1. Introduction
Wind energy has the advantages of the lowest environmental impacts, and high cost efficiency and sustainability. Wind energy contributed almost 34% of the total newly installed renewable energy capacity in 2016 [
1] and the generation of wind energy experienced a rapid growth during the past ten years worldwide [
2]. Especially, the exploitation of offshore wind energy has become an important development direction of wind energy industry [
3]. As the design water depth of offshore wind farms is becoming deeper and deeper, the foundation of offshore wind turbine (OWT) is changing from the traditional fixed-bottom type to innovative floating type, which might be more suitable and more potentially economical for deep water [
4].
Floating foundations are deeper water substructures that aimg to harness better wind resources in further out open seas. The floating offshore wind turbine (FOWT) consists of a floating platform and a mooring system connecting to the seabed. The most representative one is the “Hywind” in Norway, which is the first floating offshore wind turbine project in the world [
5]. The tension leg platform (TLP) because of its excellent performance, has gradually become an important type of structure of developing deep-sea wind resources [
6].
The U.S. National Renewable Energy Laboratory (NREL) proposed the concept of a tension-leg-type FWT in 2005 and compared it with the other wind turbines [
7]. Matha et al. comprehensively investigated the dynamic performance of a 5 MW tension-leg-type FOWT in 2009. This study confirmed the advantage of tension leg platform foundations in FWT applications [
8]. Zhao et al. [
9] preliminarily designed a multi-column TLP foundation for a 5-MW offshore wind turbine. Studies of the mini tension-leg platform have also greatly promoted the development of tension-leg-type FOWTs and also provide some important methods for analyzing the motion performance of the FOWTs equipped with tension-legs [
10,
11]. Therefore, during the past decade, more attention has been focused on the design of new TLP concepts to improve the performance of tension-leg-type FOWTs like the tension and energy efficiency.
Ren et al. [
12] proposed a tension-leg platform type floating offshore wind turbine system based on the 5 MW offshore wind turbine model. To improve the performance of the TLP system, one tentative strategy of adding mooring lines to the TLP system was proposed, and the force levels of tension legs were effectively reduced. Oguz et al. [
13] described an experimental and numerical investigation of the Iberdrola TLP wind turbine concept in realistic wind and wave conditions. The results from studies showed the benefits of such TLP structures in terms of motions which are vital to obtain a high power output from a floating offshore wind turbine.
Nevertheless, the central feature for TLP is that restraining freedom in vertical plane with tension tendons making it similar to a rigid body, while for the horizontal plane, the constraint is less, making it similar to a compliant body [
14]. Having an in depth view of the structural response of a TLP is an important issue, not only for response analysis but also for engineering design [
15]. It has previously been observed in other studies that the motion of TLPs is large in the horizontal plane [
16]. Although many researchers have done conceptual designs before, there is little published data on new tension leg conceptual designs to overcome the problem in the horizontal plane caused by this characteristic.
Therefore, in this study, a new type of tension-leg-type wind turbine connected with a series of buoys (Serbuoys-TLP) is proposed to improve the motion performance of tension-leg-type FOWTs in the horizontal plane. The coupling effects of the Serbuoys-TLP system are investigated by conducting both numerical analysis and model tests. The higher-order boundary element method is adopted to solve the boundary value problem in which multi-body hydrodynamic interactions is treated as generalized mode approach [
17]. Modal analysis is also an important means of interpreting dynamic responses [
18]. To investigate the characteristics of the Serbuoys-TLP, the modal analysis of the Serbuoys-TLP had been conducted on the commercial software platform ANSYS. The results measured in frequency and time domain analyses showed good agreements with the results of the modal analysis. Finally, the simulation of Serbuoys-TLP wind turbine under typically actual sea condition has been carried out with the consideration of winds, waves and currents. The results indicate that the Serbuoys-TLP wind turbine has a better performance in the horizontal plane compared with tradition tension-leg-type FOWT.
2. Numerical Model of the Serbuoys-TLP System
The Serbuoys-TLP system has been modeled as two rigid bodies: a TLP type FOWT and a series buoys connected tension leg in
Figure 1 [
12]. Hydrodynamic properties and the coupling interaction effects of the two rigid bodies involved in the Serbuoys-TLP system have been simulated based on AQWA code in the frequency domain and the time domain, which is flexible for modeling multi-body systems and can accommodate the introduction of both mechanical and hydrodynamic couplings between two bodies, and aerodynamic loads on the wind turbine rotor are simplified as equivalent thrusts and bending moments (with the user-force function of AQWA code) based on the design data of the NREL 5 MW wind turbine [
8].
2.1. Governing Equation in Frequency Domain
Frequency domain analysis is not only the basis of hydrodynamic analysis, but also the premise of the time domain analysis [
19]. The equation of motion is as follows:
where
is the structure mass,
is the added mass,
is the viscous damping,
is the mooring damping,
is the mooring stiffness,
is the restoring force of stillness water,
is the wave force.
The damping matrix (no radiation damping) and surge stiffness are obtained in next section, and these values should be added to the corresponding card of ANSYS-AQWA to obtain relatively accurate results.
2.1.1. Mooring Stiffness Matrix of Serbuoys-TLP in Surge and Sway Direction
The mooring stiffness matrix of traditional tension leg foundation have the same form as Serbuoys-TLP as shown in Equation (2). The derivation process of TLP is described by Chandrasekaran [
20]. With the consideration of coupling effect, derivations on the stiffness of the Serbuoys-TLP mooring lines are given (see
Section 2.3):
2.1.2. Vicious Damping of Serbuoys-TLP
Based on the linear formula of drag force, the viscous damping can be estimated by a Fourier series expansion [
21]:
where
is the velocity amplitude of structure at frequency
,
A is the motion amplitude, and
Cd has a value of 0.7.
2.2. Governing Equation in Time Domain
2.2.1. Motion Response Analysis of the Wind Turbine’s Upper Platform
It is relatively straightforward to simulate complex nonlinear coupling motions of multi-body systems with complex mooring arrangement and many other external forces, including nonlinear effect when utilizing the time domain simulation [
22]. To find the nonlinear mooring force of tendons G, each buoy force are integrated into the entire tension leg. G is introduced into the motion equation of the Serbuoys-TLP wind turbine and the motion response in the time domain is calculated, as shown in the Equation (4):
where
M and m are the mass and added mass matrix,
is the displacement.
B is the damping matrix.
is the stiffness matrix,
is the applied loading and
is the mooring force of the tendon.
2.2.2. Analysis on Motion Response of Additional Buoy
Assume the tension of a series of buoy upper and lower ends is provided by the upper and lower parts of the tendon, and the pull action line of the nodes coincides with the buoy axis. The buoy model can then be simplified as shown in
Figure 2. In time domain analysis, the buoy force equilibrium equation with tension leg and TLP platform effect can be expressed as follows:
The center of gravity (COG) of the series of buoys is located geometrically centered, and the local coordinate system located in the COG. At the beginning, the local coordinate system in the positive direction with the same global coordinate system. The displacement of the local coordinate system can be obtained by calculation, the angle of the local coordinate system can be determined though the relative spatial relationship between the buoy upper and lower nodes [
23]. The forces acting on the buoy include gravity
GB, buoyancy force
FB, pull force provided by the buoy upper and lower nodes
TP,
TPb, inertial force
FPI, drag force (considering the relative velocity between buoy and water particles)
FPf. The balance equation is shown as Equation (5).
2.3. Mooring Stiffness of the Serbuoys-TLP System
A single tendon is studied in this section, as shown
Figure 3. In order to calculate the mooring stiffness of a Serbuoys-TLP system, the buoy can be simplified as a buoyancy point. The tendon is truncated by the buoy, and the stiffness of each segment is performed based on static analysis. The following variables can be assumed to solve the mooring stiffness.
and
are the initial pre-tension in the tether and buoys, respectively. When the platform produces a unitary horizontal displacement
x under the action of horizontal force
Fx.
Lu0 and
Ld0 are the original length of the upper and lower tendon, Δ
Lu and Δ
Ld represent the elongation when the tendon has been installed.
,
and
xu,
xd represent the elongation with the tendon has been installed and the horizontal displacement of the upper and lower tendon when the platform has produced a horizontal displacement, respectively.
H is the vertical distance from the center of platform gravity to the mooring point.
At is the cross-sectional area of the tether, and
E is Young’s modulus of the tether. There are three relationships between these above physical quantities:
Because
xu and
xd are the unknown quantity, a new equilibrium equation (Equation (6)) must be added. The horizontal forces at the top and bottom of the buoy are the same:
where
k11 is the surge stiffness for one tendon, and
k11 can be rewritten as:
where Δ
Th and Δ
Lh are the variation of tension and length due to the arbitrary displacement given in the surge degree of freedom.
It can be seen from Equations (9) and (10),
x ∝
L/T, thus:
Considering
x contains
xu and
xd, so:
and
can be calculated when Equations (12) and (13) are brought into Equation (8). Based on Hooke’s law, the upper and lower section surge stiffness of the tendon are written as follows:
By the series theorem of rigidity:
so, the surge stiffness of a single tendon can be deduced as follows:
The total surge stiffness of the Serbuoys-TLP system is four times as much as that of a single tendon. When the horizontal displacements is assumed to be a small quantity, there is:
K21 = 0, as no force develops in the sway direction when an arbitrary displacement ocurrs in the surge direction.
Equilibrium of forces in the heave direction gives:
K41 = 0, as no moment develops along the roll direction when an arbitrary displacement ocurrs in in the surge direction.
Summation of moments along the pitch direction gives:
K61 = 0, as no moment develops along the yaw direction when an arbitrary displacement ocurrs in the surge direction.
3. Description of Physical Model Test
The scale model tests of the Serbuoys-TLP system have been done in the advanced wave flume laboratory located at the Harbin Institute of Technology (HIT). The numerical model is validated against the model test. Comprehensively considering the condition of the laboratory and the size of full-scale Serbuoys-TLP system, the scale ratio of the Serbuoys-TLP test model has been designed to be 1/50 with Froude’s law. The overall view of the main combined structure system and locations of installed sensors for monitoring main dynamic responses of the Serbuoys-TLP system are shown in
Figure 4. The scale model is mainly based on the scaling law of the similarity of Froude numbers. The scale test model is mainly made of organic glass, and the main design parameters of which are listed in
Table 1.
The six-DOF motions of the Serbuoys-TLP have been tracked by a stereovision measurement system with two high-quality cameras and target plates, and for details of the working principle readers can refer to reference [
12]. Considering the surge response is the most significant motion for the TLP system, an additional laser displacement sensor has been used for measuring the surge displacement of the TLP platform (assisting the stereovision measurement system).
The tension leg system in the model test has been simplified as four steel cables (stiffness equivalent to tension legs in the prototype). There is a waterproof tension sensor (with a sensitivity of 0.01 N) at the top of each tension leg to measure tension responses of each tension leg. The bottom ends of the four tension legs are connected to four heavy plates to simulate the TLP foundation.
To make sure the data sampling is synchronized, the laser displacement sensor, the stereovision measurement system, accelerometers sensor, tension/pressure sensors have been all set to record data at the same time with the same sample frequency of 100 Hz during model tests. In addition, the stereovision measurement system and waterproof tension sensors have all been calibrated before doing model tests.
5. Conclusions
This paper proposes the concept of a new type of tension-leg-type wind turbine connected with a series of buoys (Serbuoys-TLP). The complicated coupled motion characteristics of the TLP with a buoy system are investigated by means of experimental and numerical analysis. In the numerical approach, both frequency and time domain approaches have been applied. In the frequency domain, the mooring stiffness matrix of the Serbuoys-TLP is derived for accurate and efficient calculation of coupled mooring forces. The time domain simulation is applied with consideration of nonlinear factors between platform, tendon and buoys with nonlinear wave forces. The complex behaviors of time domain analysis are identified from modal analysis which is also a meaningful method for practical application of Serbuoys-TLP. From the systematic comparison between model tests, modal analysis, numerical analyses both in frequency domain and time domain, the following conclusions could be drawn:
- (1)
Under the most of the regular wave conditions, buoys attached to tension leg can effectively improve the horizontal motion, especially during surges. A TLP surge suppressive efficiency as high as 60% is seen above under some conditions; In the case of irregular waves, the results show that the buoys can effectively suppress the surge motion response of the TLP, particularly at the peak.
- (2)
Wave height and the incidence angle of waves cannot change the suppressive efficiency on the surge of TLP, but it is different from the wave period. The natural frequency of the Serbuoys-TLP has been changed due to the addition of buoys on the tension leg. Therefore, the phenomenon of wave-frequency resonance is captured in both a time domain simulation and experimental tests. On both sides of the resonance period, the suppressive effect is quite different, which needs special attention to avoid wave frequency resonance.
- (3)
The position and displacement of the buoys have a great influence on the suppressive effect. Generally speaking, A lower position and the larger displacement of buoys corresponds to a larger resonance period, and the suppressive effect is more obvious after the resonance intent. However, due to the existence of wave-frequency resonance, we can not blindly pursue the suppressive effect. Instead, modal analysis and hydrodynamic analysis should be combined to check the parametera of the buoys to get the best results.