OMAE2013 10635 VIV Marine Risers Sheared Flow Final

7/28/2019 OMAE2013 10635 VIV Marine Risers Sheared Flow Final

1/12

1 Copyright 2013 by ASME

Proceedings of the 32rd

International Conference on Ocean, Offshore and Arctic EngineeringOMAE2013

9-14 June 2013, Nantes, France

OMAE2013- 10635

NUMERICAL SIMULATION OF VORTEX INDUCED VIBRATIONSFOR MARINE RISERS SUBJECTED TO SHEARED FLOW

F. Van den AbeeleCranfield University

Cranfield, UK

J. Vande VoordeOCAS N.V.

Ghent, Belgium

F. KaraCranfield University

Cranfield, UK

ABSTRACTThe increasing demand for oil and gas, currently estimated at

135 million barrels of oil equivalent per day, keeps pushing theboundaries of offshore engineering into ever deeper waters.

Exploration and production activities in the Gulf of Mexico, for

instance, are performed in water depths exceeding 3000 meters.

For such deepwater developments, the suspended length of themarine risers adds up to several kilometers. When designing

and installing risers in (ultra)deep water, the length/diameter

aspect ratio of the marine riser can exceed L/D > 1000, and the

features of the fluid flow in depth direction can no longer be

neglected. Indeed, both the magnitude and the direction of thecurrent change with water depth, giving rise to higher

harmonics in the VIV response.

The prediction of vortex induced vibrations for deepwater risers

is very challenging, owing to the fact that the incident flows arenon-uniform and the associated fluid structure interaction

phenomena are highly complex. These complex conditions give

rise to a non linear coupled system with a large number ofdegrees of freedom, which depends on several physical and

mechanical parameters.

In this paper, 3D CFD calculations are performed to evaluate

the effect of the third dimension for risers subjected to uniformflow and sheared currents. For a uniform current velocity at the

inlet boundary, it is shown that vortex shedding in the wake of

long slender tubulars can give rise to the development of

vortices with horizontal axis, resulting in a fluctuation of theflow in the Z-direction. These three dimensional vortices are

strong enough to modulate the vortex shedding on the riser as a

function of depth. The 3D simulations with uniform current

velocity are then compared to marine risers subjected tosheared currents. It is shown that the presence of sheared

currents invokes a shift in both phase and frequency of the

vortex shedding.

VORTEX INDUCED VIBRATIONS IN MARINE RISERSWall thickness design for marine risers is based on Barlows

formula [1]

2 (1)which states that the hoop stress expressed as a function ofthe internal pressure , mean diameter and wall thickness ,is limited by the specified minimum yield stress of thematerial, multiplied by a safety factor 0.6 for hazardousservice. Additional design guidelines are applied to account forcorrosion allowance and continuity of the internal diameter.

Barlows formula (1) indicates that a smaller diameter riser

can convey hydrocarbons at a higher internal pressure. Hence,multiple small diameter risers are typically preferred over one

single large diameter riser. During the design of floating

production platforms in deepwater, it has been recognized [2]

that there is a risk of interference between adjacent production

and export risers, or possibly between other combinations of

tendons, drilling risers and production risers.

This paper presents numerical analyses to predict vortex

induced vibrations in marine risers subjected to sheared flow.The paper subsequently addresses

Wake interference and proximity effects. First, 2Dsimulations on fixed rigid cylinders are performed to

investigate wake interference and proximity effects formultiple marine risers in tandem arrangement. The

influence of end spacing on the flow pattern is studied,

and the drag and lift coefficients for both the upstream

and downstream riser are compared to evaluate

proximity effects.


2/12


Multiphysics modeling of fluid structure interaction. Inorder to predict the displacements of marine risers

experiencing vortex induced vibrations, multiphysics

modeling of fluid structure interaction is needed. Fluidstructure interaction requires co-simulation of astructural solver and a Computational Fluid Dynamics

(CFD) code. In this paper, a weakly coupled solution

is presented to estimate the VIV response of marinerisers in close proximity.

Slender risers subjected to sheared flow. Whendesigning and installing risers in (ultra)deep water, the

length/diameter aspect ratio of the marine riser can

exceed 1000, and the features of the fluid flowin depth direction can no longer be neglected. Both the

magnitude and the direction of the current change with

water depth, giving rise to higher harmonics in theVIV response. At the end of this paper, 3D CFD

calculations are performed to evaluate the effect of the

third dimension for risers subjected to uniform flow

and sheared currents.

COMPUTATIONAL FLUID DYNAMICS FOR RISERS

The simulations, reported in this paper, have been performedwith OpenFOAM, an open source CFD solver. This solver uses

the generalized version of the Navier-Stokes equations [3],

solving for the velocity field , and the pressure .When the fluid flows past a fixed cylinder like a marine riser, aregion of disturbed flow is formed, like schematically shown on

Figure 1.

In this simulation of laminar flow, the free stream velocity

is shown in green. Lower velocities are depicted in blue,

whereas yellow indicates values higher than the stream

velocity. Evidently, the velocity varies in terms of magnitude,

direction and time, and four regions can be distinguished:

1. The retarded flow is a narrow region in front of thecylinder, where the local (time-averaged) velocity islower than the free stream velocity

2. Two boundary layers attached to the surface of thecylinder

3. Two sideway regions where the local (time-averaged)velocity is higher than the free stream velocity

4. The wake, which is the downstream region ofseparated flow where the local (time-averaged)

velocity is less than the free stream velocity

The fluid flow around a circular cylinder, as shown on Figure 1,is a well-known and documented [4-6] problem in

computational fluid dynamics, and often used as a benchmark

for CFD solvers [7].

Figure 1: Regions of disturbed flow

The flow pattern in the wake of the cylinder is primarily

governed by the Reynolds number

(2)which expresses the ratio of inertia forces to viscous forces,

with the fluid flow velocity, the total outer diameter and (3)

the kinematic viscosity as a ratio of the dynamic viscosity with the density . A detailed analysis of the different flowregimes around subsea structures can be found in [8-9]. In

summary, the regimes of fluid flow across a smooth subseastructure can be divided in

Unseparated flow for very low ( 5) Reynoldsnumbers

The regime for5 40 , where a pair of Fpplvortices develop in the wake

The transition range (150 300) from laminarflow to turbulence

The regime where the vortex street is fully turbulent(300 3 10)

For even higher numbers 310 3 10,the laminar boundary layer undergoes turbulent

transition, and the wake will be narrower and

disorganized

At very high Reynolds numbers ( 3 10), re-establishment of a turbulent vortex street occurs

For the range of Reynolds numbers relevant to offshore

pipeline engineering, the flow is fully turbulent, and it becomes

increasingly difficult if not impossible- to predict the transient

flow behavior with a laminar solver for the Navier Stokesequations.


3/12


The possible options for CFD simulations at very high

Reynolds numbers are:

Direct Numerical Simulation (DNS), which solves the

Navier Stokes equations for the pressure and thevelocity components in a time-dependent domain. Thisapproach requires a very fine mesh size and very small

time steps to resolve the smallest eddies and capture

the fluctuations in the turbulent flow [10]. As a result,this approach is not economically feasible for pipeline

design.

Large Eddy Simulation (LES), where large turbulenteddies are computed in a time-dependent simulation,

whereas small eddies are predicted with a compactmodel. Indeed, smaller eddies have an isotropic (and

hence more universal) behavior, but larger eddies in

the turbulent flow tend to be anisotropic, and their

behavior is directly influenced by the problem

geometry. The viability and accuracy of Large EddySimulation for complex turbulent flows at high

Reynolds numbers is investigated in [11], but has

proven to be not feasible for full 3D analysis ofoffshore structures [12].

Reynolds Averaged Navier Stokes (RANS) turbulencemodel. In the RANS approach, all flow characteristics

are decomposed as the sum of a steady (mean) value

and a fluctuating term. This decomposition gives riseto a Reynolds stress tensor, which adds six unknowns

to the system of equations. As a result, turbulence

models are required to provide additional transportequations to close the system [13]. In this paper, an

enhanced model is used to simulate vortexinduced vibrations in multiple marine risers. The

mathematical details of the turbulence model appliedare given in the Appendix.

WAKE INTERFERENCE FOR TANDEM RISERS

During the design of floating production platforms in

deepwater, it has been recognized [2] that there is a risk of

interference between adjacent production or export risers, orpossibly between other combinations of tendons, drilling risers

and production risers. The consequences of most concern arethe possible increase in fatigue damage due to vortex induced

vibrations (VIV), and the likelihood of contact between

adjacent risers.

A large body of work has been published addressing

measurement, modeling and analysis of marine risers in tandem

arrangement [14]. A careful review of flow interferencebetween two circular cylinders in various arrangements has

been presented by Zdravkovich [15-16], including an extensive

list of references on this subject. He has also introduced a

classification of flow regimes around two circular cylinders,

depending on their relative position.

Different studies for the tandem arrangement of two

adjacent risers [2, 17-19] have shown that the changes in drag,lift and vortex shedding are not continuous. Instead, an abrupt

change for all flow characteristics is observed at a criticalspacing between the risers. An exhaustive description onproximity effects and wake interference can be found in [20],

and a comprehensive summary of VIV in tandem risers is

provided in [2]. Recent research results have been published ina.o. [21-23].

In this paper, the published data on riser interference tests

for flexible tubulars [2] will be used as experimental validation.

To simulate these experiments, a 2D CFD model is constructed,assuming fixed rigid cylinders with an outer diameter of 114.3

mm. The simulation setup, with a grid of 50 by 15, isshown on Figure 2.

Figure 2: Simulation setup to study wake interference

For the simulations of fluid flow around marine risers in

tandem arrangement, the computational grid comprises some250 000 cells. Depending on the end spacing, the dimensionless

wall distance is in the range of

20 y uy 30 (4)with the distance to the nearest wall, and the frictionvelocity defined by

u

(5)

where is the average wall shear stress. As long as (4) issatisfied, the problem is well conditioned. The enhanced model, presented in [24] and detailed in the Appendix, was

used to simulate vortex induced vibrations in multiple marine

risers in tandem arrangement.

On Figure 3, the turbulent eddy viscosity is shown for very

high ( 2.5 10) Reynolds numbers, clearly indicatingthat this enhanced eddy viscosity model is capable ofsimulating a turbulent wake with significant separation.


4/12


Figure 3: Distribution of turbulent eddy viscosity

The parametric approach, suggested in Figure 2, enablesthe investigation of risers in staggered arrangements as well, for 0. In this paper, we focus on risers in tandem arrangement( 0 with different end spacings 2 6. It has beenshown experimentally [16-18] that there is strong interference

between two cylinders in tandem arrangement for spacing

ratios with 3.5. At a spacing 3.5, a suddenchange of the flow pattern in the gap between the adjacent

risers is observed.

On Figure 4, the influence of the end spacing on the fluidflow pattern in the wake of the tandem risers is shown for a

Reynolds number 10, i.e. the two-bubble regime of thetransition in the boundary layers. These simulation results

indeed endorse the experimental observations of Allen [2],

Zdravkovich [16] and King [17]:

For small end spacing ( 3), vortex sheddingonly occurs in the wake of the downstream riser: thefree shear layers which separate from the upstream

riser are permanently re-attached to the downstream

riser. In [25], Zdravkovich refers to this type of wake

interference asquasi-steady re-attachment

.

Figure 4: Tandem risers with different end spacing


5/12


When increasing the gap ( 3) between bothrisers, a turbulent vortex street appears in the wake of

both the upstream and the downstream riser. The

vortices shed by the upstream riser coalesce with thevortex street of the downstream riser, andbinary eddystreets are observed. It can be clearly seen that there is

no re-attachment of the free shear layers separatedfrom the upstream riser to the downstream one.

Drag coefficient data [16, 18] shows that the upstream riser

takes the brunt of the burden, and that the downstream riser haslittle or no effect on the upstream one. For different values of

spacing , the drag coefficient is shown on Figure 5.

Figure 5: Drag coefficients at Re = 105

Apparently, the drag coefficient on the upstream riser is not

significantly influenced by the downstream one, but asignificant change in drag is observed on the downstream

cylinder for 3. In [2], drag coefficients are measured onrisers in tandem arrangement with increasing end spacing for

Reynolds numbers from 1 10 up to 2.5 10. OnFigure 8, for instance, the measured drag coefficients for both

upstream and downstream riser are shown for a spacing 3. The drag coefficients, predicted by the CFDsimulations at 1 10, are indicated as well, showing avery good agreement with the experimental data.

Figure 6: Drag coefficients for L = 3D [2]

Figure 6 shows that for the upstream cylinder, the drag

crisis occurs somewhat earlier (i.e. at a lower Reynolds

number) than traditional measurements of this phenomenon

[17, 18], which could be attributed to the combined effects offree-stream turbulence and cylinder displacement. Thecombination of an early drag crisis on the upstream riser and

large displacements of the downstream riser produces a larger

total drag force on the downstream riser for 1.7 10.MULTIPHYSICS: FLUID-STRUCTURE INTERACTION

The CFD simulations, presented in the previous section,

were performed on fixed, rigid cylinders. Although such

simulations are capable of identifying the proximity effects

between adjacent risers by revealing their influence on dragcoefficients and flow pattern in the wake, they cannot predict

the VIV response of the riser.

Blevins [26] pointed out that the cross-flow cylinder

vibration can significantly affect the vortex shedding. In

summary, the cylinder displacement tends to

Increase the d rag on the cylinder

Shift the vortex shedding frequency to the cylindersvibration frequency

Increase the strength of the vortices

Alter the vortex pattern and hence the vortex sheddingfrequency

Some quantitative details can be found in [26-27]. In

addition to drag coefficients, Allen [2] reports measurements

for the transverse displacements of the upstream anddownstream cylinders as well. In order to predict the

displacements of marine risers experiencing vortex induced

vibrations, multi-physics modeling of fluid structure interactionis needed.

Fluid structure interaction requires co-simulation of astructural solver and a CFD code. In a strongly coupled

solution, the fluid flow will dictate the displacements, which in

turn will influence the flow pattern. The structural

displacements are used as an input for the CFD simulation, and

the resulting pressure distribution is fed back to the structural

solver [28]. When simulating large displacements (e.g. vortexinduced vibrations), the moving mesh is severely distorted and

the strongly coupled solution procedure is prone to numericalinstabilities.

In a weakly coupled solution, the structural solver and the

CFD solver are executed sequentially. This approach provides a

better balance between accuracy and computational expense,but is only applicable when the structural response does not

significantly influence the fluid flow. In this paper, weakly

coupled simulations of fluid structure interaction are conducted

to estimate the VIV response of marine risers in closeproximity.


6/12


WEAK COUPLING

STRONG COUPLING

Figure 7: Comparison between weak and strong coupling

In the sequentially coupled simulations, we first calculate

the flow patterns to estimate the lift and drag forces exerted on

the structure. The CFD simulations are performed according tothe approach described in the previous section: the fluid domain

is modelled in 2D, and the cylinders are fixed and assumed to

be rigid (cfr. Figure 2).

On Figure 8, the calculated lift and drag forces are shown

for the downstream riser at a spacing 3, for a Reynoldsnumber 1 10. The oscillating signals reflect a fullydeveloped turbulent wake. Note that the average lift force is

zero, while the average drag force is a measure for theresistance against fluid flow.

On Figure 9, the Fast Fourier Transform (FFT) of the lift

and drag forces is shown, to reveal the frequency content of thesignals. Clearly, the dominant frequency of the drag force is

twice the lift frequency: 2 0.42Hz.

Figure 8: Lift and drag forces on the downstream riser

For the top-tensioned risers used in [2], the n-th eigenfrequency

can be estimated by [29]

f 2 (6)

with the length, the tension, the distributed mass andthe bending stiffness. In (6), the tubes are assumed to be simply

supported, straight and with constant tension. As a result, the

computed eigenfrequency is omni-directional and corresponds

to the first bending mode of the cylinder. Note that the natural

frequency (6) is a function of the tension, but is predominantlycontrolled by the bending stiffness [30].

The lowest natural frequency is calculated as = 2.35 Hz,while the measured frequency (by means of Pluck tests) was

found to be = 2.23 Hz. Numerical modal analysis (solvingthe eigenvalue problem) confirmed a lowest natural frequency

of = 2.225 Hz.

Figure 9: Frequency spectrum of lift and drag forces

As indicated in Figure 9, the drag frequency 0.42 Hzis still significantly lower than the first natural frequency of the

test tubes, so only moderate displacements are expected.


7/12


To predict the response of the downstream riser when

subjected to the lift and drag forces shown on Figure 8, the

principle of virtual work [31] is applied:

(7)

where is the boundary of the Lagrangian body , are thestress components, the strain components, the externalforces (including lift and drag ), and the unknowndisplacements. The top-tensioned test tube is modeled as a

compliant structure, with Youngs modulus = 2700 MPa anddensity

= 1050 kg/m. The displacements are simulated with

a finite element code using a transient dynamic explicit solver.

Figure 10: Predicted cross-flow displacements

The predicted cross-flow displacements of thedownstream riser are shown on Figure 10. After some 20

seconds, the signal reaches its maximum amplitude

y 0.15 (8)For the same situation (end spacing 3 diameters and

Reynolds number 105), the maximum measured transverse

displacement [2] was 0.163.On Figure 11, the transverse RMS displacement

measurements for both the upstream and downstream test tube

are shown for the range 10 2.5 10. Apparently, forthe lower Reynolds numbers ( 1.7 10, thedisplacement of the downstream cylinder is smaller than for theupstream cylinder. For higher Reynolds numbers, the down-

stream cylinder vibrates at larger transverse amplitudes than thedownstream cylinder. However, other tests have shown [32]

that for higher vibration modes [33], the downstream cylinder

always vibrates less than the upstream one, when the magnitude

of the displacements is sufficiently large.

Figure 11: Transverse displacements for L = 3D [2]

The prediction of the fluid structure interaction (FSI)

simulation is included in Figure 11 as well, showing a goodagreement with the experimental observation.

MARINE RISERS SUBJECTED TO SHEARED FLOW

In the CFD simulations presented in the previous sections,

the risers were assumed to be fixed and rigid, and the lengthdirection was not taken into account. However, when designing

and installing risers in (ultra)deep water, the length/diameter

aspect ratio of the marine riser can exceed 1000, andthe features of the fluid flow in depth direction can no longer be

neglected. In this section, 3D CFD calculations are presented to

evaluate the effect of this third dimension for risers subjected touniform and sheared currents.

In order to assess the effect of the length direction on the

flow pattern, a 3D CFD calculation was performed on a riser

with a diameter 1 meter and length 50 meter. Thecalculation grid comprised 616 000 cells. On Figure 12, the

pressure distribution on the riser is shown, and the

corresponding flow pattern is visualized as well.

Figure 12: Fluid flow simulation around 3D riser


8/12


Vortex shedding in the wake of the long slender tubular

gives rise to the development of vortices with horizontal axis,

resulting in fluctuation of the flow in the Z-direction. This

could be expected, as it is known [3] that the transport of avortex creates in itself a new vortex with perpendicular axis.The simulation shows that these 3D vortices are strong enough

to modulate the vortex shedding on a riser as a function of

depth, although the inlet boundary has a uniform currentvelocity.

On Figure 13, the lift coefficient integrated over the entire

riser length is compared with a 2D simulation for the same riser

diameter. While the dominant frequency is the same, the 3Dsignal exhibits higher harmonics, corresponding to a shift in

vortex shedding frequency as a function of depth. The

amplitude of the lift is also lower than expected based on the2D calculations. A similar trend is observed when comparing

the drag forces for a 2D and 3D simulation. In conclusion, a 2D

simulation will give rise to conservative predictions.

Figure 13: Comparison of lift forces between 2D and 3D

The prediction of vortex induced vibrations for deepwater

risers is very challenging, owing to the fact that the incident

flows are non-uniform and the associated fluid structureinteraction phenomena are highly complex [34]. These complex

conditions give rise to a non-linear, coupled system with a large

number of degrees of freedom, which depends on severalphysical and mechanical parameters. While a great deal of

attention has been devoted to riser VIV modeling andprediction, most of the studies presented in literature [35-38]only account for a uniform incident current.

A good introduction on the subject of marine risers

subjected to sheared flow is given by Vandiver [39-41], and a

limited set of experiments [29] and simulations [34] have been

published on VIV predictions for linearly sheared currents. At

the end of this paper, a 3D CFD simulation is performed on a

riser span of 50 meter, subjected to sheared flow. For thecurrent profile [42], a one-seventh power law

Vz

0 (9)

Figure 14: Marine riser subjected to sheared current

was chosen, where the flow velocity varies from 0 at theseabed to at 2 . On Figure 14, the resulting fluid

pattern around the marine riser is shown. The vortex street is

visualized in five horizontal planes, uniformly distributed overthe length of the riser. The influence of the current gradient

over the length of the riser can clearly be observed in Figure 14.

On Figure 15, the lift and drag coefficients are shown as a

function of depth. Close to the seabed ( 5 m), the riserexperiences little or no fluctuating lift, and only moderate drag.

When approaching the still water level, the lift and dragcoefficients asymptotically converge towards the 2D solution.

The presence of sheared currents invoke a shift in both phase

and frequency of the vortex shedding. As a result, the lift and

drag will be lower compared to the 3D simulation with a

uniform current speed, shown in Figure 13.

Figure 15: Lift and drag as a function of depth


9/12


CONCLUSIONS

In his pioneering paper [43], Prof. Vandiver presented the most

stringent research challenges in the prediction of vortexinduced vibrations for marine risers. In addition to the need ofacquiring high quality full-scale response data and developing

cost effective mitigation measures, he highlights a more

profound understanding of fluid structure interaction and thesimulation of sheared flow as important research topics.

This results, presented in this paper, want to contribute to the

numerical simulation of VIV for marine risers in close

proximity. The main conclusions from this work read:

Given the high Reynolds numbers involved in deep waterriser design (10 10), turbulence modeling isrequired to capture vortex shedding. The enhanced

model, proposed in [24], proves to be the most appropriateRANS closure to predict VIV.

For two risers in tandem arrangement, there is a suddenchange in flow characteristics for a critical spacing 3.5. The upstream riser takes most of the burden,while the drag coefficient on the downstream riser is lower

at 1.7 10 Multiphysics modeling of fluid structure interaction allows

predicting the VIV response of marine risers in tandemarrangement. For high Reynolds numbers, the downstream

riser often experiences higher transverse displacements

than the upstream riser.

For low Reynolds numbers, there is little effect of endspacing on the drag coefficients and displacements,

whereas the effect of end spacing is obvious and distinct

for 1.7 10 Fluid flow simulations in 3D indicate that 2D CFD

calculations will yield conservative predictions: the

amplitude of lift and drag are slightly over-estimated in 2Dsimulations.

The presence of sheared currents invoke a shift in bothphase and frequency of the vortex shedding. As a result,

the lift and drag will be lower compared to a 3D simulation

with a uniform incident current.

APPENDIX ON TURBULENCE MODELLING

The Navier-Stokes equations for incompressible Newtonian

liquids could be used for turbulent flow simulations. However,

once the flow becomes turbulent, all quantities fluctuate in timeand space with widely varied time scales and length scales. It is

theoretically possible to solve the Navier-Stokes equations for

all scales, yet the required computer resources render this

approach impracticable.

Therefore, the turbulent influence is modeled, and the most

commonly used models are the Reynolds Averaged NavierStokes (RANS) models [13]. In this RANS approach, all flow

characteristics are decomposed as the sum of a steady (mean)value and a fluctuating term. This decomposition gives rise to aReynolds stress tensor, which adds six unknowns to the system

of equations. As a result, turbulence models are required to

provide additional transport equations to close the system.

In this paper, the turbulence model was selected tosimulate wake interference in adjacent marine risers. This

model is frequently used to model turbulent flow, and was

identified by [11] as the most appropriate RANS model to

predict vortex induced vibrations in marine risers for Reynolds

numbers up to 10.The

turbulence model [44-45] is a two equation

model, providing a transport equation for the kinetic energy kt ukx ux x kx2 kd

(10)

and an additional expression for the viscous dissipation rate

t u

x Cf

k u

x Cf

k x x2 d expd2 (11)

where is a non-local function [45] of distance to the wall.The auxiliary functions read 1 and

f 1 0.41.8 exp Re

36 (12)with

Re k (13)The turbulent eddy viscosity is computed from

Cf k (14)with 0.09 and 1 exp0.0115. The valuesfor the other model constants are listed in Table 1.

Table 1: Values for the k- model constants

1.35 1.80 1.0 1.3


10/12


This standard model is widely used in computationalfluid dynamics, and was adopted by [11, 46] to predict vortex

shedding around circular cylinders at high Reynolds numbers

( 10). The model performs quite well for boundary layerflows, but is less accurate for risers in which a high mean shearrate is present or massive separation occurs (which could beexpected for risers in tandem arrangement). In these cases, the

eddy viscosity is over-predicted by the standard formulation.

Moreover, the dissipation rate equation (11) does not always

give the appropriate length scale for turbulence.

To improve the ability of the standard model topredict complex turbulent flows, an enhanced eddyviscosity model is proposed in [24]. This model consists of a

new formulation for the viscous dissipation rate

t ux x xCS C k (15)

based on the dynamic equation of the mean square vorticityfluctuation at large turbulent Reynolds numbers. In addition, a

new eddy viscosity formulation is introduced

C k (16)with

C 1A AU k (17)based on the positivity of the normal Reynolds stresses and the

Schwarz inequality for turbulent shear stresses [24]. In (17),

the coefficient is determined byU SS (18)

with 2 (19)and the parameters

4.0and

6cos, where

13cos6W (20)where

W SSSS (21)with

S SS (22)The other constants, calibrated in [24], are listed in Table 2.

Table 2: Values for the enhanced k- model constants

max0.43, 5

1.90

1.0 1.2

REFERENCES

[1] Mohitpour M., Golshan H. and murray A., Pipeline

Design and Construction A Practical Approach, Third

Edition, ASME Press (2007)

[2] Allen D.W., Henning D.L. and Lee L., Riser Interference

Tests on Flexible Tubulars at Prototype Reynolds

numbers, Proceedings of the Offshore TechnologyConference, OTC-17290 (2005)

[3] Batchelor G.K., An Introduction to Fluid Dynamics,

Cambridge University Press (1967)[4] Norberg C., Flow Around a Circular Cylinder: Aspects of

Fluctuating Lift, Journal of Fluids and Structures, vol. 15,

pp. 459-469 (2001)

[5] Rocchi D. and Zasso A., Vortex Shedding from a Circular

Cylinder in a Smooth and Wired Configuration:Comparison between 3D Large Eddy Simulation and

Experimental Analysis, Journal of Wind Engineering and

Industrial Aerodynamics, vol. 910, pp. 475-489 (2002)

[6] Norberg C., Fluctuating Lift on a Circular Cylinder:Review and New Measurements, Journal of Fluids and

Structures, vol. 15, pp. 57-96 (2003)[7] Schfer M. and Turek S., Benchmark Computations of

Laminar Flow Around a Cylinder, Flow Simulation withHigh Performance Computers II, vol. 52, pp. 547-566

(1996)

[8] Sumer B.M. and Fredsoe J., Hydrodynamics around

Cylindrical Structures, World Scientific, Signapore (1999)[9] Gourmel X., Numerical Simulation of the Flow over

Smooth and Straked Riser at High Reynolds Numbers,

M.Sc. Thesis, Cranfield University, School of AppliedSciences, Offshore and Ocean Technology (2010)

[10] Mainon P. and Larsen C.M., Towards a Time Domain

Finite Element Analysis of Vortex Induced Vibration of

Risers with Staggered Buoyancy, Proceedings of the 30th

ASME Conference on Ocean, Offshore and ArcticEngineering, OMAE2011-49046 (2011)

[11] Catalano P., Wang M., Iaccarino G. and Moin P.,

Numerical Simulation of the Flow Around a Circular

Cylinder at High Reynolds Numbers, International Journal

of Heat and Fluid Flow, vol. 24, pp. 463-469 (2003)

[12] Constantinides Y. and Oakley O., Numerical Prediction ofBare and Straked Cylinder Vortex Induced Vibrations,

Proceedings of the 25th International Conference on

Offshore Mechanics and Arctic Engineering, OMAE2006-92334, Hamburg, Germany (2006)

[13] Wilcox D.C., Turbulence Modelling for Computational

Fluid Dynamics, Second Edition, DCW Industries (1998)


11/12


[14] Kondo N., Three Dimensional Analysis for Vortex Induced

Vibrations of an Upstream Cylinder in Two Tandem

Circular Cylinders, Proceedings of the 30th

ASME

Conference on Ocean, Offshore and Arctic Engineering,OMAE2011-49655 (2011)[15] Zdravkovich M.M., Review of Flow Interference between

Two Circular Cylinders in Various Arrangements, Journal

of Fluids Engineering, vol. 99 (4), pp. 618-633 (1977)[16] Zdravkovich M.M., Flow Induced Oscillations of Two

Interfering Circular Cylinders, Journal of Sound and

Vibration, vol. 101(4), pp. 511-521 (1985)

[17] King R., Wake Interaction Experiments with Two Flexible

Circular Cylinders in Flowing Water, Journal of Soundand Vibration, vol. 45(2), pp. 559-583 (1976)

[18] Zhang H. and Melbourne W.H., Interference between Two

Cylinders in Tandem in Turbulent Flow, Journal of Wind

Engineering and Industrial Aerodynamics, vol. 41-44, pp.589-600 (1992)

[19] Allen D.W. and Henning D.L., Vortex Induced Vibration

Current Tank Tests of Two Equal Diameter Cylinders inTandem, Journal of Fluids and Structures, vol. 17, pp.

767-781 (2003)

[20] Mittal S. And Kumar V., Flow Induced Oscillations of

Two Cylinders in Tandem and Staggered Arrangements,

Journal of Fluids and Structures, vol. 15, pp. 717-736(2001)

[21] Lestang Parade E., Dual String Risers Local Behaviour,

M.Sc. Thesis, Cranfield University, School of AppliedSciences, Offshore and Ocean Technology (2010)

[22] Li L., Fu S., Yang J., Ren T. and Wang X., Experimental

Investigation of Vortex Induced Vibration of Risers withStaggered Buoyancy, Proceedings of the 30th ASME

Conference on Ocean, Offshore and Arctic Engineering,OMAE2011-49046 (2011)

[23] Corson D., Cosgrove S., Hays P.R., Constantinides Y.,

Oakley O., Mukundan H. And Leung M., CFD

Hydrodynamic Databases for Wake Interference

Assessment, Proceedings of the 30th

ASME Conference on

Ocean, Offshore and Arctic Engineering, OMAE2011-49407 (2011)

[24] Shih T.H., Liou W.W., Shabbir A., Yang Z. And Zhu J., A

New k- Eddy Viscosity Model for High Reynolds

Number Turbulent Flows, Computer Fluids vol. 24(3), pp.

227-238 (1995)[25] Zdravkovich M.M., Flow Around Circular Cylinders

Applications, Oxford University Press (2003)

[26] Blevins R.D., Flow Induced Vibration, Second Edition,

Krieger Publishing Company, Florida (1994)[27] Vandiver K.J., Drag Coefficients of Long Flexible

Cylinders, Proceedings of the Offshore Technology

Conference, Houston, Texas, OTC-4490 (1983)

[28] Tukovic Z., The Finite Volume Method for Fluid StructureInteraction with Large Structural Displacements

[29] Lie H. and Kaasen K.E., Modal Analysis Measurements

from a Large Scale VIV Model Test of a Riser in Linearly

Sheared Flow, Journal of Fluids and Structures, vol. 22,

pp. 557-575 (2006)

[30] Weimin C., Zhongqin Z. and Min Li, Effects of Varying

Tension and Stiffness on Dynamic Characteristics andVIV of a Slender Riser, Proceedings of the 30th ASME

Conference on Ocean, Offshore and Arctic Engineering,OMAE2011-49295 (2011)[31] Rao S.S., The Finite Element Method in Engineering,

Elsevier Science & Technology Books, 658 pp. (2004)

[32] Allen D.W. and Henning D.L., Vortex Induced VibrationCurrent Tank Tests of Two Equal Diameter Cylinders in

Tandem, Journal of Fluids and Structures, vol. 17, pp.

767-781 (2003)

[33] Ashiru A., Assessment of Vortex Induced Vibration

Response in Higher Harmonics Mode, M.Sc. Thesis,Cranfield University, School of Applied Ssciences,

Offshore and Ocean Technology (2007)

[34] Srinil N., Analysis and Prediction of Vortex Induced

Vibrations of Variable Tension Vertical Risers in LinearlySheared Currents, Applied Ocean Research, vol. 33, pp.

41-53 (2011)

[35] Dixon M. and Charlesworth D., Application of CFD forVortex Induced Vibration Analysis of Marine Risers in

Projects, Proceedings of the Offshore Technology

Conference, OTC 18348 (2006)

[36] Huang K., Chen H.C. and Chen C.R., Deepwater Riser

VIV Assessment by Using a Time Domain SimulationApproach, Proceedings of the Offshore Technology

Conference, OTC 18769 (2007)

[37] Ashuri H., Sadeghi K and Niazi S., A Numerical Model ofVortex Induced Vibrations on Marine Risers, Proceedings

of the 30th ASME Conference on Ocean, Offshore and

Arctic Engineering, OMAE2011-49610 (2011)[38] Song J.N., Lu L., Teng B., Park H.I., Tang G.Q. and Wu

H., Laboratory Tests of Vortex Induced Vibrations of aLong Flexible Riser Pipe subjected to Uniform Flow,

Ocean Engineering voL. 38, vol. 1308-1322 (2011)

[39] Kim Y.H., Vandiver K.J. and Holler R., Vortex Induced

Vibration and Drag Coefficients of Long Cables Subjected

to Sheared Flow, Proceedings of the Fourth International

Offshore Mechanics and Arctic Engineering Symposium,Ed. J.S. Chung, vol. 10185a (1985)

[40] Vandiver K.J. and Chung T.Y., Predicted and Measured

Response of Flexible Cylinders in Sheared Flow,Proceedings of the ASME Winter Annual Meeting

Symposium on Flow Induced Vibration, Chicago (1988)[41] Vandiver K.J., Predicting Lock-in on Drilling Risers in

Sheared Flow, Proceedings of the Flow Induced VibrationsConference, Lucerne, Switzerland (2000)

[42] Adams A.J., Atkins W.S. and Thorogood J.L., On the

Choice of Current Profiles for Deep Water Riser Design,

Proceedings of the SPE Annual Technical Conference,

Society for Petroleum Engineers, SPE 49262 (1998)[43] Vandiver K.J., Research Challenges in the Vortex Induced

Vibration Prediction of Marine Risers, Proceedings of the

Offshore Technology Conference, Houston, Texas, USA,OTC-8698 (1998)


12/12


[44] Jones W.P. and Launder B.E, Prediction of Laminarization

with a Two Equation Model of Turbulence, International

Journal of Heat and Mass Transfer, vol. 15 (1972)

[45] Chien K.Y., Predictions of Channel and Boundary LayerFlows with a Low Reynolds Number Turbulence Model,AIAA Journal, vol. 20(1), pp. 33-38 (1982)

[46] Majumdar S. and Rodi W., Numerical Calculation of

Turbulent Flow Past a Circular Cylinder, Proceedings ofthe 7th Turbulent Shear Flow Symposium, pp. 3.13-25,

Stanford, USA (1985)

OMAE2013 10635 VIV Marine Risers Sheared Flow Final

Documents