Useful Papers

1. CORNUT, Stephane F.A. and VANDIVER, J. Kim.
“Offshore VIV Monitoring at Schiehallion – Analysis of Riser VIV Response”
Proceedings of ETCE/OMAE 2000 Joint Conference: Energy for the New Millennium, New Orleans, LA, February 14-17, 2000.

During November and December 96, a drilling riser in the Schiehallion field (West of Shetlands in 360m of water) was instrumented with accelerometers to record its Vortex-Induced Vibration (VIV) response in current. A paper has already been presented on the data gathering campaign (Hassanein, 1998). The present paper concentrates on the analysis of selected samples of the recording. This emphasis of the paper is twofold. The first is the investigation of the relationship between the shear of the velocity profile and the probability of single mode dominated response. The second is the determination of the reduced velocity bandwidth, _Vr, associated with the fluid excitation of the riser. Little is known about these quantities in the high Reynolds regimes found offshore. The first direct application of this work will be to better calibrate and further develop VIV prediction programs. The results presented in this paper come from 83 samples of 28 minute long records. The raw accelerations were interpreted in terms of modal displacements (the normal modes were found from FE analysis). The current profile data are from acoustic Doppler current profile (ADCP) records that covered all but the top 60m of the water column.

2. FEI Chen-Yang and VANDIVER, J. Kim.
“A Gaussian Model for Predicting the Effect of Unsteady Windspeed on the Vortex-induced Vibration Response of Structural Members”
Proceedings of the 14th International Conference on Offshore Mechanics and Arctic Engineering, ASME, 1995.

In a previous study, the authors have shown that the expected duration of visit by the windspeed to the critical velocity interval of a structural member is an important time scale in determining the ultimate fatigue damage of the member due to vortex-induced vibration in naturally time varying winds. In this paper, a Gaussian windspeed assumption is introduced in which the expected duration of visit can be explicitly in terms of simple wind statistics. This assumption is verified with high sampling rate maritime wind data. The wind statistics necessary for calculation of the expected duration of visit are extracted from the raw wind data.

3. JONG, Jen-Yi and VANDIVER J. Kim
“Response Analysis of the Flow-Induced Vibration of Flexible Cylinders Tested at Castine, Maine in July and August of 1981”
MIT Ocean Engineering Research Report, January, 1983.

A cable strumming experiment was conducted at Castine, Maine in July and August of 1981. 75-foot long section of a 1.25-inch diameter cable, and a 1.631-inch diameter pipe were subjected to vortex induced vibration. Seven biaxial pairsof accelerometers were placed at different locations along the cable, and the pipe. Acceleration at these seven positions as well tension, tidal current velocity and drag force were simultaneously recorded. Current velocities ranged from 0 to 2.4 feet/second. A numerical double integration technique is presented in detail and used to obtain the transverse and in-line displacements. Modal identification is used to evaluate the motion in terms of the individual natural modal coordinates of the cable. Lockin and non-lockin examples are presented. Cross flow amplitudes are typically twice that of the in-line vibration. In-line response frequencies are typically twice that of the cross flow.

4. KAASEN, Karl E., LIE, Halvor, SOLAAS, Froydis, and VANDIVER, J. Kim.
“Analysis of Vortex-Induced Vibrations of Marine Risers Based on Full-Scale Measurements”
Offshore Technology Conference, Houston, Texas, May 1-4, 2000.

As a part of the Norwegian Deepwater Program (NDP) three drilling risers have been instrumented with accelerometers and rotation-rate meters for measurement of vortex-induced vibrations (VIV). In addition, current was measured at number of depths. The paper describes how the riser displacements were derived from the measurements and compared with the current. A major task has been to rid the acceleration measurements of the influence of gravity due to the riser’s rotations out of the vertical and include the measurements of angular motion in a consistent way. This has been done using modal decomposition and a least-squares method to estimate the modal weights. The main purpose of the work was to provide data for calibration of computer programs for prediction of VIV. Examples of results are given.

5. KIM, Y. H., VANDIVER, J. Kim, and HOLLER, R.
“Vortex-Induced Vibration and Drag Coefficients of Long Cables Subjected to Sheared Flows”
Proceedings of the Fourth International Offshore Mechanics and Arctic Engineering Symposium – Volume 1. Editor: Jin S. Chung. Book No. 10185A, 1985.

The vortex induced vibration response of long cables subjected to vertically sheared flow was investigated in two field experiments. In typical experiment, a weight was hung over the side of the research vessel by a cable which was instrumented with accelerometers. A typical experiment measured the acceleration response of the cable, the current profile, the tension and angle of inclination at the top of the cable. The total drag force was computed from the tension and angle measurements. Two braided Kevlar cables were tested at various lengths from 100 feet to 9050 feet. As a result of these experiments, several important conclusions can be drawn: (1) The wave propagation along the length of the cable was damped, and therefore, under most conditions the cable behaved like an infinite string; (2) Response spectra were quite broad-band, with centre frequencies determined by the flow speed in the region of the accelerometer; (3) Single mode lockin was not observed for long cables in sheared current profile; (4) The average drag coefficient of long cables subjected to sheared flow was considerably lower than observed on short cables in uniform flow; (5) the r.m.s. response was higher in regions of higher current speed. A new dimensionless parameter is proposed which incorporates the properties of the cable as well as the sheared flow. This parameter is useful in establishing the likelihood that locin may occur, as well as in estimating the number of modes likely to respond.

“Vortex-Induced Vibration Parameters: Critical Review”
ASME Offshore Technology Conference, Parts 1 and 2, 1994.

This paper presents the results of a research study to develop an empirical basis for modeling hydrodynamic vortex-induced vibrations in marine risers, tethers and other slender marine structures. Published model tests were reviewed, evaluated, including more than 150 model tests compiled to provide extensive insight and understanding of the hydrodynamic VIV parameters. The data could provide values for the VIV parameters used in a VIV analysis model. The most important VIV parameters are: the lift coefficient, the shedding frequency (Strouhal number), the correlation length, and the shedding frequency bandwidth. The empirical data are based on steady flow model tests that are applicable to long, flexible cylinders in simulating marine risers undergoing large amplitude vibrations of the order of up to one riser diameter. The empirical data account for the lock-in phenomenon that is the most important consideration to predict accurately VIV extreme response. Conclusions and recommendations are included to develop am empirical methodology that captures the hydrodynamic VIV phenomena. These recommendations provide the basis for the development of a VIV prediction model that is a significant extension from previous models in literature, because it can predict lock-in behavior of a flexible cylinder in shear flow.

7. VANDIVER, J. Kim and ROVERI, Francisco E.
“Slenderex: Using SHEAR7 for Assessment of Fatigue Damage Caused by Current Induced Vibrations”
Proceedings of OMAE 2001, 20th International Conference on Offshore Mechanics and Arctic Engineering, June 3-8, 2001, Rio de Janeiro, Brazil.

This paper focuses on the evaluation of the fatigue damage caused by current induced vibrations on the SlenderEx system. SlenderEx is a low cost drilling system being evaluated by Petrobras for fast appraisal of exploratory wells. SHEAR7 is the well-known computer program developed by MIT for assessment of fatigue damage on slender offshore structures (such as cables and risers) caused by vortes induced vibrations (VIV) originated from sheared currents. The SlenderEx system consists of a 13-3/8 inch 72 lb/ft casing connecting the mud line to a semi-submersible platform and is planned for drilling exploratory wells in water depths up to 1800 meters. At the lower end the casing penetrates some 400 meters into the soil and the upper termination is a stress joint located under the surface BOP which is guided by conventional tensioning system. Fatigue damage is firstly evaluated for a set of variables defined as the Base Case. After that a parametric study is conducted for the determination of the influence of main parameters on response. This study is warranted by the uncertainties about input parameters. The investigation consists of a parametric variation of current velocity, riser tension, lock-in bandwidth, single/multi-mode response, and stress concentration factors. A total of 88 current profiles and the corresponding probabilities of occurrence are considered in the analysis. Some of the current profiles are originally non-planar. The current velocities have then to be projected onto a plane for being analyzed with SHEAR7. The differences arising from this limitation are also evaluated.

8. VANDIVER, J. Kim and CHUNG, Tae-Young.
“Predicted and Measured Response of Flexible Cylinders in Sheared Flow”
Proceedings, ASME Winter Annual Meeting Symposium on Flow-Induced Vibration, Chicago, December 1988.

Results are presented from a flow-induced vibration experiment conducted in a sheared current. The site was an historic 1848 mill canal with a width of 58 feet. Variable headgates allowed a controllable horizontal shear to be produced. An instrumented cable 1.125 inches in diameter was deployed horizontally in flow. Response was measured for a variety of cable tensions and sheared flow profiles. A method of predicting the response of cables in sheared flow is introduced, which includes the effect of correlation length, hydrodynamic damping, lift coefficient with higher order harmonics and turbulence. Comparisons are made between predicted and measured response. The response is shown to contain significant amount of vibration up to fifth harmonic of the vortex shedding frequency. Hydrodynamic modal damping is shown to have a dramatic effect on the response, and to decrease with increasing frequency of vibration.

9. VANDIVER, J. Kim and JONG, J.-Y.
“The Relationship Between In-Line and Cross-Flow Vortex-Induced Vibration of Cylinders”
Journal of Fuids and Structures, 1, pp. 381-399, 1987.

Cable strumming experiments were conducted at Castine, Maine in 1981 and from an icebreaker in 1983. the purpose was to study the vibration characteristics of long flexible cylinders subjected to vortex-induced oscillation. Particular emphasis was placed on the investigation of the relationship between in-line and cross flow vibration. Under non-lock-in, random vibration conditions, linear spectral analysis indicated that in-line and cross-flow response were linearly independent of each other, while the results of modal analysis showed that the moving average vibration energies in these two directions were strongly related. A higher order spectral analysis was performed to demonstrate a non-linear correlation between in-line and cross-flow vibration of flexible cylinders excited by vortex shedding in both uniform and sheared flow conditions. The results of bispectral analysis demonstrated the existence of a quadratic relationship between in-line and cross-flow motion under both lock-in and non-lock-in conditions. The well-known frequency doubling phenomenon in in-line response was proven to be a result of such quadratic correlation.

10. VANDIVER, J. Kim and MAZEL, Charles H.
“A Field Study of Vortex-Excited Vibrations of Marine Cables”
Offshore Technology Conference, Paper OTC 2491, Dallas, Texas, 1976.

A variety of cables were studied under controlled conditions in the ocean. Sections of cable, 76.5 ft in length, were exposed to a spatially uniform, time-varying current. Vibration response, current velocity, and tension were simultaneously recorded. Care was taken to minimize complicating influences, such as lumped masses and nonuniform tensions. The data revealed strong interaction between the vortex shedding process and the natural frequencies of each cable. Under lock-in conditions the spanwise vibration mode shape corresponded correctly with the “lock-in” natural frequency. A cable with an antistrumming fairing was tested simultaneously with an unfaired length of the same cable; the vibration frequencies and amplitudes are compared.

11. VANDIVER, J. Kim.
“Dimensionless Parameters Important to the Prediction of Vortex-Induced Vibration of Long, Flexible Cylinders in Ocean Currents”
Journal of Fluids and Structures, 7, pp. 423-455, 1993.

Case studies drawn from 17 years of field and laboratory experiments are used to demonstrate and explain why the flow-induced vibration of long cylinders in ocean current varies from single mode lock-in to broad-band random vibration. It is shown that, with a careful consideration pf a few dimensionless parameters, the range of observed behavior is predictable. New interpretations are given to the significance of familiar parameters such as mass ratio and reduced damping. In addition, the fractional variations in flow velocity over the length of the cylinder and the number of natural frequencies within the bandwidth of vortex-shedding frequencies are shown to be of considerable importance. When consideration of the above parameters reveals that multiple mode response without lock-in is likely to occur, then hydrodynamic damping is revealed to have a powerful influence on dynamic response, and the simple product of the total damping ratio and the mode number slows one to anticipate the whole range of response behavior, from the wave propagation properties of infinite length cables to the standing wave features of short cylinders.

12. VANDIVER, J. Kim, FEI, Chen-Yang, CAMPBELL, R. Brad, and RUDGE, Daniel.
“A Procedure for Predicting the Fatigue Damage of Structural Members in Unsteady Winds”
Offshore Technology Conference, Paper No. 8081, Houston, Texas, May 6-9, 1996.

The practice of assuming full, steady state, vortex-induced-vibration response to wind is excessively conservative. This paper presents a practical method for estimating the reduction of fatigue damage rate due to the natural unsteady fluctuations in wind speed. Two dimensionless parameters are shown to be particularly important. The first is the ratio of the lock-in bandwidth to the turbulence intensity level of the wind. The second is the ratio of the length of time the wind remains in the lock-in interval to the rise time of the member to steady state response levels. The paper also shows that one must account for the discrete nature of wind aped and direction scatter diagrams in estimating the probability of occurrence of the critical wind speed.

13. VANDIVER, J. Kim, ALLEN, D. and LI, Li.
“The Occurrence of Lock-In Under Highly Sheared Conditions”
Journal of Fluids and Structures, 10, pp. 555-561, 1996.

Experimental results are presented which show that two dimensionless parameters may be used to predict the likelihood of lock-in under sheared flow conditions. One parameter is Ns, the number of potentially excited modes within the vortex-shedding frequency bandwidth generated by sheared flow. The second, ?V/Vavr, called the shear parameter in this paper, is the ratio of change in velocity of the flow over the length of the cylinder to the spatially averaged flow velocity over the length of the cylinder. Unexpected results are shown which reveal that lock-in may occur under highly sheared conditions. The probable cause of the lock-in is that, under highly sheared conditions, the power available to one particular mode may dominate all other modes. This condition is less likely to develop in flows with lower velocity gradients.

14. VANDIVER, J. Kim.
“Drag Coefficients of Long Flexible Cylinders”
Offshore Technology Conference, Paper No. 4490, Houston, Texas, May 2-5, 1983.

In the summer of 1981 a field experiment was conducted investigating the vibration response of long flexible cylinders to vortex shedding in a steady, uniform current. Two basic cylinder types were tested, both 75 feet in length. One cylinder was a cable 1.25 inches in diameter with seven pairs of internal biaxial accelerometers. The second cylinder was a steel pipe, 1.631 inches in diameter, carrying a cable inside. Drag force, current speed, tension and biaxial acceleration at seven locations were measured. Drag coefficients in excess of 3.0 were measured for both the pipe and the cable under lockin conditions.

15. VANDIVER, J. Kim.
“Predicting Lock-in on Drilling Risers in Sheared Flows”
Proceedings of the Flow-Induced Vibration 2000 Conference, June 18-22, 2000, Lucerne, Switzerland.

The kurtosis statistic is introduced as a sensitive tool for efficient preliminary analysis of flow induced vibration response data. The kurtosis of sequential blocks of time series data allows one to distinguish single mode lock-in events. The problem of predicting lock-in is then discussed. Instructional examples are introduced to illustrate the relative importance of flow-speed, power-in length and diameter, when attempting to predict single frequency dominance. When VIV from two different flow speed regions compete, it is shown that the ratio of the flow speeds cubed is an important indicator, as is the ratio of the square of the length of the power-in regions. Two example cases from measured response on a drilling riser in the North Sea are presented. SHEAR7 predictions are compared to measured results.

16. VANDIVER, J. Kim.
“Research Challenges in the Vortex-Induced Vibration Prediction of Marine Risers”
Offshore Technology Conference, Paper No. OTC 8698, Houston, Texas, May 4-7, 1998.

Current research in the prediction of vortex-induced vibration of marine risers is driven by problems in several areas. These include understanding the physics of the fluid-structure interaction, developing adequate structural dynamic modeling tools, acquiring high quality full-scale response data, finding appropriate techniques for analysis of response data, calibrating response prediction programs, and inventing cost effective suppression and protection methodologies. Problems in each of these areas are defined and key limiting issues are described.

17. VANDIVER, J. Kim.
“The Prediction of Lockin Vibration on Flexible Cylinders in a Sheared Flow”
Offshore Technology Conference, Paper No. 5006, Houston, Texas, May 6-8, 1985.

A method is proposed for the prediction of the flow induced vibration response of flexible cylinders such as cables, pipes and risers in a sheared flow. The significance of material damping is discussed. The reduced damping or response parameter plays a key role in response prediction. However, the dependence of the response parameter and therefore the response amplitude on the ratio of cylinder mass per unit length to the displaced fluid mass per unit length is shown to be widely misunderstood. Under lockin conditions, damping is important in determining the response amplitude, but cylinder mass per unit length is not.

18. VANDIVER, J. Kim,
“A New Interpretation of the Response Parameter Sg
MIT Paper, October 30, 2000.

One of the key problems in VIV response prediction in sheared flow has been the prediction of single-mode dominance in sheared flows in spite of many competing modes. This challenge has stimulated a new look into the meaning of the dimensionless parameter, which is known variously as the “response parameter”, the “reduced damping” or the Scruton number” It is known to be a rough predictor of response amplitude A/D. The various forms have small differences and there has been some debate over the years as to which is correct. Most of the controversy centers on the definitions of mass ratio and damping ratio. Our recent studies have shed some new light on this.

19. VANDIVER, J. Kim ,VIKESTAD, Kyrre and LARSEN, Carl M..
“Experimental Study of Excited Circular Cylinder in Current”
OMAE 1997.

This paper presents results from experiments with an elastically supported cylinder subjected to support motions and fluid flow. We varied the support motion amplitude, frequency and flow velocity. We show how this external disturbance influences the vortex shedding frequency, cylinder oscillation amplitude at the vortex shedding frequency and at the support oscillation frequency. Energy dissipation from the cylinder into the fluid is given in terms of the transverse drag coefficient Cd. Results show that the external disturbance has limited influence on the vortex shedding frequency, except for the case where the vortex shedding frequency coincide with the support frequency. Response from support motion tends to be more damped in fluid flow than in still water. Response at the vortex shedding frequency is reduced by the external disturbance, if the disturbance frequency is different from the vortex shedding response frequency.

20. VIKESTAD, Kyrre, LARSEN, Carl M. and VANDIVER, J. Kim.
“Damping of Vortex-Induced Vibrations”
Offshore Technology Conference, Paper No. OTC 11998, Houston, Texas, May 1-4, 2000.

Vortex-induced vibration (VIV) of a long riser in sheared current is often considered as an energy balance problem: Excitation forces in the power-in region add an equal amount of energy to the system as is dissipated by damping forces outside this region and structural damping. A riser may have different excitation and damping regions depending on the actual oscillation frequency, cross-section properties and local flow velocity. A damping model must hence be able to handle higher and lower flow velocities than the excitation velocity range. In this paper the fluid damping models proposed by Venugopal are compared with the experiments conducted by Gopalkrishnan and Vikestad. The results show that the models are conservative at high and low reduced velocities.

21. MELING Trond Stokka, JOHANNESSEN Kenneth and NYGAARD Einar
“An Assessment Of EOF Current Scatter Diagrams With Respect To Riser VIV Fatigue Damage”
OMAE 2002 - 28062

The accuracy of the current modelling is critical when considering deepwater riser fatigue damage caused by vortex induced vibrations (VIV). In the present study the use of empirical orthogonal functions (EOF) to simplify huge amounts of current measurements has been assessed. The amplitudes of the time varying principal components (PC) have been organized into bins in scatter diagram. The accuracy of this scatter diagram approach with different numbers of EOF modes involved has been evaluated in terms of riser VIV fatigue damage.

22. LARSEN Carl M. , KOUSHAN Kamran and PASSANO Elizabeth.
“Frequency And Time Domain Analysis Of Vortex Induced Vibrations For Free Span Pipelines”
OMAE 2002 – 28064

The present paper will discuss various models for calculation of vortex induced vibrations (VIV) of free span pipelines, and present a new strategy for such analyses. Applications of traditional models are presented and their limitations discussed. The new approach is based on the combination of an empirical linear frequency domain model, and a non-linear time domain structural model. The first step is to carry out the VIV analysis according to linear response theory, and next introduce the calculated hydrodynamic forces to the non-linear structural model. The benefit from using the non-linear model is to describe stresses at the shoulders more accurately, which is important since fatigue damage in many cases will be largest in this area. The conclusion is that the interaction between pipe and seafloor is crucial for accurate stress prediction, and that a non-linear time domain model will give the most accurate result.

23. NIELSEN GunnarFinn, SOREIDE Tore H and KVARME Stig Olav.:
“VIV Response Of Long Free Spanning Pipelines”
OMAE 2002-28075.

Vortex induced vibration (VIV) of free spanning pipelines in current is considered. In standard VIV estimation, one mode of oscillation is considered only. Increasing the length of the span, several modal shapes may be excited. Further, due to the sag effect of a long free span, the dynamic properties in vertical and horizontal direction of the span are different. This causes a much more complex VIV response pattern for long free spans than for short spans. The observed VIV response of long free spans during model testing is discussed. Hypotheses that may explain the observed behaviour are presented. Also a format of new design principles for long free spans is outlined.

24. VANDIVER J. Kim and MARCOLLO Hayden.
“High Mode Number VIV Experiments”
IUTAM Symposium On Integrated Modeling of Fully Coupled Fluid-Structure Interactions Using Analysis, Computations, and Experiments, 1 June-6 June , 2003.

A simple equation is presented which provides the maximum achievable mode number for a flexible cylinder, towed by the top end with a weight at the bottom end. The maximum achievable mode number, while towing in still water, is shown to depend primarily on mass ratio, length to diameter ratio and the maximum allowable angle of departure from vertical at the top end. Modal overlap in lock-in regions is shown to depend strongly on mass ratio in uniform flow, but not in sheared flow. The reduced velocity bandwidth parameter is introduced to quantify the extent of lock-in regions in sheared flow. Two shear parameters are shown to be useful in characterizing low and very high mode number response. Finite length lock-in regions are described for cylinders with infinite length dynamic properties.

25. VANDIVER J. Kim.
“A Universal Reduced Damping Parameter For Prediction Of Vortex-Induced Vibration”
OMAE 2002-28292

A dimensionless parameter, Su, is proposed which enables a clear presentation of vortex-induced vibration response data in sheared and uniform flows. The ability of the parameter to account for the effects of damping, flow velocity and power-in length is demonstrated with response data from an unusual set of experiments conducted by SHELL Development Co. The historical relationship of the new parameter to the earlier work of Owen Griffin is also presented. Key words: Vortex-induced vibration, reduced damping.

26. LIAO Jung-Chi.
“Vortex-induced Vibration of Slender Structures in Unsteady Flow”
PhD Thesis- MIT February 2002

Vortex-induced vibration (VIV) results in fatigue damage of offshore oil exploration and production structures. In recent years, the offshore industry has begun to employ curved slender structures such as steel catenary risers in deep-water offshore oil systems. The top-end vessel motion causes the slender riser to oscillate, creating an unsteady and non-uniform flow profile along the riser. The purpose of this research is to develop a VIV prediction model for slender structures under top-end periodic motions. The key approach to this problem requires identifying the dimensionless parameters important to the unsteady VIV. A set of data from a large-scale model test for highly compliant risers conducted by industry is available. The spectral analysis of the data showed a periodic pattern of the response frequencies. A constant Strouhal (St) number model was proposed such that shedding frequencies change with local inline velocities. The Keulegan-Carpenter number (KC) controls the number of vortex pairs shed per cycle. A KC threshold larger than 40 was found to have significant response for a long structure with finite length excitation region. An approximate solution to the response of an infinite beam with a finite excitation length was obtained; this solution provided an explanation for the high KC threshold. A model for an equivalent reduced damping Sg under a non-uniform, unsteady flow was proposed. This equivalent reduced damping Sg was used to establish a prediction model for the VIV under top-end periodic motions. A time domain simulation of unsteady VIV was demonstrated by using Green’s functions. The turning point problem wave propagation was solved for a pipe resting on a linearly varying stiffness foundation. Simple rules were established for conservative estimation of TDP fatigue damage with soil interactions. Guidelines for model test experiment design were provided based on dimensional analysis and scaling rules.

The Effectiveness of Helical Strakes in Supressing High Mode Number VIV”
OTC - 18276- PP

Triple helical strakes can play an important role in hte suppression of VIV on offshore platforms. This paper will present results of two filed experiments, one conducted at Lake Seneca in upstate New York and the second in the Gulf Stream near Miami, Florida. Three different distributions of triple helical strakes were tested. These experiments were designed to explore the effects of VIV on both bare pipes and pipes with strakes at mode numbers greater than the tength mode in uniform and sheared currents. At lake Seneca, bare pipes and full strake coverage pipes were tested in uniform currents. In the Gulf Stream two different configurations of Strakes were tested and compared to the VIV response of a bare cylinder. The two configurations are referred to as the the 40% coverage case and the 70% staggered coverage configuration. The results of the test showed a reduction in the amplitude of the vibration and also the frequency content of the vibrations. In particular, a large third harmonic component, which contributes significantly to the fatigue damage rate, was suppressed by the configurations with strakes. Together these reductions will greatly increase the fatigue life of the pipe.

Fatigue Damage from High Mode Number VIV”

This papers presents results from two field experiments using long flexible cylinders, suspended vertically from surface vessels. The experiments were designed to investigate vortex-induced vibration (VIV) at giher than the tength mode in uniform and sheared flows. The results of both experiments revealed significant vibration energy at the expected Strouhal frequency (referred to in this papers as the fundamental frequency) and also at two and three times the Strouhal frequency. Although higher harmonics have been reported before, this was the first time that the contribution to fatigue damage, resulting from the third harmonic, could be esttimated with some certainty. This was enabled by the direct measurement of closely spaced strain gauges in one of the experiments.

In some circumstances the largest RMS stress and fatigue damage due to VIV are caused by theses higher harmonics. The total fatigue damage rate including the third harmonic is shown to be up to forty times greater than the damage rate due to the vibration at the fundamental vortex- shedding frequency alone. This dramateic increase in damage rate due to the third harmonic appears to be associated with a narrow range of reduced velocities in regions of the pipe associated with significant flow-induced excitation.

29. JAISWAL Vivek, Vandiver J. Kim
“VIV Response Prediction for Long Risers with Variable Damping”

This paper describes the Vortex Induced Vibration response of long cylinders equipped with strajes and presents damping measurements from Gulf Stream Experiments conducted in October 2006. The experiments used a 500.4 foot long composite pipe with an outer diameter of 1.43 inches. The strakes were a triple helix design with a pitch to diameter ratio of 17.5. The pipe was equipped with varying amounts of strake coverage and was towed in the Gulf Stream which had current profiles which varied from nearly uniform to highly sheared. The measured response showed the characteristisc of travelling waves. Modeling such response using mode superposition and Green's Functions is presented.

Identifying the Power-In Region for VIV of Long Flexible Cylinders”

The primary objective of this research is to locate the source of the vortex-induced vibrations (VIV) for long flexible cylinders at high-mode number and to help determine the source region for future predictions. The two Gulf Stream tests were conducted to collect data on a scale-model pipe that was excited at high-mode numbers.
The high density of the sensors on the pipe allowed for analysis that had not previously been done. Two methodologies
are presented to locate the area of the region that is the source of the vibration.
In VIV, the current which causes the vibrations is important, because the speed of the current will determine the frequency of the vibration. Therefore, one important question is which section of the pipe will be the source of the vibrations for a known current profile. This source region is known as the power-in region. Regions on the pipe that are not a source of power instead damp the structural vibrations.
Once the region where the vibration originated has been found, the different phenomena that effect the location of the
power-in region that were discovered are shown. Four different factors are presented that effect the locations of the power-in region: the angle of the pipe with respect to the vertical, the gradient of the current direction, the current profile, and the end effects at high mode number.

A dimensionless parameter is presented which help in the prediction of VIV given a current profile. The power-in factor
predicts the region where the source of the vibration occurs using a combination of the current velocity and the source
region length.

"Insights on Vortex-Induced, travelling waves on long risers"
Journal of Fluids and Structures 25 (2009)

This paper is based on portions of a keynote presentation,which explored the boundaries of what is understood
about the vibration behavior of long cylinder sexcited by vortex shedding. The source of data is a recent field
experiment on a long flexible cylinder,densely instrumented with fiber optic strain gauges. The paper emphasis is on
previously unknown or unexplained phenomena and in some cases offers provocative insights as opposed to conclusive
proofs. Three particular topics are covered: (i)the occurrence of peak strain and fatigue damage rates at unexpected
locations, (ii) the dominance of traveling wave rather than standing wave response and(iii) the appearance of stable
cylinder trajectories,such as figure eights and crescents in pure traveling wave regions. Potential explanations are
offered and areas for promising additional research are proposed.

"Phenomena Observed in VIV Bare Riser Field Tests"

The following paper presents the results of preliminary data analysis performed on a densely instrumented bare riser
undergoing Vortex-Induced Vibration (VIV) response at high mode number. The data analysis steps are presented and show a method whereby it is possible to resolve uncertainty in the orientation of strain gauges on a riser responding to VIV. Two new phenomena are then revealed from the data analysis. The first is the occurrence of higher harmonic VIV response in directions which are not orthogonal to the cross-flow and inline directions. Secondly, evidence of riser structural response in the form of wave propagation is observed.

"Incorporating Higher Harmonics in VIV Fatigue Predictions"

Vortex-Induced Vibrations (VIV) are an important source of fatigue damage for risers in the Oil and Gas industry. Results
from recent VIV experiments by Vandiver et al. [1] indicate significant dynamic strain energy at not only the Strouhal
frequency, but also its harmonics. In certain regions of the pipe, these higher harmonics accounted for more that half of the measured RMS strain and increased fatigue damage by a factor exceeding twenty. However, the state-of-the-art in VIV prediction only accounts for the vibrations at the Strouhal frequency.
Preliminary results from a second set of experiments, described in this paper, confirm the importance of the higher
harmonics in fatigue life estimates of pipes. Further, the authors formulate an approach to incorporate the higher harmonics in VIV related fatigue design. Finally, the authors identify the estimation of the higher harmonics, in both location and magnitude, as an important area of ongoing research, the results of which will be required to implement this proposed method.

34. SWITHENBANK Susan, VANDIVER J. Kim, LARSEN Carl Martin, LIE Halvor
"Reynolds Number Dependance of Flexible Cylinder VIV Response Data"
OTC - 18276- PP

The response amplitude and the nondimensional frequency of flexible cylinder vortexinduced vibrations from laboratory and field experiments show significant trends with increasing Reynolds number from 10^3 to 2*10^5. The analysis uses complex data from experiments with wide variations in the physical parameters of the system, including length-to-diameter ratios from 82 to 4236, tension dominated natural frequencies and bending stiffness dominated natural frequencies, sub-critical and critical Reynolds numbers, different damping coefficients, standing wave and traveling wave vibrations, mode numbers from 1−25th, and different mass ratios.

"Spatial Variation of Drag on Long Cylinders in Sheared Flow"

A method is described for measuring the local drag coefficient on a long cylinder which exhibits vortex-induced vibration (VIV). Results are shown from a field experiment in which a long flexible pipe was instrumented with two-hundred and eighty fiber optic strain gauges. The measured local drag coefficients are compared to a commonly used drag coefficient
prediction formula. The formula is shown to be useful as a tool for predicting the average drag coefficients for the whole cylinder but is not able to accurately capture local variation in Cd . The local Cd measurements also reveal the location of VIV source regions.

"Partial Strake Coverage Vortex-Induced Vibrastion Benchmarking using SHEAR7v4.5"

A VIV benchmarking study was undertaken using SHEAR7v4.5 against NDP high mode VIV response laboratory data. The purpose of which was to derive an improved set of modeling parameters for partial strake coverage cases whilst not
comprising previous accuracy of shear flow bare riser response predictions. Fifty percent (50%) partial strake coverage
experimental data was utilized from both uniform and shear flow conditions while bare data was also included in the activity for reference purposes. The results showed that such an activity can derive an improved set of modeling parameters that significantly improve the ability to match experimental results and also highlight where future improvement efforts can be targeted.

37. VANDIVER J. Kim, CHENG Yongming, JAISWAL Vivek, SHESHADRI Aditi, YU Alan
"An Experimental Evaluation of Vortex-Induced Vibration of a Riser Bundle with Gaps"

VIV model test results are presented for a bundle of three parallel pipes all lying in the same plane, similar to a riser with large kill and choke lines. The rigid model was attached to a spring-mounted frame in the MIT towing tank. The horizontal model was towed in the tank and allowed to respond in free vibration to vortex-induced vibration in the cross-flow direction. The angle of attack of the model was varied from 0 to 90 degrees. The model was tested with and without helical strakes. Without strakes the model exhibited significant vibration at 0 and 90 degrees angle of attack. Strakes suppressed VIV at all angles of attack.

"Modelling Travelling Waves Using Mode Superposition"

Analysis of the data from two Vortex-Induced Vibration (VIV) experiments conducted in the Gulf Stream on a 500-foot-long, 1.43 inches diameter, flexible, tension dominated riser model revealed that the response is predominantly characterized by the presence of traveling waves. It was also observed that the location of the VIV excitation region (power-in) affects the characteristics of the response. The conventional method of modeling the excitation force as a standing wave was found inadequate to predict the location of the peak measured response accurately, especially in the cases where the excitation region is close to a boundary (the ends of the riser model).

A modified excitation force model consisting of a combination of standing and traveling wave excitation regions is demonstrated to predict the location of the peak response more accurately. This work presents the idea of modifying the VIV excitation model to include traveling wave characteristics and using mode superposition method for computing the response to this modified force. Examples of the implementation of this method are shown for the two distinct cases of the location of the power-in region - the power-in region adjacent to the boundary and the power-in region away from the boundary. Depending on the location of the power-in region, different proportions of standing and traveling wave excitations are used to yield predicted responses that match the measured response characteristics.

39. RESVANIS Themistocles and VANDIVER J. Kim
"Modelling Risers with Partial Strake Coverage"

This paper compares model test data for risers with partial strake coverage to predictions made with the Vortex-Induced Vibration (VIV) prediction program SHEAR7 Versions 4.5 and 4.6. It is shown that new features in Version 4.6 substantially enhance the capability for predicting the VIV response of risers with partial coverage. Experimental data is taken from two large L/D tests: the NDP 38 m long riser tests and the Deepstar-Miami, 500 foot long riser. New methods are described for modeling risers partially covered with helical strakes. Key SHEAR7 parameters are recommended, based on parametric investigations to calibrate the model against the available experimental data. Recommended modeling procedures are described so as to facilitate implementation by SHEAR7 users in their VIV modeling tasks

40. RAO Zhibiao, VANDIVER J. Kim, JHINGRAN Vikas, Sequeiros OCTAVIO
"The Effect of Exposure Length on Vortex-Induced Vibration of Flexible Cylinders"

This paper addresses a practical porblem; "What portion of fairing or strake coverage may be lost or damaged, before the operator must take corrective measures?". This paper explores the effect of lost fiarings (the exposure length) on Vortex-Induce Vibration (VIV) of flexible cylinders. THe source of data is a recent model test, conducted by SHELL Exploration and Production. A 38m long pipe model with varying amounts of fairings was tested. Response as a function of percent exposure length is reported. Unexpected results are also reported: (i) the flexible ribbon fairings used in the expreiments did not suppress VIV at speeds above 1 m/s; (ii) Above 1m/s, a competition was observed between VIV excited in the faired and bare regions of the cylinder, (iii) Unusual traveling wave behavior was documented--waves genereated in the bare region perriodically changed direction and exhibited varation in the VIV response frequency.

The results of the tests showed that (1) the excitation in the bare and faired regions could be identified by frequency, because the faired regions could be identified by frequency, because the faired region exhibited a much lower Strouhal number; (2) as expected, the response to VIV on the bare region increased with exposure length; (3) the response to VIV on the faired region decreased with exposure length.

41. RESVANIS Themistocles, VANDIVER J. Kim, JHINGRAN Vikas, LIAPIS Stergios
"Reynolds Number Effects on the Vortex-Induced Vibration of Flexible Marine Risers"

This paper explores the Reynolds number dependance of the Vortex-Induced Vibration (VIV) of flexible marine risers. Emphasis is placed on revealing the trends that exist between the dimensionless amplitude (A/D) and REynolds number. Data is drawn from recent towing tank experiments which used flexible cylinders of three different diameters. The 38m long pipes were exposed to uniform and sheared currents. The Reynolds number range extended from approximately 5,000 to 220,000 -well into the critical regime- with the largest diameter pipes responding in up to the the 13th mode and the smaller diameter pipe responding well above the 20th mode. The result and trends from this set of experiments are compared to previous results from laboratory and field experiments.

"Damping Parameters for Flow-Induced Vibration"
Journal of Fluids and Structures 35, 2012

A dimensionless damping parameter, c*=2cω/ρU^2, is defined for cylinders experiencing flow-induced vibration. It overcomes the limitations of "mass-damping" parameters, which first came in to use in 1955. A review of the history of mass-damping parameters reveals that they have been used in three principal variations, commonly expressed as Sc, SG and α. For spring-mounted rigid cylinders all three forms reduce to a constant times the following dimensionless group, 2c/πρD^2ω_n , where ‘c’ is the structural damping constant per unit length of cylinder and ω_n is the natural frequency of the oscillator, including, when so specified, the fluid added mass. All have been used to predict A*_max=Amax/D, the peak response amplitude for VIV. None are useful at organizing response at reduced velocities away from the peak in response. The proposed alternative, c*, maybe used to characterize VIV at all reduced velocities in the lock-in range.The simple product of A* and c* is shown to equal CL, the lift coefficient, thus providing a simple method for compiling CL data from free response measurements. Mass-damping parameters are not well-suited to the organization of the response of flexible cylinders in shearedflows or for cylinders equipped with strakes or fairings. c* is well-suited for use with sheared flows or for cylinders with partial coverage of strakes or fairings. Data from three independent sources are used to illustrate the applications of c*. It is shown that the method of modal analysis maybe used to generalize the application of c* to flexible risers.An example for a riser with partial fairing coverage is presented.

43. RAO Zhibiao and VANDIVER J. Kim
"VIV Excitation Competition Between Bare And Boyant Segments Of Flexible Cylinders"

This paper addresses a practical problem: “Under which coverage of buoyancy modules, would the Vortex Induced Vibration (VIV) excitation on buoyant segments dominate the response?” This paper explores the excitation competition between bare and buoyant segments of a 38 meter long model riser. The source of data is a recent model test, conducted by SHELL Exploration and Production at the MARINTEK Ocean Basin in Trondheim Norway. A pipe model with five buoyancy configurations was tested.

The results of these tests show that (1) the excitation on the bare and buoyant regions could be identified by frequency, because the bare and buoyant regions are associated with two different frequencies due to the different diameters; (2) a new phenomenon was observed; A third frequency in the spectrum is found not to be a multiple of the frequency associated with either bare or buoyancy regions, but the sum of the frequency associated with bare region and twice of the frequency associated with buoyancy region; (3) the contribution of the response at this third frequency to the total amplitude is small; (4) the power dissipated by damping at each excitation frequency is the metric used to determine the winner of excitation competition. For most buoyancy configurations, the excitation on buoyancy regions dominates the VIV response; (5) a formula is proposed to predict the winner of the excitation competition between bare and buoyant segments for a given buoyancy coverage.

44.FONTAINE Emmanuel et al.
"Using Model Test Data To Assess VIV Factor Of Saferty For SCR and TTR in GOM"

This paper presents results obtained as part of the DeepStar Phase 10 program on VIV Factors of Safety. The objective was to develop a general methodology to calibrate Factors of Safety for VIV-induced fatigue and to apply it to partially straked risers. This was achieved using reliability methods, accepted industry VIV prediction software and state-of-the-art model test experiments.

Most oil companies use a Factor of Safety of 20 when predicting VIV damage using VIV software tools. There are numerous software tools currently in use in industry to predict VIV damage to straked risers and each of them will have different accuracy, and therefore an intrinsic level of conservatism. Understanding the level of conservatism in different VIV prediction software is therefore critical to determining what Factor of Safety to use.

This study benchmarks the latest generation of industry accepted VIV design tools at the time of the study (2011): SHEAR7v4.6, VIVAv6.5 and VIVANAv3.7.24 against high quality VIV data from three separate straked riser experiments. A bias distribution (predicted to measured VIV damage results) is obtained for each software tool as a function of the strake coverage.

A novel reliability framework approach is then developed to incorporate all uncertainties associated with VIV fatigue prediction into a limit state function, including variability in met-ocean conditions and variability in the fatigue resistance of the material characterized by a design S-N curve. The limit state function is analyzed using First Order Reliability Methods to develop Factors of Safety for target probabilities of failure.

The general method is then applied on two case studies involving an SCR and TTR in Gulf of Mexico loop currents, but it can be easily extended to different locations and riser configurations. The resulting FoS range from about 1 to 15 for most software, and are lower than industry standards for VIV prediction. The FoS do not vary markedly for different riser configurations, indicating the possibility of reducing excess conservatism when predicting VIV damage on straked risers.