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Experimental and numerical study on the multi-body coupling dynamic response of a Novel Serbuoys-TLP wind turbine
Ocean Engineering 192 (2019) 106570
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Experimental and numerical study on the multi-body coupling dynamic response of a Novel Serbuoys-TLP wind turbine Zhe Ma a, Shaoxiong Wang a, Yin Wang a, *, Nianxin Ren b, Gangjun Zhai a a b
State Key Laboratory of Coast and Offshore Engineering, Dalian University of Technology, Dalian, 116024, China College of Civil Engineering and Architecture, Hainan University, Haikou, 570228, China
A R T I C L E I N F O
A B S T R A C T
Keywords: Offshore wind turbines (OWT) Serbuoys-TLP Dynamic analysis Model test Multibody effect
The floating wind turbine (FWT) based on the tension leg platform (TLP) plays an important role in addressing the issue of energy pinch, but the central characteristic for TLP is that in vertical direction it is similar to a rigid structure with tension tendons to restrain motion, while in horizontal direction, it seems to be compliant with less constrain. The large amplitude motions in the horizontal plane caused by this compliance will seriously affect the performance of the platform under harsh environmental conditions. To address this problem, a new type of tension leg platform wind turbine connected with a series of buoys (Serbuoys-TLP) is proposed. A timedomain simulation program (DUTMST) for the TLP and Serbuoys-TLP based on MATLAB is provided, with consideration of the multi-body coupling effect between the body, tension leg and buoy. That is, each buoy can be analysed as a separate mass structure connected on the tension leg. The accuracy of DUTMST is discussed via comparison with the results of an experiment and AQWA. The dynamic responses of TLP and Serbuoys-TLP are presented in DUTMST. The results show that the Serbuoys-TLP can significantly reduce the horizontal response of the TLP. In addition, the horizontal response suppression effects of Serbuoys-TLP are investigated by varying the wave factor and parameters of buoys. Additionally, the parameters of buoys adapted to the East China Sea are given.
1. Introduction With the exhaustion of traditional energy, the past decade has seen the rapid development of new renewable energies in many fields, such as solar energy, wave energy, tidal energy and wind energy (Bevrani et al., 2010). Floating wind turbines (FWTs), as an important component of offshore structures, is playing a key role in capturing wind energy from deep-water area and have thus attracted increasing attention in recent years (Leung and Yang, 2012). Since Heronemus (1972) proposed the concept of offshore FWTs in 1972, the spar-type wind turbine Hywind in the North Sea and the semi-submersible wind turbine WindFloat in Portuguese waters have carried out full-scale prototype sea trials and grid-connected power generation (Roddier et al., 2010; Skaare et al., 2015). As a professional institute in floating foundations for offshore wind, IDEOL has been engineering and accompanying floating offshore wind projects from conception to installation. They have also developed a series of new projects, such as Floatgen, which is installed in France and Hibiki installed in Japan (http://www.ideol-offshore.com). The damping-pool system of IDEOL has been tested and will be applied in
Japan (Beyer et al., 2015). All the recent studies above demonstrate an exciting prospect for FWTs. Compared with other FWTs, the appearance of tension-leg-type FWTs is late. The National Renewable Energy Laboratory (NREL) pro posed the concept of a tension-leg-type FWT in 2005 and compared it with spar-type and semi-submersible wind turbines (Musial et al., 2004). Matha et al. under the support of NREL, comprehensively studied the dynamic performance of a 5 MW tension-leg-type FWT in 2009. This study confirmed the superiority of tension leg platform foundations in FWT application (Matha, 2009). A TLP is a typical compliant offshore platform with a vertical mooring system. Similar to application in the offshore oil industry, the dynamic response has always been the focus of scholars’ attention because the large amplitude dynamic response will affect the normal operation of the wind turbines (Bangga et al., 2018). Several theories on the dynamic response of TLP have been proposed. Jain (1997) presented dynamic response analysis of a TLP to deterministic first order wave forces considering coupling between the degrees of freedom of surge, sway, heave, roll, pitch and yaw. Joseph et al. (2004) reported the
* Corresponding author. E-mail address: [email protected] (Y. Wang). https://doi.org/10.1016/j.oceaneng.2019.106570 Received 17 July 2018; Received in revised form 7 October 2019; Accepted 13 October 2019 Available online 22 October 2019 0029-8018/© 2019 The Authors. Published by Elsevier Ltd. This is an (http://creativecommons.org/licenses/by-nc-nd/4.0/).
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Ocean Engineering 192 (2019) 106570
results of a detailed experimental and numerical investigation of the coupled dynamic behaviour of a mini TLP. Abaiee et al. (2016) devel oped two different numerical models, the finite element model (FEM) based on the Morison equation and the boundary element model (BEM) based on a 3D diffraction/radiation theory. Some scholars also have conducted the fully-coupled dynamic analysis of TLP-FOWTs in time domain. Bae et al. (2013) developed a numerical simulation tool including aero-blade-tower dynamics and control, mooring dynamics, and platform motions. Yang et al. (2010) developed a time-domain nonlinear global-motion-analysis program for floating hulls coupled with risers/mooring lines to check the survivability of a TLP with the loss of one or two tendons by accident. Nematbakhsh et al. (2015) compared the wave load effects on a TLP wind turbine by using computational fluid dynamics and potential flow theory approaches. Studies over the past two decades have provided important infor mation on how to simulate the dynamic response of a TLP. However, data from these studies suggest that there are some disadvantages inherent in the dynamic response of a typical TLP, like the large motion response. Therefore, many of the current studies on TLPs pay particular attention to improving the structure form to reduce the dynamic response in the horizontal plane (Bachynski et al., 2012). Wang et al. (2014) proposed the conceptualization of a floating offshore wind tur bine tension leg platform (HIT-FOWT-TLP) that a concrete ballast model is arranged underneath the spoke bottom plane to serve as permanent ballast, and compared it to the traditional NREL-TLP model. Rao et al. (2012) proposed a new concept of a tension-based TLP (TBTLP) and obtained response amplitude operators (RAOs) of the TBTLP with one tension base in terms of the surge, heave and pitch, comparing it with a TLP without a tension base. These studies provide new insights into conceptual design of TLP, but the improvements mentioned above are more effective for heave. In previous studies on the design of a system with low motions, GICON®-TLP with the angled ropes is relatively mature. Adam et al. have carried out comprehensive research, including numerical simula tion and model experiments (Adam et al., 2014). A pilot plant of GICON®-TLP has been designed for this offshore location in the Baltic Sea. However, the applicable water depth of GICON®-TLP wind turbine is limited due to the economic viability with the increase of applied water depth. This paper gives the concept of a new type of tension-leg-type wind turbine connected with a series of buoys (Ser buoys-TLP), which attempts to reduce the dynamic response of the TLP in the horizontal plane. However, much of the calculation software up to now cannot consider the coupling dynamic response of a series of buoys. Therefore, this paper provides a time-domain simulation program (DUTMST), based on MATLAB, with consideration of the multi-body
coupling between the body, tension leg and buoy. Dynamic analysis of the TLP and Serbuoys-TLP by DUTMST is performed and compared to the results of an experiment and commercial software AQWA. Using the proposed program DUTMST, some numerical studies are conducted in order to highlight the effect of a few important parameters on the Serbuoys-TLP response. 2. Methodology 2.1. Proposed Serbuoys-TLP The Serbuoys-TLP is a typical TLP wind turbine, which consists of a central column, pontoons and tendons. In addition, a series of buoys are connected to the tendon legs. The wind turbine is the 5 MW model proposed by NREL. A sketch of the Serbuoys-TLP is shown in Fig. 1(a) and (b). For multibody structures, coupling forces are predominant in the analysis process. To incorporate the coupling phenomena, the equation of motion describing the dynamic equilibrium between the wind turbine foundation and buoys can be assembled as follows: € þ ½C�fxg _ þ ½K�fxg ¼ fFe g þ ½M�fxg
4 X �
� � �� Fmj fxg; xj ; t
(1)
j¼1
where [M] is the diagonal mass matrix for all six degrees of freedom, including platform mass and additional mass; [C] is the radiation damping matrix; [K] is the hydrostatic stiffness matrix; {Fe} is the vector of forcing apart from the mooring force; {Fmj} is the vector of mooring force provided by tension leg j; and x€, x_ and x are the acceleration, ve locity and displacement vectors of the platform, respectively
(x ¼ ½x; y; z; rx; ry; rz�T ). Each buoy can be analysed as a separate mass structure connected on the tension leg, establishing the buoys’ equation of motion (j ¼ 1; 2; 3; 4): � �� � � �� � � � � �� n 0 � � �o Mj x€j þ Cj x_j ¼ Fmj fxg; xj ; t þ Fmj xj ; t (2) where [Mj] is the mass matrix of buoy j for all six degrees of freedom, including buoy mass and additional mass; [Cj] is the damping matrix of buoy j; {Fmj} is the same as {Fmj} in equation (1); {F’mj}is the vector of force provided by the lower section of tension leg j; and x€j , x_j and xj are the acceleration, velocity and displacement vectors of buoy j, respectively.
(a) Sketch of the model
(b) Top view of the foundation
Fig. 1. Sketch of the Serbuoys-TLP. 2
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2.2. Numerical implementation
damping Bjk and wave forces under different wave frequencies F(ω) (Yeung et al. 1982). Ajk, Bjk and F(ω) are written as: Z ρ ! Ajk ¼ Im½ϕrk ð X Þ�nj dS (3)
The coupling effect between buoys and platform is the dominant factor in the analysis of Serbuoys-TLP. Nevertheless, the traditional software AQWA cannot consider the coupling dynamic response brought by the buoys and only equips the buoys as a tension leg with an increased diameter. Therefore, DUTMST has been developed to inves tigate the coupling dynamic response of the Serbuoys-TLP. Frequency domain analysis can only perform the linear analysis, which is cheap and easy (Low et al., 2009). To incorporate the nonlinear phenomena, DUTMST adopts time domain analysis using the Runge-Kutta (Alexander et al. 1977) step-by-step numerical integration technique to solve equations (1) and (2). The solution flow chart of DUTMST is shown in Fig. 2. As shown in Fig. 2, the kernel of DUTMST mainly consists of two parts: the obtaining of hydrodynamic parameters and the calculation of mooring force related to the displacement. The details of these two parts are showed in Section 2.3 and 2.4. ALINEread is a function to obtain the hydrodynamic results.
ω
S0
Z Bjk ¼
!
(4)
ρ Re½ϕrk ð X Þ�nj dS S0
Z FðωÞ ¼
iωρ
! ϕI ð X Þnj dS
S0
Z iωρ
! ϕd ð X Þnj dS
(5)
S0
! where ρ is water density; ω is the wave frequency; ϕrk ð X Þ is the radiation ! ! wave potential; ϕI ð X Þ and ϕd ð X Þ are the incident wave potential with unit wave amplitude and the corresponding diffraction wave potential, respectively; and nj is the unit normal vector of the floating body surface. The numerical model in AQWA is shown in Fig. 3 (a) and (b), whose size is consistent with the prototype. The models of the platform and buoys are established in AQWA separately. By means of the function (ALINEread) provided by DUTMST, we can obtain the added mass ma trix, radiation damping matrix and wave forces of the platform. It is assumed that the buoys are not affected by waves because the buoys are far from the surface of the water. For example, the maximum wave excitation force is merely 3.5t equalling to the 1.5% of a buoy displacement when wave period is 18s and buoy displacement is 250t. It indicated that the wave force acting on the buoys are negligible, and are thus not considered here. We only obtain the added mass matrix and radiation damping matrix of the buoys by ALINEread. Based on the results of the calculation in AQWA, the wave forces in DUTMST are given as:
2.3. Hydrodynamic force vectors There are three main types of study design used to identify predicted wave loads acting on offshore floating bodies: the diffraction-radiation theory (Mei et al., 1978), the Morison’s type equation (Morison et al., 1950) and computational fluid dynamics (CFD) (Nematbakhsh et al., 2013). The Morison’s type equation is an empirical formula, and the accuracy of it depends heavily on the choice of coefficients Cd and Cm. The results of CFD are relatively accurate. However, the calculation of CFD requires large amount of computation resource. (Nematbakhsh et al., 2015). Therefore, the diffraction-radiation theory may be better compared with the other two methods. One advantage of the diffraction-radiation theory is that it avoids the problem of a long calculation time. The dynamic responses of the Serbuoys-TLP can be simulated in a multi-group working condition to explore the effect of buoys. Another advantage of the diffraction-radiation theory is that this method is more mature. Many commercial software packages have utilized it to solve practical problems and obtain proven results (Zheng et al., 2004). The relevant hydrodynamic coefficients of platform and buoys are obtained by AQWA. It contains two model settings for simplifying the tension leg: a massless spring model (spring element) and a nonlinear beam model (tube element). The tube element can better consider the added mass and radiation damping. DUTMST provides a function (ALINEread) which can obtain the hydrodynamic results of any struc ture calculated by AQWA, including the added mass Ajk, radiation
FðtÞ ¼ A⋅FðωÞ⋅ei½
(6)
ωtþkðx cos χ þy sin χ Þþφ�
where A is the wave amplitude; k is the wave number; (x, y) is the barycentric coordinate of the platform; χ is the incident angle of the wave; φ is the initial phase; and F(ω) is the wave forces under different wave frequencies. Both F(ω) and φ are obtained by ALINEread. 2.4. Tension vector In the process of solving equations, we should firstly establish the relationship between tension and the position of buoys and platform. Only in this way can we achieve the positions of platform and buoys in next step through the tension in this time step. The tension calculation includes two sections, Fmj and F’mj, simplifying the tension leg as a massless spring model. The force analysis diagram is shown in Fig. 4(a). The tension vector of a tether can be given as:
(a) Serbuoys-TLP Fig. 2. Solution flow chart of DUTMST.
Fig. 3. Numerical model in AQWA. 3
(b) Buoys
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Ocean Engineering 192 (2019) 106570
2
1 ½RX� ¼ 4 0 0
0 cosðrxÞ sinðrxÞ
3 0 sinðrxÞ 5 cosðrxÞ
(12)
The coordinates of points U and D in OXYZ can also be obtained according to this method. Only need to change the fxg into the bar ycentric coordinate of the buoys fxj g and change [xp,yp,zp]T into the coordinate of point U and D in COGζηξ. In this way, the instantaneous tension of the tension leg can be calculated based on the displacements of the platform and buoys in real time. 3. Validation of the numerical model (a) Force analysis
3.1. Set-up of the physical test
(b) Coordinate system
Fig. 4. Diagram of the Serbuoys-TLP.
Fmj ¼ T0 þ
F’mj ¼
EA �! ðjPU j Lu0
�! PU Lu0 Þ �! jPU j
T0 EA �! ðjAD j þ Fb þ Ld0 4
�! AD Ld0 Þ �! jAD j
The Serbuoys-TLP model being considered is square in plan view, as shown in Fig. 1, with four buoys attached to the tension leg. To verify the accuracy of the program DUTMST, scale model tests of the Serbuoys-TLP system have been performed in the advanced wind tunnel and wave flume joint laboratory at the Harbin Institute of Technology (HIT). The experimental model of the floating wind turbine foundation is shown in Fig. 5(a), and that of the buoys is shown in Fig. 5(b). Comprehensively considering the condition of the laboratory and the size of the full-scale Serbuoys-TLP system, the scale ratio of the Serbuoys-TLP test model has been designed to be 1/50 in line with Froude scaling laws (Ren et al., 2012). The main design parameters of the Serbuoys-TLP and wave data are given in Table 1.
(7)
(8)
�! jPU j ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðxU xP Þ2 þ ðyU yP Þ2 þ ðzU zP Þ2
(9)
�! jAD j ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðxD xA Þ2 þ ðyD yA Þ2 þ ðzD zA Þ2
(10)
3.2. Comparison between numerical and experimental studies
where { Fmj } and { F’mj } are the same as in equations (1) and (2). Point P (xP, yP, zP) is the point of the tension leg attached on the foundation; points U (xU, yU, zU) and D (xD, yD, zD) are the points of the tension leg attached on the buoy; and point A (xA, yA, zA) is the tension leg anchor point. Therefore, they denote the instantaneous vector joining the endpoints of the tether. E is the Young’s modulus; A is the cross-sectional area of the tether; Lu0 and Ld0 are the initial length of the upper and lower sections of the tether, respectively; and T0 and Fb are the net force of the foundation and buoys. For the nonlinear model in the present study, the tension vector is a nonlinear function of the displacements because higher order compo nents are considered in the calculation of the instantaneous length of the tether (Cheng et al., 2018). Therefore, the acquisition of the coordinates of points P, U and D is especially important. A method of coordinate conversion is given to obtain the coordinates of the platform and the upper and lower nodes of the buoys (Sugita et al., 2016). Two right-handed Cartesian coordinate systems, OXYZ and COGζηξ, are defined in Fig. 4(b). OXYZ is the space-fixed coordinate system, where plane OXY coincides with the undisturbed calm water surface. COGζηξ is the body-fixed coordinate system, where COG coincides with the centre of gravity of the platform. The coordinate of point P (xPj yPj zPj ) in OXYZ is: 2 3 2 3 2 3 xPj xp x 4 yPj 5 ¼ 4 y 5 þ ½RZ�½RX�½RY�4 yp 5 (11) zPj zp z
The Serbuoys-TLP is a multi-body coupling system, so each buoy should be analysed as a separate mass structure. The experimental model of the Serbuoys-TLP is consistent with the DUTMST program considering buoys connected on the tension leg. Nevertheless, AQWA cannot consider the Serbuoys-TLP as a multi-body system and the buoy can only be equivalent to a tension leg with an increased diameter. However, as the basis of DUTMST, AQWA is also carried out in the process of the numerical study in order to primarily study the dynamic responses of the Serbuoys-TLP. The numerical model in AQWA is the same as in section 2.3. Considering that the surge responses usually play a dominant role for the Serbuoys-TLP floating system, we are more concerned about the surge of the TLP. The results of surge in AQWA, DUTMST and the experiment are shown in Fig. 6. Fig. 6 (a) is the time history of Serbuoys-TLP under the work condition in Table 1. The ordinate of Fig. 6 (b) is dimensionless parameters represented by the average amplitude of the time-domain results under wave period 5.66 s, 7.07 s, 8.48 s, 9.90 s, 11.31 s, 12.73 s, 14.70 s. And similar conclusions can be drawn from the two Figures. As shown in Fig. 6, the results indicate that the numerical results of both DUTMST and AQWA have a good agreement with the experimental data, although, compared with the results of DUTMST, it is illogical that the surge obtained in the AQWA are smaller than the experimental value. Because of without accounting for the damping effect completely in the scale test model, the numerical results should be larger than the
where fxg ¼ ½x; y; z; rx; ry; rz�T is the displacement vectors of the plat form; [x,y,z]T is the barycentric coordinate of the platform; [rx,ry,rz]T is the roll, pitch and yaw of the platform; and [xp,yp,zp]T is the coordinate of point P in COGζηξ. 2 3 2 3 cosðrzÞ cosðrzÞ 0 cosðryÞ 0 sinðryÞ ½RZ� ¼ 4 sinðrzÞ sinðrzÞ 0 5½RY� ¼ 4 0 sinðryÞ 0 5 0 0 1 sinðryÞ 0 cosðryÞ (a) Floating wind turbine foundation
(b) Model of the buoys
Fig. 5. Experiment model of the Serbuoys-TLP. 4
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Ocean Engineering 192 (2019) 106570
wave conditions. Based on the above research, the dynamic response of the typical TLP and Serbuoys-TLP has been simulated in DUTMST under four different wave conditions. The time histories of the surge are shown in Fig. 8 to compare the dynamic responses of the TLP and Serbuoys-TLP in the plane. From Fig. 8(a), (b) and (c), we can see that the surge of the Serbuoys-TLP is obviously less than that of the TLP. This result indicates that the Serbuoys-TLP can exhibit effective improvement in the dynamic responses compared to the TLP in the plane and exhibits a good effect in suppressing the dynamic responses of the TLP in the plane. However, the suppressive effect is different under the different wave conditions. Surprisingly, suppression of the surge of the TLP is not observed in Fig. 8(d). Instead, the surge of the Serbuoys-TLP is larger than that of the TLP under this wave conditions (wave period T ¼ 6 s). These results suggest that the suppressive effect of the Serbuoys-TLP on the dynamic responses of the TLP in the plane is affected by wave parameters. Therefore, the next section of the study was concerned with factors that affect the suppressive effect of the Serbuoys-TLP.
Table 1 Main design parameters of the Serbuoys-TLP and wave data. Parameters NTEL 5WM Wind turbine Blades and Nacelle mass (kg) Tower mass (kg) Tower Height(m) TLP platform Buoyancy (kg) Total mass (kg) Water depth (m) Centre of gravity (m) Ixx � Iyy; Izz (kg⋅m2) Spoke design (m) Tension leg (m) Parameter of buoys Buoy height (m) Buoy radius (m) Displacement (t) Installation position (m) Wave data Wave height (m) Wave period (s)
Full scale
Scaled (λ ¼ 1/50)
350,000;
2.80;
350,000 90
2.80 1.80
5214,000 2814,000 170 (0,0,-5.0) 4.5 � 109; 5.0 � 108 L ¼ 20.0; A ¼ 4.0*4.0 L ¼ 140; D ¼ 1.2; t ¼ 0.04
41.71 22.51 3.40 (0,0,-0.02) 14.40; 1.6 L ¼ 0.40; A ¼ 0.08*0.08 Equivalent steel cable
10 4.2 4*250 Z ¼ 95
0.2 0.084 4*0.002 Z ¼ 1.9
3 8.485
0.06 1.2
4.2. Influence of wave factors on the suppressive effect of the SerbuoysTLP The dynamic responses of the Serbuoys-TLP and typical TLP are calculated under 27 wave conditions consisting of different wave pe riods, wave heights and wave heading angles. These wave parameters are listed in Table 2. To display the results more conveniently, dynamic
experimental value (Teigen et al., 1998). It may be caused by the un reasonable simplification that the buoy is equivalent to a tension leg with an increased diameter in AQWA. As far as this is concerned, the results obtained in DUTMST are more logical. In addition, DUTMST is an open source program implemented by MATLAB. Therefore, it is more convenient for advanced development to investigate the factors on the suppressive effect of the Serbuoys-TLP compared with AQWA.
DUTMST AQWA
1.0
4. Discussion
0.5
Surge (m)
4.1. Comparison of the Serbuoys-TLP and a typical TLP To compare the differences between the Serbuoys-TLP and a typical TLP, DUTMST also provides a time-domain simulation program for a typical TLP, which is exactly the same as the Serbuoys-TLP except that no buoys are on the tension leg. Compared with the Serbuoys-TLP, the analysis of the typical TLP is simpler because only equation (1) needs to be solved using the Runge-Kutta step-by-step numerical integration technique. To assess the accuracy of DUTMST for the typical TLP, the time histories of the surge predicted by DUTMST are compared with the numerical results of AQWA in Fig. 7. It is worth noting that the tension leg in AQWA is also simplified to spring element here like the DUTMST. The wave data of the numerical study is the same as in Table 1 (wave period T ¼ 8.485 s, wave height H ¼ 3 m). It is apparent from Fig. 7 that the results obtained from DUTMST have good agreement with the results of AQWA. It has been verified that this trend remains under different
Surge (m)
0.8
0.7 0.6 0.5 0.4 0.3 458
460
-0.5
-1.0 100
Experiment DUTMST AQWA
462
140
t (s)
160
0.8
DUTMST
0.4 0.0
Experiment AQWA
0.6 0.4 0.2
-0.4 -0.8 400
120
420
440
460
480
180
200
Fig. 7. Surge of the typical TLP obtained with AQWA and DUTMST.
Surge (m)
1.2
0.0
0.0
500
t (s) (a) Time History of Serbuoys-TLP
4
6
8
12
(b) RAO of Serbuoys-TLP
Fig. 6. Surge response of the Serbuoys-TLP. 5
10
Wave period (s)
14
16
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Ocean Engineering 192 (2019) 106570
TLP Serbuoys-TLP
1.6
-0.8
0.8
Surge(m)
Surge(m)
0.8 0.0
TLP Serbuoys-TLP
1.6
0.8 0.6 0.4 127 128 129 130 131
-1.6 100
120
0.0
1.0 0.8
-0.8
140
t (s)
160
180
120 121 122 123 124
-1.6 100
200
120
(a) T=8.485s H=3m
180
200
TLP Serbuoys-TLP
0.8
Surge(m)
Surge(m)
-0.8
160
1.6
0.8 0.0
t (s)
(b) T=10s H=3m
TLP Serbuoys-TLP
1.6
140
1.4
1.2 121
-1.6 100
122
123
120
0.2
-0.8
124
140
0.4
0.0
t (s)
160
180
-1.6 100
200
162
163
164
120
(c) T=12s H=3m
165
140
t (s)
160
180
200
10
12
(d) T=6s H=3m
Fig. 8. Surge of the TLP simulated in DUTMST.
responses under each wave condition are represented by the average amplitude of the time-domain results between 100 s and 200 s. The surge motion amplitudes of the Serbuoys-TLP and typical TLP under wave condition A are shown in Fig. 9. The surge motion ampli tudes of the Serbuoys-TLP and typical TLP both increase gradually as the wave period increases. When the wave period is approximately 7 s, the dynamic response of the Serbuoys-TLP exhibits a peak value. Before the wave period reaches this peak, the Serbuoys-TLP cannot suppress the surge motions of the TLP, and the surge motions of it become larger than those of the TLP. After the wave period reaches this peak, the SerbuoysTLP has a good suppression effect on the dynamic response of the TLP in the plane, and the suppression effect decreases with the increase of the wave period. A possible reason for these results is that the natural fre quency of the Serbuoys-TLP coincides with the frequency of the incident wave, causing resonance. Therefore, when the parameters of the Serbuoys-TLP are determined, the dynamic responses of the SerbuoysTLP under different wave periods should be discussed. The surge motion amplitude of the Serbuoys-TLP and typical TLP under wave conditions B and C are shown in Fig. 10(a) and (b). The suppressive rates for the surge motion of the TLP are listed in Table 3. As shown in Fig. 10 and Table 3, although the surge motions of the Serbuoys-TLP and TLP are different under different wave conditions, the suppressive rate is basically constant as the wave height and wave
Surge (m)
0.8
Incident angle of wave (� )
Wave height (m)
Wave period (s)
Group A (11) Group B (9) Group C (7)
0
1
0 0; 15; 25; 45; 60; 75; 90
1; 2; 3; …; 7; 8; 9 1
3; 4; 5; …; 11; 12; 15 10 10
0.4 0.2 0.0
2
4
6
8
14
16
Wave period (s) Fig. 9. Surge contrast of the TLP and Serbuoys-TLP under working condition A.
incident angle change. When the incident angle of the wave is 90� , the surge motions of the TLP and Serbuoys-TLP are very small, so it is meaningless to discuss the suppressive rate here. 4.3. Influence of buoy factors on the suppressive effect of the SerbuoysTLP
Table 2 Regular Wave conditions. Groups
Serbouys-TLP TLP
0.6
The analysis of section 4.2 indicates that the wave period plays an important role in the suppressive effect of the Serbuoys-TLP on the dy namic responses of the TLP in the plane. The main reason is that the buoys connected on the tension leg change the natural frequency of the Serbuoys-TLP. In actual conditions, it is particularly important to investigate the applicability of buoy parameters. Therefore, the dynamic responses of the Serbuoys-TLP and typical TLP are calculated under working conditions D, E, F and G to investigate 6
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Ocean Engineering 192 (2019) 106570
0.4
Serbouys-TLP
2.4 1.6 0.8 0.0
Serbouys-TLP
0.3
TLP
Surge(m)
Surge(m)
3.2
TLP
0.2 0.1 0.0
0
2
4
6
Wave height (m)
8
-0.1 -15
10
0
15
30
45
60
75
Incident angle of wave(°)
(a) Group B
90
(b) Group C
Fig. 10. Surge contrast of the TLP and Serbuoys-TLP under working conditions B and C.
0.6
Wave condition
Suppressive rate
Wave condition
Suppressive rate
B B B B B B B B
7.71% 7.71% 7.71% 7.71% 7.70% 7.70% 7.70% 7.70%
B (H ¼ 9 m) C (θ ¼ 0� ) C (θ ¼ 15� ) C (θ ¼ 30� ) C (θ ¼ 45� ) C (θ ¼ 60� ) C (θ ¼ 75� ) C (θ ¼ 90� )
7.69% 7.70% 7.71% 7.70% 7.70% 7.69% 7.69% ——
(H ¼ 1 m) (H ¼ 2 m) (H ¼ 3 m) (H ¼ 4 m) (H ¼ 5 m) (H ¼ 6 m) (H ¼ 7 m) (H ¼ 8 m)
Surge (m)
Table 3 The suppressive rate of the Serbuoys-TLP for the surge under working conditions B and C.
Group Group Group Group
D (11) E (11) F (11) G (11)
0.2
2
4
6 8 10 Wave period (s)
12
14
Fig. 11. Surge contrast of the TLP and Serbuoys-TLP under working conditions D, E, F and G. Table 5 Suppressive rate of the Serbuoys-TLP for the surge under working conditions G. Wave condition
Suppressive rate
Wave condition
Suppressive rate
G (T ¼ 3 s) G (T ¼ 4 s) G (T ¼ 5 s) G (T ¼ 6 s) G (T ¼ 7 s)
5.15% 11.77% 27.57% 102.78% 67.97%
G G G G G
42.20% 30.37% 24.85% 21.65% 19.31%
(T ¼ 8 s) (T ¼ 9 s) (T ¼ 10 s) (T ¼ 11 s) (T ¼ 12 s)
increases with the increase displacement of the buoys, the Tp increased as well. This unusual phenomenon is because the total mass of Serbuoys-TLP increases with the increase of displacement of buoys. Therefore, we can conclude that the mass of the buoys also has a great influence on the natural frequency of the total system. rffiffiffiffiffiffiffi 2π K11 ω¼ ¼ (13) Tp M The TLP provided in this paper is more suitable for the East China Sea (Zheng et al., 2012), where the common wave periods are 6 s–8 s. Based on this trend, it is practical in the East China Sea on condition that the buoys will be located 60 m underwater and the displacement of buoys be set as 250 t. The suppressive efficiency under the corresponding working condition D is listed in Table 6. In this way, the Serbuoys-TLP can effectively suppress the horizontal dynamic responses of the TLP.
Table 4 Working conditions. Groups
0.4
0.0
the influence of the position of and displacement of buoys on the sup pressive effect of the Serbuoys-TLP. The working conditions are listed in Table 4, and each group includes 11 situations of wave periods from 3 s to 15 s (wave height H ¼ 1 m, incident angle of wave θ ¼ 0� ). The surge motions of the TLP and Serbuoys-TLP are shown in Fig. 11. A pre liminary analysis of the variation in the wave period corresponding to the peak with the buoy parameters is given. As seen from Fig. 11, the numerical results obtain a good agreement with the results of group A, and a peak value also exist in the time his tories of the Serbuoys-TLP. However, as the position of the buoys become deeper and the displacement of the buoys increases, the wave period corresponding to the peak (Tp) is larger. The suppressive effect of the Serbuoys-TLP also is influenced by the Tp. The suppressive effect under work condition G seem to be the best and the suppressive effi ciency is listed in Table 5. The change of Tp accompanied with the buoy factors may be caused by the change of mooring stiffness of SerbuoysTLP. In order to further interpret this phenomenon and discuss the in fluence of buoy factors on mooring stiffness, the static analysis of Serbuoys-TLP is carried out and the results are shown in Fig. 12. The δx in Fig. 12 is the initial offset of the platform in the surge and Fx is the horizontal restoring force caused by δx. Based on the results obtained above, we can see that the mooring stiffness will decrease as the position of the buoys become deeper. Ac cording to Eq.(16), we can observe that Tp increases with the decrease of stiffness when the total mass is constant. Therefore, the increase of Tp will occur as the position of the buoys become deeper. The mooring stiffness of Serbuoys-TLP will increase as the displacement of the buoys increase. Surprisingly, although the mooring stiffness of Serbuoys-TLP
TLP D(-60m,250t) E(-95m,250t) F(-95m,400t) G(-60m,400t)
5. Conclusions Position of buoys (m) 60 95 95 60
Displacement of buoys (t)
In this study, a concept of Serbuoys-TLP is provided firstly, and the dynamic behaviors of Serbuoys-TLP have been investigated both experimentally and numerically (using the time-domain simulation program (DUTMST)). DUTMST, which is based on MATLAB, take
4*250 4*250 4*400 4*400
7
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Ocean Engineering 192 (2019) 106570
Fx (N)
3x105
4x105
TLP Serbuoys-TLP(250 t) Serbuoys-TLP(400 t)
3x105 Fx (N)
4x105
2x105 1x105
TLP Serbuoys-TLP(-60 m) Serbuoys-TLP(-95 m)
2x105 1x105
0 -0.6 0.0
0.6
1.2
1.8
2.4
3.0
0 -0.6 0.0
3.6
x (m)
0.6
1.2
1.8
2.4
3.0
3.6
x (m)
Fig. 12. The static analysis of Serbuoys-TLP about horizontal resilience.
No. 2016YFE0200100), the Central Universities (Grant No. DUT19JC47), National Natural Science Foundation of China (Grant No. 51709040). The financial support is greatly acknowledged.
Table 6 Suppressive rate of the Serbuoys-TLP for the surge under working conditions D. Wave condition
Suppressive rate
Wave condition
Suppressive rate
D (T ¼ 3 s) D (T ¼ 4 s) D (T ¼ 5 s) D (T ¼ 6 s) D (T ¼ 7 s)
5.76% 14.77% 52.01% 54.21% 30.48%
D (T ¼ 8 s) D (T ¼ 9 s) D (T ¼ 10 s) D (T ¼ 11 s) D (T ¼ 12 s)
21.54% 17.65% 15.47% 14.04% 12.82%
References Abaiee, M.M., Ketabdari, M.J., Ahmadi, A., Ardakani, H.A., 2016. Numerical and experimental study on the dynamic behavior of a Sea-star tension leg platform against regular waves. J. Appl. Mech. Tech. Phys. 57 (3), 510–517. Adam, F., Myland, T., Schuldt, B., Großmann, J., Dahlhaus, F., 2014. Evaluation of internal force superposition on a tlp for wind turbines. Renew. Energy 71, 271–275. Alexander, R., 1977. Diagonally implicit Runge-Kutta methods for stiff odes. SIAM J. Numer. Anal. 14 (6), 1006–1021. Bachynski, E.E., Moan, T., 2012. Design considerations for tension leg platform wind turbines. Mar. Struct. 29 (1), 89–114. Bae, Y.H., Kim, M.H., 2013. Rotor-floater-tether coupled dynamics including secondorder sum-frequency wave loads for a mono-column-tlp-type fowt (floating offshore wind turbine). Ocean. Eng. 61, 109–122. Bangga, G., Guma, G., Lutz, T., Kramer, E., 2018. Numerical simulations of a large offshore wind turbine exposed to turbulent inflow conditions. Wind Eng. 42 (2), 88–96. Bevrani, H., Ghosh, A., Ledwich, G., 2010. Renewable energy sources and frequency regulation: survey and new perspectives. IET Renew. Power Gener. 4 (5), 438–457. Beyer, F., Choisnet, T., Kretschmer, M., Cheng, P.W., 2015. Coupled Mbs-Cfd simulation of the ideol floating offshore wind turbine foundation compared to wave tank model test data. In: Proceedings of the Twenty-Fifth (2015) International Ocean and Polar Engineering Conference. Kona, Big Island, Hawaii, USA. Cheng, Y., Ji, C., Zhai, G., Oleg, G., 2018. Nonlinear analysis for ship-generated waves interaction with mooring line/riser systems. Mar. Struct. 59, 1–24. Heronemus, W., 1972. Power from offshore winds. In: Proceedings of the 8th Annual Conference and Exposition on Applications of Marine Technology to Human Needs (Washington, DC). Jain, A.K., 1997. Nonlinear coupled response of offshore tension leg platforms to regular wave forces. Ocean. Eng. 24 (7), 577–592. Joseph, A., Idichandy, V.G., Bhattacharyya, S.K., 2004. Experimental and numerical study of coupled dynamic response of a mini tension leg platform. J. Offshore Mech Arct. 126 (4), 318–330. Leung, D.Y.C., Yang, Y., 2012. Wind energy development and its environmental impact: a review. Renew. Sustain. Energy Rev. 16 (1), 1031–1039. Low, Y.M., 2009. Frequency domain analysis of a tension leg platform with statistical linearization of the tendon restoring forces. Mar. Struct. 22 (3), 480–503. Matha, D., 2009. Model Development and Loads Analysis of an Offshore Wind Turbine on a Tension Leg Platform with a Comparison to Other Floating Turbine Concepts. Mei, C.C., 1978. Numerical-methods in water-wave diffraction and radiation. Annu. Rev. Fluid Mech. 10, 393–416. Morison, J.R., Obrien, M.P., Johnson, J.W., Schaaf, S.A., 1950. The force exerted by surface waves on piles. Trans. Am. Ins. Mining Metall. Eng. 189, 149–154. Musial, W., Butterfield, S., Boone, A., 2004. Feasibility of Floating Platform Systems for Wind Turbines. 42nd AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada. Nematbakhsh, A., Bachynski, E.E., Gao, Z., Moan, T., 2015. Comparison of wave load effects on a tlp wind turbine by using computational fluid dynamics and potential flow theory approaches. Appl. Ocean Res. 53, 142–154. Nematbakhsh, A., Olinger, D.J., Tryggvason, G., 2013. A nonlinear computational model of floating wind turbines. J. Fluid Eng-T. Asme. 135, 12110312. Rao, D.S.B., 2012. Hydrodynamic Analysis of Tension Based Tension Leg Platform. Ocean, Offshore and Arctic Engineering, Rio de Janeiro, Brazil. Ren, N., Li, Y., Ou, J., 2012. The effect of additional mooring chains on the motion performance of a floating wind turbine with a tension leg platform. Energies 5 (4), 1135–1149. Roddier, D., Cermelli, C., Aubault, A., Weinstein, A., 2010. Windfloat: a floating foundation for offshore wind turbines. J. Renew. Sustain. Energy 2, 0331043. Skaare, B., Nielsen, F.G., Hanson, T.D., Yttervik, R., Havmoller, O., Rekdal, A., 2015. Analysis of measurements and simulations from the Hywind demo floating wind turbine. Wind Energy 18 (6), 1105–1122. Sugita, T., Suzuki, H., 2016. A study on tlp hull sizing by utilizing optimization algorithm. J. Mar Sci Tech-Japan. 21 (4), 611–623.
consideration of the multi-body coupling effect between the foundation, tension legs and buoys. The results of DUTMST are compared with data from experiment and AQWA. The comparisons showed that the nu merical results of DUTMST obtain a better agreement with experimental results compared to the numerical results of AQWA. The following conclusions are summed up based on the numerical studies conducted with DUTMST under different working conditions: (a) The Serbuoys-TLP has a certain suppressive effect on the dynamic responses of the TLP in the plane. The highest suppressive rates under the different working conditions D, E, F and G are 54.21%, 16.62%, 24.73% and 67.97%. (b) The change of mooring stiffness of Serbuoys-TLP will accompa nied with the addition of buoys on the tendons. A wave period (Tp) which corresponds to resonance in the time histories of the surge exists. The suppressive effect is not good or even worse in the motion response of the TLP near this wave period. Therefore, the wave period should be given more attention in the application of Serbuoys-TLP. (c) As the position of the buoys becomes deeper and the displace ment of buoys increases, the wave period corresponding to Tp becomes larger. According to the static analysis method, we can draw the conclusion that both mooring stiffness and the mass of buoys have certain influence on the suppressive effect. Based on this trend, we can make the wave period corresponding to reso nance avoid the common wave periods under the actual sea conditions by changing the parameters of the buoys. And the parameters of buoys adapted to the East China Sea are given. 6. Future works Many challenges related to the feasibility of the Serbuoys-TLP system still remain, and the development of the concept for actual deployment requires further investigation. Challenges will include the redistribution of the tension, the installation process of buoys, analysis of the effect of long-term fatigue, and effective survival strategies for extreme sea cases. The study of these aspects should be included in future research. Acknowledgements This research was supported by the Fundamental Research Funds for the National Key Research and Development Program of China (Grant 8
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Teigen, P., Niedzwecki, J.M., 1998. Experimental and Numerical Assessment of Mini Tlp for Benign Environments. Wang, H., 2014. Dynamic analysis of a tension leg platform for offshore wind turbines. Power Technologies 1 (94), 42–49. Yang, C.K., Kim, M.H., 2010. Transient effects of tendon disconnection of a tlp by hulltendon-riser coupled dynamic analysis. Ocean. Eng. 37 (8–9), 667–677.
Yeung, R.W., 1982. Added mass and damping of a vertical cylinder in finite-depth waters. Appl. Ocean Res. 4 (1), 63. Zheng, C., Zhuang, H., Li, X., Li, X., 2012. Wind energy and wave energy resources assessment in the East China Sea and south China sea. Sci. China Technol. Sci. 55 (1), 163–173. Zheng, Y.H., You, Y.G., Shen, Y.M., 2004. On the radiation and diffraction of water waves by a rectangular buoy. Ocean. Eng. 31 (8–9), 1063–1082.
9
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Ocean Engineering journal homepage: www.elsevier.com/locate/oceaneng
Experimental and numerical study on the multi-body coupling dynamic response of a Novel Serbuoys-TLP wind turbine Zhe Ma a, Shaoxiong Wang a, Yin Wang a, *, Nianxin Ren b, Gangjun Zhai a a b
State Key Laboratory of Coast and Offshore Engineering, Dalian University of Technology, Dalian, 116024, China College of Civil Engineering and Architecture, Hainan University, Haikou, 570228, China
A R T I C L E I N F O
A B S T R A C T
Keywords: Offshore wind turbines (OWT) Serbuoys-TLP Dynamic analysis Model test Multibody effect
The floating wind turbine (FWT) based on the tension leg platform (TLP) plays an important role in addressing the issue of energy pinch, but the central characteristic for TLP is that in vertical direction it is similar to a rigid structure with tension tendons to restrain motion, while in horizontal direction, it seems to be compliant with less constrain. The large amplitude motions in the horizontal plane caused by this compliance will seriously affect the performance of the platform under harsh environmental conditions. To address this problem, a new type of tension leg platform wind turbine connected with a series of buoys (Serbuoys-TLP) is proposed. A timedomain simulation program (DUTMST) for the TLP and Serbuoys-TLP based on MATLAB is provided, with consideration of the multi-body coupling effect between the body, tension leg and buoy. That is, each buoy can be analysed as a separate mass structure connected on the tension leg. The accuracy of DUTMST is discussed via comparison with the results of an experiment and AQWA. The dynamic responses of TLP and Serbuoys-TLP are presented in DUTMST. The results show that the Serbuoys-TLP can significantly reduce the horizontal response of the TLP. In addition, the horizontal response suppression effects of Serbuoys-TLP are investigated by varying the wave factor and parameters of buoys. Additionally, the parameters of buoys adapted to the East China Sea are given.
1. Introduction With the exhaustion of traditional energy, the past decade has seen the rapid development of new renewable energies in many fields, such as solar energy, wave energy, tidal energy and wind energy (Bevrani et al., 2010). Floating wind turbines (FWTs), as an important component of offshore structures, is playing a key role in capturing wind energy from deep-water area and have thus attracted increasing attention in recent years (Leung and Yang, 2012). Since Heronemus (1972) proposed the concept of offshore FWTs in 1972, the spar-type wind turbine Hywind in the North Sea and the semi-submersible wind turbine WindFloat in Portuguese waters have carried out full-scale prototype sea trials and grid-connected power generation (Roddier et al., 2010; Skaare et al., 2015). As a professional institute in floating foundations for offshore wind, IDEOL has been engineering and accompanying floating offshore wind projects from conception to installation. They have also developed a series of new projects, such as Floatgen, which is installed in France and Hibiki installed in Japan (http://www.ideol-offshore.com). The damping-pool system of IDEOL has been tested and will be applied in
Japan (Beyer et al., 2015). All the recent studies above demonstrate an exciting prospect for FWTs. Compared with other FWTs, the appearance of tension-leg-type FWTs is late. The National Renewable Energy Laboratory (NREL) pro posed the concept of a tension-leg-type FWT in 2005 and compared it with spar-type and semi-submersible wind turbines (Musial et al., 2004). Matha et al. under the support of NREL, comprehensively studied the dynamic performance of a 5 MW tension-leg-type FWT in 2009. This study confirmed the superiority of tension leg platform foundations in FWT application (Matha, 2009). A TLP is a typical compliant offshore platform with a vertical mooring system. Similar to application in the offshore oil industry, the dynamic response has always been the focus of scholars’ attention because the large amplitude dynamic response will affect the normal operation of the wind turbines (Bangga et al., 2018). Several theories on the dynamic response of TLP have been proposed. Jain (1997) presented dynamic response analysis of a TLP to deterministic first order wave forces considering coupling between the degrees of freedom of surge, sway, heave, roll, pitch and yaw. Joseph et al. (2004) reported the
* Corresponding author. E-mail address: [email protected] (Y. Wang). https://doi.org/10.1016/j.oceaneng.2019.106570 Received 17 July 2018; Received in revised form 7 October 2019; Accepted 13 October 2019 Available online 22 October 2019 0029-8018/© 2019 The Authors. Published by Elsevier Ltd. This is an (http://creativecommons.org/licenses/by-nc-nd/4.0/).
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results of a detailed experimental and numerical investigation of the coupled dynamic behaviour of a mini TLP. Abaiee et al. (2016) devel oped two different numerical models, the finite element model (FEM) based on the Morison equation and the boundary element model (BEM) based on a 3D diffraction/radiation theory. Some scholars also have conducted the fully-coupled dynamic analysis of TLP-FOWTs in time domain. Bae et al. (2013) developed a numerical simulation tool including aero-blade-tower dynamics and control, mooring dynamics, and platform motions. Yang et al. (2010) developed a time-domain nonlinear global-motion-analysis program for floating hulls coupled with risers/mooring lines to check the survivability of a TLP with the loss of one or two tendons by accident. Nematbakhsh et al. (2015) compared the wave load effects on a TLP wind turbine by using computational fluid dynamics and potential flow theory approaches. Studies over the past two decades have provided important infor mation on how to simulate the dynamic response of a TLP. However, data from these studies suggest that there are some disadvantages inherent in the dynamic response of a typical TLP, like the large motion response. Therefore, many of the current studies on TLPs pay particular attention to improving the structure form to reduce the dynamic response in the horizontal plane (Bachynski et al., 2012). Wang et al. (2014) proposed the conceptualization of a floating offshore wind tur bine tension leg platform (HIT-FOWT-TLP) that a concrete ballast model is arranged underneath the spoke bottom plane to serve as permanent ballast, and compared it to the traditional NREL-TLP model. Rao et al. (2012) proposed a new concept of a tension-based TLP (TBTLP) and obtained response amplitude operators (RAOs) of the TBTLP with one tension base in terms of the surge, heave and pitch, comparing it with a TLP without a tension base. These studies provide new insights into conceptual design of TLP, but the improvements mentioned above are more effective for heave. In previous studies on the design of a system with low motions, GICON®-TLP with the angled ropes is relatively mature. Adam et al. have carried out comprehensive research, including numerical simula tion and model experiments (Adam et al., 2014). A pilot plant of GICON®-TLP has been designed for this offshore location in the Baltic Sea. However, the applicable water depth of GICON®-TLP wind turbine is limited due to the economic viability with the increase of applied water depth. This paper gives the concept of a new type of tension-leg-type wind turbine connected with a series of buoys (Ser buoys-TLP), which attempts to reduce the dynamic response of the TLP in the horizontal plane. However, much of the calculation software up to now cannot consider the coupling dynamic response of a series of buoys. Therefore, this paper provides a time-domain simulation program (DUTMST), based on MATLAB, with consideration of the multi-body
coupling between the body, tension leg and buoy. Dynamic analysis of the TLP and Serbuoys-TLP by DUTMST is performed and compared to the results of an experiment and commercial software AQWA. Using the proposed program DUTMST, some numerical studies are conducted in order to highlight the effect of a few important parameters on the Serbuoys-TLP response. 2. Methodology 2.1. Proposed Serbuoys-TLP The Serbuoys-TLP is a typical TLP wind turbine, which consists of a central column, pontoons and tendons. In addition, a series of buoys are connected to the tendon legs. The wind turbine is the 5 MW model proposed by NREL. A sketch of the Serbuoys-TLP is shown in Fig. 1(a) and (b). For multibody structures, coupling forces are predominant in the analysis process. To incorporate the coupling phenomena, the equation of motion describing the dynamic equilibrium between the wind turbine foundation and buoys can be assembled as follows: € þ ½C�fxg _ þ ½K�fxg ¼ fFe g þ ½M�fxg
4 X �
� � �� Fmj fxg; xj ; t
(1)
j¼1
where [M] is the diagonal mass matrix for all six degrees of freedom, including platform mass and additional mass; [C] is the radiation damping matrix; [K] is the hydrostatic stiffness matrix; {Fe} is the vector of forcing apart from the mooring force; {Fmj} is the vector of mooring force provided by tension leg j; and x€, x_ and x are the acceleration, ve locity and displacement vectors of the platform, respectively
(x ¼ ½x; y; z; rx; ry; rz�T ). Each buoy can be analysed as a separate mass structure connected on the tension leg, establishing the buoys’ equation of motion (j ¼ 1; 2; 3; 4): � �� � � �� � � � � �� n 0 � � �o Mj x€j þ Cj x_j ¼ Fmj fxg; xj ; t þ Fmj xj ; t (2) where [Mj] is the mass matrix of buoy j for all six degrees of freedom, including buoy mass and additional mass; [Cj] is the damping matrix of buoy j; {Fmj} is the same as {Fmj} in equation (1); {F’mj}is the vector of force provided by the lower section of tension leg j; and x€j , x_j and xj are the acceleration, velocity and displacement vectors of buoy j, respectively.
(a) Sketch of the model
(b) Top view of the foundation
Fig. 1. Sketch of the Serbuoys-TLP. 2
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2.2. Numerical implementation
damping Bjk and wave forces under different wave frequencies F(ω) (Yeung et al. 1982). Ajk, Bjk and F(ω) are written as: Z ρ ! Ajk ¼ Im½ϕrk ð X Þ�nj dS (3)
The coupling effect between buoys and platform is the dominant factor in the analysis of Serbuoys-TLP. Nevertheless, the traditional software AQWA cannot consider the coupling dynamic response brought by the buoys and only equips the buoys as a tension leg with an increased diameter. Therefore, DUTMST has been developed to inves tigate the coupling dynamic response of the Serbuoys-TLP. Frequency domain analysis can only perform the linear analysis, which is cheap and easy (Low et al., 2009). To incorporate the nonlinear phenomena, DUTMST adopts time domain analysis using the Runge-Kutta (Alexander et al. 1977) step-by-step numerical integration technique to solve equations (1) and (2). The solution flow chart of DUTMST is shown in Fig. 2. As shown in Fig. 2, the kernel of DUTMST mainly consists of two parts: the obtaining of hydrodynamic parameters and the calculation of mooring force related to the displacement. The details of these two parts are showed in Section 2.3 and 2.4. ALINEread is a function to obtain the hydrodynamic results.
ω
S0
Z Bjk ¼
!
(4)
ρ Re½ϕrk ð X Þ�nj dS S0
Z FðωÞ ¼
iωρ
! ϕI ð X Þnj dS
S0
Z iωρ
! ϕd ð X Þnj dS
(5)
S0
! where ρ is water density; ω is the wave frequency; ϕrk ð X Þ is the radiation ! ! wave potential; ϕI ð X Þ and ϕd ð X Þ are the incident wave potential with unit wave amplitude and the corresponding diffraction wave potential, respectively; and nj is the unit normal vector of the floating body surface. The numerical model in AQWA is shown in Fig. 3 (a) and (b), whose size is consistent with the prototype. The models of the platform and buoys are established in AQWA separately. By means of the function (ALINEread) provided by DUTMST, we can obtain the added mass ma trix, radiation damping matrix and wave forces of the platform. It is assumed that the buoys are not affected by waves because the buoys are far from the surface of the water. For example, the maximum wave excitation force is merely 3.5t equalling to the 1.5% of a buoy displacement when wave period is 18s and buoy displacement is 250t. It indicated that the wave force acting on the buoys are negligible, and are thus not considered here. We only obtain the added mass matrix and radiation damping matrix of the buoys by ALINEread. Based on the results of the calculation in AQWA, the wave forces in DUTMST are given as:
2.3. Hydrodynamic force vectors There are three main types of study design used to identify predicted wave loads acting on offshore floating bodies: the diffraction-radiation theory (Mei et al., 1978), the Morison’s type equation (Morison et al., 1950) and computational fluid dynamics (CFD) (Nematbakhsh et al., 2013). The Morison’s type equation is an empirical formula, and the accuracy of it depends heavily on the choice of coefficients Cd and Cm. The results of CFD are relatively accurate. However, the calculation of CFD requires large amount of computation resource. (Nematbakhsh et al., 2015). Therefore, the diffraction-radiation theory may be better compared with the other two methods. One advantage of the diffraction-radiation theory is that it avoids the problem of a long calculation time. The dynamic responses of the Serbuoys-TLP can be simulated in a multi-group working condition to explore the effect of buoys. Another advantage of the diffraction-radiation theory is that this method is more mature. Many commercial software packages have utilized it to solve practical problems and obtain proven results (Zheng et al., 2004). The relevant hydrodynamic coefficients of platform and buoys are obtained by AQWA. It contains two model settings for simplifying the tension leg: a massless spring model (spring element) and a nonlinear beam model (tube element). The tube element can better consider the added mass and radiation damping. DUTMST provides a function (ALINEread) which can obtain the hydrodynamic results of any struc ture calculated by AQWA, including the added mass Ajk, radiation
FðtÞ ¼ A⋅FðωÞ⋅ei½
(6)
ωtþkðx cos χ þy sin χ Þþφ�
where A is the wave amplitude; k is the wave number; (x, y) is the barycentric coordinate of the platform; χ is the incident angle of the wave; φ is the initial phase; and F(ω) is the wave forces under different wave frequencies. Both F(ω) and φ are obtained by ALINEread. 2.4. Tension vector In the process of solving equations, we should firstly establish the relationship between tension and the position of buoys and platform. Only in this way can we achieve the positions of platform and buoys in next step through the tension in this time step. The tension calculation includes two sections, Fmj and F’mj, simplifying the tension leg as a massless spring model. The force analysis diagram is shown in Fig. 4(a). The tension vector of a tether can be given as:
(a) Serbuoys-TLP Fig. 2. Solution flow chart of DUTMST.
Fig. 3. Numerical model in AQWA. 3
(b) Buoys
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Ocean Engineering 192 (2019) 106570
2
1 ½RX� ¼ 4 0 0
0 cosðrxÞ sinðrxÞ
3 0 sinðrxÞ 5 cosðrxÞ
(12)
The coordinates of points U and D in OXYZ can also be obtained according to this method. Only need to change the fxg into the bar ycentric coordinate of the buoys fxj g and change [xp,yp,zp]T into the coordinate of point U and D in COGζηξ. In this way, the instantaneous tension of the tension leg can be calculated based on the displacements of the platform and buoys in real time. 3. Validation of the numerical model (a) Force analysis
3.1. Set-up of the physical test
(b) Coordinate system
Fig. 4. Diagram of the Serbuoys-TLP.
Fmj ¼ T0 þ
F’mj ¼
EA �! ðjPU j Lu0
�! PU Lu0 Þ �! jPU j
T0 EA �! ðjAD j þ Fb þ Ld0 4
�! AD Ld0 Þ �! jAD j
The Serbuoys-TLP model being considered is square in plan view, as shown in Fig. 1, with four buoys attached to the tension leg. To verify the accuracy of the program DUTMST, scale model tests of the Serbuoys-TLP system have been performed in the advanced wind tunnel and wave flume joint laboratory at the Harbin Institute of Technology (HIT). The experimental model of the floating wind turbine foundation is shown in Fig. 5(a), and that of the buoys is shown in Fig. 5(b). Comprehensively considering the condition of the laboratory and the size of the full-scale Serbuoys-TLP system, the scale ratio of the Serbuoys-TLP test model has been designed to be 1/50 in line with Froude scaling laws (Ren et al., 2012). The main design parameters of the Serbuoys-TLP and wave data are given in Table 1.
(7)
(8)
�! jPU j ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðxU xP Þ2 þ ðyU yP Þ2 þ ðzU zP Þ2
(9)
�! jAD j ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðxD xA Þ2 þ ðyD yA Þ2 þ ðzD zA Þ2
(10)
3.2. Comparison between numerical and experimental studies
where { Fmj } and { F’mj } are the same as in equations (1) and (2). Point P (xP, yP, zP) is the point of the tension leg attached on the foundation; points U (xU, yU, zU) and D (xD, yD, zD) are the points of the tension leg attached on the buoy; and point A (xA, yA, zA) is the tension leg anchor point. Therefore, they denote the instantaneous vector joining the endpoints of the tether. E is the Young’s modulus; A is the cross-sectional area of the tether; Lu0 and Ld0 are the initial length of the upper and lower sections of the tether, respectively; and T0 and Fb are the net force of the foundation and buoys. For the nonlinear model in the present study, the tension vector is a nonlinear function of the displacements because higher order compo nents are considered in the calculation of the instantaneous length of the tether (Cheng et al., 2018). Therefore, the acquisition of the coordinates of points P, U and D is especially important. A method of coordinate conversion is given to obtain the coordinates of the platform and the upper and lower nodes of the buoys (Sugita et al., 2016). Two right-handed Cartesian coordinate systems, OXYZ and COGζηξ, are defined in Fig. 4(b). OXYZ is the space-fixed coordinate system, where plane OXY coincides with the undisturbed calm water surface. COGζηξ is the body-fixed coordinate system, where COG coincides with the centre of gravity of the platform. The coordinate of point P (xPj yPj zPj ) in OXYZ is: 2 3 2 3 2 3 xPj xp x 4 yPj 5 ¼ 4 y 5 þ ½RZ�½RX�½RY�4 yp 5 (11) zPj zp z
The Serbuoys-TLP is a multi-body coupling system, so each buoy should be analysed as a separate mass structure. The experimental model of the Serbuoys-TLP is consistent with the DUTMST program considering buoys connected on the tension leg. Nevertheless, AQWA cannot consider the Serbuoys-TLP as a multi-body system and the buoy can only be equivalent to a tension leg with an increased diameter. However, as the basis of DUTMST, AQWA is also carried out in the process of the numerical study in order to primarily study the dynamic responses of the Serbuoys-TLP. The numerical model in AQWA is the same as in section 2.3. Considering that the surge responses usually play a dominant role for the Serbuoys-TLP floating system, we are more concerned about the surge of the TLP. The results of surge in AQWA, DUTMST and the experiment are shown in Fig. 6. Fig. 6 (a) is the time history of Serbuoys-TLP under the work condition in Table 1. The ordinate of Fig. 6 (b) is dimensionless parameters represented by the average amplitude of the time-domain results under wave period 5.66 s, 7.07 s, 8.48 s, 9.90 s, 11.31 s, 12.73 s, 14.70 s. And similar conclusions can be drawn from the two Figures. As shown in Fig. 6, the results indicate that the numerical results of both DUTMST and AQWA have a good agreement with the experimental data, although, compared with the results of DUTMST, it is illogical that the surge obtained in the AQWA are smaller than the experimental value. Because of without accounting for the damping effect completely in the scale test model, the numerical results should be larger than the
where fxg ¼ ½x; y; z; rx; ry; rz�T is the displacement vectors of the plat form; [x,y,z]T is the barycentric coordinate of the platform; [rx,ry,rz]T is the roll, pitch and yaw of the platform; and [xp,yp,zp]T is the coordinate of point P in COGζηξ. 2 3 2 3 cosðrzÞ cosðrzÞ 0 cosðryÞ 0 sinðryÞ ½RZ� ¼ 4 sinðrzÞ sinðrzÞ 0 5½RY� ¼ 4 0 sinðryÞ 0 5 0 0 1 sinðryÞ 0 cosðryÞ (a) Floating wind turbine foundation
(b) Model of the buoys
Fig. 5. Experiment model of the Serbuoys-TLP. 4
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Ocean Engineering 192 (2019) 106570
wave conditions. Based on the above research, the dynamic response of the typical TLP and Serbuoys-TLP has been simulated in DUTMST under four different wave conditions. The time histories of the surge are shown in Fig. 8 to compare the dynamic responses of the TLP and Serbuoys-TLP in the plane. From Fig. 8(a), (b) and (c), we can see that the surge of the Serbuoys-TLP is obviously less than that of the TLP. This result indicates that the Serbuoys-TLP can exhibit effective improvement in the dynamic responses compared to the TLP in the plane and exhibits a good effect in suppressing the dynamic responses of the TLP in the plane. However, the suppressive effect is different under the different wave conditions. Surprisingly, suppression of the surge of the TLP is not observed in Fig. 8(d). Instead, the surge of the Serbuoys-TLP is larger than that of the TLP under this wave conditions (wave period T ¼ 6 s). These results suggest that the suppressive effect of the Serbuoys-TLP on the dynamic responses of the TLP in the plane is affected by wave parameters. Therefore, the next section of the study was concerned with factors that affect the suppressive effect of the Serbuoys-TLP.
Table 1 Main design parameters of the Serbuoys-TLP and wave data. Parameters NTEL 5WM Wind turbine Blades and Nacelle mass (kg) Tower mass (kg) Tower Height(m) TLP platform Buoyancy (kg) Total mass (kg) Water depth (m) Centre of gravity (m) Ixx � Iyy; Izz (kg⋅m2) Spoke design (m) Tension leg (m) Parameter of buoys Buoy height (m) Buoy radius (m) Displacement (t) Installation position (m) Wave data Wave height (m) Wave period (s)
Full scale
Scaled (λ ¼ 1/50)
350,000;
2.80;
350,000 90
2.80 1.80
5214,000 2814,000 170 (0,0,-5.0) 4.5 � 109; 5.0 � 108 L ¼ 20.0; A ¼ 4.0*4.0 L ¼ 140; D ¼ 1.2; t ¼ 0.04
41.71 22.51 3.40 (0,0,-0.02) 14.40; 1.6 L ¼ 0.40; A ¼ 0.08*0.08 Equivalent steel cable
10 4.2 4*250 Z ¼ 95
0.2 0.084 4*0.002 Z ¼ 1.9
3 8.485
0.06 1.2
4.2. Influence of wave factors on the suppressive effect of the SerbuoysTLP The dynamic responses of the Serbuoys-TLP and typical TLP are calculated under 27 wave conditions consisting of different wave pe riods, wave heights and wave heading angles. These wave parameters are listed in Table 2. To display the results more conveniently, dynamic
experimental value (Teigen et al., 1998). It may be caused by the un reasonable simplification that the buoy is equivalent to a tension leg with an increased diameter in AQWA. As far as this is concerned, the results obtained in DUTMST are more logical. In addition, DUTMST is an open source program implemented by MATLAB. Therefore, it is more convenient for advanced development to investigate the factors on the suppressive effect of the Serbuoys-TLP compared with AQWA.
DUTMST AQWA
1.0
4. Discussion
0.5
Surge (m)
4.1. Comparison of the Serbuoys-TLP and a typical TLP To compare the differences between the Serbuoys-TLP and a typical TLP, DUTMST also provides a time-domain simulation program for a typical TLP, which is exactly the same as the Serbuoys-TLP except that no buoys are on the tension leg. Compared with the Serbuoys-TLP, the analysis of the typical TLP is simpler because only equation (1) needs to be solved using the Runge-Kutta step-by-step numerical integration technique. To assess the accuracy of DUTMST for the typical TLP, the time histories of the surge predicted by DUTMST are compared with the numerical results of AQWA in Fig. 7. It is worth noting that the tension leg in AQWA is also simplified to spring element here like the DUTMST. The wave data of the numerical study is the same as in Table 1 (wave period T ¼ 8.485 s, wave height H ¼ 3 m). It is apparent from Fig. 7 that the results obtained from DUTMST have good agreement with the results of AQWA. It has been verified that this trend remains under different
Surge (m)
0.8
0.7 0.6 0.5 0.4 0.3 458
460
-0.5
-1.0 100
Experiment DUTMST AQWA
462
140
t (s)
160
0.8
DUTMST
0.4 0.0
Experiment AQWA
0.6 0.4 0.2
-0.4 -0.8 400
120
420
440
460
480
180
200
Fig. 7. Surge of the typical TLP obtained with AQWA and DUTMST.
Surge (m)
1.2
0.0
0.0
500
t (s) (a) Time History of Serbuoys-TLP
4
6
8
12
(b) RAO of Serbuoys-TLP
Fig. 6. Surge response of the Serbuoys-TLP. 5
10
Wave period (s)
14
16
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Ocean Engineering 192 (2019) 106570
TLP Serbuoys-TLP
1.6
-0.8
0.8
Surge(m)
Surge(m)
0.8 0.0
TLP Serbuoys-TLP
1.6
0.8 0.6 0.4 127 128 129 130 131
-1.6 100
120
0.0
1.0 0.8
-0.8
140
t (s)
160
180
120 121 122 123 124
-1.6 100
200
120
(a) T=8.485s H=3m
180
200
TLP Serbuoys-TLP
0.8
Surge(m)
Surge(m)
-0.8
160
1.6
0.8 0.0
t (s)
(b) T=10s H=3m
TLP Serbuoys-TLP
1.6
140
1.4
1.2 121
-1.6 100
122
123
120
0.2
-0.8
124
140
0.4
0.0
t (s)
160
180
-1.6 100
200
162
163
164
120
(c) T=12s H=3m
165
140
t (s)
160
180
200
10
12
(d) T=6s H=3m
Fig. 8. Surge of the TLP simulated in DUTMST.
responses under each wave condition are represented by the average amplitude of the time-domain results between 100 s and 200 s. The surge motion amplitudes of the Serbuoys-TLP and typical TLP under wave condition A are shown in Fig. 9. The surge motion ampli tudes of the Serbuoys-TLP and typical TLP both increase gradually as the wave period increases. When the wave period is approximately 7 s, the dynamic response of the Serbuoys-TLP exhibits a peak value. Before the wave period reaches this peak, the Serbuoys-TLP cannot suppress the surge motions of the TLP, and the surge motions of it become larger than those of the TLP. After the wave period reaches this peak, the SerbuoysTLP has a good suppression effect on the dynamic response of the TLP in the plane, and the suppression effect decreases with the increase of the wave period. A possible reason for these results is that the natural fre quency of the Serbuoys-TLP coincides with the frequency of the incident wave, causing resonance. Therefore, when the parameters of the Serbuoys-TLP are determined, the dynamic responses of the SerbuoysTLP under different wave periods should be discussed. The surge motion amplitude of the Serbuoys-TLP and typical TLP under wave conditions B and C are shown in Fig. 10(a) and (b). The suppressive rates for the surge motion of the TLP are listed in Table 3. As shown in Fig. 10 and Table 3, although the surge motions of the Serbuoys-TLP and TLP are different under different wave conditions, the suppressive rate is basically constant as the wave height and wave
Surge (m)
0.8
Incident angle of wave (� )
Wave height (m)
Wave period (s)
Group A (11) Group B (9) Group C (7)
0
1
0 0; 15; 25; 45; 60; 75; 90
1; 2; 3; …; 7; 8; 9 1
3; 4; 5; …; 11; 12; 15 10 10
0.4 0.2 0.0
2
4
6
8
14
16
Wave period (s) Fig. 9. Surge contrast of the TLP and Serbuoys-TLP under working condition A.
incident angle change. When the incident angle of the wave is 90� , the surge motions of the TLP and Serbuoys-TLP are very small, so it is meaningless to discuss the suppressive rate here. 4.3. Influence of buoy factors on the suppressive effect of the SerbuoysTLP
Table 2 Regular Wave conditions. Groups
Serbouys-TLP TLP
0.6
The analysis of section 4.2 indicates that the wave period plays an important role in the suppressive effect of the Serbuoys-TLP on the dy namic responses of the TLP in the plane. The main reason is that the buoys connected on the tension leg change the natural frequency of the Serbuoys-TLP. In actual conditions, it is particularly important to investigate the applicability of buoy parameters. Therefore, the dynamic responses of the Serbuoys-TLP and typical TLP are calculated under working conditions D, E, F and G to investigate 6
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Ocean Engineering 192 (2019) 106570
0.4
Serbouys-TLP
2.4 1.6 0.8 0.0
Serbouys-TLP
0.3
TLP
Surge(m)
Surge(m)
3.2
TLP
0.2 0.1 0.0
0
2
4
6
Wave height (m)
8
-0.1 -15
10
0
15
30
45
60
75
Incident angle of wave(°)
(a) Group B
90
(b) Group C
Fig. 10. Surge contrast of the TLP and Serbuoys-TLP under working conditions B and C.
0.6
Wave condition
Suppressive rate
Wave condition
Suppressive rate
B B B B B B B B
7.71% 7.71% 7.71% 7.71% 7.70% 7.70% 7.70% 7.70%
B (H ¼ 9 m) C (θ ¼ 0� ) C (θ ¼ 15� ) C (θ ¼ 30� ) C (θ ¼ 45� ) C (θ ¼ 60� ) C (θ ¼ 75� ) C (θ ¼ 90� )
7.69% 7.70% 7.71% 7.70% 7.70% 7.69% 7.69% ——
(H ¼ 1 m) (H ¼ 2 m) (H ¼ 3 m) (H ¼ 4 m) (H ¼ 5 m) (H ¼ 6 m) (H ¼ 7 m) (H ¼ 8 m)
Surge (m)
Table 3 The suppressive rate of the Serbuoys-TLP for the surge under working conditions B and C.
Group Group Group Group
D (11) E (11) F (11) G (11)
0.2
2
4
6 8 10 Wave period (s)
12
14
Fig. 11. Surge contrast of the TLP and Serbuoys-TLP under working conditions D, E, F and G. Table 5 Suppressive rate of the Serbuoys-TLP for the surge under working conditions G. Wave condition
Suppressive rate
Wave condition
Suppressive rate
G (T ¼ 3 s) G (T ¼ 4 s) G (T ¼ 5 s) G (T ¼ 6 s) G (T ¼ 7 s)
5.15% 11.77% 27.57% 102.78% 67.97%
G G G G G
42.20% 30.37% 24.85% 21.65% 19.31%
(T ¼ 8 s) (T ¼ 9 s) (T ¼ 10 s) (T ¼ 11 s) (T ¼ 12 s)
increases with the increase displacement of the buoys, the Tp increased as well. This unusual phenomenon is because the total mass of Serbuoys-TLP increases with the increase of displacement of buoys. Therefore, we can conclude that the mass of the buoys also has a great influence on the natural frequency of the total system. rffiffiffiffiffiffiffi 2π K11 ω¼ ¼ (13) Tp M The TLP provided in this paper is more suitable for the East China Sea (Zheng et al., 2012), where the common wave periods are 6 s–8 s. Based on this trend, it is practical in the East China Sea on condition that the buoys will be located 60 m underwater and the displacement of buoys be set as 250 t. The suppressive efficiency under the corresponding working condition D is listed in Table 6. In this way, the Serbuoys-TLP can effectively suppress the horizontal dynamic responses of the TLP.
Table 4 Working conditions. Groups
0.4
0.0
the influence of the position of and displacement of buoys on the sup pressive effect of the Serbuoys-TLP. The working conditions are listed in Table 4, and each group includes 11 situations of wave periods from 3 s to 15 s (wave height H ¼ 1 m, incident angle of wave θ ¼ 0� ). The surge motions of the TLP and Serbuoys-TLP are shown in Fig. 11. A pre liminary analysis of the variation in the wave period corresponding to the peak with the buoy parameters is given. As seen from Fig. 11, the numerical results obtain a good agreement with the results of group A, and a peak value also exist in the time his tories of the Serbuoys-TLP. However, as the position of the buoys become deeper and the displacement of the buoys increases, the wave period corresponding to the peak (Tp) is larger. The suppressive effect of the Serbuoys-TLP also is influenced by the Tp. The suppressive effect under work condition G seem to be the best and the suppressive effi ciency is listed in Table 5. The change of Tp accompanied with the buoy factors may be caused by the change of mooring stiffness of SerbuoysTLP. In order to further interpret this phenomenon and discuss the in fluence of buoy factors on mooring stiffness, the static analysis of Serbuoys-TLP is carried out and the results are shown in Fig. 12. The δx in Fig. 12 is the initial offset of the platform in the surge and Fx is the horizontal restoring force caused by δx. Based on the results obtained above, we can see that the mooring stiffness will decrease as the position of the buoys become deeper. Ac cording to Eq.(16), we can observe that Tp increases with the decrease of stiffness when the total mass is constant. Therefore, the increase of Tp will occur as the position of the buoys become deeper. The mooring stiffness of Serbuoys-TLP will increase as the displacement of the buoys increase. Surprisingly, although the mooring stiffness of Serbuoys-TLP
TLP D(-60m,250t) E(-95m,250t) F(-95m,400t) G(-60m,400t)
5. Conclusions Position of buoys (m) 60 95 95 60
Displacement of buoys (t)
In this study, a concept of Serbuoys-TLP is provided firstly, and the dynamic behaviors of Serbuoys-TLP have been investigated both experimentally and numerically (using the time-domain simulation program (DUTMST)). DUTMST, which is based on MATLAB, take
4*250 4*250 4*400 4*400
7
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Ocean Engineering 192 (2019) 106570
Fx (N)
3x105
4x105
TLP Serbuoys-TLP(250 t) Serbuoys-TLP(400 t)
3x105 Fx (N)
4x105
2x105 1x105
TLP Serbuoys-TLP(-60 m) Serbuoys-TLP(-95 m)
2x105 1x105
0 -0.6 0.0
0.6
1.2
1.8
2.4
3.0
0 -0.6 0.0
3.6
x (m)
0.6
1.2
1.8
2.4
3.0
3.6
x (m)
Fig. 12. The static analysis of Serbuoys-TLP about horizontal resilience.
No. 2016YFE0200100), the Central Universities (Grant No. DUT19JC47), National Natural Science Foundation of China (Grant No. 51709040). The financial support is greatly acknowledged.
Table 6 Suppressive rate of the Serbuoys-TLP for the surge under working conditions D. Wave condition
Suppressive rate
Wave condition
Suppressive rate
D (T ¼ 3 s) D (T ¼ 4 s) D (T ¼ 5 s) D (T ¼ 6 s) D (T ¼ 7 s)
5.76% 14.77% 52.01% 54.21% 30.48%
D (T ¼ 8 s) D (T ¼ 9 s) D (T ¼ 10 s) D (T ¼ 11 s) D (T ¼ 12 s)
21.54% 17.65% 15.47% 14.04% 12.82%
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consideration of the multi-body coupling effect between the foundation, tension legs and buoys. The results of DUTMST are compared with data from experiment and AQWA. The comparisons showed that the nu merical results of DUTMST obtain a better agreement with experimental results compared to the numerical results of AQWA. The following conclusions are summed up based on the numerical studies conducted with DUTMST under different working conditions: (a) The Serbuoys-TLP has a certain suppressive effect on the dynamic responses of the TLP in the plane. The highest suppressive rates under the different working conditions D, E, F and G are 54.21%, 16.62%, 24.73% and 67.97%. (b) The change of mooring stiffness of Serbuoys-TLP will accompa nied with the addition of buoys on the tendons. A wave period (Tp) which corresponds to resonance in the time histories of the surge exists. The suppressive effect is not good or even worse in the motion response of the TLP near this wave period. Therefore, the wave period should be given more attention in the application of Serbuoys-TLP. (c) As the position of the buoys becomes deeper and the displace ment of buoys increases, the wave period corresponding to Tp becomes larger. According to the static analysis method, we can draw the conclusion that both mooring stiffness and the mass of buoys have certain influence on the suppressive effect. Based on this trend, we can make the wave period corresponding to reso nance avoid the common wave periods under the actual sea conditions by changing the parameters of the buoys. And the parameters of buoys adapted to the East China Sea are given. 6. Future works Many challenges related to the feasibility of the Serbuoys-TLP system still remain, and the development of the concept for actual deployment requires further investigation. Challenges will include the redistribution of the tension, the installation process of buoys, analysis of the effect of long-term fatigue, and effective survival strategies for extreme sea cases. The study of these aspects should be included in future research. Acknowledgements This research was supported by the Fundamental Research Funds for the National Key Research and Development Program of China (Grant 8
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Yeung, R.W., 1982. Added mass and damping of a vertical cylinder in finite-depth waters. Appl. Ocean Res. 4 (1), 63. Zheng, C., Zhuang, H., Li, X., Li, X., 2012. Wind energy and wave energy resources assessment in the East China Sea and south China sea. Sci. China Technol. Sci. 55 (1), 163–173. Zheng, Y.H., You, Y.G., Shen, Y.M., 2004. On the radiation and diffraction of water waves by a rectangular buoy. Ocean. Eng. 31 (8–9), 1063–1082.
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