doi:10.1007/s13344-020-0061-1

Motion Responses Analysis for Tidal Current Energy Platform: Quad-Spar and Catamaran Types

doi: 10.1007/s13344-020-0061-1

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Corresponding author: MUKHTASOR, E-mail: mukhtasor@oe.its.ac.id

摘要

Abstract: One approach to support floating tidal current turbines is by using a moored catamaran, a barge type platform. Considering its low draft, one might expect that it performs best at typical straits with sea states of small wavelets to small waves. The problem is that the high rotational motion responses of the catamaran due to wave loads tend to reduce the turbine performance. This paper looks for a possibility to deteriorate these rotational responses by introducing a platform with four buoyant legs referred to as a quad-spar considering its good stability performance. The platforms are moored by four catenary cables as their mooring system. The motion response modeling was undertaken by Computational Fluid Dynamic (CFD) simulation based on three-dimensional potential flow theory. Considering sea states of straits with typical tidal current energy potentials, the environmental load was set on random wave with the significant wave height, H_s, of about 0.09 to 1.5 m and the wave period, T, of about 1.5 to 6 s corresponding to the wave frequency, $ \omega $ , of about 1.1 to 4.2 rad/s. This study found that lower motion responses can be satisfied by the quad-spar, in which its yaw, roll and pitch responses are on average about 5%, 44%, and 38%, respectively, compared to those of the catamaran. This result indicates that the quad-spar is more effective in reducing rotational motion responses needed to keep a high performance of the tidal current energy system.
- floating platform /
- tidal current energy /
- CFD simulation /
- catamaran platform /
- quad-spar platform

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Figure 1. Illustration of a moored catamaran model (not to scale).

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Figure 2. Comparison of maximum pitch angle curve for the catamaran.

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Figure 3. Free-floating pitch RAO comparison.

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Figure 4. Twin turbines-loaded catamaran (front view).

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Figure 5. Twin turbines-loaded quad-spar (front view).

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Figure 6. Catamaran (a) and quad-spar (b) as supporting platform under meshing condition.

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Figure 7. Arrangements of mooring system of catamaran (bottom view).

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Figure 8. Arrangements of mooring system of quad-spar (bottom view).

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Figure 9. Illustration of incident wave direction (top view).

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Figure 10. Effect of the presence of the turbines on roll response of quad-spar (a) and catamaran-typed (b) platforms.

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Figure 12. Effect of the presence of the turbines on yaw response of quad-spar (a) and catamaran-typed (b) platforms.

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Figure 13. Significant wave height effect on roll response.

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Figure 15. Significant wave height effect on yaw response.

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Figure 11. Effect of the presence of the turbines on pitch response of quad-spar (a) and catamaran-typed (b) platforms.

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Figure 14. Significant wave height effect on pitch response.

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Figure 16. Maximum tension of mooring cables.

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Figure 17. ITTC wave spectra.

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Figure 18. Roll spectral response of quad-spar (a) and catamaran (b) with turbines under quartering seas condition.

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Figure 20. Yaw spectral response of twin turbines-loaded quad-spar (a) and catamaran (b) under quartering seas condition.

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Figure 19. Pitch spectral response of twin turbines-loaded quad-spar (a) and catamaran (b) under head seas condition.

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Table 1. Verification of numerical method

Parameter of catamaran ( $ \lambda /L) $	Experimental maximum pitch RAO (°/cm)	Numerical maximum pitch RAO (°/cm)	Percentage of difference (%)
0.8	0.79	0.85	6.7
1.0	0.95	0.98	3.6
1.2	0.99	1.02	2.9
1.5	1.12	1.16	3.4
1.8	1.38	1.45	4.4
2.0	1.26	1.30	3.1
2.2	1.22	1.28	4.5
2.5	0.98	1.02	3.8
3.0	0.90	0.95	5.1

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Table 2. Parameters of catamaran and quad-spar as power station

Parameter	Symbol	Value	Unit
Demi-hull separation	S	14.4	m
Breadth of demi-hull	B	2	m
Height of demi-hull	H_c	2	m
Diameter of quad-spar	D_q	2.06	m
Height of quad-spar	H_q	5.62	m
Height of deck	H_d	1	m
Breadth of deck	B_d	18.4	m
Length of deck	L_d	24	m
Draft of Catamaran	T_c	1.2	m
Draft of quad-spar	T_q	4.82	m
Diameter of turbine	D	4	m
Length of span	L_s	5.5	m

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Table 3. Perfomance parameters

Parameters	Twin turbines-loaded catamaran	Twin turbines-loaded quad-spar
Total weight (kg)	118060	118060
$ {K}_{xx} $ (m)	1.21	1.52
$ {K}_{yy} $ (m)	1.21	1.52
$ {K}_{zz} $ (m)	0.02	0.1
Defeaturing tolerance (m)	0.1	0.1
Maximum element size (m)	0.4	0.4
Number of nodes	29658	30769
Number of elements	29721	30821

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Table 4. Coordinates of anchor

Number of mooring cable	Coordinate of anchor (m)
Number of mooring cable	x	y	z
1	64.14	33.2	−35
2	64.14	−33.2	−35
3	−64.14	33.2	−35
4	−64.14	−33.2	−35

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Table 5. Properties of mooring system

Terms	Specification	Unit
Number of mooring cables	4	−
Length of mooring cables	75	m
Diameter of mooring cables	58	mm
Weight of mooring cables/ unit length	67	kg/m
Pretension of mooring cables	35.55	kN

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Table 6. The difference of maximum tension in Cable 3

${H}_{\rm{s} }$ (m)	Maximum tension (kN)		Percentage of difference (%)
${H}_{\rm{s} }$ (m)	Catamaran-typed platform	Quad-spar platform	Percentage of difference (%)
0.09	1.70	1.57	7.87
0.18	1.79	1.61	10.28
0.27	1.89	1.65	12.56
0.35	1.97	1.69	14.47
0.44	2.07	1.74	16.46
0.53	2.17	1.78	18.22
0.62	2.27	1.82	19.82
0.71	2.37	1.87	21.24
0.8	2.47	1.91	22.52
0.89	2.56	1.96	23.67
0.98	2.66	2.00	24.69
1.07	2.75	2.06	25.35
1.16	2.87	2.11	26.73
1.25	3.02	2.16	28.53
1.34	3.18	2.22	30.28
1.43	3.34	2.28	31.73
1.5	3.48	2.34	32.70

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Table 7. Steel plate estimates

Type	Estimation of floater area (m²)	Number of steel plate requirement	Estimation of steel plates prices needed (US$)
Twin turbines-loaded catamaran	270.63	30	5139.46
Twin turbines-loaded quad-spar	158.74	18	3083.68

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