CFD Study of the Non-Linear Physical Phenomena of the TLP of a 15-MW-Class FOWT under Extreme Waves

Abstract

In this study, a numerical simulation was conducted to investigate the non-linear physical phenomena of a tension leg platform (TLP) of a 15-MW-class floating offshore wind turbine (FOWT). Computational fluid dynamics was employed as the numerical tool, and a deforming mesh technique was used to describe the moving body. To examine the non-linear physical phenomena, an irregular wave was generated with a focus on head sea conditions. The springing and ringing responses were calculated from the numerical simulation results, and the relations between the motions and dynamic tensions of the 15-MW-class FOWT TLP were investigated. From the irregular wave impact simulation, it was found that the springing response via the wave sum frequencies and the ringing response occurred at approximately three times the wave peak frequency. Additionally, whipping simulations were conducted under a focused wave. The results show that the response in pitch resonance frequency was caused by the wave impact. The numerical results of this study could be used as fundamental data for FOWT TLP design.

1. Introduction

The pursuit of carbon neutrality has led to heightened interest in the utilization of renewable energy sources. Among the strategies for using renewable energy, there has been a notable increase in the research and development efforts for floating offshore wind turbine (FOWT) systems. FOWT systems generally use representative platforms, such as semi-submersible platforms, spars, and tension leg platforms (TLPs) [1]. Among these, TLPs have a similar shape to semi-submersible platforms but are noteworthy because of their small weight and small vertical motion characteristics. Previously, TLPs were mainly used as offshore platforms in the Gulf of Mexico and dry tree usage areas. Recently, there has been an increase in the utilization of TLP-type platforms for offshore wind turbine systems. Due to the strong tendon stiffness in TLPs, high-frequency motion responses of the platforms, known as “ringing” and “springing” phenomena, can occur, and these phenomena affect the fatigue damage of tendons. Therefore, the highly resonant motion responses of TLPs should be considered during their design phase.

In [2], a model test was performed for a Hutton TLP and the springing phenomenon was first observed. It was shown that the springing phenomenon occurred via wave sum frequencies. Therefore, many researchers have studied springing phenomena using numerical approaches.

In [3,4,5,6], TLP motions via wave sum frequencies were calculated using frequency domain analyses using the panel method. Furthermore, the non-linear characteristics of TLP tendons were calculated via time domain analyses in [7,8]. In [9], the springing responses of square and triangular TLPs were systematically studied via time domain analysis. Numerical approaches have mainly focused on the ringing and springing phenomena.

In [10], a time domain analysis revealed that the frequency of the ringing phenomenon was three to five times that of the wave frequency. To capture the ringing response, a series of studies using perturbation theory were conducted in [11,12]; however, the ringing responses could not be captured via theoretical approaches. In [13,14], techniques for directly solving the non-linear boundary conditions at each time point were attempted, but the ringing responses were overestimated. In [15], a time domain simulation that included Morison’s drag was performed to capture the ringing response. The time domain simulation results were directly compared with the experimental results; the authors found that the ringing responses of the numerical and experimental approaches were in good agreement. According to [16], research on the ringing response has been attempted using various methods, but a clear analysis method and procedure has not yet been established. Analytical and numerical studies have been conducted on offshore platforms. The springing phenomenon was identified to be caused by the sum frequency components of waves. The ringing phenomenon is known to occur in a frequency range of approximately three to five times the wave frequency. However, it remains challenging to accurately simulate this phenomenon either analytically or numerically.

In terms of the FOWT system of a TLP-type platform, studies on non-linear physical phenomena, such as springing and ringing responses, have recently been conducted. In [17], it was explained that the sum frequency effects on a TLP-type FOWT are more important than other excitations because of the lower energy of the aerodynamics at high frequencies. The sensitivities of the ringing response to platform stiffness and viscous damping for four TLP-type FOWTs were investigated in [17]. From the results, large extreme loads due to the ringing response occurred on the TLP-type FOWTs of large center columns, and the TLP-type FOWTs with pitch per bending natural periods of 3–4 s were largely affected by the ringing response. In [18,19], time domain analyses were performed for TLP-type FOWTs, and the numerical results were compared with the experimental results obtained in [18,19]. The authors demonstrated that second-order wave loads must be considered for an accurate numerical simulation. In TLP-type FOWT-related studies, time domain analyses are commonly employed, and significant efforts are being dedicated to considering springing and ringing phenomena.

To capture non-linear physical phenomena, computational fluid dynamics (CFD) can provide better insights. In [20], the global performance of a TLP-type FOWT was evaluated using a CFD method under regular waves and the CFD results were directly compared with the time domain analysis results, demonstrating good agreement between both. However, limited research has been conducted on non-linear physical phenomena. Owing to the significant time and cost requirements of CFD analysis, the performance evaluation of an FOWT mainly relies on regular waves. Therefore, implementing non-linear physical phenomena, such as springing and ringing, using CFD is relatively difficult.

In this study, a CFD approach was attempted under irregular waves to capture the springing and ringing phenomena in a TLP-type FOWT. From the CFD simulation results, the vertical motion characteristics of the TLP-type FOWT and the non-linear physical phenomena of the tendon and platform of the FOWT were investigated. In addition, under a focused wave, the characteristics of the motion and tendon tension responses of the TLP-type FOWT were investigated using whipping simulations.

2. Numerical Set-Up

2.1. Model

In this study, a numerical simulation was performed for a 15-MW-class TLP-type FOWT. Figure 1 shows the 15-MW-class FOWT, which corresponds to the IEA 15-MW reference wind turbine [21]. The TLP shown in Figure 1 was designed by the Korea Research Institute of Ships and Ocean Engineering (KRISO), which will be modified in the future to further enhance its performance. The TLP in Figure 1 has a shape similar to that of a semi-submersible platform to ensure stability during wet towing. The stability of the TLP during wet towing was ensured by using three rectangular columns. Furthermore, structural safety could be ensured through braces between the center and the three rectangular columns.

Table 1. Main dimensions of the TLP.

Parameter		Value
Water Depth (m)		137
Length Overall/Beam Overall (m)		74.25/84.11
Radius between the Center and Outer Columns (m)		42.5
Center Column Diameter (m)		10
Center Colum Height (m)		33
Outer Column Square Width (m)		10.5
Outer Column Height (m)		28
Freeboard_Center Column (m)		15
Freeboard_Outer Column (m)		10
Ponton Width/Depth (m)		8/4.5
Deck Width/Depth (m)		4/3
Draft (m)		18
Displacement (ton)		11,123
COG (m)		(0, 0, 41.3)
Moment of Inertia (kg·m2)		(2.83 × 1010, 2.83 × 1010, 6.53 × 109)
Number of Tendons		9 (3 per each column)
Total Pre-Tension (ton)		3782
Tendon Axial Stiffness (kN)		1,799,000
Tendon Modeling		Linear Spring
Resonance Period(s)	Surge	46.72 (0.134 rad/s)
	Heave	2.18 (2.882 rad/s)
	Pitch	3.00 (2.094 rad/s)

summarizes the main TLP dimensions.

2.2. Environmental Conditions

The non-linear physical phenomena of the 15-MW-class FOWT TLP were investigated under irregular waves. The target installation site for the 15-MW-class FOWT is near Ulsan, South Korea. The significant wave height and peak period for 50-year return periods at the target site are 11.8 m and 15.1 s, respectively. Springing and ringing phenomena can be difficult to evaluate in detail because strong green water phenomena can occur at high wave heights. To avoid these strong green water phenomena, in this study, the significant wave height was reduced by 60%, resulting in a significant wave height of 7.08 m. Additionally, for a CFD simulation, it is challenging to perform a long-term 3 h simulation at full scale. In this study, a 30 min CFD simulation was conducted, and the spectrum of the 30 min CFD simulation was matched to the JONSWAP spectrum. Figure 2 shows the spectra and time history of the irregular waves, and

Table 2. Irregular wave conditions.

Parameter	Value
Spectrum	JONSWAP
Tp (s)	15.1
Hs (m)	7.08 (60% of 11.8 m, 50-year return periods)
γ	2.5

summarizes the wave conditions.

In the case of TLP, whipping can occur owing to the strong wave impact; therefore, the whipping simulation was performed under focused wave conditions. In this study, the focused wave in [22] was generated, which exhibited a maximum wave amplitude of 11 m and a peak wave frequency of 0.524 rad/s (12.0 s). In addition, only wave heading was considered as the head sea condition. Figure 3 shows snapshots of the generated wave, while Figure 4 shows the time histories of the experimental results in [22] and the simulation results of this study. As shown in Figure 3, the high wave approached the measuring point, and the wave was broken after passing the measuring point. In the whipping simulation, the TLP was placed at the measurement point. In addition, the numerical simulation results at the measurement point were in good agreement with the experimental results in [22], as shown in Figure 4.

2.3. Numerical Method

In this study, the focus was on the non-linear physical phenomena of the TLP alone; therefore, the 15-MW FOWT was excluded. However, the global inertia of the FOWT was considered in the numerical simulation, despite it being for a TLP simulation. Figure 5 illustrates the numerical grid system. Grid convergence tests were already conducted in [23], so the grid system in Figure 5 refers to [23]. The CFD software used was STAR-CCM+ 11.06V, and a full-scale simulation was conducted. A trimmed mesh type was used, and the number of meshes was approximately three million. To account for viscous effects, such as springing and ringing phenomena, seven prism layers were applied near the TLP, and a y+ value of 1000 was set. Two refinement zones were used for irregular wave generation, and the aspect ratio (dx/dz) of these zones was set to 5. The size of one of the refinement zones was 1.2 times the significant wave height, while that of the other was 2.4 times the significant wave height. Figure 6 shows the numerical domain size and boundary conditions. As shown in Figure 6, the numerical domain size was determined based on the wavelength of the wave peak period. The boundary conditions were as follows: the inlet boundary condition was a velocity inlet boundary condition; the outlet boundary condition was a pressure outlet boundary condition; the top boundary condition was a symmetry boundary condition; and the wall boundary conditions were applied to the bottom, object, and sides.

Table 3. Numerical schemes.

Item	Value
Discretization Scheme	Finite Volume Method (FVM)
Pressure and Velocity Field	Semi-Implicit Method for Pressure-Linked Equations (SIMPLE)
Time Step	Adjustable Time Step (target CFL = 0.5)
Sub-iterations	10
Convection Schemes	Second-order Upwind
Temporal Schemes	Second-order Implicit
Turbulence Model	(Laminar Flow)
Mesh Motion	Deforming Mesh
Simulation Time	30 min (1800 s)

summarizes the numerical schemes. To capture the high-frequency non-linear physical phenomena, an adjustable time step was applied and the target CFL number was set to 0.5. Additionally, second-order upwind and second-order implicit schemes were applied to the discretization schemes of the convection and temporal terms, respectively. In this study, a laminar flow simulation was performed, with a focus on the platform motion and tendon tension characteristics.

3. Results

3.1. Springing and Ringing Phenomena

Figure 7 shows snapshots of the TLP motion under irregular waves. The time range was 1323–1338 s, and the maximum wave height occurred at approximately 1330 s, as shown in Figure 2b. As shown in Figure 7, the TLP exhibited a mean surge motion with a set-down. A strong wave impact occurred when the high wave approached the TLP. A weak green water phenomenon was observed on the deck of the TLP. A large surge motion of the TLP occurred when the wave re-impacted the back column of the TLP. After the wave passed over the TLP, a slight forward movement was observed.

Figure 8 shows the coordinate system and tendon numbering. The body-fixed coordinate system is the same as the earth-fixed coordinate system. Nine tendons were installed at the bottom of the TLP, and tendons #1, #4, and #7 were the center tendons in each column. Figure 9 shows the TLP surge, heave, and pitch motion time histories. Throughout the numerical simulation, the TLP exhibited a mean surge motion combined with wave-induced and low-frequency motions. Regarding the heave motion time history, the mean heave motion occurs via the mean surge motion, a phenomenon known as “set-down”. Additionally, the low-frequency heave motion was caused by the surge motion. Consequently, it can be concluded that the surge and heave motions are coupled in the case of a TLP. Throughout the numerical simulation, wave-induced small heave and pitch motions were observed. Notably, within a time window of approximately 1320 s, large surge, heave, and pitch motions were observed when the wave with the maximum height impacted the TLP.

Figure 10 shows the dynamic tension time histories of the TLP tendons. In the case of tendon #1, the dynamic tension was relatively smaller than that of tendons #4 and #7 due to the occurrence of the mean surge motion of the TLP. In this study, only the head sea condition was considered; therefore, the dynamic tensions of tendons #4 and #7 were identical. As shown in Figure 10, the dynamic tensions consist of components at both the wave frequency and high frequencies, with large dynamic tensions observed within the time window around 1320 s.

The dynamic tension time history of tendon #7 was expanded within the time window between 1300 and 1400 s, as shown in Figure 11. From 1300 to 1400 s, it can be observed that the dynamic tension of tendon #7 exhibits various responses. In this dynamic tension, responses occur at three times the wave frequency and are related to the pitch resonance. The response at approximately three times the wave frequency corresponds to the ringing phenomenon, whereas the response associated with the pitch resonance arises from the springing phenomenon caused by the wave sum frequency. The springing phenomenon occurs continuously throughout the numerical simulation because of the wave components of the sum frequency in irregular waves. Furthermore, the ringing phenomenon occurs because of the impulsive force of the steep wave upon impact.

Figure 12 shows the FFT results for platform motions and dynamic tensions. As shown in Figure 2a, the wave energy is very small in the frequencies associated with the ringing and springing phenomena. Furthermore, it can be observed that the effect of heave–pitch coupled motion is very small in the FFT result for heave motion under this wave condition. The low-frequency response can be seen in the FFT results for the surge and heave motions. It can also be observed that surge and heave motions are coupled in the case of a TLP-type platform, as the low-frequency heave motion response occurs via surge motion. In the dynamic tensions of tendons #4 and #7 and in pitch motion, a ringing response was observed at approximately three times the wave frequency. Additionally, it is noticeable that tendon #1 was less sensitive to the ringing response due to its lower tension. Furthermore, the FFT results for dynamic tensions for all three tendons have their resonance frequencies. It is necessary to consider the tendon resonance frequency when a tendon stiffness is determined in the design stage. However, it can be found that the tendon resonance frequency has little effect on platform motion. The springing response caused by the wave sum frequency is noticeable in the FFT results for pitch motion and dynamic tensions.

3.2. Whipping Phenomenon

Figure 13 shows snapshots from the whipping simulation at the moment of wave impact. The waves were focused in front of the TLP and a large wave hits the platform. After the wave hit the platform, large amounts of green water appeared on the deck of the TLP. The large green water hits the columns in the following order: front, center, and rear columns.

The TLP motion time histories are shown in Figure 14. As shown in the surge motion time history, a surge offset occurred with the green water phenomenon after the wave hit the front columns. The TLP moved slightly forward and the green water hit the center column. The largest surge offset occurred after the green water hit the center column. Finally, the green water hit the rear column. The magnitudes of the heave motion changed when the green water hit the columns in the following order: front, center, and rear columns. As shown in the pitch motion time history, as the wave impacts occurred sequentially, various frequencies occurred.

Figure 15 shows the dynamic tension time history for the tendons. Similar to the dynamic tensions of the TLP tendons under irregular waves, the dynamic tension of tendon #1 was the smallest. In addition, the dynamic tensions of tendons #4 and #7 were the same. Interestingly, large dynamic tensions occurred in tendons #4 and #7, such as impacts when green water hit the front and center columns. However, when the green water hit the rear column, no impact-like dynamic tension occurred in tendons #4 and #7. It is possible that some of the energy of the green water dissipated after the green water hit the center column. It can be observed that the largest dynamic tensions of tendons #4 and #7 occurred when the green water hit the center column, and the dynamic tensions of tendons #4 and #7 had various frequencies owing to green water impacts.

Figure 16 shows the FFT results for the TLP tendon motions and dynamic tensions from the whipping simulation. Similar to the motion responses of the TLP under irregular waves, the heave–pitch coupled motion was very small. In addition, a structural pitch response occurred owing to the wave impact, and it can be observed that the responses by pitch resonance motion occurred in the dynamic tensions of tendons #4 and #7. As shown in the dynamic tensions of tendons #4 and #7, the tensions caused by waves, as well as the tensions caused by pitch resonance motion, were large. Therefore, when a wave impact occurs, the tension of the tendons can increase significantly owing to the pitch resonance motion caused by the whipping phenomenon.

4. Conclusions

A numerical simulation of non-linear physical phenomena on a 15-MW-class TLP-type FOWT system was conducted under irregular wave conditions. Based on the numerical simulation results, the following conclusions were drawn:

• In terms of the low-frequency motion, the surge–heave coupled motion occurred because of the set-down caused by the surge motion. In addition, the effect of the heave–pitch coupled motion was minimal under this wave condition.
• In this study, the resonance frequency of the tendons occurred. The resonance frequency of a tendon should be considered when determining its stiffness during the design stage. However, the tendon resonance frequency has little effect on the TLP motion.
• In the irregular wave simulation, ringing and springing responses were observed. In the ringing and springing frequencies, the wave energy was very small in this study; therefore, it was clearly observed that the ringing and springing phenomena occurred owing to the impulse forces and the wave sum frequency, respectively.
• In this study, a whipping simulation was performed. Green water impacts occurred in the following order: front, center, and rear columns, and large surge offsets occurred after the green water impacts each column. It can be observed that the tensions from the wave and pitch resonance motion were large. After the green water hit the deck of the TLP, the pitch resonance motion occurred via the whipping phenomenon, and a large tendon tension could occur by the pitch resonance motion via the whipping phenomenon.
• In future work, the numerical simulation results of this study will be validated using model tests. In addition, in further numerical simulations, various wave and heading conditions will be considered to account for non-linear physical phenomena contributing to the TLP motions and changes in tension.