKeeping () Validation Studies Contents: Page D Hydrodynamic Coefficients for Simple Shapes... Box Section... Triangle Section... Cylindrical Section... 7 D Forces and Phase Angles at Multiple Headings for Simple Barge Geometries... 8 D Forces and Phase Angles at Multiple Headings for a Tanker Hull... 7 Absolute and Relative RAOs and Accelerations for the Flokstra Containership... RAOs for KCS with Weight Distribution in Head Seas and Zero Speed... References and Additional Resources... Validation Studies ()

2 D Hydrodynamic Coefficients for Simple Shapes The most fundamental computation performed by SeaKeeping is the solution of the twodimensional radiation problem for each section. The solution leads to the two-dimensional hydrodynamic added mass and damping coefficients, and the two-dimensional complex diffraction forcing amplitude for the section. In this validation study, these twodimensional results are compared to model test data published by Vugts (968). Three different geometries were analyzed: a box section, a triangular section, and a cylindrical section, as shown by Figure. For the box, three beam-to-draft (B/T) ratios were also analyzed. The beam factor (see User s Manual) was taken at the default value of 8 for all box shaped sections, and for the triangular and cylindrical sections. The resulting non-dimensional coefficients, and the total heave, sway, and roll forcing amplitudes are given by Figure through Figure 7. In most cases, fair to good agreement between the experimental data and the computational result is obtained. Appreciable differences, such as the case in roll for the triangular and cylindrical section, are attributable to neglecting viscosity, flow-separation, and other significant nonlinearities evident in the real-world flow. Further deviation is observed in the cylindrical section in roll and swayinto-roll. Here, theoretical results are practically zero, as viscous effects account for most of the experimental observations. These assumptions are typical of two-dimensional potential flow based solvers, such as the one used by SeaKeeping, and the deviations are expected. Figure. Vugts Two-Dimensional Section Geometries In the case of roll for the box section at B/T = and B/T = 8, the experimental data is corrected for the difference between the origin, O, and the section s vertical center-ofgravity, CG, as outlined by Vugts (968). In these cases, a note has been included in the plot legend. The computational results were also obtained about the origin, or CG, to maintain consistency with Vugts conventions. Results about the origin when B/T = and B/T = 8 were obtained by setting the VCG equal to the draft. In all other cases, the VCG was taken at. m as indicated. In all cases, a wave heading of 9 degrees was used to match the experimental conditions. Validation Studies ()

3 a/ρab a/ρa a/ρa Box Section , B/T=, B/T=, B/T=8 Vugts, B/T= Vugts, B/T= Vugts, B/T= (b/ρa)(b/g) / ω(b/g) / ω(b/g) / Figure. Sway Added Mass and Damping (a /b ) Box Section 7 6, B/T=, B/T=, B/T=8 Vugts, B/T=, ζa=. Vugts, B/T=, ζa=. Vugts, B/T=8, ζa= (b/ρa)(b/g) / ω(b/g) / ω(b/g) / Figure. Heave Added Mass and Damping (a /b ) Box Section (b/ρab)(b/g) / , B/T=, CG=O, Vugts, CG=O ω(b/g) / ω(b/g) / Figure. Sway-into-Roll Added Mass and Damping Coefficient (a /b ) Box Section, B/T = Validation Studies ()

4 a/ρab., B/T=, O Vugts, O (b/ρab)(b/g) / a/ρab ω(b/g) / ω(b/g) / Figure. Sway-into-Roll Added Mass and Damping Coefficient (a /b ) Box Section, B/T = , B/T=8, O Vugts, O (b/ρab)(b/g) / ω(b/g) / ω(b/g) / Figure 6. Sway-into-Roll Added Mass and Damping Coefficient (a /b ) Box Section, B/T = 8 a/ρab , B/T=, CG=O Vugts, CG=O, φa=. Vugts, CG=O, φa=. Vugts, CG=O, φa= (b/ρab )(B/g) / ω(b/g) / ω(b/g) / Figure 7. Roll Added Mass Moment of Inertia and Damping Coefficient (a /b ) Box Section, B/T = Validation Studies ()

5 a/ρab a/ρa... (b/ρab )(B/g) /...8, B/T=, CG Vugts, CG, φa=. Vugts, CG, φa= ω(b/g) / ω(b/g) / Figure 8. Roll Added Mass Moment of Inertia and Damping Coefficient (a /b ) Box Section, B/T = a/ρab....., B/T=8, CG Vugts, CG, φa=. Vugts, CG, φa=. (b/ρab )(B/g) / ω(b/g) / ω(b/g) / Figure 9. Roll Added Mass Moment of Inertia and Damping Coefficient (a /b ) Box Section, B/T = 8 Triangle Section. Vugts... (b/ρa)(b/g) / ω(b/g) / ω(b/g) / Figure. Sway Added Mass and Damping Coefficient (a /b ) Triangle Section Validation Studies ()

6 a/ρab (b/ρab)(b/g) / a/ρa. Vugts, ζ a= (b/ρa)(b/g) / ω(b/g) / ω(b/g) / Figure. Heave Added Mass and Damping Coefficient (a /b ) Triangle Section -., CG=O Vugts, CG=O ω(b/g) / ω(b/g) / Figure. Sway-into-Roll Added Mass and Damping Coefficient (a /b ) Triangle Section.. (b/ρab )(B/g) /..., CG=O Vugts, CG=O, φa=. a/ρab ω(b/g) / ω(b/g) / Figure. Roll Added Mass Moment of Inertia and Damping Coefficient (a /b ) Triangle Section Validation Studies (6)

7 a/ρab a/ρa a/ρa Cylindrical Section Vugts (b/ρa)(b/g) / ω(b/g) / ω(b/g) / Figure. Sway Added Mass and Damping Coefficient (a /b ) Cylinder Section. Vugts, ζ a= (b/ρa)(b/g) / ω(b/g) / ω(b/g) / Figure. Heave Added Mass and Damping Coefficient (a /b ) Cylinder Section , CG=O Vugts, CG=O (b/ρab)(b/g) / ω(b/g) / ω(b/g) / Figure 6. Sway-into-Roll Added Mass and Damping Coefficient (a /b ) Cylinder Section Validation Studies (7)

8 ., CG=O. Vugts, CG=O, φa=..8 (b/ρab )(B/g) /.. a/ρab ω(b/g) / ω(b/g) / Figure 7. Roll Added Mass Moment of Inertia and Damping Coefficient (a /b ) Cylinder Section D Forces and Phase Angles at Multiple Headings for Simple Barge Geometries The three-dimensional wave excitation force and moment amplitudes and phase angles were compared with results from the D diffraction panel code. The data used in this study was digitized from plots published by J.M.J. Journée, see References and Additional Resources. Two different barge-like geometries were used: a box-barge and a triangular barge. The box-barge has a beam of m, a length of m, and a draft of m, yielding a beam-to-draft ratio of. The VCG was set at the waterline, or m. The triangular barge had beam of.6 m, a length of m, and a draft of m. The barges were evaluated at wave headings of,, 6, and 9 degrees. Forward speed is zero and water depth is infinite. The beam factor and length factor (see the User s Manual for details) were left at the default values of 8. and., respectively. The results are shown by Figure 8 through Figure. In all cases, the agreement is quite satisfactory. Because SeaKeeping uses a more robust treatment of the normal vectors than other strip-theory codes, it is able to capture more of the D effects. This appears to be most evident at higher frequencies, where diffraction typically plays a greater role in the total forcing. Due to the symmetry of the barge geometries, the sway and roll forcing are zero at a wave heading of zero degrees, as evidenced by the seemingly blank plot. The phase angles at these headings are meaningless and are therefore omitted. Validation Studies (8)

9 Amplitude (kn-m) Figure 8. Sway Forcing Amplitude and Phase, Heading: - Box Barge Figure 9. Heave Forcing Amplitude and Phase, Heading: - Box Barge Figure. Roll Moment Amplitude and Phase, Heading: - Box Barge Validation Studies (9)

10 Amplitude (kn-m) Figure. Sway Forcing Amplitude and Phase, Heading: - Box Barge Figure. Heave Forcing Amplitude and Phase, Heading: - Box Barge Figure. Roll Moment Amplitude and Phase, Heading: - Box Barge Validation Studies ()

11 Amplitude (kn-m) Figure. Sway Forcing Amplitude and Phase, Heading: 6 - Box Barge Figure. Heave Forcing Amplitude and Phase, Heading: 6 - Box Barge Figure 6. Roll Moment Amplitude and Phase, Heading: 6 - Box Barge Validation Studies ()

12 Amplitude (kn-m) Figure 7. Sway Forcing Amplitude and Phase, Heading: 9 - Box Barge Figure 8. Heave Forcing Amplitude and Phase, Heading: 9 - Box Barge Figure 9. Roll Moment Amplitude and Phase, Heading: 9 - Box Barge Validation Studies ()

13 Amplitude (kn-m) Figure. Sway Forcing Amplitude and Phase, Heading: - Triangle Barge Figure. Heave Forcing Amplitude and Phase, Heading: Triangle Barge Figure. Roll Moment Amplitude and Phase, Heading: - Triangle Barge Validation Studies ()

14 Amplitude (kn-m) Figure. Sway Forcing Amplitude and Phase, Heading: - Triangle Barge Figure. Heave Forcing Amplitude and Phase, Heading: - Triangle Barge Figure. Roll Moment Amplitude and Phase, Heading: - Triangle Barge Validation Studies ()

15 Amplitude (kn-m) Figure 6. Sway Forcing Amplitude and Phase, Heading: 6 - Triangle Barge Figure 7. Heave Forcing Amplitude and Phase, Heading: 6 - Triangle Barge Figure 8. Roll Moment Amplitude and Phase, Heading: 6 - Triangle Barge Validation Studies ()

16 Amplitude (kn-m) Figure 9. Sway Forcing Amplitude and Phase, Heading: 9 - Triangle Barge Figure. Heave Forcing Amplitude and Phase, Heading: 9 - Triangle Barge Figure. Roll Moment Amplitude and Phase, Heading: 9 - Triangle Barge Validation Studies (6)

17 D Forces and Phase Angles at Multiple Headings for a Tanker Hull The three-dimensional total forcing amplitudes and phase angles for the full-scale crude oil tanker hull Macoma were computed and compared to data from the D panel method code. The data used in this study was digitized from plots published by J.M.J. Journée (). An isometric view and body plan of the submerged hull geometry are given by Figure. The geometry file was developed from poor quality digitized lines drawings, so some error is expected in the conversion of the lines to the geometry file. Section Editor was utilized to develop and edit the model, and additional stations were added using the built-in interpolation feature. The origin was placed at the aft-most station shown in the isometric and body view. Figure. Crude Oil Tanker "Macoma" Submerged Hull Geometry The hull dimensions and loading condition are given in Table. The hull is assumed to be in deep water. Validation Studies (7)

18 LOA. m LCG 6.68 m, fwd O LWL. m TCG. m, O BWL 7.8 m VCG 8.9 m, O 9,.88 MT LCF m, fwd O CB.8 - GMT.9 m Draft 8.9 m k m Trim. Deg, aft k 77. m Heel. Deg k6 77. m Table. Crude Oil Tanker "Macoma" Details The hull was subjected to a range of wave frequencies ranging in period from 9.8 sec (. rad/s) to 6. sec (. rad/s) with a constant amplitude of meter at wave headings of,, 6, 9,,, and 8 degrees. The hull was also held at zero forward speed. The Beam Factor and Length Factor were taken at their default values of 8 and, respectively. The results are plotted against the data in Figure through Figure 6. In most cases, very good agreement is observed. At wave headings of and 8, the forcing amplitudes in sway are effectively zero, therefore the phase angles are omitted Figure. Sway Forcing Amplitude and Phase, Heading: Figure. Heave Forcing Amplitude and Phase, Heading: Validation Studies (8)

19 Amplitude (kn-m) Figure. Roll Forcing Amplitude and Phase, Heading: Figure 6. Sway Forcing Amplitude and Phase, Heading: Figure 7. Heave Forcing Amplitude and Phase, Heading: Validation Studies (9)

20 Amplitude (kn-m) Figure 8. Roll Forcing Amplitude and Phase, Heading: Figure 9. Sway Forcing Amplitude and Phase, Heading: Figure. Heave Forcing Amplitude and Phase, Heading: Validation Studies ()

21 Amplitude (kn-m) Figure. Roll Forcing Amplitude and Phase, Heading: Figure. Sway Forcing Amplitude and Phase, Heading: Figure. Heave Forcing Amplitude and Phase, Heading: Validation Studies ()

22 Amplitude (kn-m) Figure. Roll Forcing Amplitude and Phase, Heading: Figure. Sway Forcing Amplitude and Phase, Heading: Figure 6. Heave Forcing Amplitude and Phase, Heading: Validation Studies ()

23 Amplitude (kn-m) Figure 7. Roll Forcing Amplitude and Phase, Heading: Figure 8. Sway Forcing Amplitude and Phase, Heading: Figure 9. Heave Forcing Amplitude and Phase, Heading: Validation Studies ()

24 Amplitude (kn-m) Figure 6. Roll Forcing Amplitude and Phase, Heading: Figure 6. Sway Forcing Amplitude and Phase, Heading: Figure 6. Heave Forcing Amplitude and Phase, Heading: Validation Studies ()

25 Amplitude (kn-m) Figure 6. Roll Forcing Amplitude and Phase, Heading: 8 Absolute and Relative RAOs and Accelerations for the Flokstra Containership The heave, pitch, and roll absolute RAOs, relative heave RAOs, and vertical accelerations were computed for several Critical Points on the full-scale Flokstra containership hull. The responses computed by SeaKeeping were then compared to model test data obtained by (Zhou, Zhou, & Xie, 996) at the seakeeping basin at the China Ship Scientific Research Center (CSSRC). Figure 6. Flokstra Containership Submerged Hull Geometry Validation Studies ()

26 The responses were computed for two different forward speeds: knots (Fr=.) and knots (Fr=.). In addition, wave headings of 8,, and 9 degrees in deep water were analyzed. An isometric view and body plan of the hull are given by Figure 6. The hull offsets were digitized from scanned and printed lines, so there are some imperfections in the model. Additional stations were added using the interpolation features in Section Editor. The origin was placed.88 m aft of the forward-most station shown. The dimensions and loading condition used for the computational results are given by Table. LOA 87. m LCG. m, aft O LWL 87. m TCG. m, O BWL. m VCG.9 m, O 6,9. MT LCF 9.97 m, aft O CB.6 - GMT. m Draft.8 m k.7 m Trim. Deg, aft k m Heel. Deg k m Table. Flokstra Containership Details Table gives the locations of each Critical Point as well as the overall center of gravity (CG). The locations of the points were selected to match, as best as possible, the probe locations on the model during testing. # Description L T V Orig. Sta7 CL DK.a Orig. Sta Stbd DK.a 6.6s Orig. Sta Stbd DK.a.97s 8.66 Orig. Sta Stbd DK 8.a.s 8.66 Orig. Sta7 Stbd DK.a.6s 8.66 Table. Flokstra Critical Points In general, the results show fair to good agreement with the experimental data. Of note is the influence of non-wave potential damping in roll. The experimental work noted a significant increase in roll damping at higher speeds and at 9 wave headings. The computational results do not include any additional roll damping other than wave potential damping. The computational results therefore over-predict the roll response in beam seas, especially at the higher speed, near roll resonance, as evidenced in the roll RAO and relative motion RAOs. In addition, dynamic swell up affects are not included in the computational results, and while the influence of the dynamic waterline was not discussed in the experimental work, it is expected that this accounts for some additional deviation from the computational results. Moreover, there is some ambiguity as to the exact measurement locations of the probes, and noted possibilities for experimental error in the experimental relative responses. Despite these deviations, the computational results are consistent with expectations, and exhibit useful predictions of the experimental observations. Validation Studies (6)

27 Roll RAO (deg/deg) Pitch RAO (deg/deg) Heave RAO (m/m) Figure 6. CG Heave RAO, Speed: kn (Fr=.), Heading: Figure 66. CG Pitch RAO, Speed: kn (Fr=.), Heading: Figure 67. CG Roll RAO, Speed: kn (Fr=.), Heading: 8 Validation Studies (7)

28 Rel. Heave RAO (m/m) Rel. Heave RAO (m/m) Vertical Acceleration ( m s /m s ).... Figure 68. Point Vertical Acceleration, Speed: kn (Fr=.), Heading: Figure 69. Point 6 Relative Heave RAO, Speed: kn (Fr=.), Heading: Figure 7. Point 8 Relative Heave RAO, Speed: kn (Fr=.), Heading: 8 Validation Studies (8)

29 Heave RAO (m/m) Rel. Heave RAO (m/m) Rel. Heave RAO (m/m).... Figure 7. Point Relative Heave RAO, Speed: kn (Fr=.), Heading: Figure 7. Point Relative Heave RAO, Speed: kn (Fr=.), Heading: Figure 7. CG Heave RAO, Speed: kn (Fr=.), Heading: Validation Studies (9)

30 Vertical Acceleration ( m s /m s ) Roll RAO (deg/deg) Pitch RAO (deg/deg) Figure 7. CG Pitch RAO, Speed: kn (Fr=.), Heading:.... Figure 7. CG Roll RAO, Speed: kn (Fr=.), Heading:.... Figure 76. Point Vertical Acceleration, Speed: kn (Fr=.), Heading: Validation Studies ()

31 Rel. Heave RAO (m/m) Rel. Heave RAO (m/m) Rel. Heave RAO (m/m).... Figure 77. Point 6 Relative Heave RAO, Speed: kn (Fr=.), Heading:.... Figure 78. Point 8 Relative Heave RAO, Speed: kn (Fr=.), Heading:.... Figure 79. Point Relative Heave RAO, Speed: kn (Fr=.), Heading: Validation Studies ()

32 Pitch RAO (deg/deg) Heave RAO (m/m) Rel. Heave RAO (m/m).... Figure 8. Point Relative Heave RAO, Speed: kn (Fr=.), Heading: Figure 8. CG Heave RAO, Speed: kn (Fr=.), Heading: Figure 8. CG Pitch RAO, Speed: kn (Fr=.), Heading: 9 Validation Studies ()

33 Rel. Heave RAO (m/m) Vertical Acceleration ( m s /m s ) Roll RAO (deg/deg).... Figure 8. CG Roll RAO, Speed: kn (Fr=.), Heading: Figure 8. Point Vertical Acceleration, Speed: kn (Fr=.), Heading: Figure 8. Point 6 Relative Heave RAO, Speed: kn (Fr=.), Heading: 9 Validation Studies ()

34 Rel. Heave RAO (m/m) Rel. Heave RAO (m/m) Rel. Heave RAO (m/m).... Figure 86. Point 8 Relative Heave RAO, Speed: kn (Fr=.), Heading: Figure 87. Point Relative Heave RAO, Speed: kn (Fr=.), Heading: Figure 88. Point Relative Heave RAO, Speed: kn (Fr=.), Heading: 9 Validation Studies ()

35 Roll RAO (deg/deg) Pitch RAO (deg/deg) Heave RAO (m/m) Figure 89. CG Heave RAO, Speed: kn (Fr=.), Heading: Figure 9. CG Pitch RAO, Speed: kn (Fr=.), Heading:.... Figure 9. CG Roll RAO, Speed: kn (Fr=.), Heading: Validation Studies ()

36 Rel. Heave RAO (m/m) Rel. Heave RAO (m/m) Vertical Acceleration ( m s /m s ).... Figure 9. Point Vertical Acceleration, Speed: kn (Fr=.), Heading:.... Figure 9. Point 6 Relative Heave RAO, Speed: kn (Fr=.), Heading:.... Figure 9. Point 8 Relative Heave RAO, Speed: kn (Fr=.), Heading: Validation Studies (6)

37 Heave RAO (m/m) Rel. Heave RAO (m/m) Rel. Heave RAO (m/m).... Figure 9. Point Relative Heave RAO, Speed: kn (Fr=.), Heading:.... Figure 96. Point Relative Heave RAO, Speed: kn (Fr=.), Heading: Figure 97. CG Heave RAO, Speed: kn (Fr=.), Heading: 8 Validation Studies (7)

38 Vertical Acceleration ( m s /m s ) Roll RAO (deg/deg) Pitch RAO (deg/deg) Figure 98. CG Pitch RAO, Speed: kn (Fr=.), Heading: Figure 99. CG Roll RAO, Speed: kn (Fr=.), Heading: Figure. Point Vertical Acceleration, Speed: kn (Fr=.), Heading: 8 Validation Studies (8)

39 Rel. Heave RAO (m/m) Rel. Heave RAO (m/m) Rel. Heave RAO (m/m).... Figure. Point 6 Relative Heave RAO, Speed: kn (Fr=.), Heading: Figure. Point 8 Relative Heave RAO, Speed: kn (Fr=.), Heading: Figure. Point Relative Heave RAO, Speed: kn (Fr=.), Heading: 8 Validation Studies (9)

40 Pitch RAO (deg/deg) Heave RAO (m/m) Rel. Heave RAO (m/m).... Figure. Point Relative Heave RAO, Speed: kn (Fr=.), Heading: Figure. CG Heave RAO, Speed: kn (Fr=.), Heading: Figure 6. CG Pitch RAO, Speed: kn (Fr=.), Heading: 9 Validation Studies ()

41 Rel. Heave RAO (m/m) Vertical Acceleration ( m s /m s ) Roll RAO (deg/deg).... Figure 7. CG Roll RAO, Speed: kn (Fr=.), Heading: Figure 8. Point Vertical Acceleration, Speed: kn (Fr=.), Heading: Figure 9. Point 6 Relative Heave RAO, Speed: kn (Fr=.), Heading: 9 Validation Studies ()

42 Rel. Heave RAO (m/m) Rel. Heave RAO (m/m) Rel. Heave RAO (m/m).... Figure. Point 8 Relative Heave RAO, Speed: kn (Fr=.), Heading: Figure. Point Relative Heave RAO, Speed: kn (Fr=.), Heading: Figure. Point Relative Heave RAO, Speed: kn (Fr=.), Heading: 9 Validation Studies ()

43 RAOs for KCS with Weight Distribution in Head Seas and Zero Speed The heave and pitch RAOs for the full-scale KRISO Container Ship (KCS) hull geometry were computed in head seas and zero speed and compared to : scale model test data. An isometric view and body plan of the hull geometry file is given by Figure. The origin was placed amidships at.7 ft aft of the forward-most station. Table also gives the dimensions and the loading condition as specified in GHS. The weight distribution used in the computations is shown by Figure. The pitch and yaw gyradii were computed automatically from the weight distribution and are given in Table. This distribution is the full-scale version of the experimental weight distribution of the model during testing. Figure. KCS Hull Geometry Validation Studies ()

44 Heave RAO (Ft/Ft) Pitch RAO (Deg/Ft) LOA 8. Ft LCG. Ft, aft O LWL 78.9 Ft TCG. Ft, O BWL.76 Ft VCG 7. Ft, O,.6 LT LCF.9 Ft, aft O CB.9 - GMT. Ft Draft. Ft k. Ft Trim. Deg, aft k.6 Ft Heel. Deg k6.6 Ft Table. KRISO Container Ship Details Figure. KCS Computational Full-Scale Weight Distribution The experimental RAOs were measured at LBP/ and on centerline. A GHS Critical Point was placed at this location, and the RAOs shown by Figure were computed at this point. In general, the computational and experimental results are in good agreement , ζa:. in, ζa:. in Figure. Heave and Pitch RAOs, Speed: kn, Heading: Validation Studies (), ζa:. in, ζa:. in

45 References and Additional Resources Journee, J. (). Verification and Validation of Ship Motions Program SEAWAY. Delft: Delft University of Technology Ship Hydromechanics Laboratory. Retrieved Jan., 8 Vugts, J. (968). The Hydrodynamic Coefficients for Swaying, Heaving, and Rolling Cylinders in a Free Surface. International Shipbuilding Progress,. Retrieved Jan., 8, from Zhou, Z.-Q., Zhou, D.-C., & Xie, N. (996). A Seakeeping Experiment Research on Flokstra Container Ship. Validation Studies ()