reduction of viv using suppression devices—an empirical approach

8/11/2019 Reduction of VIV using suppression devicesAn empirical approach

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Marine Structures 18 (2005) 489510

Reduction of VIV using suppression devicesAn

empirical approach

Gro Sagli Baarholma,, Carl Martin Larsenb, Halvor Liea

aMARINTEK, P.O. Box 4125 Valentinlyst, N0-7450 Trondheim, Norwayb

Centre for Ships and Ocean Structures (CeSoS), NTNU, N-7491 Trondheim, Norway

Received 14 April 2005; received in revised form 2 January 2006; accepted 20 January 2006

Abstract

Helical strakes are known to reduce and even eliminate the oscillation amplitude of vortex-induced

vibrations (VIV). This reduction will increase the fatigue life. The optimum length and position of the

helical strakes for a given riser will vary with the current profile.

The purpose of the present paper is to describe how data from VIV experiments with suppressingdevices like fairings and strakes can be implemented into a theoretical VIV model. The computer

program is based on an empirical model for calculation of VIV. Suppression devices can be

accounted for by using user-defined data for hydrodynamic coefficients, i.e. lift and damping

coefficients, for the selected segments.

The effect of strakes on fatigue damage due to cross flow VIV is illustrated for a vertical riser

exposed to sheared and uniform current. Comparison of measured and calculated fatigue life is

performed for a model riser equipped with helical strakes. A systematic study of length of a section

with strakes for a set of current profiles is done and the results are also presented.

r 2006 Elsevier Ltd. All rights reserved.

Keywords: Vortex induced vibrations; Suppression devices; Marine risers

1. Introduction

Vortex induced vibrations are known to contribute significantly to fatigue damage for

deepwater risers and free span pipelines. The tools for VIV analysis that are presently used

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0951-8339/$ - see front matterr 2006 Elsevier Ltd. All rights reserved.

doi:10.1016/j.marstruc.2006.01.003

Corresponding author. Tel.: +4773 59 56 88; fax: +47 73 59 57 76.E-mail address: [email protected] (G.S. Baarholm).
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by the industry are semi-empirical, meaning that the response models rely only on

empirical coefficients.

Empirical models for VIV prediction of slender marine structures have been applied

since the early eighties. The models have traditionally been based on data from oscillation

tests with short (two-dimensional) cylinder sections, and some assumptions on applicationof such results for a slender beam with an unlimited number of eigenfrequencies and

modes. The simplest model can handle uniform current and uniform cross sections, and is

based on the assumption that the response will appear at an eigenfrequency and have the

shape of the associated eigenmode, see Larsen and Bech[1]. There is a long evolution from

that stage to todays models, and the research effort that has made this improvement

possible has been substantial. An overview of recent research on aspects of VIV related to

empirical models is presented by Larsen[2].

A strong effort has been seen at several institutions aiming at improving these methods,

and new versions of computer programs like SHEAR7, Vandiver[3], VIVA, Triantafyllou

[4], and VIVANA, Larsen et al. [5]have been released. Parallel to this work we have also

seen progress made on alternative methods based on direct numerical simulations [6].

Strakes are used to reduce vortex-induced vibrations and belong to a larger group of

VIV suppression devices. During the years, several experiments have been conducted to

measure the effect of these devices. Some attempts have also been done to implement the

effect of strakes and other suppression devices in empirical models. So far it seems that the

existing methods are premature. Effort must be put into understanding the physics as well

as implementation and verification against experimental data.

2. Theoretical background

The purpose of this section is to give a brief introduction to the analysis method applied

by VIVANA, and to describe how suppression devices can be accounted for in this model.

A more detailed presentation of this theory is given by Larsen [5]. The model is based on a

general three-dimensional beam finite-element model that in principle can account for

variation of current and cross section properties along the structures. The element theory is

described by Fylling et al. [7].

2.1. Basic concepts

The present version of the model is based on some basic concepts:

1. The response takes place at a limited number of discrete frequencies that are all

eigenfrequencies, but with an added mass as a function of the local flow conditions. The

added mass coefficient is a function of the local flow condition, the oscillation frequency

and the cross section geometry.

2. The current profile is unidirectional and always in a plane defined by the slender stretch

or perpendicular to this plane.

3. VIV are assumed to have a cross-flow component only, meaning that oscillation in the

current direction is not accounted for.4. A structure in sheared current will normally have one or more excitation zones (energy

input) and damping zones (energy dissipation). There will be a balance between energy

input and energy dissipation during one cycle at dynamic equilibrium, see Fig. 1.

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5. The excitation force is given by

FL 12rCLDU2Dl, (1)

whereCLis a lift coefficient. The magnitude of this coefficient is given by the local flowcondition, the cross section geometry, oscillation amplitude and frequency.

6. Damping outside the excitation zone is defined by a damping coefficient also which is a

function of the same parameters as the lift coefficients.

The structural model and the method for dynamic response analysis are based on

fundamental principles well known from finite element theory, while all hydrodynamic

coefficients are empirical, found from two-dimensional experiments on rigid cylinder

sections.

2.2. Hydrodynamic coefficients

The analysis model is based on empirical coefficients for lift force, added mass and

damping. All coefficients will depend on the non-dimensional frequency

^f foscDU

, (2)

wherefoscis the oscillation frequency, D is the diameter andUis the flow velocity. BothD

andUmay vary along the riser, which means that all coefficients also may vary.

The lift coefficient CL will depend on the oscillation amplitude A as well as on the

frequency. This is obtained by use of lift coefficient curves as shown in Fig. 2. CL is heregiven as function of the non-dimensional amplitude A/D. The lift coefficient curves are in

addition a function of the non-dimensional frequency. Hence, if the response frequency is

known, the CL versus A/D curve will be known at any location along the riser.

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UC

Low flowvelocity

damping

High flowvelocity

damping

Largeamplitudedamping

A

D

A

D

=f

Uc

Energyin

Energyin

0.125 0.2

Excitationzone

f0D

CL=0

Fig. 1. Energy balance for vibrating riser in sheared current.

G.S. Baarholm et al. / Marine Structures 18 (2005) 489510 491


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The added mass coefficient is assumed to be independent of the amplitude and is

therefore given as a simple function of the frequency only.

The damping model proposed by Venugopal [8] is used in the Gopalkrishnan VIV

model. It is partly based on Fylling et al. [7] experiments on an oscillating cylinder.

Gopalkrishnan [9] made other experiments and confirmed that the damping model is

conservative, meaning that real damping normally is higher than that predicted by the

model. The model applies different formulations for damping in high and low flow velocity

regions. This VIV model includes in addition a damping term for high response amplitude

in order to take the self-limiting character of VIV into account. The term follows directly

from the lift coefficient curve in Fig. 2. If the amplitude exceedsA=DCL0, the liftcoefficient becomes negative. This means that the phase of the lift force shifts and the forcewill act opposite to the velocity. Hence, the lift force will dissipate energy and thereby

contribute to damping. This effect is in particular important for cases with uniform flow

velocity.Fig. 1 illustrates the energy balance for a case with all the mentioned damping

types.

2.3. Identification of response frequencies

Before a dynamic analysis can be carried out, it is necessary to find the static equilibrium

condition. The next step will be to identify possible response frequencies for VIV.A response frequency is assumed to be an eigenfrequency, but since added mass will vary

with frequency and flow velocity, iterations are required. Such iterations must be carried

out for a large number of eigenfrequencies.

A subset of response frequency candidates will define the complete set of possibly active

frequencies. These are found from an excitation range criterion defined in terms of an

interval for the non-dimensional frequency where excitation can take place. The present

study applies an interval of

0:125o ^fo0:2. (3)

This is a pragmatic choice based on the results in Gopalkrishnan[9]. By use of this intervalone can find an excitation zone for each response frequency, and eigenfrequencies without

an excitation zone cannot become active. Excitation zone identification is illustrated in

Fig. 1.

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CL

A/DD CL=0

))A

Fig. 2. Example of possible lift coefficient curves for two different non-dimensional frequencies ^f.

G.S. Baarholm et al. / Marine Structures 18 (2005) 489510492


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The next step is to decide which eigenfrequency will dominate. The dominating

frequency is identified according to the excitation parameter, gexc, defined as

gexc

ZLE U2D3

A

D

CL0dl, (4)

where A=DCL0 is found from the lift coefficient curve, seeFig. 2. A=DCL0 depends onthe non-dimensional frequency ^f. LE is the length of the excitation zone. The frequency

candidates are ranked according to the numerical value of this integral and the dominating

frequency has the largest value. The dominating frequency will retain its complete

excitation zone in the subsequent response analysis. The division of the remaining regions

into excitation zones for the non-dominating response frequencies will be discussed later.

2.4. The response analyses

The frequency response method is used to calculate the dynamic response at the

dominating frequency identified in the previous step. The analysis applies an iteration that

is needed since lift and damping coefficients depend on the local response amplitude.

A part of this iteration is to obtain correct phase between lift force and response at all

positions along the pipe. The result of this analysis hence gives complete information of

exciting forces and damping coefficients along the pipe.

The frequency response method is well suited for this application since the loads are

assumed to be acting at a known discrete frequency. Use of the finite element method will

give a dynamic equilibrium equation that may be written as

Mrt C_rt Krt Rt, (5)whereMis the mass matrix,Cis the damping matrix andKis the stiffness matrix.r, _r, rare

the displacement, velocity and acceleration vectors, respectively. The external loads will in

this case be harmonic, but loads at all degrees of freedom are not necessarily in phase. It is

convenient to describe this type of load pattern by a complex load vector X with harmonic

time variation at frequency o:

Rt Xeiot. (6)

The response vector is expressed as

rt xeiot. (7)Eqs. (6) and (7) can be introduced into (5). The mass and damping matrices can be split

into structural and hydrodynamic parts. Hence we have

o2MS MHx ioCS CHx Kx X. (8)The damping matrixCSrepresents structural damping and will normally be assumed to be

proportional to the stiffness matrix. CH contains terms from hydrodynamic damping.

Elements in the external load vector X are always in phase with the local response velocity,

but a negative lift coefficient will imply a 1801 phase shift and hence turn excitationto damping. Since the magnitude of the lift coefficient depends on the response amplitude

(cf.Fig. 2), iteration is needed to solve the equation. Note that the response frequency is

fixed during this iteration.

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The response vectorxis complex and is hence able to describe a harmonic response at all

nodes, but the responses may have different phase. This means that the response will not

necessarily appear as a standing wave, but may also have contribution from travelling

waves. From a mathematical point of view x is equivalent to a complex mode as found

from a damped eigenvalue problem.The iteration will identify a response shape and amplitude that gives consistency

between the response levels, lift coefficients and the local flow condition. The mode shape

corresponding to the selected response frequency is used as an initial estimate for the

response vector, but the final result is not defined in terms of normal modes.

In the general case, the dominating frequency will not have an excitation zone

that covers the total riser length. Consequently, excitation may take place at

other frequencies in zones outside the primary zone. A similar analysis must therefore

be carried out for other frequencies, but the excitation zone for these frequencies

will be reduced according to the zone already taken by the more dominating ones. Hence,

zone overlaps are avoided, and the dominating frequency will have the largest possible

zone.

A fundamental assumption is that the responses from the frequencies involved can be

linearly superimposed. This assumption has never been verified by dedicated experiments.

Nevertheless, linear superposition of contributions from a set of discrete response

frequencies has often been assumed as basis for empirical methods [3] and is generally

recognized to give conservative results.

3. Hydrodynamic damping model

Elements outside of the excitation zone will add damping to the system. The damping

model for the bare riser in the VIV model consists of a low velocity model and a high

velocity model. The term refers to current velocities that are lower or higher than the

velocity within the excitation zone. The damping on sections equipped with VIV

suppression devices is calculated using the lift curves valid for the actual suppression

device. Note that the lift coefficient curves are used to calculate both excitation forces and

damping for the section with suppression devices. This means that lift coefficient curves as

illustrated onFig. 2must be known for the cross section shape in question for a sufficiently

large range of the non-dimensional frequency ^f. An illustration of the damping

and excitation zones for a riser partly equipped with VIV suppression devices is shown

inFig. 3.

3.1. Bare riser

For the bare riser the damping model proposed by Venugopal[8] is applied. The model

is partly based on experiments done by Gopalkrishnan [9] in driven cylinder oscillation

tests. Miliou et al. [6] verified that the model is conservative also for the case where the

response consists of two frequencies: one corresponding to the local vortex sheddingfrequency and the other at either higher or lower frequency.

The damping force coefficient on a cylinder section with diameter D, oscillating with

cross-flow amplitude ofx0, frequency o, in a fluid with density r, viscosity n, and incident



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velocity U(if current), is given as

1. Damping in still water:

csw oprD2

2

2ffiffiffi

2p

ffiffiffiffiffiffiffiffiffiReop ksw

x0

D 2

" #, (9)

where Reo oD2=n. The first part corresponds to the skin friction according to Stokeslaw. The second part is the pressure-dominated force. The factor kswis a value found from

curve fitting to be 0.25.

2. Low reduced velocity damping:

c1 csw rDUcvl. (10)The damping is increasing linearly with respect to the incident flow velocity. The coefficient

cvlwas found to be 0.18 based on measurements.

3. High reduced velocity damping:

c2 rU2

ocvh. (11)

This coefficient is independent of the amplitude ratio. The coefficient cvhwas found to be

0.2 based on measurements.

The force coefficient above has dimensions [(N/m)/(m/s)] and corresponds to the

Fdamp cf _x part of the dynamic equilibrium equation. It is straightforward to find thecorresponding non-dimensional negative lift coefficients that yield the same damping

(or energy dissipation).Fig. 4shows that the Venugopal[8]damping model is conservative

compared to the results from the experiments both for low- and high-reduced velocities.The dots mark the measured lift coefficient found from the experiments, while the lines

show the lift coefficient predicted by the Venugopal damping model. The experiments are

conducted with sub-critical flow conditions.

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Strakes

riser

Damping

zone

Dampingzone

Barerisers

fmin

fmax

Venugopal (high velocity)damping

f(z)

Damping and excitation

force from lift curves forriser with strakes

U(z) D(z)

Excitation force from liftcurves valid for bare riser

Venugopal (low velocity)

damping

Zone, LE

Excitation

Fig. 3. Damping and excitation zones for partly straked riser.



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3.2. Riser with VIV suppression devices

A riser can be partly covered with VIV suppression devices, such as strakes. Strakes willnormally not contribute to excitation, but only to damping. In the present model a straked

segment can be defined to be within the excitation length. However, the effect on the

damping is taken into account when computing the excitation parameters.

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Fig. 4. Low- and high-reduced velocity-damping results compared to model, Vikestad et al.[10].



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Fig. 3shows a sketch of a vertical riser with uniform cross section exposed to sheared

current. The excitation zone for a given response frequency is shown with black arrow. The

straked segments consist of an excitation zone and a damping zone. The damping on the

upper part of the riser is calculated using the lift curves defined for the sections with

suppression devices. This implies that the lift coefficients must be negative for allfrequencies and all A/D ratios. In the damping zone, the damping contribution is

calculated using

ccl rDU2CL

2oA , (12)

whereCLis the lift coefficient. An example of lift curves for strakes is shown inFig. 5for a

set of non-dimensional frequencies, MARINTEK [12]. The strake height is 15% of the

diameter.

If the lift coefficient in the excitation zone is negative, the lift force will dissipate energy andwe will have a damping contribution. The damping coefficient is calculated using Eq. (12).

This implies that the damping model is identical to the model used in the excitation zone.

So far, only the damping on sections exposed to current is treated. However, there is

damping on a segment with zero current, i.e. still water damping. For straked segments,

the still water damping is found using the still water damping coefficient, csw, defined as

csw oprD2

2 1 A

D

2" #Fstill, (13)

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0 0.2 0.4 0.6 0.8 1 1.2 1.4-5

-4.5

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

A/D [-]

CL

[-]

Strakes-STK.150

f=0.677 [-]

f=0.304 [-]

f=0.195 [-]

f=0.144 [-]

f=0.115 [-]

f=0.096 [-]

f=0.084 [-]

f=0.074 [-]

Fig. 5. Lift curves for strakes with strake height 15% of the diameter, Huse and Sther[11].



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whereFstill is a scaling coefficient. This coefficient must be found from decay tests in still

water. The still water damping coefficient as a function of the A/Dratio is shown inFig. 6

together with the data points.

3.3. Hydrodynamic damping, CH

The coefficients in the hydrodynamic damping matrix for an element are found in the

standard FEM way:

CijZ

l

cxNixNjxdx, (14)

whereNdenotes the shape functions for the element. c(x) represents any of the previous

defined damping coefficientscsw,c1,c2,cfand ccl. Note that these shape functions must be

the same when calculating the damping as for the mass and the stiffness matrix.

4. Case study

The VIV model is in the following sections used to calculate vortex induced vibrations

and the corresponding fatigue life on a vertical riser exposed to uniform and sheared

current. The maximum current speed is in both cases 0.5 m/s. Finally, the theoretical model

is used to calculate the fatigue damage on a model riser (High Mode VIV test) and the

results are compared to experimental data, MARINTEK [12]. The current profiles and

current speeds applied are listed inTable 3together with the corresponding test numbers.The risers are partly covered with strakes. The strakes are in all cases applied from the

top of the riser. The strakes have a height of 0.14D and the pitch is 5D. The lift curves for a

very similar profile with 5D pitch and 0.15D height are used as input to the numerical

model. The lift curves are shown in Fig. 5.

The physical properties of the riser models are shown inTable 1. The structural damping

ratio is 1% for all cases.

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0.0

5.0

10.0

15.0

20.0

25.0

0.00 0.20 0.40 0.60 0.80 1.00 1.20

A/D [-]

csw

[kg/ms]

Fig. 6. Still water damping using general lift curves.



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4.1. SN-curves

The fatigue damage is calculated using Miner summation assuming Rayleigh distributed

stress ranges and counting the stress cycles using rainflow counting.

The SN-curve is defined as

log Ni log a m log Dsi, (15)whereais the scale parameter and m is the slope parameter. Niis the number of cycles to

failure at stress range Dsi.

Throughout the analysis, the D curve NORSOK standard [13] is applied. The curve

chosen is valid for specimens in seawater exposed to free corrosion. Since this SN-curve

consists of one segment, applying other curves with m 3 will just introduce a scaledifference in the estimated fatigue damage. The choice of curve is therefore of less

importance in this study.

The SN-data applied are listed in Table 2.

The stress concentration factors are set to 1.0 for all cases. The thickness of the pipe is

less than the reference thickness. Hence, no thickness correction is applied.

4.2. Vertical riser in uniform and sheared current

The dominating mode as a function of the strake coverage is shown in Fig. 7. It can be

seen that the dominating mode for uniform current is constant and equal to 10 for all

cases. This is as expected since the dominating mode is determined using the excitation

parameter (Eq. (4)). The excitation parameter is equally reduced for all mode candidatesand the frequency rank will be defined by the parameter A=DCL0 only. Hence, the samefrequency will always be selected, independent of the length of the bare riser. The

dominating mode number for sheared current is decreasing as the strake coverage is

increasing. This is the consequence of applying strakes from the top of the riser in

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Table 1

Physical property of risers

Parameters Vertical riser Model riser

Total length between pinned ends 612 m 38.00 m

Outer diameter 0.5 m 27 mm

Wall thickness 15 mm 3.0 mm

Bending stiffness 1.39 105 kNm2 37.2 Nm2Axial stiffness 4.7 106 kN/m2 5.09 105 NMass (air filled) 179.5 kg/m 0.761 kg/m

Table 2

SN-curve

SN-curve log K m Ref. thickness (mm)

D 11.687 3.0 25



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combination with a triangular current profile, meaning that excitation will take place at a

lower current speed for increasing length of the straked section.

The excitation length is plotted inFig. 8. The frequency candidates are ranked according

to the numerical value of the excitation parameter. The primary frequency will retain the

complete excitation zone in the succeeding response analysis. One consequence of this is

that the excitation zone that covers the straked section of the riser will still be considered as

excitation even if the lift curve is negative and gives a negative lift, i.e. only damping

contribution. This is illustrated inFig. 8showing the excitation length as a function of the

strake coverage. Based on the above, the excitation length for uniform current will always

be constant. However, the excitation length for the sheared current case will decrease, sincedominating mode number decreases.

When the excitation lengths are determined, the response analysis can be conducted. The

lift coefficient for bare riser, 25% and 58% strake coverages as a function of the water

ARTICLE IN PRESS

Dominating Mode

0

2

4

6

8

10

12

0 80604020

Strake coverage [%]

sheared

uniform

Fig. 7. Dominating mode in uniform and sheared current as a function of strake coverage.

Excitation Length

0

100

200

300

400

500

600

700

sheared

uniform

0 80604020

Strake coverage [%]

Fig. 8. Excitation lengths in uniform and sheared current as a function of strake coverage.



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depth, is shown inFig. 9. Results for both sheared and uniform current are included. As

can be seen, the lift coefficient for a bare riser is always positive for the sheared current

case. This is because the (A/D) ratio is small and large amplitude damping is hence

avoided. For the uniform current case, the lift coefficient is negative at some parts of the

riser. This is due to large amplitude damping. Adding strakes on the top part of the riser,the lift coefficient becomes negative on the straked part. The strakes contribute to a

negative lift, i.e. damping. Increasing the strake coverage to 58%, the riser in the uniform

ARTICLE IN PRESS

-2 -1 0 1-600

-500

-400

-300

-200

-100

0

CL[-] C

L[-]

Waterdepth[m]

Uniform

-0.5 0 0.5 1-600

-500

-400

-300

-200

-100

0Sheared

0% strakes

25% strakes

58% strakes

Fig. 9. Lift coefficient for dominating modes for strake coverages 0% (bare riser), 25% and 58% for riser in

uniform and sheared current.

Fatigue life [years]

0.0

0.1

1.0

0 4020 60

Strake coverage [%]

uniform

Fig. 10. Fatigue life as a function of strake coverage, uniform current profile.



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current case experiences a large negative excitation force. For the corresponding case when

the riser is exposed to sheared current, the lift coefficient is positive in the excitation zone,

but negative where strakes are found within the excitation zone. This is basically the result

of the excitation zone only being on the bare riser part. One should remember that the

damping is properly accounted for on the straked part of the riser. The lift curves for thestraked segments are used when the damping force is calculated.

Finally, the fatigue life is calculated. The minimum fatigue life for uniform and sheared

current is shown inFigs. 10 and 11as a function of the strake coverage. As can be seen, the

fatigue life increases as the strake coverage increases. The increment is significantly larger

for the sheared current cases. The increase in fatigue life is influenced by curvature and

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Fatigue life [years]

1

100

10000

1000000

100000000

6040200

Strake coverage [%]

sheared

Fig. 11. Fatigue life as a function of strake coverage, sheared current profile.

Table 3

Test number of the selected cases for VIV simulations

Uniform

u (m/s) Bare riser 5D pitch and 0.14D height

VIVANA: 100% 90% 75% 50%

Experiments: 91% 82% 62% 41%

0.9 2070 6070 6670 7270 7870

1.0 2080 6080 6680 7280 7880

1.1 2090 6090 6690 7290 7890

Shear

u (m/s) Bare riser 5D pitch and 0.14D height

VIVANA: 100% 90%

Experiments: 91% 82%

0.9 2370 6370 69701.0 2380 6380 6980

1.1 2390 6390 6990

The strake coverage used in the experiments and VIV simulation is shown in percent.



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response amplitude. As already mentioned, the mode number is constant for the uniform

case while the mode number decreases for sheared current. For the latter case, this implies

that the curvature decreases as well. Hence, the increase in fatigue life for sheared current is

a result of the combination of reduced mode number and response amplitude. The main

contribution to the increase in fatigue life for the uniform case is the reduction in responseamplitude and consequently a smaller change in fatigue life.

The intention of this study is solely to illustrate the use of the program. The results are

not verified by tests. However, the next section makes a comparison with test results.

4.3. Model riser in sheared and uniform current

The model riser is exposed to sheared and uniform current. The strake coverage in the

experiments varies from 41% to 91%. In the experiments, the model riser did not have a

continuous strake section. Since the model riser is heavily instrumented, there wereintervening gaps. This implies that a riser with 91% strake coverage is a model of a riser

completely covered with strakes. For 91% and 82% strake coverage the distribution of

strakes is uniform along the riser. For 62% and 41% coverage the strakes were removed

from the riser such that the highest current region remained covered during the linear shear

flow tests. In the experiments, two different strake configurations were tested out.

However, in this study one has been concentrating on the test with strakes with 5D pitch

and 0.14D height that resembles the strakes in Fig. 5as accurately as possible.

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0 10 20 30 40

103.8

103.5

103.2

Case No.:2070

0 10 20 30 4010

5

1010

Case No.:6670

0 10 20 30 4010

2

104

106

108

Case No.:7270

Position [m] Position [m]

Fatiguelife[yrs]

Fatiguelife[yrs]

VIVANA

experiments

0 10 20 30 4010

3

104

105

Case No.:7870

Fig. 12. Fatigue life (top left: bare riser, top right: 90%/82% strakes, bottom left: 75%/62% strakes, bottom

right: 50%/41% strakes). Uniform current Umax 0.9m/s.



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The cases chosen for comparison with the theoretical model are listed in Table 3.

Totally 24 cases are chosen for this study. For the case of simplicity, the gap between the

strakes used for the instrumentation during the experiments is not accounted for in the

VIVANA simulations. The area covered with strakes will therefore be somewhat larger

than in the tests. The strake coverage used in the simulations and experiments are found inTable 3.

The fatigue distributions for the uniform current cases are shown in Figs. 1214. The

figures show the envelope fatigue life curves from the top of the riser (pos 0) to thebottom (pos 38) calculated by VIVANA. In addition, the fatigue life calculated frommeasured bending strain is included. As can be seen, not all the cases listed in Table 3are

reported in terms of fatigue plots. This is because the theoretical model did not calculate

the fatigue damage if the cross flow displacement was found to be less than 1% of the

diameter. Nor is fatigue damage reported if the riser is completely covered with strakes

only contributing to damping. These cases are considered to have zero VIV fatigue

damage.

Looking atFigs. 1214it seems that the calculated fatigue life corresponds adequately to

fatigue life found from measured strains for cases with strake coverage of 41% and 62%.

Note that an amplitude error ofe will be amplified by e3 (exponent) for fatigue damage

because of the SN curve exponent. For cases with 82% and 91% strake coverage, the

strake model fails to represent the observed behaviour.

ARTICLE IN PRESS

0 10 20 30 40

104

103

102

Case No.:2080

0 10 20 30 4010

4

106

108

1010

Case No.:6680

0 10 20 30 40

102

104

106

108Case No.:7280


Fatiguelife[yrs]

Fatiguelife[yrs]

VIVANA

experiments

0 10 20 30 40

103

104

105

Case No.:7880


right: 50%/41% strakes). Uniform current Umax 1.0m/s.



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ARTICLE IN PRESS

0 10 20 30 4010

2

103

104

Case No.:2090

0 10 20 30 4010

4

106

108

1010

Case No.:6690

0 10 20 30 4010

2

104

106

108

Case No.:7290


Fatiguelife[yrs

]

Fatiguelife

[yrs]

VIVANA

experiments

0 10 20 30 4010

3

104

105

Case No.:7890


right: 50%/41% strakes). Uniform current Umax

1.1m/s.

0 10 20 30 4010

4

105

106

Case No.:2370

0 10 20 30 4010

4

105

106

Case No.:2380

0 10 20 30 40103

104

105

Case No.:2390

Position [m]

Fatiguelife[yrs]

Fatiguelife[yrs]

VIVANA

experiments

Fig. 15. Sheared current cases (top left: 0.9 m/s, top right: 1.0 m/s, bottom left: 1.1 m/s). Bare riser.



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Fig. 15 shows the fatigue life distribution for the bare riser exposed to sheared

current. The fatigue life calculated with the VIV model seems to be larger than the

fatigue life found using the measured strain. When the model is equipped with strakes, the

VIV model reports insignificant fatigue damage. Hence, no plots are presented for these

cases.

The cross flow displacements estimated using VIVANA for the same cases and

compared to the measured displacement are shown in Figs. 1619. As can be seen, the

displacement compares well with the measured results for the cases with strake coverage41% and 62%. Comparison of dominating modes and frequencies are shown in Table 4.

The main visual observations are summed up inTable 5. It seems that the results can be

divided into three categories. The categories are bare riser, partly straked riser and fully

straked riser. The VIV model is able to calculate the fatigue damage reasonably good for

the cases with 41% and 62% strake coverage, but for the cases where the riser is almost

completely covered with strakes the VIV model is inadequate. This is because the physical

characteristics for the partly straked riser are similar to a bare riser, while the fully straked

riser has other characteristics not implemented in VIVANA.

In MARINTEK[14]it is found that the 5D strakes have significantly different physical

characteristics compared to the 17.5D strakes. The VIV response using 5D strakes can beestimated using the existing VIV tools for partly covered strakes. However, the

characteristics of the 17.5D strakes do not resemble a bare riser and hence the VIV

tools will fail to work. This phenomenon is also mentioned by Frank et al. [15].

ARTICLE IN PRESS

0 10 20 30 400

0.005

0.01

0.015

0.02

Case No.:2070

0 10 20 30 400

2

4

6 10

-3 Case No.:6670

VIVANA

experiments

0 10 20 30 400

0.002

0.004

0.006

0.008

0.01

Case No.:7270


A/D

rms

[-]

A/D

rms

[-]

0 10 20 30 400

0.005

0.01

0.015

0.02

Case No.:7870

Fig. 16. Displacement standard deviation given on non-dimensional form (A/D). (Top left: bare riser, top right: 90%/

82% strakes, bottom left: 75%/62% strakes, bottom right: 50%/41% strakes). Uniform current Umax

0.9 m/s.



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ARTICLE IN PRESS

0 10 20 30 400

0.005

0.01

0.015

0.02

0.025Case No.:2080

0 10 20 30 400

2

4

6

Case No.:6680

VIVANAexperiments

0 10 20 30 400

0.005

0.01

0.015Case No.:7280


A/D

rms

[-]

A/D

rms[

-]

0 10 20 30 400

0.005

0.01

0.015

0.02

Case No.:7880

10-3

Fig. 17. Displacement standard deviation given on non-dimensional form (A/D). (Top left: bare riser, top right:

90%/82% strakes, bottom left: 75%/62% strakes, bottom right: 50%/41% strakes). Uniform current

Umax 1.0m/s.

Table 4

Dominating modes and frequencies from experiments and simulations

Current

profile

Umax (m/s) Test no. Strake

coverage (%)

Dominating mode Mode frequency (Hz)

Experiments Simulations Experiments Simulations

Uniform 0.9 2070 0 6 9 5.0 6.2

1.0 2080 0 7 10 7.5 6.3

1.1 2090 0 8 12 6.4 7.0

0.9 6670 82 6 6 3.4 4.3

1.0 6680 82 7 6 3.5 4.8

1.1 6690 82 8 8 4.1 5.3

0.9 7270 62 9 9 5.2 5.6

1.0 7280 62 9 10 5.5 6.3

1.1 7290 62 10 12 6.1 6.9

0.9 7870 41 8 9 5.1 5.6

1.0 7880 41 9 10 5.7 6.3

1.1 7890 41 9 12 6.2 6.9Shear 0.9 2370 0 6 6 4.6 4.3

1.0 2380 0 7 6 4.9 4.8

1.1 2390 0 7 8 8.5 5.3



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ARTICLE IN PRESS

0 10 20 30 400

0.005

0.01

0.015

0.02

0.025Case No.:2090

0 10 20 30 400

2

4

6Case No.:6690

VIVANA

experiments

0 10 20 30 400

0.005

0.01

0.015Case No.:7290

Position [m]

0 10 20 30 400

0.005

0.01

0.015

0.02Case No.:7890

10-3

A/D

rms[

-]

A/D

rms

[-]

Fig. 18. Displacement standard deviation given on non-dimensional form (A/D). (Top left: bare riser, top right:

90%/82% strakes, bottom left: 75%/62% strakes, bottom right: 50%/41% strakes). Uniform current Umax

1.1m/s.

0 10 20 30 400

0.005

0.01

0.015Case No.:2370

0 10 20 30 400

0.005

0.01

0.015Case No.:2380

VIVANA

experiments

0 10 20 30 400

0.005

0.01

0.015

0.02Case No.:2390

Position [m]

A/D

rms

[-]

A/D

rms

[-]

Fig. 19. Displacement standard deviation given on non-dimensional form (A/D). Sheared current cases (top left:

0.9 m/s, top right: 1.0 m/s, bottom left: 1.1 m/s). Bare riser.



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5. Conclusions

A theoretical VIV model is presented. The theoretical model is implemented in a

computer program based on an empirical model for calculation of VIV. Suppression

devices can be accounted for by using user-defined data for hydrodynamic coefficients, i.e.

lift and damping coefficients, for selected segments.

The theoretical model can cover cases with up to approximately 75% coverage of VIV

suppression devices. For these cases the bare riser controls the VIV behaviour (frequency,

mode, etc.).

For larger coverage the straked riser takes control of the VIV behaviour. Model tests

indicate a different physical behaviour depending on the pitch and height of the strake

triple start. The behaviour seems to be strongly dependent on pitch and height of the

strakes. In general, the responding frequencies and mode numbers are lower than for the

cases controlled by the bare riser.

Acknowledgements

The present work has been supported by the Norwegian Marine Technology Research

Institute (MARINTEK), the Norwegian Deepwater Program (NDP) and the Centre of

Excellence on Ships and Ocean Structures (CeSOS) at the Norwegian University of

Technology and Science (NTNU).

References

[1] Larsen CM, Bech A. Stress analysis of marine risers under lock-in conditions. Proceedings from the 5th

OMAE conference, Tokyo; 1986.

[2] Larsen CM. Empirical VIV models. WVIVOS, workshop on vortex-induced vibrations of offshore

structures. Sao Paulo, Brazil; 1416 August 2000.

[3] Vandiver JK, Li L. SHEAR7 V4.2f program theoretical manual. Department of Ocean Engineering MIT,

Massachusetts, USA; 2003.

[4] Triantafyllou MS, Triantafyllou GS, Tein D, Ambrose BD. Pragmatic riser VIV analysis. OTC 10931; 1999.

[5] Larsen CM, Vikestad K, Yttervik R, Passano E. VIVANA, theory manual. MARINTEK Report,

Trondheim, Norway; 2000.

[6] Miliou A, Sherwin SJ, Graham JMR. Three-dimensional wakes of curved pipes. OMAE2002-28308; 2002.[7] Fylling IJ, Larsen CM, Sdahl N, Ormberg H, Engseth AG, Passano E, et al. RIFLEXtheory manual.

SINTEF Report STF70 F95219, Trondheim; 1995.

[8] Venugopal M. Damping and response prediction of a flexible cylinder in a current. PhD thesis, Department

of Ocean Eng, MIT; 1996.

ARTICLE IN PRESS

Table 5

VIVANA fatigue damage trends

Current profile Percentage coverage 5D strakes

Bare riser Partly straked riser

(41% and 62%)

Fully straked riser (82% and 91%)

Uniform Reasonable Reasonable Insignificant VIV response for VIVANA

Sheared Reasonable Insignificant VIV response for VIVANA



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[9] Gopalkrishnan R. Vortex-induced forces on oscillating bluff cylinders. ScD thesis, Department of Ocean

Engineering, MIT, and Department of Applied Ocean Physics and Engineering, WHOI, USA; 1993.

[10] Vikestad K, Larsen CM, Vandiver JK. Norwegian deepwater program: damping of vortex-induced

vibrations. OTC Paper 11998, Houston, TX, USA; 2000.

[11] Huse E, Sther LK. VIV excitation and damping of straked risers. 20th international conference on offshore

mechanics and arctic engineering. Rio de Janeiro, Brazil; 2001.

[12] MARINTEK report: NDP riser high mode VIV tests. main report. 2004-03-24, DRAFT report no.

512394.00.01 (Confidential).

[13] NORSOK Standard. Design of steel structuresAnnex Cfatigue strength analysis; 1998.

[14] MARINTEK report: NDP riser high mode VIV testsCTR02: modal analysis, 2004-05-12. DRAFT report

no. 590002.00.02 (Confidential).

[15] Frank WR, Tognarelli MA, Slocum ST, Campbell RB, Balasubramanian SR. Flow-induced vibration of a

long, flexible, straked cylinder in uniform and linearly sheared currents. OTC 2004 / OTC16340; 2004.


reduction of viv using suppression devices—an empirical approach

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