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CROSS SECTION VIV MODEL TEST FOR NOVEL RISER GEOMETRIES

Jaap de Wilde

MARIN (Maritime Research Institute Netherlands)Haagsteeg 2 / P.O. Box 28

6700 AA WAGENINGEN, The Netherlands

A. Sworn and H. CookBP

N. Willis and C. Bridge

2H Offshore

Abstract

The global loads and fatigue life of deepwater risers or riser bundles in current are oftendominated by Vortex Induced Vibrations (VIV). Semi-empirical prediction program such as

Shear7 and VIVARRAY are still the most commonly used tools for analyzing the VIV response

of such systems. These programs rely on large databases with experimentally determinedhydrodynamic coefficients.

A new test apparatus has been developed for measuring the hydrodynamic VIV coefficients on

an oscillating model of the riser in uniform and steady current. A 3.4 m long section of the risercan be tested at full scale dimensions and real current speeds. Tests are carried out at different

tow speeds, oscillation frequencies and amplitudes. Tests at full scale Reynolds numbers reveal

new insights in the Reynolds scale effects and reduce uncertainties of such effects in the designprocess.

An efficient test strategy has been developed for finding the peak lift loads of a new riser

geometry or configuration. About 50 tests are needed for each flow orientation. A non-circularriser bundle can be tested for 8 flow angles between 0 and 360 degrees, using steps of 45

degrees. Over 400 tests can be conducted in about 2 weeks time.

Symbols

A : amplitude of oscillationCd : drag coefficient

CLv : lift coefficient in phase with velocity

CLa : lift coefficient in phase with acceleration

Cm : added mass coefficientD : cylinder diameter

fn : natural frequency of riser mode shape n

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fo : oscillation frequencyfs : vortex-shedding frequency

Re : Reynolds number

St : Strouhal numberU : flow velocity

Ur : reduced velocity

1. Introduction

One of the great challenges in the offshore industry is still the assessment of the motions of a

circular cylinder in waves and current for application to risers or riser bundles in water depths up

to 3,000 m (10,000 feet). Here the global loads and the fatigue life are often dominated byVortex Induced Vibrations (VIV). VIV can be of major concern because of the increase in drag

loads and the high fatigue damage means high investment and maintenance costs of the risers.

In ocean currents, alternating vortices will develop on the riser which can excite the riser in oneor more of its natural frequencies. Resonant type VIV happens when the vortex shedding

frequency gets close to one of the natural frequencies. Due to the so-called lock-in effect, the

correlation length increases as well as the vortex strength. Lock-in also leads to vortex inducedvibrations over a much wider range of oscillation frequencies than would be expected for normal

resonance. At lock-in the vortex shedding somehow adapts itself to the oscillation frequency.

Vortex induced vibrations are self-limiting at amplitudes around one times the cylinder diameter

(A/D = 1). The fatigue damage can still be large due to the high frequency and concentration of

the stress variations in the anti-nodes of one or more excited modes.

Figure 1: MARIN High Reynolds VIV test apparatus

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2. Vortex shedding and lock-in VIV

A cylinder in a steady cross flow develops a flow field that depends on the flow velocity, the

geometry and the surface roughness. The flow regimes can be classified into several Reynoldsregimes. The Reynolds number denotes the ratio between the inertial and viscous forces in the

flow:

=UD

Re

For Reynolds numbers above 40 a classical von Karman vortex street develops in thedownstream wake. Two opposite vortices are generated every cycle and are transported

downstream with nearly the free flow velocity.

Figure 2: Von Karman type vortex street.

Offshore riser systems operate at Reynolds numbers well above 10,000, where the following

Reynolds regimes can be distinguished [1]:

Sub-critical regime: 2,000 < Re < 200,000The turbulent vortex street has an almost constant vortex shedding frequency (St 0.20). Theboundary layer is laminar up to the separation point at about 80 from the upstream stagnationpoint. The drag coefficient of a smooth circular cylinder in the sub-critical Reynolds regime is

very constant with a value close to 1.2.

Critical regime: 200,000 < Re < 500,000The boundary layer becomes unstable, but separates before becoming turbulent. The width of the

wake decreases and the drag coefficient drops to a value near 0.3. The vortex shedding frequency

is very variable.

Supercritical regime: 500,000 < Re < 3,500,000There is first a laminar separation at about 100 from the stagnation point. The flow becomesturbulent and then re-attaches, forming a separation bubble before finally separating from the

body near 140. The regime is recognised with a drag coefficient increasing from 0.5 to 0.7. Thewake is disorganised and the shedding frequency is very variable.

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The in-line drag of a cylinder is proportional to its diameter and the square of the flow velocity:

=d

d 212

FC

D v

The vortex shedding frequency is proportional to the free flow velocity and inverselyproportional to the diameter. The Strouhal number denotes the proportionality constant:

= sf D

StU

The drop of the drag coefficient in the critical Reynolds regime is known as drag crises or

drag bucket. The drag coefficient of a very smooth cylinder can drop from about 1.2 to as low

as 0.3, as shown in the next figure based on NACA wind tunnel measurements [2].

Sub-critical Super-criticalCritical

Re

Cd

St

Sub-criticalSub-critical Super-criticalSuper-criticalCriticalCritical

Re

Cd

St

Figure 3: Drag coefficient and Strouhal number for Reynolds 104to 2 x 106

3. Lock-in VIV

The VIV phenomenon happens in the so-called lock-in region, where the vortex shedding

frequency collapses onto the natural frequency. Lock-in VIV has been widely explored, and it isknown to be associated with:

increase of the correlation length, increase of vortex strength,

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increase of response bandwidth, self-limiting nature at approximately 1 diameter, and increase of the in-line drag.

The lock-in phenomena is clearly demonstrated with the experimental Feng data [3]:

Figure 4: Frequency and amplitude response in the lock-in regime

Two regions can be distinguished in the lock-in region (5 < Ur < 8):

s nf f The vortex shedding frequency is higher than the natural frequency. The added

mass coefficient is usually smaller than 1. The lock-in results in a downward shift

of the vortex shedding frequency. The vortex shedding frequency now adapts to

the natural frequency.

Outside the lock-in regime (Ur < 5 or Ur > 8) the response follows the vortex sheddingfrequency, but the response is very small. Often a figure-of-eight type response is found for 2

degrees of freedom pipe motions.

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-1.500

-1.000

-0.500

0.000

0.500

1.000

1.500

-1.500 -0.500 0.500 1.500

Figure 5: Figure-of-eight VIV response

4. Modal response in sheared current

The VIV analysis of a deepwater riser in sheared current is still a major challenge. Specialisedgroups work on improving and calibrating existing prediction tools, developing new numerical

tools using computational fluid dynamics (CFD), new model tests techniques or performing full

scale measurements.

A deepwater riser can be excited at different locations along it length, in different modes and at

different frequencies, resulting in interesting phenomena such as:

mode interference, multi-mode response mode switching.

The response may even not consist of true modes, but rather of travelling waves that carry

energy from one area of the riser to others. The mode response in sheared current can bedemonstrated with the following simplified example. A vertical riser in a linear shear is

considered, with zero current speed at the seabed and maximum speed at the water surface.

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dL

T

Flow

D

Figure 6: Simplified riser in sheared current

In the next graph, the lock-in regions (5 < Ur < 8) are highlighted for the first seven modes. It is

however unlikely that all these modes will participate simultaneously, because of the self-limiting nature of the VIV and the limited amount of energy that can be extracted from the

vortex shedding process. In fact, the more powerful modes tend to dominate. In this example the

more energetic modes are excited at the top of the riser, where the flow velocity is the highest.The largest excitation region can de observed for modes 4 and 5.

Ur5 8

1.0

0

max

f1

f2

f3

f4f5

f6f7WD

V

=rUT

UD

Ur5 8

1.0

0

max

f1

f2

f3

f4f5

f6f7WD

V

=rUT

UD

Figure 7: Example of modal response in sheared current

5. Fatigue damage

The fatigue damage is one of the major concerns for the design of deepwater riser systems. The

stress fluctuations cause small defects in the pipe material to grow, which in the long term can

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lead to riser damage or even failure. The fatigue capacity of a material can be expressed in thenumber of stress cycles to failure (S-N curve):

=mfailureN S C

In which N is the number of cycles to failure and S is the amplitude of the stress fluctuations.The power m and the constant C depend on the material properties, the mean tension and the

stress range. S-N relations are determined empirically.

The fatigue analysis requires accurate predictions of the modes, amplitudes and frequencies. The

importance of the response amplitude is evident, reducing the fatigue life with the m th power (m

is typically 3 to 5). The importance of the mode number can be understood when comparing the

fatigue damage of a single mode response with that of several participating modes. In the firstcase the damage is always accumulating at the same locations in the anti-nodes, whereas the in

the latter case the damage tends to be more distributed over the riser. An example of the large

variation in predicted fatigue life is presented in the next table.

Table 1: Variation in predicted fatigue life

Current

Speed

Mode

No.Fatigue Life for A/D =

U[m/s]

n[-]

0.25 0.50 0.75 1.00 1.25

0.50 9 46.5 years 5.8 years 1.7 years 265 days 136 days

1.00 17 133 days 17 days 5 days 2 days 1 day

1.50 26 8 days 36 hours 11 hours 5 hours 2 hours

6. Riser VIV analysis

VIV prediction tools, such as Shear7 or VIVARRAY, have been developed for the analysing the

VIV response of deepwater risers, [4] and [5]. The semi-empirical approach has been in use for afew decades and has faced a lot of criticism. In spite of this, it survived and it is still the most

commonly used approach in the industry. The phenomenological approach is based on the

assumption that the fluid forces can be locally described by a non-linear oscillator, whichdescribes the excitation of vortex shedding process in terms of oscillating lift forces at the

Strouhal frequency or as so-called negative damping. The self-limiting nature of the oscillation

amplitude is taken care of by the non-linear description of these forces. This approach has

survived for a long time because it is adjustable to experimental results and describes the knownphenomena quite well.

The mathematical core of the programs basically involves a generalised equation of motiondescribing the riser oscillations around the global shape:

( ) + + =

2 2 2

l2 2 2

z z z zm B EI T F x,

t x xt x xt

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Most programs solve this equation mode-by-mode in the frequency domain. Finite elementmethods (FEM) are used for analysing the structural part, on the left hand side of the equation.

Strip theory is used to describe the alternating vortex shedding loads on the right hand side of the

equation. An extensive database is used with non-dimensional lift and added mass coefficients,which have been obtained from experiments. Solutions are found in an iterative process to deal

with the strongly non-linear behaviour of the lift coefficients. This part represents in fact the truenature of the hydro-structural VIV problem, in which the motions are excited by the fluid flowbut the fluid flow itself depends again on the structural motions.

CurrentCurrent

Figure 8: Strip theory approach for a slender riser

FLUID

FORCES

FLUID DYNAMICS STRUCTURAL

DYNAMICS

FLUID/STRUCTURE

MOTIONS

VIV RESPONSE

-1.500

-1.000

-0.500

0.000

0.500

1.000

1.500

-1.500 -0.500 0.500 1.500

FLUID

FORCES

FLUID DYNAMICS STRUCTURAL

DYNAMICS

FLUID/STRUCTURE

MOTIONS

VIV RESPONSE

-1.500

-1.000

-0.500

0.000

0.500

1.000

1.500

-1.500 -0.500 0.500 1.500

Figure 9: Fluid structure interaction for VIV

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The program returns for each individual mode:

oscillation amplitudes, oscillation frequency, drag loads,

fatigue life.

The interpretation of the multi-mode response is mostly left to the user.

7. High Reynolds test apparatus

A new test apparatus has been developed for measuring the vortex shedding loads on an

oscillating cylinder at full scale Reynolds numbers, [6] and [7]. A 3.4 m section of the riser istowed while being oscillated at the same time. The forces on the cylinder are measured and can

be processed to obtain the dimensionless coefficients for calibration of the VIV prediction

programs. The measurements at full scale Reynolds numbers provide new insights in the scaleeffects when entering the critical regime. The existing lift coefficient databases are mostly

populated with data from sub-critical experiments. The new apparatus may also be used for

testing new and non-symmetrical riser geometries and configurations, including straked risers,

riser bundles, piggy-back risers, risers with staggered buoyancy, drilling risers with kill andchoke lines, etc. In 2002 the set-up was used for testing a dual pipe riser system for Conoco

Phillips [8]. The test up has also been used for testing the efficiency of various strake geometries.

The development of the set-up started in 1999 as an in-house research activity and continued

afterwards for the VIVARRAY JIP. The set-up, pictured below, consists of:

(1) vertical struts arrangement,

(2) linear bearings,

(3) test pipe,

(4) large circular end plates,

(5) vertical drive shafts,

(6) oscillator with gearing and crank wheels

(7) 30 kW electric motor.

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67

5

4

3

2

1

1. Vertical struts.

2. Linear bearings

3. Test pipe.

4. End plates.

5. Drive shafts.

6. Oscillator

7. 30 kW elect ric mot or.

67

5

4

3

2

1

67

5

4

3

2

1

1. Vertical struts.

2. Linear bearings

3. Test pipe.

4. End plates.

5. Drive shafts.

6. Oscillator

7. 30 kW elect ric mot or.

Figure 10: High Reynolds VIV test apparatus

The test pipe is horizontally suspended at mid depth from the carriage on two streamlined strutswith linear bearings. The oscillation is forced by the oscillator using a crank-shaft mechanism.

The oscillation frequency and amplitude can be accurately adjusted from test to test. The

overhead carriage runs on rails over the 210 m long towing tank of 4 m width and 4 m depth.

The 165 kW engine can deal with over 10 kN of drag loads at tow speeds up to 4 m/s. Thecarriage can run in both forward and backward direction, which means that the cylinder is either

pushed or pulled trough the tank. Both directions show a uniform flow field with low turbulence.

The apparatus is capable of:

- maximum cylinder drag load of 10 kN.

- maximum vertical cylinder loads of 10 kN

- maximum tow speed of 4 m/s- maximum oscillation frequency of 3 Hz

- maximum oscillation amplitude of 330 mm

An example of the measured forces is presented in the next graph and shows the cylinder motion,

velocity, acceleration, the in-line drag force, the total cross flow force, the cross flow lift force

after inertia removal and the instantaneous energy transfer from the fluid to the pipe. A positive

mean value of this signal over an integer number of cycles means a nett excitation.

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Figure 11: Example of measured time traces

8. Data analysis

In general, the oscillating lift forces of the vortex shedding process show a phase shift with the

cylinder motions, which can for harmonic signals be expressed as follows:

z(t) Asin( t)=

L L 0F (t) F sin( t ) or= +

L L 0 L 0F (t) F sin cos( t) F cos sin( t)= +

The in-phase and the out-of-phase lift forces relate respectively to the added mass and the power

transfer from the fluid to the cylinder respectively. The power transfer can be either positive

(exciting) or negative (damping). The lift coefficient in-phase with the velocity and the lift

coefficient in-phase with the acceleration can be defined as follows:

L 0

Lv 212

F sin

C DL U

= andL 0

La 212

F cos

C DL U

=

The added mass coefficient can be calculated from the in-phase lift forces:

L0 0M 2 2

04

F cosC

D L(2 f ) A

=

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Using the same sign conventions as Gopalkrishnan [9], a positive Clv coefficient denotes power

transfer from the fluid to the cylinder oscillation and a positive Cla coefficient denotes a negative

added mass.

9. Test strategy

An efficient test strategy has been developed in collaboration with 2H Offshore and BP, for

finding the non-dimensional input coefficients for Shear7 calculations on an asymmetric riserconfiguration. The difficulty here is to find the input coefficients in such a way that sufficient

resolution is guaranteed, without expanding the test matrix too much. The three independent test

parameters are:

tow velocity (Reynolds number) oscillation frequency (reduced velocity) oscillation amplitude (amplitude ratio)

We needed about 50 individual tests for every flow angle. Eight flow angles were tested: 0, 45,

90, 135, 180, 225, 270 and 315. Over 400 tests were conducted in about 2 weeks.

Series A: 6 non-oscillating tests.Series B: 10 reduced velocity sweep tests at 0.75 A/D

Series C: 10 reduced velocity sweep tests at 0.25 A/D

Series D: 4 reduced velocity sweep tests at 0.50 or 1.2 A/DSeries E: 2 tests at the peak reduced velocity

Series F: 4 Reynolds sweep tests at 0.75 A/D

Series G: 4 Reynolds sweep tests at 0.25 A/DSeries H: 4 Reynolds sweep tests at 0.5 or 1.2 A/D

Series I: 6 spare tests

A pictorial plot of the above test matrix is presented in Figure 12 with the sub-critical

Gopalkrishnan data for a circular cylinder in the background. The lock-in area is scanned in twodirections. A reduced velocity sweep (horizontal traverse) was executed to find the location of

the peak in the bell curve, which appears not to be trivial for a non circular riser geometry. The

amplitude sweep (vertical traverse) yielded the onset lift coefficient, the maximum lift

coefficient and the zero crossing A/D value.

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Single Smooth Pipe Test Matrix

Superimposed onto Gopalkrishnan (1993) Data

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Strouhal Number, St - fD/V (-)

Amplitude,

A/D(-)

Re 40000 Re 80000 Re 160000 Re 360000

Figure 12: Pictorial summary of test matrix

The lift and added mass coefficients obtained from our recent experiments on a smooth circularcylinder are plotted in Figure 13 as a function of the reduced velocity. The oscillation amplitude

and Reynolds number were kept constant at respectively 0.5 A/D and Reynolds 40,000. It can be

observed that the lift coefficient peaks at a reduced velocity of 6, with a maximum value of 0.9.

It can also be observed that the added mass coefficient rapidly crosses the Cm = 1 line at thesame peak value. This phenomenon is associated with a distinct transition from one vortex

shedding system to another (i.e. 1p to 2p transition). For our bundle tests we used this transition

to localize the peak lift coefficients from initial tests at a coarse reduced velocity grid.

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Smooth Bare Pipe,

Lift Coefficient and Added Mass with Reduced Velocity

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 2 4 6 8 10 12 14 16

Reduced Velocity, V/fD (-)

LiftCoefficient,CLV

(-)

-1

-0.5

0

0.5

1

1.5

2

2.5

3

AddedMass,

Cm(

-)

A/D 0.5, Re 40000 A/D 0.5, Re 360000 Cm, A/D 0.5, Re 40000 Cm, A/D 0.5, Re 360000

Figure 13: Reduced velocity sweep on smooth pipe

An example of the Reynolds sensitivity for the smooth pipe is presented in Figure 14. Similarlyas for a non-oscillating cylinder, the drag coefficient drops when entering the critical Reynolds

regime. The sensitivity for the amplitude ratio and the reduced velocity can also be observed

from the graph. For the oscillating smooth cylinder we measured drag coefficients between 0.5

and 2.0. The non-oscillating drag coefficient of this cylinder dropped from 1.2 in the sub-criticalregime to 0.3 in the critical regime.

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Smooth Pipe, Drag Coefficient with Reynolds Number

0

0.5

1

1.5

2

2.5

0 50 100 150 200 250 300 350 400

Reynolds Number, Re (x103)

DragCoefficient,Cd(-)

A/D 0.5, Vr 6.0 A/D 0.5, Vr 7.0 A/D 0.5, Vr 8.0 A/D 0.5, Vr 10.0

Figure 14: Reynolds sensitivity for smooth pipe

10. Results bare pipe

Contour plots of the measured lift force coefficient in-phase with the velocity are presented in

Figure 15 and 16. Figure 15 shows our new data for a roughened cylinder at Reynolds 40,000.The other figure was derived from Gopalkrishnan [9] data for a smooth cylinder data at Reynolds

10,000. The figures reveal a complex dependence of the lift coefficient as a function of thereduced velocity and the amplitude. A similarly complex dependency can be observed for the

added mass and the drag coefficient (not presented here). This type of lift coefficient contour

plots forms the bases of the databases in semi-empirical VIV prediction tools.

Both figures show a clear peak of the lift coefficient in the lock-in region for reduced

velocities between 5 and 7 and amplitude of about 0.5 diameter. The highest lift coefficient is

about 1. The Clv = 0 line denotes the boundary between positive and negative energy transfer orpositive and negative damping. Negative damping means excitation by the vortex shedding

process. The highest amplitude crossing from positive to negative lift coefficients occurs at about

one diameter, in agreement with the self-limiting nature of the VIV phenomenon.

Recent results for a smooth and rough cylinder at sub-critical and critical Reynolds numbers

were reported by Ding et. al. [10].

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Figure 15:Lift coefficient in phase with velocity, Contour plot Clv with Ur and A/D

Single rough pipe, Reynolds 40,000, MARIN new test apparatus, 2004

2.9 3.1 3.3 3.6 3.8 4.2 4.5 5.0 5.6 6.3 7.1 8.3 10.0 12.5 16.70

0.2

0.4

0.6

0.8

1

1.2

Reduced velocity Ur [-]

A/D [-]

Lift coefficient in phase with velocity: Clv [-]

-5.7--5.4 -5.4--5.1 -5.1--4.8 -4.8--4.5 -4.5--4.2 -4.2--3.9 -3.9--3.6 -3.6--3.3 -3.3--3.0

-3.0--2.7 -2.7--2.4 -2.4--2.1 -2.1--1.8 -1.8--1.5 -1.5--1.2 -1.2--0.9 -0.9--0.6 -0.6--0.3

-0.3-0.0 0.0-0.3 0.3-0.6 0.6-0.9

Figure 16:Lift coefficient in phase with velocity, Contour plot Clv with Ur and A/D

Smooth circular pipe, Reynolds 10,000, Gopalkrishnan, MIT, 1993

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11. Conclusions and recommendations

A new test apparatus has been developed for measuring the hydrodynamic input coefficients for

calibration of semi-empirical VIV prediction programs such as Shear7 or VIVARRAY. A 3.4 mlong section of the riser or the riser bundle can be tested at full scale dimensions and real current

speeds. The tests at full scale Reynolds numbers reveal new insights in the Reynolds scale effectsand reduce uncertainties in the design process.

Based on the results presented in this paper and recent experience with the new set-up, the

following conclusions and recommendations seem justified:

1. The hydrodynamic input coefficients for calibration of semi-empirical VIV prediction

programs can be tested with the new apparatus, using a 3.4 m long model.

2. The new test apparatus has been successfully calibrated for a smooth and a rough circular

cylinder at Reynolds 40,000. Comparison with existing sub-critical data is good.

3. Distinct scale effects can be observed when comparing results from critical with sub-criticalReynolds experiments. For oscillating circular cylinders this has been reported before, but for

non-circular oscillating cylinders such data is very scarce.

4. An efficient test strategy has been developed for finding the peak lift loads of a riser bundle

geometry. About 50 tests are needed for each flow orientation. A non-circular riser bundle

can be tested for 8 flow angles between 0 and 360 degrees, using steps of 45 degrees. Over400 tests can be conducted in about 2 weeks time.

5. Experiments were carried out with one degree of freedom oscillations in cross flow direction.

It seems worthwhile however, to explore further on two degrees of freedom oscillations withcombined in-line and cross flow motions, including figure-of-eight type motions.

6. Non-circular riser geometries can show a large sensitivity of the mean lift load coefficient for

the flow angle. In those cases it is recommended to check the potential for galloping type

instabilities. The instability criterion0

y Ld

C CC

=

= +

can be used as a first check.

12. Acknowledgement

The authors would like to thank the BP management for their support in development of the new

test set-up and for the permission to publish some of the results presented in this paper.

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13. References

[1] Blevins, R.D., Flow induced vibrations, Krieger publishing company, Malabar, Florida, second

edition, 2001.

[2] Delany, N.K. and Sorensen N.E., Low speed drag of cylinders of various shapes, NACA technical

note 30338, Washington, 1953.

[3] Feng, C.C., The Measurements of Vortex-Induced Effects in Flow Past Stationary and Oscillating

Circular and D-section Cylinders, M.A.Sc. Thesis, University of British Columbia, 1968.

[4] Vandiver, J.K. and Li,. L., Shear7 V4.3 program theoretical manual, MIT, Cambridge, USA, 2003.

[5] Triantafyllou, M.S., VIVARRAY user manual, David Tein Consulting Engineers, Houston, USA, 2003.

[6] de Wilde, J.J. & Huijsmans, R.H.M.,Experiments for High Reynolds Numbers VIV on Risers, ISOPE,

Paper 2001-JSC-285, 2001.

[7] de Wilde, J.J., Huijsmans, R.H.M. & Triantafyllou, M.S.,Experimental Investigation of the Sensitivity

to In-line Motions and Magnus-like Lift Production on Vortex-Induced Vibrations, ISOPE, Paper

2003-JSC-270, 2003.

[8] Gu, G.Z. et. al., Technical feasibility of tubing risers, Offshore Technology Conference, OTC paper

15100, Houston, USA, 2003.

[9] Gopalkrishnan, R., Vortex-Induced Forces on Oscillating Bluff Cylinders, D.Sc. thesis, Department of

Ocean Engineering, MIT, Cambridge, USA, 1993.

[10] Ding, Z.J., et. al., Lift and damping characteristics of bare and straked cylinders at riser scale

Reynolds numbers, Offshore Technology Conference, OTC paper 16341, Houston, USA, 2004.

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