Author Contributions
Conceptualization and methodology, N.A. and E.G.; Experimental investigation and analysis, E.G., and A.P.; Software and validation, A.P.; Writing—original draft preparation, A.P.; Writing—review and editing, A.P., E.G., N.A., and C.C.; Supervision, N.A., E.G., C.C., and I.P.; funding acquisition, N.A., E.G. All authors have read and agreed to the published version of the manuscript.
Figure 1.
Australian Maritime College’s Model Test Basin (AMC MTB) experimental setup (left), with the main dimensions of the floating oscillating water column (FOWC) model shown on the right side.
Figure 1.
Australian Maritime College’s Model Test Basin (AMC MTB) experimental setup (left), with the main dimensions of the floating oscillating water column (FOWC) model shown on the right side.
Figure 2.
(a) FOWC axis and degree of freedom definition, blue depicting the submerged volume. (b) panel mesh on the FOWC device.
Figure 2.
(a) FOWC axis and degree of freedom definition, blue depicting the submerged volume. (b) panel mesh on the FOWC device.
Figure 3.
Time series of experimental free decay tests: (a) heave-free decay test and (b) pitch-free decay test.
Figure 3.
Time series of experimental free decay tests: (a) heave-free decay test and (b) pitch-free decay test.
Figure 4.
Interrogation of experimental free decay tests: (a) heave component during heave-free decay test and (b) pitch component during pitch-free decay test.
Figure 4.
Interrogation of experimental free decay tests: (a) heave component during heave-free decay test and (b) pitch component during pitch-free decay test.
Figure 5.
(a) Heave response amplitude operator (RAO) and (b) pitch response amplitude operator (RAO).
Figure 5.
(a) Heave response amplitude operator (RAO) and (b) pitch response amplitude operator (RAO).
Figure 6.
(a) Heave displacement during heave decay test, (b) pitch rotation during heave decay test, (c) pitch rotation during pitch decay test, (d) heave displacement during pitch decay test, (e) heave spectral response, and (f) pitch spectral response.
Figure 6.
(a) Heave displacement during heave decay test, (b) pitch rotation during heave decay test, (c) pitch rotation during pitch decay test, (d) heave displacement during pitch decay test, (e) heave spectral response, and (f) pitch spectral response.
Figure 7.
(a) Time series of surge displacement of free decay tests and (b) the corresponding spectral density plot.
Figure 7.
(a) Time series of surge displacement of free decay tests and (b) the corresponding spectral density plot.
Figure 8.
Experimental and numerical results for regular waves (H = 1.404 m for all cases; T = 7.2–14.4 s).
Figure 8.
Experimental and numerical results for regular waves (H = 1.404 m for all cases; T = 7.2–14.4 s).
Figure 9.
Experimental and numerical results for an operational, irregular sea state (Hs = 1.584 m, Tp = 9.012 s): (a) wave spectral density, (b) heave spectral density, (c) pitch spectral density, and (d) surge spectral density.
Figure 9.
Experimental and numerical results for an operational, irregular sea state (Hs = 1.584 m, Tp = 9.012 s): (a) wave spectral density, (b) heave spectral density, (c) pitch spectral density, and (d) surge spectral density.
Figure 10.
Experimental and numerical results for an elevated, irregular sea state (Hs = 3.384 m, Tp = 14.598 s): (a) wave spectral density, (b) heave spectral density, (c) pitch spectral density, and (d) surge spectral density.
Figure 10.
Experimental and numerical results for an elevated, irregular sea state (Hs = 3.384 m, Tp = 14.598 s): (a) wave spectral density, (b) heave spectral density, (c) pitch spectral density, and (d) surge spectral density.
Figure 11.
(a) Plan view of the FOWC with mooring arrangement and incident wave directions, (b) three-dimensional representation of the mooring arrangement.
Figure 11.
(a) Plan view of the FOWC with mooring arrangement and incident wave directions, (b) three-dimensional representation of the mooring arrangement.
Figure 12.
Numerical results of maximum tensions in the mooring lines for Test Cases 1–5.
Figure 12.
Numerical results of maximum tensions in the mooring lines for Test Cases 1–5.
Figure 13.
Mean tensions (kN) in mooring lines for Cases 1–5 over a 3 h storm duration and under varied incident wave directions and sea states.
Figure 13.
Mean tensions (kN) in mooring lines for Cases 1–5 over a 3 h storm duration and under varied incident wave directions and sea states.
Figure 14.
Significant values of the moored FOWC device motions in (a) surge, (b) sway, (c) heave, (d) roll, (e) pitch, and (f) yaw for all test cases (data withheld for Case 5 at incident waves angles of 90°, 135°, and 180°).
Figure 14.
Significant values of the moored FOWC device motions in (a) surge, (b) sway, (c) heave, (d) roll, (e) pitch, and (f) yaw for all test cases (data withheld for Case 5 at incident waves angles of 90°, 135°, and 180°).
Figure 15.
Mooring line tensions pre- and post-failure of Line 4 at 1800 s for (a) Case 1, (b) Case 2, (c) Case 3, and (d) Case 4.
Figure 15.
Mooring line tensions pre- and post-failure of Line 4 at 1800 s for (a) Case 1, (b) Case 2, (c) Case 3, and (d) Case 4.
Figure 16.
Motions of the moored FOWC device in (a) surge, (b) roll, (c) sway, (d) pitch, (e) heave, and (f) yaw following the simulated failure of Line 4 at 1800 s.
Figure 16.
Motions of the moored FOWC device in (a) surge, (b) roll, (c) sway, (d) pitch, (e) heave, and (f) yaw following the simulated failure of Line 4 at 1800 s.
Table 1.
Main particulars of the experimental model and test setup.
Table 1.
Main particulars of the experimental model and test setup.
Description | Model Scale (1:36) | Designed Full Scale | Units |
---|
FOWC structure | Mass displacement | 27.0695 | 1.263 × 106 | Kg |
LCG (from heave plate aft edge) | 0.420 | 15.12 | M |
VCG (from keel) | 0.246 | 8.856 | M |
Draft | 0.400 | 14.4 | M |
Mass Moments of Inertia (Ixx, Iyy, Izz) | 3.719, 3.683, 4.881 | 0.225 × 109, 0.223 × 109, 0.295 × 109 | kg·m2 |
Soft moorings | Spring stiffness | 647.8 | 839632 | N/m |
Pre-tension | 29.43 | 1.37 × 106 | N |
AMC MTB | Water depth | 0.893 | 32.15 | m |
Regular wave conditions | Wave height | 0.039 | 1.404 | m |
Wave periods | 0.8–5 | 4.8–30 | s |
Irregular wave conditions | Significant wave heights | 0.044, 0.094 | 1.584, 3.384 | m |
Peak periods | 1.502, 2.433 | 9.012, 14.598 | s |
Table 2.
Input parameters for the external lid.
Table 2.
Input parameters for the external lid.
Description | Value | Units |
---|
Lid damping factor | 0.0655 | - |
Gap for external lid | 14.4 | m |
Table 3.
Heave and pitch natural period and damping particulars.
Table 3.
Heave and pitch natural period and damping particulars.
Degree of Freedom | TN (s) | ζ (%) | External Viscous Force/Moment |
---|
Experimental | Numerical |
---|
Heave | 23.742 | 22.71 | 2.99 | 164,240.03 N/m/s |
Pitch | 23.477 | 22.71 | 3.19 | 7,911,707.55 N·m/rad/s |
Table 4.
Surge natural period, damping particulars, and mooring pre-tension.
Table 4.
Surge natural period, damping particulars, and mooring pre-tension.
TN (s) | ζ (%) | External Viscous Force (N/m/s) | Mooring Pre-Tension (N) |
---|
Experimental | Numerical |
---|
124.29 | 124.7 | 9.0 | 60153.9 | 2.51 × 106 |
Table 5.
Comparison between experimental and numerical results for heave, pitch, and surge response in regular waves for H = 1.404 m.
Table 5.
Comparison between experimental and numerical results for heave, pitch, and surge response in regular waves for H = 1.404 m.
Condition | Heave (m) | Pitch (Degrees) | Surge (m) |
---|
Experimental | AQWA | Experimental | AQWA | Experimental | AQWA |
---|
Run 1 (T = 7.2 s) | 0.214 | 0.213 | 0.601 | 0.623 | 0.204 | 0.328 |
Run 2 (T = 8.4 s) | 0.278 | 0.256 | 0.500 | 0.428 | 0.257 | 0.408 |
Run 3 (T = 10.2 s) | 0.283 | 0.308 | 0.482 | 0.128 | 0.296 | 0.494 |
Run 4 (T = 14.4 s) | 0.704 | 1.073 | 2.930 | 4.333 | 0.708 | 0.539 |
Table 6.
Comparison between experimental and numerical results for irregular wave conditions.
Table 6.
Comparison between experimental and numerical results for irregular wave conditions.
Condition | | Hs (m) | Tp (s) | Heave (m) | Pitch (Degrees) | Surge (m) |
---|
Operational | Experiment | 1.584 | 9.012 | 0.54 | 1.848 | 3.204 |
AQWA | 1.602 | 8.814 | 0.73 | 3.139 | 3.197 |
Elevated | Experiment | 3.384 | 14.598 | 2.700 | 11.311 | 6.768 |
AQWA | 3.349 | 14.79 | 3.056 | 11.953 | 3.29 |
Table 7.
FOWC catenary mooring characteristics.
Table 7.
FOWC catenary mooring characteristics.
Description | Value | Units | Description | Value | Units |
---|
Chain grade | R3 studless | - | Added mass coefficient | 1 | - |
Chain diameter | 76 | mm | Number of mooring lines | 4 | - |
Mass/unit length in air | 126 | kg/m | Fairlead locations (x,y,z) | +/– 15.1, +/– 15.1, 0.0 | m |
Submerged mass/unit length | 100.5 | kg/m | Anchor locations (x,y,z) | +/– 491, +/– 491, –100 | m |
Minimum breaking load (MBL) | 4.8843 × 106 | N | No. of cable elements | 100 | - |
Stiffness (EA) | 6.3 × 108 | N | Line length | 715 | m |
Transverse drag coefficient | 2.4 | - | Safety factor (SF) | 2.0 | - |
Longitudinal drag coefficient | 1.15 | - | | | |
Table 8.
Sea-state conditions for the FOWC mooring study.
Table 8.
Sea-state conditions for the FOWC mooring study.
Case No. | Description | Input Parameters | Spectral Analysis | Wave Directions (Degrees) |
---|
Hs (m) | Tp (s) | Hs (m) | Tp (s) | Hmax (m) |
---|
1 | Operational | 1.25 | 8.00 | 1.25 | 8.19 | 2.38 | 0, 45, 90, 135, 180 |
2 | Moderate | 2.50 | 8.00 | 2.50 | 8.19 | 4.75 |
3 | Rough | 4.00 | 12.00 | 4.00 | 12.47 | 7.55 |
4 | Very rough | 6.00 | 12.00 | 6.01 | 12.47 | 11.2 |
5 | Survivable | 9.00 | 12.00 | 9.02 | 12.47 | 16.74 |
Table 9.
Maximum tension (kN) in the mooring lines over a 3 h storm duration and under varied incident wave directions and sea states.
Table 9.
Maximum tension (kN) in the mooring lines over a 3 h storm duration and under varied incident wave directions and sea states.
Wave Direction (Degrees) | Case 1 | Case 2 | Case 3 | Case 4 | Case 5 |
---|
Max. Tension/Line No. | Max. Tension/Line No. | Max. Tension/Line No. | Max. Tension/Line No. | Max. Tension/Line No. |
---|
0 | 219.7/Line 2 | 320.1/Line 1 | 340.76/Line 2 | 621.6/Line 2 | 3411/Line 1 |
45 | 222.1/Line 3 | 301.4/Line 1 | 370.2/Line 1 | 517.7/Line 1 | 2933/Line 1 |
90 | 227.9/Line 1 | 367.9/Line 1 | 373.2/Line 1 | 2056/Line 1 | 10,450/Line 2 |
135 | 242.7/Line 4 | 518.5/Line 4 | 387.7/Line 4 | 1480/Line 1 | 20,511/Line 2 |
180 | 221.7/Line 1 | 329.7/Line 3 | 398.8/Line 1 | 750.5/Line 3 | 4995/Line 3 |