Study on Vortex-Induced Motions of A New Type of Deep Draft Multi-Columns FDPSO

A numerical simulation and an experimental study on vortex-induced motion (VIM) of a new type of deep draft multi-columns floating drilling production, storage and offloading (FDPSO) are presented in this paper. The main dimension, the special variable cross-section column and the cabin arrangement of the octagonal pontoon are introduced based on the result. The numerical simulation is adapted to study the effects of current incidence angles and reduced velocities on this platform’s sway motion response. The 300 m water depth equivalent truncated mooring system is adopted for the model tests. The model tests are carried out to check the reliability of numerical simulation. The results consist of surge, sway and yaw motions, as well as motion trajectories. The maximum sway amplitudes for different types of offshore platform is also studied. The main results show that the peak frequencies of sway motion under different current incidence angles and reduced velocities vary around the natural frequency. The analysis result of flow field indicates that the change of distribution of vortex in vertical presents significant influences on the VIM of platform. The trend of sway amplitude ratio curve of this new type FDPSO differs from the other types of platform. Under 45° current incidence angle, the sway amplitude of this new type of FDPSO is much smaller than those of other types of offshore platform at 4.4 ≤ Vr ≤ 8.9. The typical ‘8’ shape trajectory does not appear in the platform’s motion trajectories.


Introduction
FDPSO (floating drilling production, storage and offloading) is a new type of integrated ocean platform, consisting of full-function of drilling, storage, well completion. It can shorten the oil and gas production cycle largely and reduce investment. There are three kinds of structural forms: ship shape, cylinder shape and multi-columns shape. According to the specification of American Petroleum Institute (2010): the influence of the vortex-induced motion (VIM) characteristics on multi-columns platforms such as SEMI, TLP and FDPSO must be considered in the preliminary design. The VIM can cause periodic oscillation to the platform, as increases the fatigue damage of chain and the riser. On the other hand, compared to the cylindrical platforms such as spars, the VIM of multi-columns platform is usually more complex due to the mutual influence between the columns and the pontoon. As the concept of multi-columns FDPSO is quite more recent, there are much less relevant researches about it. The present researches about the vortex-induced vibration (VIV) and wake-induced vibration (WIV) still have reference value for this paper.
A large number of experimental results and analytical models about VIM are presented for the interaction among multi-columns. The arrangement modes of the column are mainly series, parallel, and staggered (Sumner, 2004;Sumner et al., 2005). The VIV characteristics of multi-columns structure in different arrangement modes are quite different from that of single column structures.
In addition to the arrangement modes, the difference between the main dimension of columns shows a great influence on the VIV. To and Lam (2007) investigated the VIV response of a flexibly mounted circular cylinder located in the rear of a larger cylinder. Their results show that the upstream larger cylinder can amplify the vibration of the downstream cylinder.
An experimental study on WIV response of cones with an in-line arrangement were carried by Zeinoddini et al. (2014). The results reveal that for cones in in-line arrangement, the amplitudes of transvers motion and in-line motion do not decrease with the increase of the spacing ratio unlike uniform cylinders do. Additionally, because of the three dimensional feature of the cones, the vortices shedding from the upstream tapered cylinder grow weak at a smaller spacing ratio. Obviously, this experiment provides a reference to study the VIV of the new type deep draft FDPSO with variable cross-section columns.
The WIV of two staggered cylinder has been investigated by Assi et al. (2014) in a flume with Reynolds number between 2000 and 25000. Trajectories and dynamic response curves of displacements were given in the study. The WIV is found to be weaker as the initial position of the downstream cylinder is more far away from the centreline of the upstream cylinder. Thus, it is significant for researching the interaction mechanism between the columns of multi-columns platform under different current incidence angles.
Based on Reynolds-averaged method, the VIM of the four cylinders with different current incidence angles and reduced velocities were simulated by Zhao and Cheng (2012). The numerical results show that the current incidence angle is significant on the response of the four-cylinder system, and the lock-in region for 45° current incidence angle is the narrowest. Korbijn et al. (2005) studied the dynamic responses and mooring characteristics of an octagonal FDPSO in the frequency domain and time domain by using SESAM software. The experiment was carried out in the tank of St Petersburg Ship Scientific Research Center of Russia. Based on the researches on the platform motion responses, the VIM characteristics of FDPSO were studied. Gu et al. (2014) took a review of the research on VIM of a new deep draft multi-columns FDPSO, which provide some basic ideas and steps for the study of VIM of this new type FDPSO.
By using the finite-analytic Navier-Stokes (FANS) code in conjunction with a moving overset grid approach, Chen and Chen (2016) studied the full scale and the 1:70 model platforms to check the scale effect. Additionally, three corner geometries were simulated. The VIM was found to be sensitive to the corner rounding. Meanwhile, the numerical simulation data were compared with experimental data, demonstrating the capability of the present computational fluid dynamics (CFD) approach.
The VIMs of several typical multi-columns platforms, such as semi-submersible platform and tension leg platform (TLP), were contrastively analysed by Waals et al. (2007). The effects of excitation length, mass ratio, current velocities and current incidence angles on the VIM performance of platform are discussed. By considering the coupling action between different degrees of freedom, the VIM characteristics of the TLP were studied numerically by Kim et al. (2011). Then, the numerical simulation results were compared with model test data for a multi-columns floating platform. The result indicates that the agreement between model tests results and CFD simulations is encouraging at low reduced velocity region. Pontaza et al. (2015) presented CFD simulations of VIM response for a platform with four round columns in the model scale. The comparisons of measured and predicted responses show good agreement. The result shows that the 45° current incidence angle has diminished sway responses relative to the 0° current incidence angle.
A TLP for Southeast Asian environment is investigated using a series of model tests and CFD analysis by Tan et al. (2016). The result shows that the hull without appurtenances has higher responses and more VIM-like behaviors compared to the hull with appurtenances. Based on VIM model tests using the large scaled semisub models with two kinds of column intervals, the VIM interference influence between the columns has been clarified by Fujiwara et al. (2016). The result indicates that columncolumn interaction of hydrodynamic force acting on fore and aft columns is weak in the lower fluid velocity and becomes relatively stronger in the higher fluid velocity. Obviously, due to the different intervals between cross-sections, this result is useful for the future improvement of the new type FDPSO.
The current incidence angle also presents a great influence on the VIM of the platform. Magee et al. (2011) carried out model tests for researching the VIM characteristics of a TLP operating in Southeast Asia. Two current incidence angles and two different drafts were studied in the model tests. The results consist of surge, sway and yaw motions, as well as motion trajectories. It shows that yaw responses with the 0° current incidence angle are more significant than those with 45° current incidence angle. Column aspect ratio affects response mainly for 45° current incidence angle and not much for 0°.
Moreover, Gonçalves et al. (2015) carried out experiments on the VIM phenomenon of deep-draft Semi-Submersible platforms. The effects of incidence angles and two types of columns, rounded square sections (SRC-model) and circular columns (CC-model) were investigated. Circular columns and square-rounded columns present different behavior in terms of transverse response for different incidence angles, and the CC-model presents common features with the new type FDPSO. Bai et al. (2014) conducted model tests on the VIM of a deep draft semi-submersible platform with square-rounded columns under different current incidence angles. The study mainly focused on the lock-in range of VIM. It shows that the sway response amplitude is larger with 135° current incidence angle. There is no lock-in phenomenon with 180° current incidence angle and 90° current incidence angle, which differs from the results of the new type FDPSO. An experimental study on VIM of the semi-submersible platform with square-rounded columns is presented by Gonçalves et al. (2012). Model tests were carried out to check the influence of different headings and hull appendages on motion trajectory, yaw motion and transverse motion of the platform. The results show that the largest transverse amplitudes occurred around 40% of the column width with incidence angles of 30° and 45°. The largest yaw motions were verified with the angle of 0°, which also differs from the results of the new type FDPSO.
In this paper, the new type of deep draft multi-columns FDPSO possesses four variable cross-section columns, hence the vortex shedding distribution is typically dependent on current incidence angle and current velocity. Com-pared with traditional deep draft semi-submersibles, the three-dimensional feature of the variable cross-section column is more complex with mutual interference between the pontoons and the columns. The purpose of this paper is to provide some reference for the study of VIM characteristics on the new deep draft multi-columns FDPSO.

Description of the FDPSO platform
The general arrangement of the new type of FDPSO platform is shown in Fig. 1. The dimensions and hydrodynamic parameters are listed in Table 1. The hull of the FDPSO consists of an octagonal buoyancy structure (pontoon) and four columns. The water ballast tanks, oil storage, solid ballast and four lower pump rooms are arranged in the pontoons. The scaling factor 1:80 is adopted in the numerical simulation and model test.

Ocean environment and working conditions
The current incidence angles of 0°, 15°, 30° and 45° are used in the numerical simulation. Only current incidence angles of 0° and 45° are chosen for the model tests. The reduced velocity V r is an important dimensionless parameter in the study of VIM, which is expressed as follows: where U is the current velocity and f n is the natural frequency. The value of D is 20.02 m, which represents the projected length of the single column's cross-section on a plane perpendicular to the current incidence angle. The detailed coordinate system and the specific of current incidence angle are shown in Fig. 2. The displacement in the x direction represents the surge motion, while the displacement in the y direction represents the sway motion. α is the current incidence angle. The current velocity conditions are shown in Table 2. The corresponding Reynolds number for the prototype is about 1.026×10 7 -6.156×10 7 , with the corresponding Reynolds number for the model of 1.4×10 4 -

Numerical modeling
The method combining Lattice Boltzmann Method (LBM) and Large Eddy Simulation (LES) is used to simulate the three-dimensional flow field around the variable cross-section columns. In the simulation, the D3Q19 lattice model is used for velocity discretization (Qian et al., 1992).

Simulation of flow field
In the continuum space with discrete velocities, the three-dimensional Boltzmann transport equation can be discretized on the lattice as: (2) The collision operator is generally modelled as a relaxation of the particle distribution functions (PDFs) towards an equilibrium state. e ax , e ay , and e az are the components of the unit vector of discrete velocity e a in x, y, and z directions, respectively. The subscript a is the identifier of the 19 discrete velocities. A single-relaxation time (SRT) based on the Bhatnagar-Gross-Krook (BGK) approximation is used: f eq a where f a is the probability distribution functions for each discrete velocity, is the local equilibrium probability distribution function, and τ is the relaxation time defined as: where υ is the coefficient of viscosity and T is the temperature. From a statistical point of view, the system is made up of a large number of elements that are macroscopically equivalent to the problem investigated. The macroscopic density and linear momentum can be computed as: For a three-dimensional model, the D3Q19 model are illustrated in Fig. 3.
The local equilibrium function is generally derived from a Maxwell-Boltzmann distribution with the same macroscopic variables of the pre-collision state, ensuring the mass and momentum conservation. It is defined as: where u is the macroscopic velocity; ω a are the weighting constants to preserve the isotropy; c s is the speed of sound; ∆x is the space step; and ∆t is the constant time step. For the D3Q19 model, the weighting constants and discrete velocities are defined as follows: With the increase of Reynolds number, the viscosity decreases, and the maximum velocity gradient will affect convergence. Then, the LES method is adopted in this study. The basic idea of the LES is to simulate the large scale structure directly, and to simulate the small scale structure by establishing the Subgrid Scale (SGS). It is suitable for unsteady three-dimensional flow simulation. Owing to the adoption of lattice BGK model, the filtration in physical space does not affect the probability distribution function f a and the local equilibrium probability distribution function . The turbulent viscosity coefficient corresponding to relaxation time is calculated by Smagorinsky model (Smagorinsky, 1963): Therefore, τ also changes with the local viscosity υ, and the relaxation time τ will not be fixed.
The laminar viscosity coefficient is defined as: The turbulent viscosity coefficient is defined as: s where c s is the Smagorinsky constant; ∆x is the filter scale, namely the minimum space step; is the strain rate tensor.
In LBM-LES method, the strain rate tensor can be expressed as follows:

Governing equation
In order to facilitate the numerical calculation, the platform is only allowed to move in the horizontal plane in the simulation. The motion of the platform is predicted by the motion equation.
For sway motion: (16) for surge motion: for yaw motion: where x, y and θ denote the in-line, transverse and yaw displacements, respectively; C x , C y , and C θ represent the damping coefficients of in-line, transverse and yaw motions, respectively; ζ x , ζ y , and ζ θ represent the structural damping ratios of in-line, transverse and yaw motions, respectively; m is the mass of the platform; J is the moment of inertia according to yaw motion; f nx , f ny , and f nθ represent the structural natural frequencies of in-line, transverse and yaw motions, respectively; K x , K y , and K θ represent the mooring system stiffnesses of in-line, transverse and yaw motions, respectively. M θ is the moment acting on yaw motion; F 1 and F d are the lift and drag force, respectively.

Experimental setups
5.1 Arrangement of the mooring system and equivalent truncation design The FDPSO's mooring system is composed of four groups with total 16 chain-polyester type mooring lines. As shown in Fig. 4, in each group, the interval angle between adjacent mooring lines is 5°. The distances between anchor and the center of the platform are 2440 m.
The operating depth is 1500 m for the prototype. Even with the scaling factor of 1:80, the model's mooring system is too large for the basin. Therefore, it is necessary to adopt equivalent truncation mooring system, and the schematic of the truncated model is shown in Fig. 5. In the equivalent truncation design, Stansberg et al. (2002) has given the detailed introduction for the method of truncated system's se-lection and design. According to their result, the following principles are accounted: to model the correct total, horizontal restoring force characteristic; to model the correct quasi-static coupling between vessel responses; to model a representative level of mooring and riser system damping, and current force; to model representative single line tension characteristics (at least quasi-static). The vertical truncation factor of mooring ropes is 5 (γ=5). More details of the mooring lines system after being truncated are presented in Table 3.
The static force characteristics of the mooring system (full or truncated) are displayed in Fig. 6a. The tension characteristics of single mooring line (full or truncated) are shown in Fig. 6b. From Fig. 6, we can find: before and after equivalently truncated, the horizontal restoring force characteristic of whole mooring system and the top tension characteristic of single mooring line are roughly the same.
This experiment was carried out in the State Key Laboratory of Ocean Engineering in Shanghai Jiao Tong University. The dimensions of the basin are 50 m×30 m×6 m. Testing time for each case in the model test was defined corresponding to 3 hours in prototype. According to the scaling factor 1:80, the water depth is set at 3.75 m corresponding to the prototyped truncated water depth of 300 m. In the present tests, the Froude numbers of the model and prototype were kept in the same, which means the similarity of the gravitational force and inertia force is satisfied. Based on the law of similarity, the relationships of physical variables between prototype and model are listed in Table 4, where λ means the linear scale ratio and γ means the specif-  The main body of the model is made of plexiglass. The FDPSO model is hollow for adjusting gravity center easily. The surface of the FDPSO model is painted with waterproof material to enhance the structural strength and water resistance. The gravity center position is adjusted by changing the weights on the inertial moment frame.
Internal circulation mode is adopted in the current generation system. High power pump draws the water in the pool through the pipeline. The high-pressure water flow is ejected from the nozzle of the pipes. Because a plurality of nozzles are arranged evenly on each pipe along the width direction of the pool, the water jet is relatively uniform with a uniform and stable flow inside the basin.
A photo of the FDPSO in the model test is shown in Fig. 7. The data were captured with a sampling frequency of 40 Hz. All of the measured data in the model tests have been transferred to the full scale in this study.

Natural period and dimensionless damping coefficient
of the FDPSO A free decay experiment is carried out to determine the platform's natural period and damping parameters. In this experiment, no environmental load but initial displacement or initial rotation angle is imposed on the platform. By analyzing the damping curve of each freedom motion, the natural period and damping coefficient of platform's motion are gained. The results for the prototype are exhibited in Table 5.

Characteristics of the time domain and frequency domain of the VIM
To focus on the VIM response characteristic of the platform, only the surge, sway and yaw motion are detailed illustrated. The motion responses are presented from 500 s to 2000 s.
Time series of the three-degree-of-freedom (3DOF) motion responses for the FDPSO are shown in Fig. 8. The equilibrium position and the maximum amplitude of the surge motion increase with the increase of the reduced velocity with two current incidence angles. At the reduced velocity  Fig. 6. Force characteristics of mooring system before and after truncation. of 6.7 ≤ V r ≤ 11.1, the equilibrium position of surge with the current incidence angle of 45° is larger than that with 0°a ngle. As shown in Fig. 8, with 0° incidence angle, the sway motion of the platform is regular at the reduced velocity 4.4 ≤ V r ≤ 8.9. But with the incidence angle of 45°, the regularity of sway motion is poor. From Fig. 8e and Fig. 8f, it can be observed that compared with the surge and sway motion, the yaw motion is more intensive and severe. Additionally, the yaw motion is more severe with 45° current incidence angle than that with 0° angle.
Power spectrum densities (PSD) of the surge the motion are presented in Fig. 9. With 0° current incidence angle, a peak frequency of the surge motion of the platform at each reduced velocity except V r =11.1 occurs near 0.063 rad/s, which is close to the natural frequency of surge. There is only one peak frequency of the spectrum of the surge motion at the reduced velocity V r ≤ 4.4. But there are two spectral peaks at the reduced velocity 6.7 ≤ V r ≤ 8.9. The vortex shedding of each column varies along the column length. This leads to less chance of synchronization for the downstream column suffering the vortex shedding of upstream column. Hence, the surge motion is irregular and unpredictable. With 45° current incidence angle, the frequency peaks of the surge motion gradually assemble in the low frequency region as the reduced velocity increases. Fig. 10 presents the PSD of the sway motion with 0° and 45° current incidence angles. It is noted that the spectrum peak frequency in each case is around the natural frequency of the sway motion, which shows that the reduced velocities ranging from 2 to 13 have little effect on the peak frequency of this new FDPSO's sway motion. With 0° current incidence angle, with the increase of the reduced velocity, the spectral density at the peak frequency firstly increases, and then decreases. The largest spectral density at the peak frequency occurs at V r =6.7. With 45° current incidence angle, with the increase of the reduced velocity, the spectral density at the peak frequency increases. Fig. 11 presents the spectrum response characteristic of yaw motion. For both 0° and 45° current incidence angles, the wide range of the spectrum response of the yaw motion can be found. Owing to the irregular shape, multiple dissimilar vortices occur along the vertical of the variable section column at the same time. These vortices will influence each other and result in the three-dimensional effect of the variable section column larger than those of the long straight cylinder. The peak frequency of yaw motion at each reduced velocity is close to the natural frequency.

Characteristics of trajectories
As shown in Fig. 12, the trajectory of the platform motion never shows the typical '8' shape for two incidence angles. The dominant sway motion occurs at low reduced velocity region with the regular motion trajectory with 0°c urrent incidence angle. The surge motion of the platform cannot be ignored at high reduced velocity region. With 45°c urrent incidence angle, both the surge and the sway motions increase with the increase of the reduced velocities. But the growth rate of the surge is larger than that of the sway, which means that the platform trajectory tends more and more like 'oval'.

Validation analysis
The numerical simulation results are compared with the experimental results only for α = 0° with V r =6.7 in this paper. Comparisons of the time series and the maximum sway   Fig. 11. Spectrum response characteristic of yaw.

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GU Jia-yang et al. China Ocean Eng., 2018, Vol. 32, No. 1, P. 1-13 amplitudes between the measured data and the numerical simulations are presented in Fig. 13. As shown in Fig. 13a, the simulation result of sway motion is smaller than the experimental value. This may due to that the sway motion of the platform in the model test is also affected by the roll, pitch and heave motions which are not considered in simulation. In Fig. 13c and Fig. 13d, the surge motion and the yaw motion are presented. Unlike the sway motion, the simulation results of the surge and yaw motions are larger than the experimental values. From  Fig. 13b, it also can be seen that with the increase of the reduced velocity, the difference between simulation and model test results are more obvious. Both experimental and simulation results present initial branch and lower branch, which indicates that the horizontal simplification does not affect the VIM features of the platform. A good agreement between numerical and experimental results is generally ob-served. This provides confidence to the CFD model to test other cases which are not experimental tested.

Effect of the current incidence angle
Simulations are carried out for the current incidence angles of α = 0°, 15°, 30° and 45°. The comparisons of the sway motion between different current incidence angles are shown in Fig. 14. With the current incidence angle changing from 0° to 45°, the range of initial branch of the sway amplitude ratio curve increases. Under 30° current incidence angle, the lower branch has disappeared, and the sway amplitude eventually remains steady. The tendency of the sway amplitude ratio curve under 0° current incidence angle is similar to that under 15° current incidence angle, while the tendency of sway amplitude ratio curve under 30° and  GU Jia-yang et al. China Ocean Eng., 2018, Vol. 32, No. 1, P. 1-13 9 45° current incidence angles are similar. However, the peak frequencies of the sway motion are close to the natural frequency for all of current incidence angles. This indicates that the current incidence angles have little effect on the peak frequencies of the sway motion. It can be seen from Fig. 14a, with the increase of the current incidence angle, the value of the sway amplitude ratio at V r =6.7 drops off gradually. This phenomenon will be further explained in the next section.

Sway amplitude characteristics of the VIM
The time series results from the model tests are analyzed statistically as follows.
Maximum sway amplitude Nominal sway amplitude where max[Y(t)] is the maximum displacement, min[Y(t)] is the minimum displacement, and σ[Y(t)] is the standard deviation of the sway amplitude. The results are shown in Fig. 15. There are sway responses of five types of multicolumns platform under two current incidence angles. Under 0° current incidence angle, the results of the sway motion verify the existence of a resonant behavior on the VIM of this new type of the FDPSO for the reduced velocity 6.0≤V r ≤8.0. However, with the increase of the reduced velocity, the difference between the maximum amplitude and nominal amplitude becomes larger. The instability of the sway motion increases with the reduced velocity, as the maximum amplitude of the sway motion at V r = 13.3 increases suddenly. The instability may be caused by the coupling effects between motions of different degrees of freedom.
Under 0° incidence angle, the amplitude of the sway motion of this new type FDPSO is relatively smaller compared with other types of offshore platform with obvious resonance phenomena. However, under 45° current incidence angle, there is no obvious resonance phenomena. Obviously, the sway amplitude of this new type of FDPSO is much smaller than that of other types of offshore platform at 4.4 ≤ V r ≤ 6.7 under 45° current incidence angle. This may be caused by the variation column diameter along the column length. The vortex shedding from each column varies along the column length. This leads to less chance of synchronization.
Similar to the circular column(CC-model), the amplitude of this new type FDPSO's sway amplitude ratio curve under the 0° incidence angle is larger than that under 45° incidence angle at 4.4 ≤ V r ≤ 6.7. This is different from a  semi-submersible platform with four square columns (Waals et al., 2007), as well as a four rigidly coupled circular cylinders in a square configuration (Zhao and Cheng, 2012).

Flow field
The vorticity fields and the vector diagrams of fluid motion at V r =6.7 are given in Figs. 16-19. Where H means the total height of the pontoon and column, and Z is the vertical height above the bottom of the pontoon. Z/H=0.6 is located at the maximum diameter of the column, while Z/H=0.4 is located at the minimum diameter of the column. In order to analyze the three-dimensional characteristics of the platform's variable cross-section columns clearly, only the flow fields near the columns are chosen to be present.
From these figures, it is can be seen that for each cur-rent incidence angle, the vortex shedding mode is irregular. Under 0° current incidence angle, the downstream column disturbs the vortex shedding from the upstream column. Under 15° current incidence angle, the distribution of the vortex at Z/H=0.6 is similar to that of the vortex at Z/H=0.4. Under 30° current incidence angle, the distribution of vortex Z/H=0.4 differ from that of Z/H=0.6, which is caused by the variation column diameter along the column length. The vorticity in most areas of the flow field is relatively large. However, as shown in Fig. 14, the amplitude of the sway motion under 30° current incidence angle is not the largest. Thus, the vorticity of the vortex behind the column is not the determining factor for the VIM of the platform. The difference in the distribution of the vortex in the vertical may weak the excitation force on the platform.
Under 45° current incidence angle, large difference in  The ratio between the maximum and minimum diameter of the column merit further research to find the best value to reduce the VIM on the platform.

Conclusions
In the present study, experimental tests and numerical simulation were carried out to investigate a new type of deep draft multi-columns FDPSO's VIM characteristic. In the model tests, the equivalent truncation design was adopted and coupling effects between motions of different degrees of freedom were taken into account. The numerical simulation is adopted to study the effect of current incidence angles on the sway motion response of the platform and to analyze the three-dimensional characteristics of flow field. The sway amplitudes for different types of offshore platform were analyzed. The following conclusions can be drawn.
(1) The peak frequency of the sway motion in each case is close to the natural frequency of the sway motion. This reveals that the vortex shedding frequency and current incidence angles have little effect on the peak frequencies of the sway motion. With the current incidence angle changing from 0° to 45°, the range of initial branch of the sway amplitude ratio curve increases. Under 30° current incidence angle, the lower branch has disappeared, and the sway amplitude remains steady.
(2) The yaw motion under 45° current incidence angle is larger than that under 0° angle, especially at high flow velocity. The peak frequencies of the yaw motion are also close to the natural frequency.
(3) The platform trajectories do not show the typical '8' shape. Sway motion plays a major role in the VIM of the platform at low flow velocity region. At high flow velocity region, the surge motion reaches a relatively large value.
(4) With the increase of the reduced velocity, the nominal amplitude of the sway motion under 0° current incidence angle increases firstly and then decreases. Under 45° current incidence angle, the sway amplitude of this new type of FDPSO is much smaller than those of other types of offshore platform at 4.4 ≤ V r ≤ 8.9. The trend of this new type FDPSO' sway amplitude ratio curve differs largely from those of the other types of the platform. However, similar to the circular column(CC-model), this new type FDPSO's sway amplitude under the 0° incidence angle is larger than that under 45° incidence angle at 4.4 ≤ V r ≤ 6.7.
(5) At high flow velocity, the sway motion is irregular, Without considering the effects of the platform with six degrees of freedom motion coupling, the simulated maximum amplitudes of the sway motion are smaller than that in experimental tests.
(6) Under 30° current incidence angle, the distribution of the vortex at Z/H=0.4 differs from that at Z/H=0.6, which is caused by the variation column diameter along the column length. The change of the distribution of the vortex along the vertical may weak the sway motion of the platform, but will not change the peak frequencies of the sway motion.