A Novel 10 MW Floating Wind Turbine Platform—SparFloat: Conceptual Design and Dynamic Response Analysis

Abstract

New conceptual designs for floating offshore wind platforms (FOWPs) are crucial for deep-sea wind power generation, increasing power output, lowering construction costs, and minimizing the risk of damage. While there have been various conceptual designs, tailored solutions for the South China Sea are limited due to the relatively harsh environment. This study proposes a novel 10 MW FOWP—“SparFloat”, which combines the advantages of a semi-submersible platform and Spar platform to cater for the sea conditions of the South China Sea. By systematically adjusting the distance between columns and the diameters of the side column and heave plate, the impact of geometrical changes in the platform on its dynamic response is investigated for the purpose of design optimization. The results highlight that roll/pitch natural periods are predominantly governed by restoring stiffness, whereas heave motion exhibits a higher sensitivity to added mass and radiation damping. Increasing the inter-column distance and side column diameter enhances stability and reduces roll/pitch natural periods, while enlarging the heave plate diameter extends the heave natural period. Time-domain simulations using a coupled FAST-AQWA framework confirm that the optimized design meets rule requirements, verifying the robustness and suitability of the SparFloat concept for the challenging environment of the South China Sea.

1. Introduction

As one of the most important renewable energy resources, offshore wind energy is receiving growing attention. In 2023, despite the macroeconomic challenges faced by the sector in some key markets, the wind industry installed 10.8 GW of new offshore wind capacity. The Global Wind Energy Council (GWEC) forecasts that 410 GW of new offshore wind capacity will be installed in the next ten years, bringing offshore wind deployment in line with global targets to install 380 GW by 2030 [1]. Floating offshore wind turbines (FOWTs) have arisen as a promising means of accessing massive wind energy resources in deep water, where the existing fixed-type offshore wind turbine is no longer practical. There are four predominant types of floating offshore wind platform (FOWP): (1) Spar-type, (2) Semi-submersible, (3) Tension Leg Platform (TLP), and (4) Barge-type [2]. Among them, the spar-type and semi-submersible platforms have emerged as the most frequently pursued designs, owing to the discernible limitations observed in the TLP and barge types [3]. However, Spar-type platforms achieve sufficient inertia by increasing the distance between their center of gravity (CoG) and center of buoyancy (CoB), necessitating considerable water depth. Conversely, semi-submersible platforms exhibit a well-established structural design that is adaptable to varying water depths, for which the stability is achieved through substantial static stiffness, though they are more susceptible to wave forces [4].

Recent developments in the field of FOWP have led to noteworthy projects and concepts. The Fukushima FORWARD project [5] introduced an “Advanced Spar” platform hosting a 7 MW wind turbine. Zhang et al. [6] designed a fully submersible FOWP, combining semi-submersible and spar characteristics. A comprehensive numerical model created using OpenFAST and AQWA revealed that the proposed platform significantly improves hydrodynamics and recovery capabilities. Bai et al. [7] presented a 10 MW OUCwind semi-submersible platform for shallow waters, showing enhanced stability by increasing the column distance. In comparison with 10 MW OO-Star, OUCwind performs well in sway and anchor tension, but displays higher wave responses in surge and heave. Cao et al. [8] designed a four-column platform called SPIC for a 200 m water depth and 10 MW wind turbine, connecting columns with pontoons and braces. Recently, Yao et al. [9] proposed a new spar-buoy with a porous shell. Zhao et al. [10] proposed a new semi-submersible platform modified from the traditional OC4-DeepCwind platform.

Researchers have been actively exploring the dynamic responses of FOWTs under combined wind–wave–current actions through numerical simulations and model tests; see references [11,12,13,14] for state-of-the-art reviews. Chen et al. [15] designed a spar-type FOWT based on the OC3 Hywind model and conducted experiments. An optimized anemometer arrangement on a disc plane was proposed to enhance wind field measurements. Ha et al. [16] introduced a ‘Real-Time Hybrid Simulation’ for evaluating a 10 MW class FOWT. The technique’s repeatability was validated and compared with fully coupled analysis results, demonstrating its reliability. Model tests aim to generate coupled motion and load data for FOWTs, refining the design analysis and validating the numerical codes. Mei and Xiong [17] examined the impact of second-order hydrodynamic loads on a 15 MW FOWT. Their results revealed that the second-order wave excitation increases surge motion, and neglecting second-order hydrodynamics underestimates pitch, heave, and yaw motions under extreme conditions. Zhao et al. [18] employed FAST for fully coupled simulations of a 10 MW FOWT under different environmental conditions. It was shown that ignoring the second-order difference-frequency wave loads leads to underestimated low-frequency responses, while the second-order sum-frequency wave loads notably affect the structural dynamics. An aero-hydro-servo-elastic coupling framework called F2A (FAST2AQWA) was developed and validated by Yang et al. for the simulation of FOWTs [19,20]. Furthermore, the fatigue damage to the tendon of a TLP-type FOWT was estimated by F2A, and the results demonstrated lower error rates compared to those of FAST. Shen et al. [21] used F2A to analyze V-shaped and triangle-shaped FOWTs (called “V-FWT” and “Tri-FWT”, respectively) under extreme conditions. The results showed that V-FWT had slightly reduced stability compared to Tri-FWT, but displayed better economic and hydrodynamic performance.

The combination of numerical simulations and model tests has significantly contributed to the development of offshore wind technology. To delve deeper into the conceptual design of FOWPs, this study introduces a novel 10 MW floating offshore wind platform called “SparFloat” (shown in Figure 1), which aims to combine the merits of semi-submersible and spar-type platforms while mitigating their respective drawbacks. The SparFloat design features a robust deep-draft spar-like central column that provides significant inertial stability by lowering the platform’s center of gravity (CoG). This deep-draft central column enhances the platform’s heave and pitch performance, making it less susceptible to wave-induced motions. Additionally, four side columns are incorporated to offer substantial static stability, akin to semi-submersible platforms, allowing for adaptability across various water depths. The integration of these design elements results in improved overall stability and motion performance, as well as potential reductions in material usage and installation costs.

The subsequent sections are structured as follows. Section 2 presents the methodology. In Section 3, the initial parameters of SparFloat are introduced, exploring the impact of variations in the main geometrical parameters on the platform dynamics and optimization of the platform. Section 4 employs time-domain analysis to conduct fully coupled simulations of aero-hydro-mooring interactions on the optimized model. Finally, conclusions are drawn in Section 5.

2. Solution Method and Verification

Traditional offshore platforms have primarily focused on analyzing the impact of marine environmental factors such as waves, currents, and tides, as well as the constraints imposed by mooring systems. The wind loads on the above-water components of these platforms typically account for approximately 10–20% of the total environmental loads, making their contribution relatively minor. However, this is not the case for FOWPs. The towering masts and large blades of these mega-sized floating wind turbines result in substantial bending moments when exposed to wind loads. The significant wind-induced tilting moments pose a considerable challenge to the platform’s stability [22]. In computational analyses, it becomes essential to include wind loads and establish a comprehensive methodology that couples aerodynamic, hydrodynamic, and mooring loads [23].

2.1. Aerodynamic Load

Aerodynamic loads are computed through the Blade Element Momentum (BEM) theory. This method assumes the independence of each blade element, without interactions among them. The aerodynamic load on each blade element is determined solely by the lift and drag coefficients ($C_l$ and $C_d$). This results in expressions for both thrust and torque, as follows:

$$dT={\displaystyle \frac{1}{2}}{\rho }_a{W}^{2}Nc\left(C_l\mathit{cos}\varphi +C_d\mathit{sin}\varphi \right)dr$$

(1)

$$M={\displaystyle \frac{1}{2}}{\rho }_a{W}^{2}Nc\left(C_l\mathit{sin}\varphi +C_d\mathit{cos}\varphi \right)rdr$$

(2)

where ${\rho }_a$ is the density of air; $W$ is the relative velocity of the blade with reference to the flow; $N$ is the number of blades; $c$ is the chord of the blade; $\varphi$ is the flow angle; and $r$ is the radius.

2.2. Hydrodynamic Load

When analyzing the impact of waves on marine structures, both the potential flow and viscous effects play crucial roles [24]. In cases where marine systems have dimensions significantly larger than wave parameters like the wave height and wavelength, the potential flow dominates, and the impact of viscous effects is typically minor. So, the total load ($F_{total}$) can be written as follows [25]:

$$F_{total}=F_{FK}+F_S+F_R+F_D$$

(3)

where $F_{FK}$ denotes the Froude–Krylov force, including the buoyancy force; $F_S$ denotes the diffraction force; $F_R$ denotes the added mass and damping force; and $F_D$ denotes the drag force.

However, for slender components within smaller marine structures (e.g., cross braces), viscous effects become significant and must be factored into hydrodynamic load calculations using Morison’s equation [26]. The segment force $dF$ on a finite length $dz$ of a cylinder is as follows:

$$dF={\rho }_w{\displaystyle \frac{\pi D^2}{4}}dz{C}_{M}a+{\displaystyle \frac{{\rho }_W}{2}}{C}_{D}dz\left|u\right|u$$

(4)

where ${\rho }_w$ is the density of sea water; $dF$ denotes the horizontal force, with the direction of positive force as the wave propagation direction; $D$ denotes the cylinder diameter; $a$ and $u$ are the flow acceleration and velocity, respectively; and $C_M$ and $C_D$ are the mass and drag coefficients, respectively.

2.3. Mooring Load

The Dynamic Analysis Method (DAM) and the Quasi-Static Analysis Method (QSAM) are two fundamental approaches used for calculating the mooring forces. DAM takes into account the structural dynamics and environmental loads, utilizing dynamic equations to simulate the time domain response of the structure [27]. In contrast, QSAM is a simplified approach that assumes gradual changes in response. It neglects dynamic effects and inertia forces, and determines the equilibrium states and mooring forces through static equations [28].

DAM considers a wider range of dynamic effects and parameters, providing more accurate results, but with higher computational complexity. On the other hand, QSAM offers cost-effective computations and results accepted by rules. However, because it overlooks dynamic effects and inertia forces, the calculated mooring responses might be conservative. Consequently, American Bureau of Shipping (ABS) rules [29] stipulate that when utilizing QSAM for mooring analysis, a more cautious safety margin is required (as indicated in

Table 1. Safety factors for mooring lines, as specified in ABS rules.

Loading Condition	Analysis Method	Design Condition of Mooring System	Safety Factor
Design load cases	DAM	Intact	1.67
		Damaged condition with one broken line	1.05
	QSAM	Intact	2.00
		Damaged condition with one broken line	1.43
Survival load cases	DAM	Intact	1.05
	QSAM

).

2.4. Coupling Framework F2A

The National Renewable Energy Laboratory (NREL) developed FAST to offer a time domain simulation tool that encompasses aero-hydro-servo-elastic aspects. Its core version includes modules such as AeroDyn, ElastDyn, HydroDyn, and ServoDyn [30], which are connected for time domain analysis. However, due to limitations in FAST’s HydroDyn module, particularly concerning the hydrodynamics for floating platforms, the integration of external hydrodynamic software is necessary to replace HydroDyn and facilitate real-time data exchange with other FAST modules. To address this issue, Yang et al. [19] introduced a coupling framework F2A that combines certain features of FAST (version 7.02) with AQWA (version 19). Figure 2 illustrates the utilization of the position, velocity, and acceleration data computed in AQWA for assessing the dynamic responses of the upper structures of the wind turbine. Concurrently, FAST subroutines are employed to compute tower base loads, serving as external forces integrated into AQWA to solve the subsequent equation of motion for the platform:

$$M\ddot{{\rm X}}(t)+C\dot{{\rm X}}(t)+K{\rm X}(t)+{\int }_0^{t}h(t-\tau )\ddot{{\rm X}}(\tau )d\tau =F(t)$$

(5)

where $M$ is the total mass matrix; ${\rm X}\left(t\right)$ is the displacement at time $t$; $F\left(t\right)$ is the total external force vector; $C$ and $K$ are the damping and stiffness matrices, respectively; and $h\left(t\right)$ is the acceleration impulse function matrix:

$$h(t)={\displaystyle \frac{2}{\pi }}{\int }_0^{\infty }B\left(\omega \right){\displaystyle \frac{\mathit{sin}(\omega t)}{\omega }}d\omega$$

(6)

where $B\left(\omega \right)$ is the radiation damping at wave frequency $\omega$.

DAM considers a wider range of dynamic effects and parameters, providing more accurate results but with higher computational complexity. On the other hand, QSAM offers cost-effective computations and results accepted by rules. However, because it overlooks dynamic effects and inertia forces, the calculated mooring responses might be conservative. Consequently, ABS rules stipulate that when utilizing QSAM for mooring analysis, a more cautious safety margin is required (as indicated in Table 1).

2.5. Verification of F2A

To validate the accuracy of the F2A module, standard operational conditions are chosen for the OC4-DeepCwind platform [31]; these are shown in Figure 3. The numerical results generated by the F2A module are subsequently cross-referenced with those in [32]. The test conditions utilize Jonswap wave spectra and a constant wind speed, as outlined in

Table 2. List of test conditions.

Conditions	Wind Speed (m/s)	Significant Wave Height (m)	Spectral Peak Period (s)	Peak Factor
Test	16.11	7.1	12.1	2.2

.

Table 3. Comparison of test results and numerical results.

DOF Motion		Test Results	Numerical Results	Relative Error
Surge/m	max	14.1	12.288	12.8%
	min	1.53	1.912	24%
	mean	5.9	5.837	1.06%
Pitch/°	max	2.17	1.864	14%
	min	2.16	1.95	9.7%
	mean	0.071	0.078	9.8%
Heave/m	max	4.9	4.463	8.9%
	min	1.17	0.945	18.8%
	mean	1.87	1.792	4.1%

presents the obtained numerical results and the comparison with experimental data, revealing relative errors of 1.06%, 9.8%, and 4.1% for the surge, pitch, and heave degrees of freedom (DOF) motion, respectively. Notably, the relative errors for the minimum values of surge and heave are 24% and 18.8%, respectively. These deviations are likely attributable to the influence of transient wave conditions and subtle discrepancies in the damping and added mass effects between the numerical model and the experimental setup. Despite these deviations, the numerical model exhibits a high degree of reliability in accurately capturing the platform’s overall dynamic behavior. The low relative errors observed in the mean values across all DOFs indicate that the model effectively represents a steady-state response under coupled aerodynamic, hydrodynamic, and mooring interactions. These findings are consistent with previous studies, which have demonstrated that extreme conditions tend to yield larger discrepancies compared to mean responses. This evaluation underscores the robustness of the numerical model for both conceptual design and dynamic performance analysis.

3. Design Considerations

In the design of FOWP, the stability and seakeeping of the platform serve as crucial reference indicators. Classification societies (e.g., [33]) have defined the calculation methods and corresponding specifications used for assessing the stability performance of offshore floating structures. To achieve good seakeeping performance, the platform’s natural periods must keep away from the typical incident wave periods (5~20 s) in the specific sea area [33]. In practice, it is desirable to ensure that the natural period for heave motion is at least 20 s, while that for either roll or pitch motion is larger than 25 s. This mitigates the occurrence of significant resonance effects with incident waves.

3.1. Intact Stability Verification Method

The intact stability check curve for offshore floating platforms is shown in Figure 4, where ${\theta }_1$ is the first intercept, ${\theta }_2$ is the down-flooding angle, and ${\theta }_3$ is the second intercept [34]. Two criteria need to be satisfied: (1) the area ratio $\phi =(A+B)/(B+C)$ ≥ 1.3, and (2) the righting moment should be always positive.

The thrust force $F_{thrust}$ generated by wind on the turbine blades can be calculated using the following:

$$F_{thrust}={\displaystyle \frac{1}{2}}{\rho }_a{C}_T{A}_{thrust}{V}_{hub}^2$$

(7)

where $C_T$ is the thrust coefficient, $A_{thrust}$ denotes the swept area of the blades; and $V_{hub}$ denotes the 10 min mean wind speed at the hub height. Figure 5 shows the thrust and power curves for the NREL 5 MW and DTU 10 MW wind turbines [35,36].

According to the rules of the China Classification Society [37], the wind loading on the nacelle and tower can be calculated using the following:

$$F_{wind}={\displaystyle \frac{1}{2}}{\rho }_a{C}_s{C}_h{A}_{wind}{V}_{wind}^2$$

(8)

where $F_{wind}$ denotes the steady wind force; $C_s$ denotes the shape coefficient; $C_h$ denotes the height coefficient; $A_{wind}$ denotes the projected area; and $V_{wind}$ denotes the 10 min mean wind speed at a given elevation above the still water level (SWL).

The overturning moment can be expressed as the product of the overturning force ($F_{thrust}$ and $F_{wind}$) and the lever arm [37]. It is consequently divided into two terms:

$$M=F_{thrust}{H}_{hub}+F_{wind}{H}_z$$

(9)

where $H_{hub}$ is the height of the hub center, and $H_z$ denotes the distance between the point of wind pressure and the CoG.

The restoring stiffness in the heave and pitch directions can be determined as follows:

$$C_{33}={\rho }_{w}g{A}_w$$

(10)

$$C_{55}={\rho }_{w}gV\left({\displaystyle \frac{{\int }_{A_w}{x}^{2}dS}{V}}+z_b-z_G\right)$$

(11)

where $C_{33}$ denotes the heave restoring stiffness; $C_{55}$ denotes the pitch restoring stiffness; ${\rho }_w$ denotes the sea water density; $g$ is the gravitational acceleration; $A_w$ denotes the water plane area; $V$ denotes the displaced volume; and $z_b$ and $z_G$ denote the vertical positions of CoB and CoG, respectively. The natural period can be calculated as follows:

$$T=2\pi \sqrt{{\displaystyle \frac{M+M_a}{K}}}$$

(12)

where $M$ and $M_a$ denote the mass and added mass, respectively; and $K$ denotes the restoring stiffness.

3.2. Viscous Drag Correction

To account for the viscous effects, the drag force on small components (e.g., braces) can be calculated as follows:

$$F_{drag}={\displaystyle \frac{1}{2}}{C}_D{\rho }_{w}A(u_x-\dot{x})\left|u_x-\dot{x}\right|$$

(13)

where $C_D$ is the non-dimensional drag coefficient, $A$ is the projected area, $u_x$ denotes the fluid particle velocity, and $\dot{x}$ denotes the structural velocity. In AQWA, for the purpose of drag correction, an additional damping of 8% of the critical damping $D_c$ is used [22]; this is defined as follows:

$$D_c=2\sqrt{(M+M_a)K}$$

(14)

3.3. Conceptual Design of SparFloat Model

In the conceptual design of SparFloat, the DTU 10 MW wind turbine has been employed. This wind turbine, known for its robust specifications, is characterized by a three-bladed configuration and is rated for wind speeds up to 11.4 m/s. The wind turbine’s parameters are provided in

Table 4. Main parameters of DTU 10 MW wind turbine.

Parameter	DTU 10 MW
Rated wind speed	11.4 m/s
Cut-in wind speed	4.0 m/s
Cut-out wind speed	25.0 m/s
Rotor diameter	178.3 m
Minimum rotor speed	6.0 rpm
Maximum rotor speed	9.6 rpm

[36].

Table 5. Main parameters of tower.

Parameter	Tower
Height of tower top above SWL	119.0 m
Diameter of tower top	5.5 m
Diameter of tower base	8.3 m
Tower mass	451.0 t
Height of center of mass above SWL	61.0 m

outlines the principal parameters of the tower structure, an essential component that facilitates the connection between the rotor-nacelle assembly and the platform. Notably, the tower is conical in shape, in order to optimize the structural integrity. It is worth mentioning that the diameter of the tower’s base is aligned with that of the central column, ensuring a secure and seamless connection.

The dimensions of the original SparFloat model are presented in Figure 6, and other pertinent parameters are detailed in

Table 6. Geometrical parameters of the original SparFloat platform.

Displacement	Steel Usage	Draft	HCG (From Waterline)	Ixx	Iyy	Izz
16,111 t	4280.7 t	47 m	−26.8 m	2.72 × 1010 kg·m2	2.72 × 1010 kg·m2	3.63 × 109 kg·m2

. It is noteworthy that the original SparFloat platform exhibits a displacement of 16,111 t, successfully downsizing the platform for ultra-large FOWTs. This downsizing leads to a steel requirement of only 4280.7 t, well below the targeted design objective of 500 t/MW [38], thereby significantly reducing material costs. Additionally, a concrete ballast with a diameter of 28 m and a thickness of 7 m is placed at the base of the central column. The SparFloat features a draft of 47 m, resulting in a draft clearance of 13 m since the water depth is 60 m (see Figure 6b). However, to prevent the platform from grounding, rigorous requirements are imposed on the performance of the heave motion. It is essential to minimize the heave motion of the platform. The relationships between the platform’s geometrical parameters, stability, and seakeeping performance are explored by varying the distance between the main column and side columns ($S$), the diameter of the side column ($D_{sc}$), and the diameter of the heave plate ($D_{hp}$), while other parameters are kept unchanged, as shown in Figure 6c. For the original SparFloat model, $S$ = 28 m, $D_{sc}$ = 10 m, and $D_{hp}$ = 24 m.

Figure 7 shows the righting and overturning moment curves of SparFloat under operational conditions (wind speed is 11.4 m/s) at a 45° critical axis. The results reveal that SparFloat exhibits a first intersection angle of 8.7°, with an area ratio under the curve amounting to 2.44, thus aligning with the IMO rules.

Table 7. Hydrostatic stiffness and natural periods of SparFloat.

Platform Motion	Hydrostatic Stiffness	Natural Period
Heave	3,704,153 N/m	25.75 s
Roll/Pitch	23,935,082 N·m/°	33.94 s

shows the static stiffness and natural periods of SparFloat. The results reveal that the natural periods for heave, roll, and pitch significantly deviate from the typical range of the incident wave periods at 5~20 s, validating the reliability of the platform design.

3.4. Influence of Inter-Column Distance ($S$)

The impact of varying the inter-column distance over the relative range from −20% to 20% with a step increment of 5% on different platform properties is presented in Figure 8. Figure 8a indicates that an increase in $S$ modestly raises the platform displacement, with each 5% increment in the inter-column distance leading to an approximately 0.3% increase in platform displacement. Additionally, the ratio between the areas of the righting and overturning moment curves grows nearly linearly with the inter-column distance, i.e., about 2% to 2.5% for every 5% increase in $S$, indicating enhanced stability. Figure 8b reveals no significant correlation between the heave motion restoring stiffness and the inter-column distance. Increasing the inter-column distance does not alter the restoring stiffness, as it is more closely linked to the waterplane area. The added mass for the heave motion slightly decreases about 0.2% to 0.25% for every 5% increase in $S$. On the contrary, the restoring stiffness and added mass for the roll and pitch motions notably increase by about 6% to 6.5% for every 5% increment in $S$. Figure 8c demonstrates the minimal effects of varying the inter-column distance on the heave natural period. This stems from the limited sensitivity of the heave motion’s restoring stiffness and added mass to the change in inter-column distance (as indicated by Equation (12)). Conversely, the natural periods of the roll and pitch decrease notably with an increased inter-column distance, i.e., decreasing about 2% to 5% for every 5% increase in $S$. Interestingly, despite a similar increase in the damping stiffness and added mass for the roll and pitch motions, the natural periods decline. This suggests that the restoring stiffness predominantly influences the platform’s natural period, while the impact of added mass is comparably minor. This is due to the fact that the added mass term is an order of magnitude smaller than the mass term in the equation of motions.

Figure 9 depicts the alterations in the wave force (F-K wave force and diffraction wave force) with the wave period. For the wave force in the heave direction, as shown in Figure 9a, distinct patterns emerge over different period ranges labeled as I, II, and III. In Zone I (T = 3.28~7.26 s), the wave force rises and then falls, peaking at T = 5.6 s. Increasing $S$ by 5% leads to an approximately 110 kN (or 4.18%) rise in the wave force at T = 5.6 s. In Zone II (T = 7.26~17.32 s), the wave force decreases with the period, peaking at T = 9.94 s. Interestingly, in this zone, the wave force inversely relates to the inter-column distance. Every 5% increase in $S$ reduces the wave force by around 180 kN (or 4.54%) at T = 9.94 s. In Zone III (T = 17.32 s and beyond), the wave force rises again with the period, though the increasing rate gradually slows. Obviously, the change in the inter-column distance has a negligible impact on the heave wave force throughout Zone III. Figure 9b reveals a similar trend in roll/pitch wave forces, which is also divided into Zones I, II, and III. Zones I and II display a similar behavior to that of heave force, while Zone III demonstrates an initial increase followed by a subsequent decrease in the roll/pitch forces with increasing period. In Zone I (T = 2.72~4.58 s), the roll/pitch forces slightly rise with the increase in $S$. For every 5% increment in $S$, the roll/pitch forces increase by 57 kN·m, or 4.91% at T = 3.6 s. Similarly, during Zone II (T = 4.58~12.88 s), the roll/pitch forces grow with the inter-column distance, rising by 73 kN·m (or 4.12%) for every 5% increment in $S$ at T = 6.33 s. Notably, Zone III witnesses the minimal wave force change, which is nearly invariant to the inter-column distance.

Figure 10a illustrates the trend in the radiation damping for heave motion. Zone I (T = 3.28~7.26 s) exhibits an increasing and then decreasing trend as the period increases. A larger inter-column distance leads to higher radiation damping, and every 5% increase in $S$ augments the damping by about 180 kN, or 9.47% at T = 4.93 s. Zone II (T = 7.26~17.32 s) mirrors the period-related fluctuations of Zone I, but correlates oppositely to the inter-column distance. For each 5% increase in $S$, the radiation damping reduces by roughly 190 kN (or 9.26%) at the peak period T = 8.65 s. Zone III shows stable radiation damping, regardless of the period or inter-column distance, eventually approaching zero. Figure 10b demonstrates the changes in radiation damping for roll/pitch motions. As period increases, Zones I and II reveal rising and falling trends, respectively, but are minimally impacted by the inter-column distance. However, Zone II displays a slight increase in radiation damping with an increase in the inter-column distance. The difference in radiation damping between the −20% and 20% change in $S$ is 230 kN·m. The radiation damping in Zone III is consistently maintained at zero.

3.5. Influence of Side Column Diameter ($D_{sc}$)

Expanding on the original SparFloat model, this sub-section delves into the impact of altering the side column diameter on the platform’s stability and seakeeping performance. The results, depicted in Figure 11, reveal insightful trends. Figure 11a indicates that as the side column diameter increases, the area ratio grows nearly linearly, expanding by around 8–8.7% for every 5% increase in $D_{sc}$. In Figure 11b, a positive correlation exists between the restoring stiffness and the side column diameter. The heave and roll/pitch restoring stiffnesses rise almost linearly as the side column diameter increases. A 5% increase in $D_{sc}$ corresponds to an increase of roughly 8–8.5% in the heave restoring stiffness and 15~16% in the roll/pitch restoring stiffness. Additionally, the heave added mass slightly decreases with the side column diameter: a 5% increase in $D_{sc}$ leads to an approximately 1.2% reduction in heave added mass. Conversely, the roll/pitch added mass remains nearly unchanged. Figure 11c reveals a clear inverse relationship between the side column diameter and the natural periods of the heave and roll/pitch motions. As $D_{sc}$ increases by 5%, the heave natural period decreases by about 3% to 8%, while the roll/pitch natural period decreases by about 6%.

Figure 12 and Figure 13 provide the variations in wave force and radiation damping with the side column diameter. Figure 12a illustrates the wave force changes in the heave direction. It is evident that increasing the side column diameter linearly reduces the wave forces in Zones I and Ⅱ. A 5% increase in $D_{sc}$ corresponds to a significant reduction in wave force, namely, decreasing by 6.87% (or 180 kN) in Zone I, and 5.06% (or 200 kN) in Zone II. Notably, Zone III exhibits a steady increase in the wave force, rising by 330 kN for every 5% increment in $D_{sc}$. Figure 12b presents the wave force changes in the roll/pitch direction. The results reveal that the change in the side column diameter has a minimal impact in Zone I. A critical period emerges at T = 6.54 s in Zone II: before and after this period, a 5% increase in $D_{sc}$ yields a 4.04% (70 kN·m) rise and a 6.8% (103 kN·m) reduction in wave force, respectively. Zone III witnesses a slight increase in wave force with an increase in the side column diameter, which gradually tapers as the period increases. In Figure 13a, radiation damping in the heave direction consistently decreases with the increasing side column diameter in both Zones I and II. Zones I and II, respectively, experience a reduction of 11.07% (210 kN) or 8.78% (180 kN) with a 5% increase in $D_{sc}$. Additionally, Zone III shows a slight increase in radiation damping with the increase in the side column diameter. Figure 13b outlines the radiation damping changes in the roll/pitch direction, highlighting the relatively minor impact of varying the side column diameter.

3.6. Influence of Heave Plate Diameter ($D_{hp}$)

Figure 14 presents how the change in heave plate diameter affects the platform stability and seakeeping performance. Figure 14a shows that a larger heave plate diameter slightly increases the displacement, but marginally affects the area ratio, implying its limited influence on stability. Figure 14b reveals the minor effects of the heave plate diameter on restoring stiffness for heave and roll/pitch motions. However, the impact on added mass is significant, which increases by 8–11% with every 5% increase in $D_{hp}$. Figure 14c shows a linear rise in the heave natural period, which increases about 3.5–4% with a 5% increase in $D_{hp}$, while the roll/pitch natural periods are basically unaffected.

Figure 15 and Figure 16 illustrate the effects of varying the heave plate diameter on the wave forces and radiation damping, respectively. Figure 15a presents the changes in wave forces along the heave direction. It is clear that in Zones I and Ⅱ, each 5% increase in $D_{hp}$ results in an increase of 370 kN (14.06%) and 550 kN (13.88%), respectively. Conversely, Zone III exhibits reduced wave forces with larger heave plate diameters, gradually diminishing with extended periods. Figure 15b shows the wave force variations in the roll/pitch direction. During Zone I, the wave forces exhibit minimal sensitivity to the change in heave plate diameter. Zone II reveals rising forces with a larger heave plate diameter: a 5% increase in $D_{hp}$ leads to a 160 kN·m (9.19%) rise in wave force. Zone III indicates a slight decrease in wave force with an expanded heave plate diameter. Figure 16a displays the variation in radiation damping in the heave direction. Zones I and II show significant increases as the heave plate diameter increases. A 5% increase in $D_{hp}$ leads to a force increase of 490 kN (25.92%) and 640 kN (31.06%) in Zones I and II, respectively. However, Zone III remains constant regardless of the heave plate diameter variation. Figure 16b demonstrates that the radiation damping in the roll/pitch direction is relatively insensitive to the change in the heave plate diameter in Zones I and III. Conversely, Zone II shows gradual increases with a larger heave plate diameter: a 5% increase in $D_{hp}$ leads to a 48 kN·m (9.08%) rise in radiation damping.

3.7. Results Analysis and Model Optimization

The analysis reveals that the natural period of the platform exhibits a significant dependence on both the restoring stiffness and the mass (including added mass), as described by Equation (12). An increase in restoring stiffness leads to a reduction in the natural period, while an increase in mass or added mass results in a considerable extension of the natural period. However, the sensitivity of the natural period to these parameters differs between heave and roll/pitch motions. As shown in Figure 8, with an increasing inter-column distance, both the restoring stiffness and the added mass in the roll/pitch directions increase, yet the natural periods in these directions show a decreasing trend. This observation indicates that the roll/pitch natural periods are predominantly governed by the restoring stiffness, whereas the influence of added mass is relatively minor. The reduced sensitivity to added mass can be attributed to its limited contribution to the rotational inertia in the roll/pitch directions, which constrains its impact on the corresponding natural periods.

Based on the above analysis, it is concluded that increasing the inter-column distance improves stability but reduces roll/pitch natural periods. Nevertheless, as long as these periods remain within manageable limits, the extension of the inter-column distance from the original value of 28 m to 32 m seems to be reasonable, despite the potential increase in fatigue loads, which requires careful consideration. Enlarging the side column diameter enhances stability but lowers the heave and roll/pitch natural periods. Since the heave natural period is already 25.12 s and well beyond the typical incident wave range of T = 5–20 s, a further reduction is deemed impractical. Expanding the heave plate diameter minimally affects stability but significantly increases the heave natural period, while posing challenges to structural integrity due to increased wave forces. Therefore, the original values for the side column diameter and heave plate diameter are advisable. To summarize, the optimized SparFloat model has the following dimensions: $S$ = 32 m, $D_{sc}$ = 10 m, and $D_{hp}$ = 24 m.

4. Time Domain Results and Analysis

Based on the optimized SparFloat model, comprehensive time domain simulations are conducted by coupling aerodynamics, hydrodynamics, and mooring dynamics. Aerodynamic loads are computed using the blade element momentum theory, hydrodynamic loads are assessed using potential flow theory, and the mooring system analysis is executed through a quasi-static analysis method. This study aims to explore the dynamic response of SparFloat and the tension on the mooring system under different wind and wave conditions.

4.1. Environmental Conditions

This study considers three different environmental conditions. The Jonswap wave spectrum (with a wave peak enhancement factor of 2) and the NPD wind spectrum are used in analysis, with specific details provided in

Table 8. List of flow parameters in South China Sea region under different environmental conditions.

Environmental Condition	Significant Wave Height	Peak Wave Period	Wind Speed	Incident Angle
DLC	0.5 m	4.5 s	11.4 m/s	0°~45°, 90°
ELC	7.3 m	11.1 s	28.6 m/s	0°~45°, 90°
SLC	12.1 m	17 s	51.4 m/s	0°~45°, 90°

. For the “Design Load Condition (DLC)” [39], the floating wind turbine is operating under normal operational conditions at a rated wind speed. The “Extreme Load Condition (ELC)” is an extreme sea condition with a 50-year return period. The “Survival Load Condition (SLC)” produces responses with a very low probability of being exceeded during the design life, and the FOWT can endure such responses without causing catastrophic consequences. The “SLC” condition is used to check the robustness of the mooring system.

4.2. Design of Mooring System

The mooring system is essential for providing the restoring force and ensuring the structural stability of SparFloat. A schematic diagram of the mooring system is presented in Figure 17, with its main parameters summarized in

Table 9. Parameters of the mooring system.

Mooring Parameters	Value
Number of mooring lines	8
Depth to anchors below SWL	60 m
Depth to fairleads above SWL	5 m
Unstretched mooring line length	468 m
Equivalent mooring line diameter	0.116 m
Wet weight	296 kg/m
Axial stiffness	5.98 × 108 N
Breaking strength	9.4 × 106 N

. The catenary mooring system comprises 8 mooring lines. They are divided into four groups that spread symmetrically about the center of the platform. The two adjacent mooring lines in each group are laid out in a parallel configuration. The mooring lines consist exclusively of chains throughout their entire length. The fairlead, positioned 5 m above the waterline, is connected to each of the four side columns. The anchors, located on the seafloor, lie at a depth of 60 m below the waterline. The mooring lines possess a breaking strength of 9.4 × 10⁶ N, and the safety factor requirements can be found in Table 1. A safety factor is calculated as follows:

$$\sigma ={\displaystyle \frac{F_{break}}{T_{max}}}$$

(15)

where $F_{break}$ is the breaking strength, and $T_{max}$ is the maximum mooring tension.

4.3. Analysis of Dynamic Response

Seakeeping performance is crucial for FOWTs, with specific requirements for motion responses. During operational conditions, the platform’s mean and maximum roll/pitch motions must not surpass 5° and 10°, respectively. In extreme conditions, these limits expand to 8° and 15°, respectively [33]. Specifically, in the case of the floating platform designed for the South China Sea, ensuring minimal heave motion during survival conditions is crucial to prevent potential bottom contact and grounding risks.

Figure 18 depicts SparFloat’s maximum motion responses under various incident angles during the DLC condition. The roll motion is highly sensitive to incident angles, whereas the pitch motion shows less sensitivity and the heave motion is negligibly small. Notably, the most significant roll response occurs at a 90° incident angle, reaching 9.87°. The corresponding time domain curve is depicted in Figure 19a, with an average roll response at 4.91° at a 90° incident angle, satisfying the rule requirements. Similarly, the largest pitch response occurs at a 0° incident angle, peaking at 6.77°. Figure 19b displays the time domain curve, with an average pitch response of 3.33°, which also meets the rule criteria.

Figure 20 shows a histogram displaying the maximum motion response of SparFloat under varying incident angles under ELC condition. Compared to the DLC condition, the heave motion increases considerably, reaching a maximum amplitude of 1.37 m. However, this heave response remains relatively subdued, highlighting the platform’s robust design. Additionally, both roll and pitch motions are reduced under the ELC condition compared to the DLC condition. This effect is due to extreme conditions causing wind speeds to exceed the turbine’s cut-out speed, leading to turbine parking and a consequent reduction in aerodynamic thrust.

The results further indicate that under the ELC condition at a 90° incident angle, the most pronounced response is observed in roll motion, peaking at 7.08°. The corresponding time domain curve is illustrated in Figure 21a, which has a mean value of 4.03° and complies with the rules. At a 0° incident angle, the most significant motion occurs in the pitch motion, reaching a maximum value of 4.58°. The time domain curve is depicted in Figure 21b, demonstrating a mean response of 1.73°, which also conforms to the rules.

Figure 22 presents the time domain curve of heave response under the SLC condition at a 0° incident angle. The maximum negative heave response of 3.99 m is obtained at 9400 s, leaving an under-keel clearance of 9.01 m that is sufficiently safe. These findings reveal that the heave response during the SLC condition remains insignificant, demonstrating the platform’s freedom from grounding risk.

4.4. Analysis of Mooring Tension

The mooring system plays a crucial role in maintaining the floating platform’s position against higher-order wave drift forces and ensuring the platform remains stationary at its equilibrium position. Table 1 presents the ABS classification rules for the mooring safety factors calculated using the QSAM, mandating that the mooring safety factor should surpass 2 for the intact condition during both DLC and ELC, and exceed 1.43 for the damaged condition. For SLC conditions, the mooring safety factor calculated using the QSAM should be higher than 1.05.

Figure 23 presents the minimum mooring safety factors at various incident angles under DLC and ELC conditions. The red dashed line shows the minimum safety factor required by the rules. The results indicate that under both intact and damaged conditions, the mooring system of SparFloat complies with the rules and maintains an ample safety margin. This confirms the rationality of the platform and mooring system designs. Further analysis reveals that the mooring safety factor is minimum when the incident angle is 90°, due to larger high-order drift forces causing an increase in the roll motion response of the platform and subsequently tightening the mooring lines.

Figure 24 shows the minimum mooring safety factors at various incident angles under the SLC intact condition. All the results satisfy the rules, but at a 90° incident angle, the safety factor, at about 1.11, is marginally above the threshold of 1.05, indicating a slight safety margin for the mooring system under the SLC condition.

5. Conclusions

Combining the structural advantages of the spar-type and semi-submersible platforms, a new floating platform named “SparFloat” is designed for the typical sea conditions of the South China Sea. Variations in the platform dimensions, such as the inter-column distance, side column diameter and heave plate diameter, are investigated to optimize the design. The optimized platform is then subjected to fully coupled time domain simulations, confirming its rationality and reliability. The following conclusions can be drawn:

(1)

The stability and seakeeping performances of the platform are significantly affected by the platform’s restoring stiffness and mass. With an increase in the restoring stiffness, stability improves but seakeeping worsens. The mass of the platform has a significant impact on both aspects, whereas the impact of added mass is relatively minor. Notably, the seakeeping is affected not only by the restoring stiffness and mass, but also by external environmental loads.

(2)

The inter-column distance significantly impacts the platform’s dynamic response. A 5% increase in the column distance enhances the platform stability by about 2.5% and decreases the natural period of roll/pitch motion by 3–8%. The diameters of the side column and the heave plate also influence the platform dynamics. An increase of 5% in the side column diameter enhances the platform stability by 8.7%, and decreases the natural period of roll/pitch motion by 6%. As the heave plate diameter increases, the natural period of heave motion rises, but that of roll/pitch motion remains constant. This is because the roll/pitch natural periods are primarily governed by the restoring stiffness, and the added mass has a negligible effect on the roll/pitch periods due to its minimal contribution to the platform’s rotational inertia.

(3)

Fully coupled time domain simulations are conducted on the optimized SparFloat model. The results demonstrate that the platform’s motion responses meet classification rules under all conditions, with the heave motion remaining consistently conservative. Furthermore, the mooring force analysis aligns with the classification rules, with a sufficient safety margin for DLC and ELC, but with a slight safety margin for the SLC condition.

This study confirms the rationality and reliability of the SparFloat design, emphasizing the critical influence of geometric parameters on the platform’s dynamic behavior. To further enhance the design’s practicality and broaden its applicability, future research will prioritize validation through scaled model tests and comprehensive numerical simulations under extreme environmental conditions. Additionally, the potential deployment of the SparFloat platform in diverse offshore regions and its scalability for accommodating larger wind turbines will be systematically investigated, with the aim of advancing its feasibility and adaptability for a wider range of applications in the offshore wind energy sector.