Investigation of Long riser viv.pdf

Paper No. 2004-EF-005 De Wilde 1 of 6

Laboratory Investigation of Long Riser VIV Response

Jaap J. de Wilde and René H.M. HuijsmansMaritime Research Institute Netherlands (MARIN)

Wageningen, The Netherlands

ABSTRACT

In order to address the response of a long cylindrical riser in current,design codes (like Vandiver, 1983) require lift and drag coefficients of2-D sections. Uncoupling the flexible response from the loading thesedesign codes will determine the flexural response based on sectionalstiffness and mass coefficients. However the physics of VIV behaviorindicate that the hydroelastic response is significant. Therefore a studyhas been initiated to research the 3-D response of a part of a long riserin current by experiments.

A circular steel pipe of 16 mm diameter and 12.6 m long was towedhorizontally in a towing tank at speeds between 0.5 and 3.0 m/s andwith pretensions between 0.5 and 2.5 kN. Measurements were made ofthe drag loads, the acceleration and the bending moments. State-of-the-art fibre optical measuring techniques were deployed to obtain detailedinsight into the complex VIV response of the test pipe. The firstanalysis of the test data shows a very complex response, includingstrong coupling between cross flow and in-line motions, beating, multi-mode response, traveling wave response, etc. Further analysis willcontinue and additional results will be published later.

KEY WORDS: Vortex; vibration; VIV; riser; high mode; experi-ments; fibre optics.

INTRODUCTION

One of the great challenges in the offshore industry is still theassessment of the motions of a circular cylinder in waves and currentfor application to risers or riser bundles in water depths up to 3,000 m(approximately 10,000 feet). Here the fatigue life of the riser is oftendominated by Vortex-Induced Vibrations (VIV). Also the importantconcern of riser interference is largely governed by VIV.

There is a great difficulty in predicting the response of a long span ofriser in current. The riser may respond in several possible modes, but itis most often uncertain whether the riser will predominantly respond inone or a few modes or that it will respond in several modessimultaneously (Blevins, 2001; Triantafyllou et al., 1999 and Vandiver,1983 and 1993). The response may also transit from one mode to

another or from one set of modes to another, even in steady uniformcurrent. Non-stationary response may occur as well, including modeswapping or traveling waves. Full scale measurements, model tests andtheoretical considerations indicate that all of these types of behaviorcan occur for deep water risers, especially in sheared current situations.For the riser design and the VIV analysis it is of key importance tounderstand when single mode response dominates or when severalmodes will be excited simultaneously.

High quality experiments showing high mode VIV behavior of longrisers or cables are rare (Hong et al., 2002; Kleiven, 2002 and Larsen,Vandiver, Vikestad, and Lie, 1997), especially at high Reynoldsnumbers (Allen and Henning, 1997; Allen and Henning, 2001 andSimantiras and Willis, 1999). Prototype measurements on real risers arepresently undertaken, but results have not been published yet in openliterature. Such measurements as well as model scale experiments aremuch needed for the better understanding of the high mode responsebehavior and for the validation of semi-empirical VIV prediction tools,as well as the latest developments in CFD. Laboratory experimentsrequire a large test facility to accommodate sufficient riser length, evenfor relatively low Reynolds numbers and relatively small L/D ratios.Moreover a strong and stiff carriage is needed to cope with the largedrag loads and pretensions.

A large amount of instrumentation is required to capture the complexspatial VIV response of a long riser in detail. The pipe motions of everypossible mode need to be measured in at least two degrees of freedom(cross flow and in-line) with sufficient accuracy and at a sufficientsampling rate. Obviously, the instrumentation and cabling should benon-intrusive and preferably be placed inside the tests pipe.

TEST DESCRIPTION

Model Basin

The experiments were conducted in MARIN’s Shallow Water towingtank in Wageningen, The Netherlands. The basin is 15.8 m wide by 220m long and is equipped with an overhead carriage. The water depth inthe basin is 1.15 m. The carriage has a velocity range of 3 m/s and apower supply of 4 x 15 kW. The horizontal test pipe was supported by


TransducerTensioner

Test pipe

Carriage

1.15 m

15.8 m

Water levelRail

TransducerTensioner

Test pipe

Carriage

1.15 m

15.8 m

TransducerTensioner

Test pipe

Carriage

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15.8 m

Water levelRail

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two vertical struts from the carriage. A threaded end was used foradjusting the initial pretension in still water. Some flexibility was builtinto the vertical struts to reduce the increase of the mean tension in thepipe during towing and also to reduce the dynamic variations in pipetension. The maximum measured in-line deflection of the test pipe wasless than 1.0 m or less than 8% of the pipe length.

Fig. 1. Test set-up for towing 12.6 m horizontal pipe (cross section)

Test Pipe and Test Set-Up

The test pipe was a seamless thin walled steel pipe of 16 mm outerdiameter and 0.8 mm wall thickness. Steel end caps were welded oneach end for mounting the pipe between the two vertical struts. Auniversal joint was placed on both ends to obtain a pinned connectionwithout bending moments, adding about 2 x 50 mm to the totaleffective pipe length from joint to joint. The load cells were locatedbetween the universal joints and the struts. The pipe was filled withtank water.

Fig. 2. Test pipe with load cells and universal joint

The properties of the test pipe are summarized in the next table atmodel scale. The pipe surface was reasonably smooth.

Table 1. Properties of test pipe

Parameter Symbol Unit ValueDiameter D mm 16Length L m 12.6Axial stiffness EA N 8.02E6Bending stiffness EI Nm2 232Mass ratio m+ - 2.29

The effective lateral stiffness of the vertical struts was 51 kN/m andacts as axial springs on both ends of the test pipe. The test pipe itselfhad a total axial stiffness of 640 kN/m, which is much higher. Theeffective horizontal and vertical stiffness of the end supports are veryhigh.

Instrumentation and Data Acquisition

The carriage speed was measured by means of an encoder on a fifthwheel on the carriage. The drag loads were measured on both pipe endsby means of strain gauge type load cells. The vertical (lift) loads andthe axial loads were measured in the same way. The instrumentationwas calibrated and checked for linearity prior to the testing.

Small two-component accelerometers were mounted inside the pipe attwo location, respectively at 6.04 m and 9.32 m from the right end ofpipe, excluding the 50 mm of the universal joint. Special steel houseswere manufactured for each location, in which two accelerometers (xand z) could be firmly mounted. The pipe was cut at the two locationsand the steel houses were welded in between. The steel houses werekept small as possible to minimize the influence on the pipe properties.However, in future correlation studies it might still be necessary to takethe locally different mass and bending stiffness properties into account.The electrical cables of the accelerometers were fed through the pipe.All signals were sampled at 250 Hz.

Fibre Optic Measuring Technique

The right-hand side of the test pipe was instrumented with 40 opticalfibre strain gauges. Four fibres of approximately 0.3 mm diameter weremounted in small axial grooves in the pipe surface, at 90 degrees angle:top, bottom, fore and aft. The small grooves were carefully machined inthe pipe surface and filled with resin after the fibres had been placedinside, to keep a smooth pipe surface. A total of 10 Fibre BraggGratings (FBG) were burned in each fibre, using a spatially varyingpattern of intense UV light. A specialized company in UK wasresponsible for the preparation of the optical fibres and the mounting inthe pipe surface. The FGB strain gauges were located at 0.375, 0.750,1.125, 1.500, 1.875, 2.250, 2.625, 3.000, 3.750 and 4.500 m from theright end of the test pipe, excluding the 50 mm of half a universal joint.

Fig. 3. Instrumentation of test pipe with 40 FGB strain gauges

Each Bragg grating serves as a wavelength selective mirror, whichreflects light with a wavelength corresponding to the so-called Braggwavelength �B (Doyle, 2003). The rest of the light propagates down thefibre uninterrupted. Physical or mechanical properties such astemperature or stress may affect the reflected wavelength, which in ourcase was deployed to construct an optical strain gauge. Because of thevery constant temperature of the water in the basin (less than 1 degreeCelsius variation), the temperature effect could be disregarded and themeasured shift in wavelength was as a direct measure of the localstrain.


Drag load

0.0000

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Cd [-

]

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Bragg grating burned in coreof optical fibre

cladding

0.3

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Bragg grating burned in coreof optical fibre

cladding

Fig. 4. Schematic drawing of Bragg grating in optical fibre

A W3/4250 FBG unit was used for the interrogation of the 40 opticalstrain gauges. The sampling rate was 250 Hz. The unit illuminates thefour fibres with a swept-wavelength light source and measures thereflected light by means of a photodiode detector. Wavelength-divisionmultiplexing (WDM) is used to address the different sensors in eachline.

TEST RESULTS AND DISCUSSION

Theoretical VIV Response of Tensioned Beam

The natural frequencies of a tensioned beam are given by the followingrelation (Timoshenko, Young and Weaver, 1974):

( )2

4 2 22 4

12n

a

L T EIf n nEI m m L

ππ π

= ++

(1)

The mode number (n) represents the number of half waves in theresponse shape. The other parameters are the pipe length (L), the axialtension (T), the bending stiffness (EI), the mass per unit length (m) andthe added mass (ma). Our test pipe of 16 mm diameter had a mass in airof 0.461 kg and an added mass of 0.201 kg per unit length (assumingCm = 1 in still water). The natural frequencies of the first 12 modes at1.0 kN pretension are given in Table 2. The vortex shedding frequencyat 1.0 m/s current speed is 12.5 Hz, assuming a Strouhal number of 0.2.Lock-in VIV response can therefore be expected for mode 6 or 7 at thisspeed.

Table 2. Natural frequencies of test pipe in still water at 1.0 kNpretension

Mode Frequency Mode Frequency123456

1.55 Hz3.17 Hz4.92 Hz6.85 Hz9.00 Hz

11.41 Hz

789

101112

14.11 Hz17.12 Hz20.45 Hz24.11 Hz28.12 Hz32.48 Hz

The mode shape of an oscillating uniform beam can be represented by asinusoid:

nn yA sin

Lπφ � �= � �

� �(2)

in which y is the co-ordinate along the cylinder length and A theamplitude of the oscillation. The bending moment is proportional to thecurvature and can be found by double differentiation of the shape:

2 2 2

2 2n A n n yM EI sin

Ly Lφ π π∂ � �= − = � �

� �∂(3)

The bending moment is also proportional the difference in strain on twoopposing sides of the circular test pipe. In our case the measureddifferences in strain "Top - Bottom" and "Fore - Aft" were regarded asa measure of respectively the cross-flow and in-line curvature at eachlocation. Using of a Taylor series expansion the displacement at aposition y can be expressed by:

221

0 0 02 2z zz( y ) z( y ) ( y y ) ( y y ) ...y y

∂ ∂= + − + − +∂ ∂

(4)

This relation shows how the displacements can be derived from themeasured curvatures. This step, involving an inverse matrix operationfor each time step, has not been carried out yet.

Drag Loads

In Fig. 5 the drag coefficient of the vibrating cylinder is plotted as afunction of the tow speed. The mean tension in the experimentsincreased with the tow speed from 0.45 kN in still water to 2.5 kN atthe maximum tow speed of 3.0 m/s. The Reynolds numbers are all inthe sub-critical regime (7,000 < Re < 43,000).

Fig. 5. Measured drag coefficient as a function of the tow speed

The vibrations of the cylinder lead to higher drag loads than for thesame cylinder kept stationary at the same speed, which is known as“drag amplification”. The drag amplification factor in our tests is about2 at small speeds and decreases for increasing speeds. At 3.0 m/s thedrag coefficient of about 1.37, which is only slightly above the normaldrag coefficient for a stationary smooth cylinder of Cd = 1.2. It shouldbe noted that no corrections were made for the end effects and the dragon the universal joints.


Flow+x

+z

Flow+x

+z

AX1

9.8 Hz

AX1

9.8 Hz

AZ1

9.8 Hz

19.6 Hz

AZ1

9.8 Hz

19.6 Hz

Motion Response

Time traces of the measured motions at the pipe mid are presented inFig. 6. These motions were derived by double integration of themeasured accelerations. The tow speed was 1.0 m/s and the meantension 0.9 kN.

Fig. 6. Time traces of measured motions at pipe mid

The amplitude ratios are respectively A/D = 0.35 for the cross flowoscillations and A/D = 0.64 for the in-line oscillations. A trajectory plotof the cross flow versus in-line motions is presented in Fig. 7.

Fig. 7. Trajectory plot of cross flow vs. in-line motions at pipe mid

A "lying banana" type motion is observed. In general "figures of eight"or "standing bananas" type trajectory plots are expected for the vortex-induced vibrations of a circular pipe. Our unexpected result deservesfurther investigation. Possibly the dynamic tension in our experimentwas higher than for most real marine risers. The trajectory plots of thecurvature, presented at the end of this paper, show unexpected complexresponses at the different locations of the pipe as well.

Spectral density plots of the measured accelerations are presented inFig. 8. Response peaks can be observed at 9.8 and 19.6 Hz, corre-sponding to Strouhal numbers of respectively 0.16 and 0.31. The higherfrequency is twice the lower frequency. It is assumed that thesefrequencies are related respectively to the cross-flow excitation (twoopposing cross flow vortices per cycle) and the in-line excitation (twoin-line vortices per cycle). The theoretical calculated natural frequen-cies of mode 5 and 6 are close to the lower frequency peak in thespectral density plot. It should, however, be noted that the naturalfrequencies of lock-in VIV can significantly deviate from thetheoretical values, due to the large variability of the added mass.

Fig. 8. Spectral density plot of measured accelerations at pipe mid

The unexpected response will be further investigated after submissionof this paper. The following comments seem appropriate at this stagehowever:

- The sign convention of the signals in Figs. 6, 7 and 8 has beencarefully checked and no error was found. The cabling of theaccelerometers was checked prior to the test, by rotating the pipe instill water and measuring the gravity component.

- The stiffness of the vertical struts is 51 kN/m at each side, which ismuch lower than the axial stiffness of the steel pipe itself (640kN/m), but may still be high enough to induce significant dynamictension in the pipe for the higher response modes and responseamplitudes. The measured dynamic tension in the presented test101008 was approximately 10% of the mean tension. The meantension provided the main restoring mechanism. The contributionof the bending stiffness was relatively small.

- Dynamic end effect, complex non-linear response or strongcoupling between cross-flow and in-line motions may also beresponsible for the unexpected results. It seems worthwhile tocheck for possible Mathieu instabilities (Hagedorn, 1988).

The dynamic tension is not normally considered in the responseanalysis of marine risers. Calculations are often based on the linearizedbeam equation:

2 2 2

2 2 2

� �∂ ∂ ∂ ∂ ∂ ∂� �+ + − =� �� ∂ ∂ ∂� �∂ ∂ ∂� ��

y y y ym b T EI L( x,t )t x xt x x

(5)

Finally it should be noted that the scaling of our experiment toprototype dimensions is not straightforward. Froude scaling is not theobvious choice, because gravity is not an important parameter in theexperiment. Instead it is proposed to scale as follows:

- geometrical scale: �:1 (e.g. 50:1)- velocity scale: 1:1- tension: �

2:1 (e.g. 2500:1)


14

103 2 1

410

3 2

Trajectory Plots of Curvature Derived from FBGMeasurements

Trajectory plots of the measured curvature are presented in Fig. 10. Thecurvature in z direction is plotted against the curvature in x direction.The 10 plots correspond to the 10 FBG strain gauge locations along thepipe, as shown in Fig. 9. Presented is about 2 seconds of the test.

Fig. 9. Locations of curvature trajectory plots

The response was very different at each of the 10 locations, which wasalso expected for the long pipe. Not expected, however, was thecomplex shape of the trajectories. Similarly as for the motions in Fig. 7,the curvature response does not resemble much of a "figure of eight".However some cyclic repetition can still be recognized in plots.Plotting the same graphs for a shorter duration shows thatapproximately the same path is followed every cycle, where each cycleconsists of a number of distinct lobes. Swapping from one type ofmotion to another does not occur in the presented part of the test.

Because the curvature is presented and not the actual displacements theresults cannot be compared directly with "figure of eight" type plots.However, the plots in Fig. 10 still show how complex the VIV responseof the long riser can be, even in uniform current. Further analysis isneeded to get more insight in this complex behavior. One of the futureaims is to learn more about the mode participation and to compare ourmeasurements with the results of VIV prediction tools. The analysistechniques described by Kleiven (2002) for identifying the VIV vibrationmodes by use of the Empirical Orthogonal Functions technique will beused.

CONCLUSIONS

The vortex-induced vibrations of a horizontal cylindrical pipe in a crossflow situation were investigated at small scale in a tow tank for a rangeof tow speeds and pretensions. The slender test pipe with a length overdiameter ratio of 788 exhibited VIV response with a high modalcontent. Conventional accelerometers and state-of-the-art optical fibrestain gauges were successfully deployed for capturing the complexresponse behavior.

Based on the preliminary results presented in this paper, it can beconcluded that the vibrational response of the long pipe is much morecomplex than expected. Single mode response with a stable sinusoidalmode shape was not observed, at least not for the tests with the highertow speeds. For presented test in this paper (1.0 m/s and 0.9 kN) it isassumed that mode 5 or 6 was dominant, but also much higher modesand double frequency modes (mode 11 or 12) participated.

The observed "lying banana" trajectory at the pipe mid is intriguing anddeserves further investigation. In general "figures of eight" or "standingbananas" type trajectory plots are found for the vortex-inducedvibrations of a circular pipe. Possibly the relatively high dynamictension plays a role in our experiments.

Further analyses will be carried out to derive the motion response fromthe measured curvature at the 10 locations of the optical strain gaugemeasurements. Next it will be attempted to identify the VIV vibrationmodes from the experiments. Finally it seems worthwhile to validatesemi-empirical VIV prediction programs against our test results.

REFERENCES

Allen, DW and Henning, DL (1997). “Vortex-Induced Vibration Testsof a Flexible Smooth Cylinder at Supercritical Reynolds Numbers,”Proceedings of the International Offshore and Polar EngineeringConference, Honolulu, USA.

Allen, DW and Henning, DL (2001). “Prototype Vortex-InducedVibration Tests for Production Risers,” Offshore TechnologyConference, Paper OTC 13144, Houston, USA.

Blevins, RD (2001). “Flow Induced Vibrations,” Second Edition,Krieger Publishing Company, Malabar, Florida.

Brida, D and Laneville, A (1993). “Vortex-Induced Vibrations of aLong Flexible Cylinder,” Journal of Fluid Mechanics, Vol 250, pp481-508.

Doyle, C (2003). “An Introduction to Bragg Gratings and InterrogationTechniques,” Smart Fibres.

Hagedorn, P (1988). “Non-linear Oscillations”, Clarendon Press,Oxford.

Hong, S, Choi, YR, Park, JB, Park, YK and Kim, YH (2002).“Experimental Study on Vortex-Induced Vibration of Towed Pipes,”Journal of Sound and Vibration, Vol 249, pp 649-661.

Kleiven, G. (2002). “Identifying VIV Vibration Modes by Use of theEmpirical Orthogonal Functions Technique,” OMAE2002-28425.

Larsen, CM, Vandiver, JK, Vikestad, K and Lie, H (1997). “VortexInduced Vibrations of Long Marine Risers - Experimental Investi-gations of Multi-Frequency Response,” BOSS, pp 455-468.

Marcollo, H and Hinwood, J (2002). “Mode Competition in a FlexibleCylindrical Riser,” International Mechanical Engineering Congressand Exposition.

Simantiras, P and Willis, N (1999). “Investigation on Vortex InducedOscillations and Helical Strakes Effectiveness at Very HighIncidence Angles,” Proceedings of the International Offshore andPolar Engineering Conference, Brest, France.

Timoshenko, S, Young, DH and Weaver, W (1974). “VibrationProblems in Engineering,” Fourth Edition, John Wiley & Sons.

Triantafyllou, MS, Triantafyllou, GS, Tein, D and Ambrose, BD(1999). “Pragmatic Riser VIV Analysis,” Offshore TechnologyConference, Paper OTC 10931, Houston, USA.

Vandiver, JK (1983). “Drag Coefficients of Long Flexible Cylinders,”Offshore Technology Conference, Paper OTC 4490, Houston, USA.

Vandiver, JK (1993). “Dimensionless Parameters Important to thePrediction of Vortex-Induced Vibration of Long Flexible Cylindersin Ocean Currents,” Journal of Fluids and Structures, Vol 7, pp 423-455.

Willden, R and Graham, G (2002). “Multi-Modal Vortex-InducedVibrations of a Vertical Riser Pipe Subject to a Uniform CurrentProfile,” Conference of Bluff Body Wakes and Vortex-InducedVibrations BBVIV3, pp 229-232.


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Fig. 10. Curvature trajectory plots derived from FBG strain gauges

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Investigation of Long riser viv.pdf