Simulation of the Flow Around an Offshore Structure for Wind

Turbines

Jose Pedro Nunes Teixeira Vaz Morenojose.moreno@ist.utl.pt

Instituto Superior Tecnico, Universidade de Lisboa, Lisboa, Portugal

December 2016

Abstract

Offshore industry has been growing during the last years. The deep understanding of the interactionof waves and currents with offshore structures is a crucial factor in safe and economical technology design.This work is focused on a gravity based foundation (GBF) offshore structure for eolic turbines that isbeing developed in the scope of the DemoGRAVI3 project. The goal of this work is to perform CFDsimulations of the flow around the captive GBF structure cross section for different current headingsin order to obtain the hydrodynamic force coefficients. Free surface effects and the fluid/structureinteraction will be neglected. The ReFRESCO code [1] is used to perform the simulations with thepurpose of solving the unsteady RANS equations with the k − ω SST turbulence model. Two basicpillar geometries were considered in the project design, i.e., a GBF offshore structure was initiallycomposed by cylinder pillars and changed to chamfer pillars. The main conclusions of this work were:considering the range of incoming current angles studied, the angle of β = 180◦ is the one that has thelowest loading applied on the offshore structure; On the other hand, β = 90◦ presents the most complexflow with the highest loading applied on the offshore structure; The numerical uncertainty associatedwith this study is not negligible; The flow behavior is much more complex for a single chamfer cylinderpillar than for a single smooth cylinder pillar and, as consequence, higher loads are observed for theformer. Keywords: CFD, Offshore Structure, Hydrodynamic Loading, RANS, DemoGRAVI3

1. Introduction

The subject of study in this work is a GravityBased Foundation (GBF) GRAVI3 technology forwind turbines substructures developed within theframework of the European funded project De-moGRAVI3, that allows a more cost-effective so-lution for wind energy applications in diverse Eu-ropean offshore wind areas. This technology con-sists on a mixed concrete-steel self-buoyant bottomstanding GBF made by three concrete caissons sup-porting a steel tripod.In order to develop applications in the offshore in-dustry, it is required to perform several analysis fordesign purposes. The full-scale testing would bethe best option to verify any application. However,it is too expensive and the use of a ”trial and er-ror” methodology with a full-scale structure is notpossible. Alternatives must be considered and twooptions to estimate the hydrodynamic loads andflow behavior around an offshore structure mightbe used: physical models or mathematical models.The main goal of this work is to determine the hy-drodynamic loading applied on the GRAVI3 off-shore structure using mathematical models. Thisstructure will be subjected to different forces caused

by a combination of different environmental condi-tions (wind speeds, waves, tidal and currents) wheninstalled. Plus, one of the innovations of this tech-nology is that the wind turbine and the GBF areassembled onshore. Since the transport will be car-ried out using the assembled global structure, it isrequired to evaluate the potential consequences ofthis process.Several simplifications were introduced in problemmodeling. Simulations were carried out using acaptive structure, i.e., the structure was static andthe fluid/structure interaction (FSI) was not con-sidered. The free surface effects were neglected atthis stage. Simulations were performed in two di-mensions, resulting in a study of the hydrodynamicloading caused by the incoming current on the basicgeometry cross-section of the GBF structure. TheCFD study will be carried out using a viscous-flowcode that solves multiphase unsteady incompress-ible flows using RANS equations with the volume-of-fluid (VOF) method (ReFRESCO [2]).In the initial design, the GRAVI3 offshore struc-ture was formed by three concrete caissons withcylindrical shape. In order to assess the numeri-cal uncertainty associated with this study, it was

1

required to carry out several simulations with dif-ferent grid refinements. These simulations shouldhave been performed with the final geometry of in-terest. However, in order to obtain faster results,simulations around a single smooth cylinder werecarried out to assess the discretization and iterativeerrors. Simultaneously, the implications of usingwall functions (WF) to model the wall shear stresswere investigated.During the development of the DemoGRAVI3project, for manufacturing reasons, there was achange in the geometry to a cylindrical chamfershape. Plus, a study of the transport and opera-tion conditions was released by the DemoGRAVI3consortium of companies and the incoming currentfree stream velocity was reduced. Due to these rea-sons, two simulations were carried out using thenew geometry of a single chamfer pillar in orderto check the grid and iterative convergence. More-over, it was possible to better understand the differ-ences between both single pillar geometries as wellas the Reynolds dependence of the hydrodynamicnon-dimensional coefficients for the new geometry.Figure 1 illustrates the differences between the ini-tial and the settled geometry for the DemoGRAVI3project.

(a) Cylinder PillarsOffshore Structure

(b) Chamfer PillarsOffshore Structure

Figure 1: Change in DemoGRAVI3 Structure

Finally, the main objective was to estimate the hy-drodynamic force coefficients on the full scale threechamfer pillars substructure cross section. Thisstudy was performed for a constant steady currentwith different incoming angles.The structure of this paper is the following: Sec-tion 2 explains the key concepts required to betterunderstand this work. Section 3 presents the math-ematical model implemented. Section 4 shows thesummarized results obtained for the simulations ofthe flow behavior around single cylinder and cham-fer pillars. The results obtained for the flow behav-ior around the GBF offshore structure cross sectionare also presented. Finally, section 5 presents themain conclusion as well as some suggestions for fu-ture work.

2. Background

The GBF cross section geometry with three chamferpillars is very peculiar and, because of that, thereis a lack of literature to perform a background in-vestigation. However, to study a wide range of off-shore applications, one of the areas of fluid mechan-ics that has great interest in these scope is the studyof ”bluff body” flows.The study of bluff bodies for research and academicpurposes is usually associated with flow behavioraround cylinders. However, the simulations per-formed in this work considered full-scale geometriesand as consequence, very high Reynolds numbers.For these conditions, the literature about cylindersis non-existent. Nevertheless, the background in-vestigation will be focused on a two dimensionalanalysis of the flow behavior around a single cylin-der with the main goal of understanding the keyaspects of these type of flows.The geometry was changed during the project de-velopment and a background investigation was car-ried out about the flow behavior around the newchamfer cylindrical geometry. There is no informa-tion available for this specific geometry. Although,there are some investigations about the effects ofthe corner cut-offs of square cylinders. In order tohave more information about these works, see [3],[4] and [5].In the literature of ”bluff body” flows, the forcesthat characterize the flow are usually decomposedin two different directions as illustrated in figure 2,one that is parallel with the flow direction (dragforce) and the direction perpendicular to this one(lift force).

Figure 2: Forces applied on Cylinder

The drag force can be decomposed in two differenttypes of contributions known as pressure force andfriction force. The pressure force is a consequenceof the pressure difference between the rear and thefront of the cylinder. On the other hand, the frictionforce is caused by the shear stress on the cylinderwall. For very high Reynolds number, the effects ofthe friction force are negligible when compared withthe pressure force effects. The drag force is usuallypresented as a non-dimensional quantity, the drag

2

coefficient defined by:

CD =FD

12ρU

2∞D

=Fx

12ρU

2∞D

(1)

where FD is the drag force.The steady current flows around complex geome-tries are characterized, besides the drag force paral-lel to the flow, by an oscillating force perpendicularto the flow that is created due to the vortex shed-ding mechanism. It can be verified that an upwardlift is felt when a vortex is being created downwardthe cylinder and a downward lift is created whenthe opposite occurs.For the purpose of the study of the vortex-inducedvibrations around smooth cylinder, the lift non-dimensional coefficient is going to be used and de-fined as:

CL =FL

12ρU

2∞D

=Fy

12ρU

2∞D

(2)

The oscillating lift coefficient is defined as

C ′L =F ′L

12ρU

2∞D

=FL − FL12ρU

2∞D

(3)

being F ′L the difference between the instantaneousforce (FL) and the mean force (FL). The Lift Co-efficient standard deviation is computed using:

CL,R.M.S = (C2L)

12 =

√√√√√ N∑n=1

C ′2L

N(4)

where N is the number of time steps in the simula-tions sample. Similar analysis will be used for theR.M.S. of the drag coefficient in this work.The alternate shedding behavior that is observed inthe wake of a cylinder is common to ”bluff body”flows. This vortex behavior that is influenced bythe Reynolds Number is characterized by anothernon-dimensional quantity. The Strouhal Numberthat is given by:

St = St(Re) =fvD

U∞(5)

where fv is the vortex-shedding frequency, D is thecylinder diameter and U∞ is the flow velocity.

3. Problem Scope and Methodology3.1. Mathematical ModelsThe RANS equations were used to model the flowbehavior in this work. The approach of this modelconsists in emsemble-averaging of all the quantitiespresent in the Navier-Stokes equations. Consideringthe fluid as a Newtonian incompressible fluid, thecontinuity equation of the mean flow (equation 6)

and the resultant unsteady RANS equations (equa-tion 7) are presented below:

∂Vi∂xi

= 0 (6)

ρ∂Vi∂t

+∂

∂xj(ρViVj+ρv′iv

′j) = − ∂p

∂xi+∂τij∂xj

+ρbi (7)

where Vi is the mean velocity, p is the mean pres-sure, bi the mean body forces, ρ the fluid density,τij are the mean viscous stress tensor components

and ρv′iv′j is the Reynolds Stress Tensor (RST).

The turbulence model used in this work is thek − ω SST model developed by Menter [6].

3.2. Numerical GridThe grids in this work were generated using the util-ities blockMesh and SnappyHexMesh available onthe open source software OpenFOAM [7]. The gridgeneration process using OpenFOAM is divided in2 key steps: creation of a fully hexahedral block-structured mesh containing the whole domain of thestudy using the blockMesh utility; mesh adjustmentand refinement near the geometry surface subject ofstudy enabling the creation of non-hexahedral cellsusing the SnappyHexMesh utility. The resultantmesh will be unstructured with full hexahedral orhexahedral dominant cells.The global scheme for the grids used in all the sim-ulations of this work is illustrated in figure 3 andconsist in eight different blocks with different levelsof refinement and grading according to the zones ofinterest in the study. In order to design the differ-ent geometries inside the block 4, it is required toconstrain all other blocks that forms the solutiondomain.

Figure 3: Key Blocks In Grid Generation

Block 4 is illustrated as a circle. However, it is go-ing to be adjusted and refined in order to assureacceptable results for the different geometries.

3.2.1 Smooth Cylinder

In order to evaluate the difference between the useof wall functions (WF) and the direct applicationof the no slip (NS) condition to model the shear

3

stress at the geometry surface, it was required todesign two grids. Both of them, are multi-blockstructured. Table 1 shows the differences betweenthe two grids.

Mesh N◦ofcells y2 LRef

NS Mesh 129450 4.4 · 10−7 24WF Mesh 107540 4 · 10−4 24

Table 1: Differences between NS and WF mesh

Block 4 is subdivided into four new blocks with de-creasing grading towards the geometry surface. Theblock design scheme and grid are illustrated in fig-ure 4.

Figure 4: Smooth Cylinder Block 4 Grid Charac-teristics

(a) Scheme of Block 4 inSmooth Cylinder

Simulations

(b) Grid Illustration ofBlock 4

To estimate the discretization error associated withthe grids that are being designed, a grid refinementstudy using WF was carried out. During this study,the iterative error was evaluated.The grid convergence study was performed usingthree different meshes. Table 2 shows the differ-ences between the grids according to their refine-ment ratio, being Mesh A, the coarser mesh andMesh C, the finest mesh.

Table 2: Total Number of Cells (N◦Cells) and GridRefinement Ratio (h1

hi)

Mesh A B CN◦Cells 107540 182754 275974h1/hi 1.6 1.23 1

3.2.2 Chamfer Cylinder

Chamfer cylinder cross-section can be defined as asquare cylinder which has the corners cut off bya certain length. The geometry will be defined bythe ratio between the length of the corner cutoff (C)and the reference length (Lref ). The chamfer cylin-der reference length is the largest distance betweentwo opposite sides in the chamfer cylinder. For thisparticular case, the corner cutoff will have a lengthof C = 5.09m and a reference length of Lref = 27m,resulting in a Chamfer Geometry Ratio (CGR) of

18.9%. Figure 5 illustrates the dimensions speci-fied.

Figure 5: Schematics of the Chamfer geometry

Two simulations using different incoming headingvelocities were performed to study the flow behav-ior around the chamfer cylinder. One, which consid-ered an inlet velocity of U∞ = 10 m/s while otherconsidered U∞ = 1 m/s.The grid scheme was the same used in the smoothcylinder and exhibited in figure 3, where the block4 is subdivided into 8 blocks. Figure 6 presents theBlock 4 scheme and the resultant grid.

(a) Scheme of Block 4 inChamfer Cylinder

Simulations

(b) Grid Illustration ofBlock 4

Figure 6: Chamfer Cylinder Block 4 Grid Charac-teristics

Table 3 presents the main differences between thetwo grids for the different inlet boundary condition.

Table 3: Grid Characteristics for the ChamferCylinder Simulations

Reynolds Number N◦ of Cells y2 (m)2.7 · 107 103600 0.0042.7 · 108 143000 0.0004

3.2.3 Global Structure Cross Section

In order to analyze the flow around the global struc-ture cross section, it is required to design a grid thatenables the rotation of the structure for several flowangles. The incoming flow heading angle (β) is mea-sured relative to the point RO as illustrated on fig-ure 7. The colors of the different pillars will be keptin section 4 to easily understand the differences in

4

the hydrodynamic loading applied to each of them.

Figure 7: Global Structure Geometry

The global mesh was divided into two distinct re-gions: inner and outer mesh. The inner mesh iscomposed by the block 4 as the outer mesh is formedby all the other blocks. Inside the inner mesh, twodifferent arrangements were done: one to design thesurface geometries of the three chamfer cylinders,and another to enable the rotation of the outermesh. Table 4 shows the differences between thegrids for the range of incoming current angles thatwill be studied in the scope of this work.

Table 4: Number of cells of each mesh for the dif-ferent β

Angle of Attack (β) 0◦ 90◦ 180◦

N◦Cells 409640 407760 405460

Figure 8 illustrates the block boundaries and thedynamic movement of the outer mesh relative tothe inner mesh.

Figure 8: Boundary Conditions

3.3. Boundary ConditionsThe boundary conditions can be summarized as fol-lowed:

• The inlet is defined by a Dirichlet boundarycondition as a free stream velocity that is de-composed in different vectors according to flow

direction. The velocity magnitude is 10m/sin the smooth cylinder case and 1m/s in theglobal structure simulations. Both velocitiesare used in the single chamfer cylinder simu-lations. The inlet turbulence quantities weredefined as follows: the turbulent kinetic energywas defined as k = 1.5·10−4 ·U2

∞ and turbulent

dissipation as ε = 0.09k2

Re·10−8 .

• The top and bottom boundaries held free slipboundary conditions, which means that thereis no shear stress on the side walls.

• The outlet condition is defined as outlet pres-sure, where the pressure is equal to the staticpressure of the fluid.

• Since this is a two dimensional flow, the pillarsof the structure are considered to have infinitelength. The symmetry boundary condition isapplied on the front and back (lateral bound-aries).

• The geometries surfaces of the pillars are de-fined as walls where two different approacheswere used. In the smooth cylinder, the wallshear stress was modeled using the direct ap-plication of the NS condition, while in the othersimulations, WF were applied.

All the cells in the domain were initialized using theinlet conditions with relative pressure equal to zero.The reference pressure is the hydrostatic pressure.

4. ResultsThe quantities of interest of this work are the dragcoefficient (CD), lift coefficient (CL) and Strouhalnumber (St).Forces are calculated as a sum of two different com-ponents: pressure force obtained by integration ofthe pressure in the surface of the geometries andshear force by integration of the wall-shear stress inthe pillars surfaces.To compute the vortex shedding frequency, an esti-mation of the power spectral density (PSD) of theoscillating lift force in time is calculated. The PSDis obtained by using a Discrete Fourier transforma-tion to study the frequency domain.All the simulations were performed using emsemble-averaged RANS equations, which means that all thequantities computed in this work are not instanta-neous values. Therefore, maximum and minimumvalues may differ from those measured instanta-neously. Every time flow parameters are discussed,they are always emsemble-averaged values.The results obtained are not time accurate. Thesimulations were started with an uniform velocityfield. The variation of the quantities of interest atthe ”start” of the CFD simulations were removed.

5

The simulations were ran for a longer time thanwhat is presented during this work.

4.1. Single Pillars4.1.1 Smooth Cylinder

Two ways of modeling the wall shear stresses wereconsidered. The first is the direct application ofthe no slip (NS) condition which models the viscoussub-layer of the boundary layer; The other consistsin using wall functions (WF) assuming the flow tohave a completely turbulent boundary layer.From the simulations carried out, as expected, theflow is ”fully” turbulent. The difference betweenthe wall shear stress modeling methods is not sig-nificant and there are several sources of forced ap-proximations and numerical uncertainties that willbe more serious in the following simulations. Usingthe direct application of the NS condition wouldresult in an extra computational time that will beavoided. Considering that the main goal is to studythe global structure cross-section, it is acceptable touse WF to model the flow behavior.The numerical uncertainty due to discretization hastwo sources: time and space. The temporal dis-cretization error will not be calculated in this work.The Grid Convergence Index [8] is used to estimatean error band for the RE solution of the results ob-tained from the two most refined grids. The resultsare shown in the table 5:

Table 5: Grid Convergence Index [%]

GCI CDAV GCLRMS

GCIAB 1.7 16.3GCIBC 1.14 13.842

From the results obtained, it is possible to saythat the estimations of RE solutions for the non-dimensional quantities are CD = 0.285, CLRMS

=0.128 and St = 0.41. The associated error bandis 1.14%, 13.842% and approximately 0% for eachof the quantity of interest in the most refined grid,respectively.The flow behavior presents a regular vortex shed-ding, i.e., the flow separation occurs always on thesame locations and one vortice is being formed andreleased at each side alternately. This behavior hasa well defined frequency and occurs periodically,which results in periodically variation of the lift co-efficient and well defined peak of a PSD and Stnumber. The near wake region is also very well de-fined, short and narrow which is characteristic of avery high Reynolds number flow.The result obtained for the average drag coefficientshows a low discretization error. On the other hand,the standard deviation of the lift coefficient presentsa significant numerical uncertainty. These values

might increase or decrease in the following simula-tions and the level of trust in the results are ques-tionable, being more problematic for the CL,RMS ,which presents a larger GCI.

4.1.2 Flow around Chamfer Cylinder

The flow behavior around the chamfer cylinder ge-ometry was subject of study for two incoming cur-rent velocities. Depending on the geometry ofstudy, the flow dependence of the Reynolds numberis different. Instead of performing one simulationand assume the hydrodynamic non-dimensional co-efficients to compute the forces, it was required toperform two simulations. Moreover, it is possibleto assess the Reynolds number influence for bothconditions.The results obtained for the drag and lift coefficientsare plotted in the figure 9 and figure 10.

(a) CL at Re = 2.7 · 107 (b) CD at Re = 2.7 · 108

Figure 9: Drag Coefficient Pattern for the flowaround the Chamfer Cylinder Geometry

(a) CL at Re = 2.7 · 107 (b) CL at Re = 2.7 · 108

Figure 10: Lift Coefficient Pattern for the flowaround the Chamfer Cylinder Geometry

The solution obtained for the non-dimensional co-efficients is not what is expected. The use ofensemble-averaged RANS equations to flow mod-eling should not be characterized by solutions withrandom non-periodic behaviors. The main goal ofusing the RANS equations is to remove the ran-domness of turbulence by using a turbulence model,resulting in periodic oscillations of the mean flowvariables. However, the average values of the dragcoefficient are similar for both Reynolds number(CD ' 2).The variation in time of the drag and lift coeffi-cients suggests a very complex flow that has a large

6

number of frequencies associated. Despite the factthat the simulations with different Reynolds num-ber have different PSD for the different frequencies,it is verified a certain level of agreement between thevortex shedding frequencies in different situations.

4.2. Flow around Global Structure Cross SectionFive simulations were produced for different incom-ing currents of 0◦, 90◦ and 180◦ to model the flowaround the GBF structure cross section.The first simulation performed considered an in-coming current of β = 0◦ using a time step of∆t = 0.32 s. Further, the simulation for an in-coming current of β = 90◦ required a very low timestep to satisfy the desired iterative convergence tol-erance. To approximate the discretization error intime between all the simulations, a second simu-lation was carried out for an incoming current ofβ = 0◦ using a time step of ∆t = 0.02 s. After con-cluding the simulations using this small time stepfor all the proposed incoming currents, the grid forβ = 90◦ was refined in order to observe the solutiongrid dependence. This condition was selected toperform the grid refinement because it representedthe situation with the most complex flow behavior.

4.2.1 0◦ Degrees

The results for the small time step (∆t = 0.02s) arepresented in table 6.

Table 6: Results Obtained for β = 0◦ using a timestep of ∆t = 0.02s

β = 0 CDAV GCLAV G

CLRMSSt

Red Pillar 1.11 0 0.15 0.12Blue Pillar 1.66 -0.68 0.83 0.23

Green Pillar 1.66 0.68 0.82 0.23

The differences in the results obtained for bothtime steps are not significant. This means that dis-cretization errors must be controlled by the gridresolution in space.The flow behavior for the incoming current of β =0◦ around the GBF structure is simpler than for thesingle chamfer cylinder. In this case, the flow be-havior seems statistically converged since the meanflow variables of interest presents a periodic andwell defined pattern.The value of the average drag coefficient is differentfor each pillar. The red pillar has the lowest valuewhile the other two share the higher values. Com-paring to the results observed for the average dragcoefficient of the single pillar, all these values arelower.The wake control that is enhanced by both of pillars(green and blue) in the rear of the red pillar is themain cause for the forces reduction. The red pillar

wake width is reduced and the vortex formation issuppressed. As consequence, the standard devia-tion of the lift coefficient is very low. In the presentcondition, due to the symmetry of the GBF struc-ture, the red pillar average lift coefficient is zero.Green and blue pillars present a similar flow be-havior around them. The drag and lift coefficientsshare the same pattern in time. However, thesequantities have a different phase in relation to oneanother. The drag coefficient has the same average,maximum and minimum values for both pillars. Onthe other hand, the lift coefficient has a symmetricbehavior, i.e., the maximum force on the green pil-lar is equal to the minimum force on the blue pillarand vice-versa. The inner region between the pil-lars is characterized by higher fluid velocities andlower pressures. As consequence, the lift coefficientis larger in the direction towards the center of thegeometry for the green and blue pillars. Neverthe-less, the average value and the standard deviationof this quantity is equal for both pillars.The variation in time of the non-dimensional coef-ficients applied on the different pillars are shownin figure 11. The reference length for the non-dimensional total forces is Lref = 61 m while foreach pillar is Lref = 27 m. The total forces appliedon the GBF structure is the sum of the forces ap-plied on each pillar.

(a) Drag Coefficient (CD)

(b) Lift Coefficient (CL)

Figure 11: Forces applied on the different pillarsfor β = 0◦

The lift coefficient of each pillar was studied in the

7

frequency domain and the PSD as function of theStouhal number is presented in figure 12.

Figure 12: PSD Of The Lift Coefficient for β = 0◦

The vortex shedding frequency of the GBF struc-ture is characterized by several frequencies derivedfrom the different pillars. The red pillar has a verywell defined dominant frequency with a weak vor-tex shedding mechanism. On the contrary, boththe green and blue pillars are composed by severalvortices being shed at different frequencies. Two ofthese shedding frequencies are dominant and one ofthem is similar to the dominant frequency of the redpillar. The separation points for the GBF structureare much better defined than in one single pillar. Asa consequence, fluid detachment and reattachmentlocations are very well defined between periods.

4.2.2 180◦ Degrees

The results obtained for this simulation are pre-sented in table 7.

Table 7: Results obtained for β = 180◦ using a timestep of ∆t = 0.02s

β = 180 CDAV GCLAV G

CLRMSSt

Red Pillar -0.23 0 0.63 0.08Blue Pillar -1.69 0.18 0.22 0.19

Green Pillar -1.69 -0.18 0.21 0.19

Comparing with the hydrodynamic loading appliedon the different pillars respectively, the results ob-served for the incoming current of β = 180◦ showsa lower drag coefficient. The standard deviation ofthe lift coefficient is lower for the blue and greenpillars. The red pillar presents an increase of thisquantity. The results show smaller oscillation ofboth non-dimensional quantities, being the load-ing on the GBF structure much better distributedamong all the pillars.The red pillar shows the lowest drag coefficient. Alow pressure region is created around the stagna-tion point in the front of the red pillar due to thefact that it is located in the wakes of both greenand blue pillars. Simultaneously, the low pressure

region in the wake of the red pillar oscillates alter-natively between one side and the other during aperiod.The non-dimensional variables variation in time isillustrated on figure 13.

(a) Drag Coefficient (CD)

(b) Lift Coefficient (CL)

Figure 13: Forces applied on the different pillarsfor β = 180◦

The GBF structure is symmetric relative to the in-coming flow. The average lift coefficient is equal tozero for the red pillar due to this feature.Like in the situation for the incoming current fromβ = 0◦, green and blue pillars share a similar flowbehavior around them. Despite having differentpatterns from the simulation using β = 0◦, thedrag and lift coefficient have the same propertiesexplained previously, i.e., these quantities have adifferent phase in relation to one another havingthe same average, maximum and minimum valuesfor the drag coefficient and symmetric values (themaximum force on the blue pillar is equal to theminimum force on the green pillar and vice-versa)for the lift coefficient.The near wakes around the different pillars are verywell defined. The separation locations are fixed be-tween cycles, i.e., despite alternating between oneside and the other according to the vortex sheddingphenomena, the fluid detachment/reattachment isalternate but fixed. As consequence, it is observeda periodic flow behavior.The results obtained for the dominant and non-dominant frequencies are plotted in figure 14.

8

(a) Dominant Frequencies

(b) Non Dominant Frequencies

Figure 14: PSD of the Lift Coefficient for β = 180◦

The vortex shedding mechanism is characterizedby several frequencies. The vortices shed from thegreen and blue pillars are weak due to the presenceof the red pillar. As result, these pillars are charac-terized by smaller a lower standard deviation of thelift coefficients. On the other hand, the red pillarhas the dominant vortex shedding frequency. Forthis flow configuration, the most energetic vorticesare formed around the red pillar.

4.2.3 90◦ Degrees

The flow behavior around the GBF structure withan incoming current from β = 90◦ resulted in themost complex flow compared to the situations pre-sented previously.The results obtained for an incoming current angleof β = 90◦ are shown in table 8.

Table 8: Results obtained for β = 90◦ using a timestep of ∆t = 0.02s

β = 90 CDAV GCLAV G

CLRMSSt

Red Pillar 1.44 0.52 0.66 0.1Blue Pillar 0 0.84 1.17 0.1

Green Pillar 2.15 0.27 0.4 0.1

The hydrodynamic loading applied is different foreach of the pillars. The average drag coefficient islarger on the green pillar than in the red and bluepillars. The lower drag coefficient is observed onthe blue pillar being this value negative in sometime intervals. Due to the asymmetry, the average

lift value applied on the different pillars is not equalto zero. The standard deviation of this quantity ishigher for the blue pillar and lower for the greenpillar. Nevertheless, the lift coefficient values aremainly positive for all the pillars. Comparing withthe other simulations, the loading distribution be-tween the pillars is more unbalanced.The non-dimensional variables variation in time isillustrated on figure 15.

(a) Drag Coefficient (CD)

(b) Lift Coefficient (CL)

Figure 15: Forces applied on the different pillarsfor β = 90◦

On contrary to what was shown in the previous in-coming current angles, for β = 90◦ the results arenot what is expected for a RANS solution. Like-wise the single chamfer cylinder simulation, theemsemble-averaged variables show a non-periodicbehavior between cycles.The study of the frequency domain of the lift co-efficient shows a very well defined frequency peak,which means that the vortex shedding frequencyis very well defined. However, the mean variablesmagnitude change between cycles due to the flowbehavior pattern change between periods.Further grid independence assessment was carriedout for this incoming flow heading. The average,mimimum and maximum values obtained for thenon-dimensional quantities are in the range thatwas obtained for the coarser grid. Therefore, thediscretization error in space is not the cause for thenon-periodic behavior that was observed.

9

5. Conclusions

The main goal of this work is to provide a quali-tative assessment of the hydrodynamic coefficientsof the global structure cross section in several flowincoming headings. The study is focused on the fol-lowing key variables: the drag coefficient (CD), thelift coefficient (CL), and the Strouhal number (St).The main conclusions of this paper are the follow-ing:

- Considering the range of angles of attack stud-ied in this work, the simulations carried outwith the GBF structure cross section show thatthe incoming current from β = 180◦ is the bestoption to transport the assembled structure.Also, the hydrodynamic loading applied on theoffshore structure is lower during operation us-ing this configuration. The structure is sym-metric relative to the flow direction. This re-sults in lower mean quantities peaks and loweraverage values of the drag and lift coefficients.

- The results obtained for the incoming currentheading from β = 90◦ present the worst situ-ation that can be selected in the range of thestudied angles. The hydrodynamic loading ap-plied on the different pillars is unbalanced. Asa consequence, larger oscillations are observedfor some of the pillars while almost no loadingis applied on another.

- The use of a chamfer geometry in the offshorestructure pillars will imply a higher flow com-plexity in comparison to the simple cylindergeometry. This will result in higher hydrody-namic loads and higher number of vortex shed-ding frequencies.

- The numerical uncertainty associated with thestudy for the smooth cylinder is significant andmainly dominated by the discretization error.The discretization error associated with thedrag coefficient and Stouhal number is accept-able while larger errors are noticed for the liftcoefficient. Nonetheless, finer grids should beused to mitigate this discretization uncertainty.The assessment of the discretization error intime was not performed.

- In the single chamfer cylinder pillar, a non-periodic behavior was obtained. The qualityof the results obtained in these simulations isquestionable. This behavior might be the re-sult of a poor turbulence modeling, the solu-tion is not statistically converged or the ”real”flow behavior is not periodic. In order to ac-cess the quality of these results, it is requiredto perform experiments.

- Compared to the direct application of the NScondition, the use of WF to model very highReynolds number flows is acceptable since theboundary layer is ”fully” turbulent.

Several studies can be suggested to future worksince there is always space to improvement in aR&D project of an innovative technology such asthe GBF structure:

- To better understanding of the flow behavior,it is suggested to carry on the simulations formore angles of incoming currents in order tounderstand the influence of the currents ap-plied to the structure. Introducing the effectsof the free surface (both with incident and re-flected waves) and the fluid/structure interac-tion would also be important.

- Further studies about the numerical uncer-tainty of the simulations with the GBF offshorestructure should be performed.

References[1] MARIN. A community based open-usage cfd

code for the maritime world, 2016. [accessed in3-12-2016].

[2] Vaz G. and Hoekstra M. Theoretical and nu-merical formulation of fresco. Technical report,Maritime Research Institute of The Nether-lands, 2008.

[3] Sparrow E., Tong J., Tse J., and AbrahamJ. P. Using corner chamfers to reduce the dragof flat-sided columns. Proceedings of the ICE- Engineering and Computational Mechanics,168(2):79–88, 2015.

[4] Tamura T. and Miyagi T. The effect of turbu-lence on aerodynamic forces on a square cylin-der with various corner shapes. Journal of WindEngineering and Industrial Aerodynamics, 83(1-3):135–145, 1999.

[5] Yamagishi Y., Kimura S., Oki M., andHatayama C. Effect of Corner Cutoffs on FlowCharacteristics. 2009.

[6] Menter F. Zonal two equation k−ω turbulencemodels for aerodynamic flows. AIAA Journal,1993.

[7] Greenshields C. J. OpenFOAM-Open SourceCFD toolbox. CFD Direct Ltd., 2015.

[8] Roache P. J. Verification and Validation inComputational Science and Engineering. Her-mosa Publishers, 1998.

10