GU Jia-yang,XIE Yu-lin,WU Jie

(a.Marine Equipment and Technology Institute;b.School of Naval Architecture and Marine Engineering, Jiangsu University of Science and Technology,Zhenjiang 212003,China)

Study on Vortex-induced M otion Characteristics of Variable Cross Section M ulti-column of a New Type of Deep Draft FDPSO

GU Jia-yanga,b,XIE Yu-linb,WU Jieb

(a.Marine Equipment and Technology Institute;b.School of Naval Architecture and Marine Engineering, Jiangsu University of Science and Technology,Zhenjiang 212003,China)

The software Fluent combined with detached eddy simulation(DES)is used to study the characteristics of a FDPSO variable section column vortex-induced motion.The variable section column vortex-induced motion is simplified into a mass-spring-damp system.The numerical simulations are done by calculating the instantaneous lift and drag forces of column and applying Reynolds-Averaged solver for the Navier-Stokes equation,then dynamic mesh technique is applied to update the flow field while UDF program is used to solve the differential equation of motion.The characteristics of variable section column flow around and vortex-induced motions at different flow velocity are studied.Drag coefficient,lift coefficient,vortex-induced motion amplitude and trajectory are discussed, too.The results indicated that three dimensional numerical models are more advantaged in simulation of high Reynolds number flow around a single column,and there are multiple vortices interacting with each other in the rear of the variable section column,which restrains the lift and drag effect of vortex on the column.When the reduced velocity ranges from 6 to 9,there is no obvious‘lockin’phenomenon.The transverse vibration amplitude of variable section column vortex-induced motions is about 1.2D at reduced velocity 4.5.The stream-wise equilibrium position increases with the increase of reduced velocity.The trajectory of variable section column is disordered and appears‘8’shape.

variable section column;vortex-induced motions;dynamic mesh; user defined functions

0 Introduction

Along with the development of ocean engineering technology and equipment,many newplatform concepts are proposed,such as floating drilling production,storage and offloading (FDPSO).FDPSO combines the characteristics of offshore drilling equipment and FPSO,which possesses the function of drilling,oil production,storage and transportation.FDPSO breaks through the traditional engineering application mode of drilling platform for development of deepwater oil and gas field,which gets the attention of many oil companies for the strong ability to withstand harsh environment and work in ultra deep water area.The structure form of FDPSO contains three types(Fig.1):ship type,cylinder type and multi-column type.The first multi-column FDPSO was invested by the United States OIL&GAS company and built by the Nantong COSCO Shipping Engineering Co.,Ltd.The main body of the platform is eight sides shaped floating,which consists of 4 columns and 2 riser platforms.The maximum operating depth of FDPSO is 3 000 meters.

Fig.1 Three typical FDPSO forms

Vortex Induced vibration(VIV)is a common fluid-solid coupling problem in the field of ocean engineering.When the current flows through the column of the platform with a certain velocity,the flow separation is generated due to the viscous effect and adverse pressure.The vortices shed and break out periodically at the rear of the column which causes the platform to move back and forth in a certain period,and this phenomenon is called vortex-induced motion (VIM).VIM has a negative impact on the structural safety of platform and increases the damage of chain and the riser fatigue.If the influence of vortex induced motion is not considered in the design of the platform,the insufficient estimation in the design of anchor and riser stress prediction problems will cause anchor and riser design parameters small,which increases the platform security risks and even leads to serious consequences.

The column section form of deepwater offshore platform is mainly round or square.Many researchers have carried out the research on vortex induced motion characteristics of single column platform.Williamson et al[1]is the first one to conduct systematic study for VIV of an elastically mounted rigid cylinder,whose study results have an important guiding role for the VIM of single column and multi-column platform.Zhao et al[2]used CFD method to conduct numerical simulation of multi-cylinder vortex induced motion under the working condition: the flow approaching angles ranges from 0°to 45°,the column spacing ratio is 3,the reduced velocity ranges from 1 to 20,and the study result showed that the change of the flow approach-ing angle has a great influence on the vortex induced motion of multi-column.Based on the theoretical analysis,Li et al[3]carried out the numerical simulation for the flow around and VIM of square column which explained the intrinsic mechanism behind the VIM,and compared mechanical behavior,motion amplitude and trajectory of the cylinder and square cylinder.With combination of model test and CFD calculation,Wang et al[4]studied the wake flow field,vortex shedding excitation and VIM characteristics of a cylinder under different conditions.The large eddy simulation(LES)method was used to calculate the vortex induced motion of Spar platform at different reduced velocity by Zhao et al[5],which proved the reliability of the solver NAOE-FOAM-SJTU in the simulation of the VIM.

In recent years,the influence of the cross section on the VIM of the column has attracted the attention of the academic circles,but the current research mainly focused on 2D section form,research on 3D complex variable section column is seldom reported.Xu et al[6]have conducted numerical simulation for the flow induced vibration of elastically mounted columns with different cross section,the effect of section shape on the vibration form and the influence of the stream-wise vibration on the transverse vibration are analyzed,as well.Gu et al[7-8]have studied the difference in VIM of two typical different section columns and the effect of filleting radius of square column on vortex-induced characteristics,and it has been found that the VIV of square column does not have the lock-in phenomenon which occurs in the VIV of circular cylinder,but the amplitude appears‘beat’rule and the‘beat’region differs caused by different filleting radius.In addition,the trajectories of square columns with different filleting radius are discussed.

So far,the phenomenon of VIV has not been studied deeply and comprehensively.This paper presents a new FDPSO variable section column.The hydrodynamic characteristics,vortex induced motion response and trajectory of this FDPSO are different from the traditional single cylinder or square column,so the research on VIM characteristics of these has great directive significance to the design of FDPSO.

1 Numerical com putation models

1.1 Governing equations for Computational Fluid Dynamics

Mass and momentum conservation equations for incompressible viscous fluid are given by:

1.2 Dynamical governing equation in dimensionless forms

1.3 Calculation model

In this paper,the FDPSO variable section column is zoomed with a scale of 1:80 during numerical simulation.Main parameters of the variable section column are given in Tab.1,and the shape is shown in Fig.2.

Tab.1 M ain parameters of the variable section column

Fig.2 The variable section column

1.4 Computational domain and grid division

The grid distribution of computational domains is shown in Fig.3;the local grid distribution of variable section column is shown in Fig.4.Cartesian coordinate system is adopted in the computational domain,the stream-wise parallel to the X axis,the transverse parallel to Y axis,and Z axis is vertical.After conversion,the average of variable section column diameter is D=0.28 m(D is characteristic length for computational fluid dynamics).

The VIM of variable cross-section column is simplified into mass-spring-damp system, the coupled motion of stream-wise and transverse is considered,the center of the variable section column is 5D away from the two laterals,5D away from the upstream boundary,and 20Daway from the downstream boundary.In the vertical,the height of variable section column is about 2D.The body-fitted grids were applied along the variable section column surface.The combination of quadrilateral grids and triangle grids are used in the whole domain.Dense grids are used in the vicinity of the variable section column,and the relatively sparse grids are used in the outer region.

Fig.3 Grid distribution of computational domains

Fig.4 Local grid distribution of the variable section column

In the same size of the computational domain,compared with two dimensional numerical simulations,the three-dimensional numerical simulation increases the amount of calculation. The complete numerical simulation for the near wall turbulence of the structure is very difficult,so detached eddy simulation(DES)is used to reduce the number of grids.DES model simulates the near wall flow by wall function.There is only need to locate first node at viscous layer without refined grids,which will save computing resources.According to the experience of using DES model,Atkins[9]suggested that the thick of first layer grids y+should be set between 30 and 100,which ensures that the first layer of grid is located in an area where the turbulence is fully developed.

Fluent separation solver is used to carry out calculation with the DES turbulence model and non steady first-order implicit method,SIMPLEC algorithm is used to couple the pressure and velocity of momentum equation,and momentum,turbulent kinetic energy and dissipation rate are displayed in the form of the second order upwind to reduce numerical dissipation. The boundary conditions are as follows:the surface of the variable section column is assumed to be smooth with no-slip.The velocity inlet is adopted at the left of computational domains. The outflow boundary is adopted at the right of computational domains.The symmetry is set at other boundaries.The inflow is uniform stream.

2 Results and analysis

2.1 Flow field analysis

The 3D pathlines behind the variable section column at Uc=0.112 m/s are given in Fig.5. The flow separation occurs when the fluid flows through the variable section column.Irregular spiral pathlines present in the rear of the column which indicates the complex and disordered flow field characteristics caused by irregular object surface.The‘circle’trajectory occurs when the fluid flows through the variable section column,which means the production of multiple vor-tices.The interaction of vortices relaxes the force on the structure produced by the vortices, which will reduce vortex energy and suppress the VIV of the structure.

The vortex structure in z direction at Uc=0.224 m/s are given in Fig.6.There are obvious interaction and mutual involvement between vortices near the rear of variable section column. The complicated vortex distribution shows the complexity of the flow field around the variable section column,and makes a good explanation for the irregularity of the lift and drag coefficient of the variable section column.

Fig.5 3D pathlines behind the variable section column

Fig.6 Vortex structure in z direction of variable section column

2.2 Analysis of drag coefficient and lift coefficient

The calculation result of the lift coefficient and drag coefficient of variable section column is intercepted in stable stage,the time history curve of lift coefficient is transformed by the Fast Fourier Transform(FFT),lift and drag characteristics are also discussed,as shown in Fig.7.

Fig.7 Time series and FFT analysis of Cl&Cdunder different cases

From Fig.7,it is found that the lift coefficient and drag coefficient of variable section column show high randomness,which is determined by the complexity of the three-dimensional flow field and the anisotropy of the vortex.The period of lift coefficient and drag coefficient is difficult to find a stable multiple relationships as a cylinder.Under different cases,the lift coefficient Cltakes 0 as the center to do the reciprocating oscillation in a instability state,but the mean value is still about 0.The lift coefficient ranges from-0.2 to 0.2.The drag coefficient Cdis stable at about 0.65.The above results prove that the variable cross section can reduce the lift force of the fluid on the structure.From the view of frequency domain analysis,the frequency of vortex shedding is irregular,and then the multiple peaks and the band of energy concentration arise.Especially in the high flow rate condition,the vortex shedding of the column is disordered,mutual influenced and suppressed.The reason of the irregular vortex shedding frequency is that there are a large number of small scale vortexes separating from the column when the large scale vortexes shed from the column,and the period of large scale vortex is long while the period of small scale vortex is short.Lift and drag coefficients of variable section column numerical model are shown in Tab.2.

Tab.2 Lift and drag coefficients of variable section column numerical m odel under different cases

On the whole,the flow around characteristics and the wake vortex structure of the variable section columns are so complicated that it is difficult to find a certain law,which can only be analyzed from the macro level.Due to the irregular shape,the rear of the variable section column may have multiple vortices at the same time.These vortices will influence each other and result in the three-dimensional effect of the variable section column larger than that of the cylinder.The reduction of drag coefficient proves that the variable section column has a good effect on the drag and VIM of the platform in the practical engineering application.But the complex structure will increase the difficulty of the construction of the platform.

2.3 Transverse VIM locking range and Stream-wise equilibrium position

Reduced velocity Uris an important dimensionless parameter in the study of VIM.In order to carry out comparative analysis,at Urranging from 1.5 to 9,the time history curve ofstream-wise and transverse amplitude are intercepted in stable stage.The left is transverse amplitude motion response spectrum in the same time stage,as shown in Fig.8.

Fig.8 Time series and FFT analysis of variable section column x/D&y/D at different reduced velocity

The VIM of variable section column has weak regularity,and the transverse amplitude exhibits fluctuation at the same reduced velocity.In the stream-wise,the VIM of variable section column also shows weak regularity at high speed.From response spectrum,it is found that when Ur=1.5,two bands of energy concentration arise.But with the increase of the reduced velocity,the two bands of energy concentration are synthesized to one.Firstly,the period of the transverse VIM response spectrum peak decreases with the increase of reduced velocity,and then keeps stable,gradually decreases after Ur>9.

（A/D）maximumand（A/D）nominalare used to represent VIM response amplitude,the transverse amplitude is expressed as follows:

where max（ Y（t ））is the maximum displacement,min（ Y（t ））is the minimum displacement, σ（ Y（t ））is the standard deviation of the transverse amplitude.

The transverse amplitude of variable section column at different velocity is shown in Fig.9.Whether the maximum amplitude or the nominal amplitude,the maximum value occurs at Ur=4.5.The maximum value of the maximum amplitude is 1.18D,and the maximum value of nominal amplitude is 1.08D.The statistics of the transverse amplitude obtained by two kinds of statistical methods has great difference,which reveals the instability of the transverse amplitude.This instability is also found in the lift coefficient during the numerical simulation of the flow around.On the whole,the trends of transverse amplitudes are similar under the two kinds of statistical methods,both increase with the increase of reduced velocity,gradually decline after reaching the turning point,and there is no obvious‘lock-in’phenomenon.

In addition to the transverse vibration,the stream-wise vibration which occupies a non dominant position is also an important response.The stream-wise amplitude of variable section column under different reduced velocity is shown in Fig.10,and it is found that the streamwise equilibrium position increases with the increase of reduced velocity.

Fig.9 Transverse amplitude of variable section column at different reduced velocity

Fig.10 Stream-wise amplitude of variable section column at different reduced velocity

2.4 Trajectory

Fig.11 Variable section column trajectories at different reduced velocity

According to the time history curve of stream-wise and transverse vibration,the trajectories are drawn to analyze the characteristics and trends of variable section column VIM at different reduced velocity,as shown in Fig.11(X axis and Y axis are done by non-dimensionalmethod).Due to the frequency of stream-wise VIM is two times of the transverse,the trajectories of variable section column appears‘8’shape or‘banana’shape.As the amplitude value of the stream-wise motion is different from the transverse motion,the width of trajectories is different,too.The trajectory becomes‘fat’with the amplitude becomes larger.

3 Conclusions

The finite volume method is used to simulate the characteristics of a FDPSO variable section column VIM.This paper emphatically analyzes the drag coefficient,lift coefficient,motion amplitude and trajectory.Fourth-order Runge-Kutta program is used to solve differential equation,the solving program is embedded into UDF,the transient dynamic response is transferred to the column by the DEFINE_CG_MOTION macro function,as well as the dynamic mesh technique is used to update the flow field.The conclusions are summarized as follows:

(1)In the high Reynolds number flow around a single column,the physical quantities of flow field and structure have great changes in vertical direction and shows strong three-dimensional characteristics,thus the three dimensional numerical model is more advantage.

(2)There may be multiple vortices in the rear of the variable section column at the same time,and the interaction between vortices restrains the lift and drag effect of vortex on the column.

(3)VIM of a single column should go through a slowly steady process.Finally,this column will take periodic motion at a certain point away from origin in the flow direction.When the reduced velocity ranges from 6 to 9,there is no obvious‘lock-in’phenomenon.The transverse vibration amplitude of variable section column VIM is about 1.2D at reduced velocity 4. 5.The stream-wise equilibrium position increases with the increase of reduced velocity.

(4)The trajectory of variable section column is disordered and appears typical‘8’,which is caused by the irregular time course of the stream-wise and the transverse motion.The trajectory of variable section column will change along with the reduced velocity.

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新型深吃水多立柱FDPSO變截面立柱渦激運(yùn)動(dòng)特性研究

谷家揚(yáng)a，b，謝玉林b，吳介b

（江蘇科技大學(xué)a.海洋裝備研究院；b.船舶與海洋工程學(xué)院，江蘇鎮(zhèn)江212003）

文章采用FLUENT軟件結(jié)合分離渦法對(duì)某新型深吃水多立柱FDPSO變截面立柱渦激運(yùn)動(dòng)特性開(kāi)展了研究。將變截面立柱渦激振動(dòng)系統(tǒng)簡(jiǎn)化為質(zhì)量-彈簧-阻尼模型，引入雷諾平均應(yīng)力模型求解不可壓縮粘性Navier-Stokes方程，通過(guò)計(jì)算出流場(chǎng)作用于柱體的瞬時(shí)升力與阻力，并基于UDF程序求解運(yùn)動(dòng)微分方程同時(shí)運(yùn)用動(dòng)網(wǎng)格技術(shù)實(shí)現(xiàn)流場(chǎng)更新，實(shí)現(xiàn)了對(duì)變截面立柱渦激運(yùn)動(dòng)的數(shù)值模擬。對(duì)不同來(lái)流速度下變截面柱繞流和渦激運(yùn)動(dòng)特性進(jìn)行了研究，分析了變截面柱阻力系數(shù)、升力系數(shù)、運(yùn)動(dòng)幅值和運(yùn)動(dòng)軌跡等，研究發(fā)現(xiàn)：在高雷諾數(shù)單柱繞流模擬中采用三維數(shù)值模型更具優(yōu)勢(shì)，變截面柱后方同一時(shí)間內(nèi)可能有多個(gè)旋渦產(chǎn)生，旋渦之間相互影響，抑制了旋渦對(duì)柱體的升阻力作用；在折合速度6～9范圍內(nèi)，變截面柱未出現(xiàn)明顯“鎖定”現(xiàn)象；變截面柱渦激運(yùn)動(dòng)的橫蕩振幅峰值在Ur=4.5，約為1.2D；變截面柱流向平衡位置隨著折合速度增加而增加；變截面柱運(yùn)動(dòng)軌跡出現(xiàn)了典型的“8”字形，但變截面柱的軌跡相對(duì)較紊亂。

變截面柱；渦激運(yùn)動(dòng)；動(dòng)網(wǎng)格；UDF

U357

A

谷家揚(yáng)（1979-），男，博士，江蘇科技大學(xué)副教授，通訊作者，E-mail：gujayang@126.com；謝玉林（1994-），男，江蘇科技大學(xué)碩士研究生；吳介（1991-），男，江蘇科技大學(xué)碩士研究生。

U357

A

10.3969/j.issn.1007-7294.2016.09.003

1007-7294（2016）09-1098-11

Received date：2016-04-20

Foundation item:Supported by National Natural Science Foundation of China(51309123);the Open Foundation of State Key Laboratory of Ocean Engineering(1407);Sponsored by‘Qing Lan Project’of Colleges and Universities in Jiangsu Province and the Collaborative Innovation Center Funded Projects in Jiangsu University(High Technology Ship Category)

Biography：GU Jia-yang(1979-),male,associate professor,corresponding author,E-mail:gujiayang@126.com; XIE Yu-lin(1994-),male,master graduate student; WU Jie(1991-),male,master graduate student.