VIV on Free Span of Pipelines

download VIV on Free Span of Pipelines

of 12

description

Fatigue from vortex-induced vibrations of free span pipelines using statistics of current speed and direction

Transcript of VIV on Free Span of Pipelines

  • March 15, 2003 16:34

    Proceedings of OMAE032003 22nd International Conference on Offshore Mechanics and Arctic Engineering

    June 8-13, 2003, Cancun Mexico

    OMAE2003-37223

    FATIGUE FROM VORTEX-INDUCED VIBRATIONS OF FREE SPAN PIPELINESUSING STATISTICS OF CURRENT SPEED AND DIRECTION.

    Rune [email protected]

    Norwegian University of Scienceand Technology (NTNU)

    Department of Marine TechnologyOtto Nielsens vei 10

    7491 TrondheimNorway

    Carl M. [email protected]

    Norwegian University of Scienceand Technology (NTNU)

    Department of Marine TechnologyOtto Nielsens vei 10

    7491 TrondheimNorway

    Gunnar K. [email protected]

    Norsk HydroE&P Research Centre

    P.O. Box 71905020 Bergen

    Norway

    ABSTRACTA section of a sub sea pipeline that is suspended between

    two points on an uneven seafloor is often referred to as a freespan pipeline. Pipelines, installed on a seabed with a highlyirregular topography, may have to be designed with several freespans. If a free span is exposed to a current flow, vortex-inducedvibrations (VIV) of the suspended part of the pipeline may occur.These vibrations may cause unacceptable fatigue damage in thestructure.

    Statistical distributions of current speed and direction closeto a small mountain on the seabed (approximately 20 m high and40 m wide) are established based on full-scale measurements ofthe current velocity in the area.

    Some results from recent model tests of VIV in free spanpipelines, including some tests in which the flow direction wasnot perpendicular to the longitudinal axis of the pipe, are shown.These results indicate that it is sufficient to use the componentof the current velocity vector that is normal to the pipe whenusing empirical models for estimating the response due to vortexshedding.

    An existing empirical model for analysis of VIV [1] is ex-tended such as to include oscillations in the same plane as thecurrent flow (in-line VIV).

    The effect of including the directional variability of the cur-

    rent when estimating the VIV fatigue damage, using the extendedVIV model on a typical free span pipeline, is demonstrated, andfound to be of great importance. A parameter study, in whichthe length of the free span is varied, is also carried out. The con-clusion from this study is that a reduction of free span lengthaffects the parameters that govern the accumulation of fatiguedamage differently. Stresses are increased, but the number ofcurrent conditions capable of inducing VIV is reduced when thelength of the span is reduced. It is therefore difficult to predictwhether the accumulated damage will increase or decrease whenthe span length is reduced, and detailed analyses are required foreach particular free span and current distribution.

    The damage from in-line VIV is generally lower than thedamage from the cross flow VIV for all but the shortest spanlengths.

    INTRODUCTIONWhen leaving the relativeley flat continental shelf, and mov-

    ing into deeper water, a more irregular bottom topography is of-ten encountered. On-bottom pipelines from off-shelf fields, re-quired to climb onto the continental shelf, may have to be in-stalled so that parts of the pipeline are suspended freely betweentwo fixed points. Freely suspended parts of the pipeline is usu-

    1 Copyright c 2003 by ASME

  • ally referred to as free spans. This type of structure may alsobe found closer to the coast when crossing rough topographysuch as one may find in the vicinity of fjord sills, see Bjerkeet al. [2]. The hydrodynamic loading on free span pipelines be-low the shelf edge is mostly due to current flow. Wind generatedsurface waves does not significantly influence the flow patternsclose to the sea bed at this water depth. It is well known thatcurrent flow may cause vortex induced vibrations (VIV) in freespan pipelines. This phenomenon has been investigated in a se-ries of research programs, see Marchesani et al. [3] and Bryndumet al. [4] and references therein for an overview. The motivationfor such a considerable research effort has been to gain insightand understanding of the process, and to manifest this insight ina set of design guidelines for free-spanning pipelines. Parame-ters such as turbulence in the flow, proximity of the sea bed, pipesagging, flow inclination angle relative to the longitudinal axis ofthe pipe, pipe-soil interaction and the dynamic coupling betweenadjacent free spans all influence the vortex shedding induced re-sponse of the pipe.

    The quality of a fatigue life estimate of a given free spanat a given location depends upon the quality of the input to theanalysis and, of course, upon the goodness of the analysis toolitself. Several tools are available. Det Norske Veritas have issueda set of guidelines [5]. These guidelines are developed on thebasis of the aforementioned free span VIV research programs.There are also several computer programs available that aim atpredicting the VIV-response correctly, see e.g. Vandiver et al.[6], Larsen et al. [7], Triantafyllou [8] and Furnes and Berntsen[9].

    Strong current perpendicular to the pipe will cause largeVIV-amplitudes and, consequently, large fatigue damage in a freespan. The pipeline can be accepted only if it is documented thatthe fatigue life of all spans is above an acceptable limit. Since thedirection of the current relative to the pipeline axis is importantwhen it comes to VIV response, it is necessary to include currentdirectionality in the statistical description of the current.

    Bjerke et al. [2] reported results from current measurementsin rough topography close to a fjord sill in Norway. The pur-pose of the study was to provide a design basis for the Troll Oilpipeline for transportation of oil from the Troll field to the westcoast of Norway. This study concluded that the near seabed cur-rents close to the fjord sill were dominated by sporadic sill over-flows of heavy Atlantic water intruding the deeper parts of theNorwegian Trench. Mathiesen [10] presented analyses of nearbottom current measurements over irregular seabeds for four lo-cations outside the coast of Norway, and Mathiesen et al. [11]discussed various aspects of the flow over irregular topographyusing measurements and numerical models.

    In the present paper we use the distribution of current speedand direction obtained from recent measurements close to thesea bed in an area off the shelf break outside the coast of Mid-Norway, see Figure 1. This is the area where the Ormen Lange

    12o W

    6o W

    0o

    6o E

    12o E

    18o E

    57 oN

    60 oN

    63 oN

    66 oN

    69 oN Sviny section

    Ormen Lange

    Figure 1. LOCATION OF THE ORMEN LANGE GAS FIELD AND THESTOREGGA SLIDE AREA. DEPTH BETWEEN THE CONTOUR LINESIS 200 METERS. CONTOUR LINES BELOW 2600 METERS ARE NOTDRAWN.

    gas field is situated. Some 8000 years ago a large underwa-ter slide took place in this area, and the bottom topography istherefore very irregular. The distribution of current speed anddirection, obtained from the measurements, is applied in a VIV-analysis of a typical free span pipeline. First, we use only thestatistical distribution of the current speed, neglecting the direc-tional distribution of the current, and calculate the VIV of thefree span as if the pipe was always exposed to flow perpendicu-lar to its longitudinal axis. Next, we include the information wehave about the current direction and decompose the current ve-locity vector into a perpendicular component and an axial com-ponent. The perpendicular component is then used in the VIVcalculations. The calculations are carried out for a set of differ-ent free span lengths, and for different global orientations of thefree span.

    CURRENT MEASUREMENTSData were logged at four nearby stations in the vicinity of

    a small peak (height 30 meters, diameter 60 meters) at awater depth of approximately 680 meters. The logging stationsare located on the slope from the continental shelf to the deeperocean, see Figure 1. We use the data logged 20 meters above the

    2 Copyright c 2003 by ASME

  • 6- XG90o, East

    YG, 0o/360o, North

    South

    West

    1HVH

    Figure 2. COORDINATE SYSTEM.

    top of the peak for the purpose of this study.The recorded data consist of time-traces sampled at 1 Hz.

    The length of each time-trace is 34.2 minutes (2050 seconds),and the time-traces were recorded once every two hours. A totalof 800 time traces were obtained during the entire measurementperiod (October 18 until December 25), and these time traces arereferred to as HF (high frequency) time-traces in the following.

    The data were recorded according to the traditional conven-tion that the x-axis is directed towards the east, the y-axis is di-rected towards the north and the z-axis is directed vertically up-wards. See Figure 2 for an illustration of the coordinate systemused.

    We calculate three values of the 10 minute mean horizontalspeed, VH , on each HF time-trace and the corresponding horizon-tal flow directions, H (see Figure 2).

    The 2D probability density function for VH and H is definedby

    p(v,)dvd = P[(vVH v+dv) ( H +d)] (1)

    p(v,)dvd = 1

    where v is some horizontal speed and is some direction. Prob-ability density functions for one of the variables are obtained by

    0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

    5

    10

    15

    p(v)

    v (m/s)

    0 50 100 150 200 250 300 3500

    0.1

    0.2

    0.3

    0.4

    0.5

    p()

    (deg.)

    Figure 3. PROBABILITY DENSITY FUNCTIONS.

    integration over the other variable.

    p(v) =

    p(v,)d (2)

    p() =

    p(v,)dv

    Plots of p(v) and p() for the current meter which was positioned20 meters above the top of the peak can be seen in Figure 3.

    VIV-ANALYSIS PROCEDUREWe have used the VIVANA computer program system for

    the VIV-analyses in the present paper. VIVANA in its originalform predicts the vortex-induced vibrations perpendicular to theflow direction, i.e. the cross flow response. It is, however, alsopossible for the vortex shedding to excite the pipe in-line withthe current flow direction. This type of response is referred toas in-line VIV. Finally, it is possible that the cross flow motionof the pipe induces oscillations in the in-line direction, see e.g.Furnes and Berntsen [9]. We consider cross-flow VIV and in-lineVIV in this paper. Oscillations induced by the cross-flow motionof the pipe, however, are not considered.

    Cross-flow VIV in VIVANAA thorough description of the theoretical background for the

    analysis method implemented in VIVANA for predicting cross

    3 Copyright c 2003 by ASME

  • Cross flow model.

    Inline model.

    A/D

    A/D

    (A/D)CL=0

    (A/D)CL=0

    (A/D)CL,max

    (A/D)CL,max

    CL,0

    CL,max

    CL,max

    Figure 4. LIFT COEFFICIENT MODELS IN VIVANA.

    flow VIV is given by Larsen et al. [1]. A brief outline will begiven in the following.

    VIVANA applies nonlinear 3D finite element technique forsystem modeling and static analysis. The specific VIV-analysisstarts with finding a static solution for the forces and displace-ments of the structure to be analysed for a given current condi-tion. Several eigenvalue analyses are then carried out in orderto arrive at the possible response frequencies. The added massalong the cylinder is given as a function of a non-dimensionalfrequency, defined by

    f = fosc,CF DU

    where fosc,CF is the cross-flow oscillation frequency of the struc-ture, D is the diameter of the cylinder and U is the cross flowspeed. Several eigenvalue analyses are necessary in order to,through an iteration, find oscillation frequencies which are con-sistent with the added mass. Once the candidates for the responsefrequency (or frequencies) have been established, excitation anddamping zones along the cylinder are defined based on empiricaldata. Energy is put into the system in the excitation zones andremoved through the damping zones. If there are no dampingzones, which will be the case for most free spans where the crossflow speed is uniform along the pipe, damping is introduced bya self limiting mechanism. When the amplitude exceeds a cer-tain limit the lift coefficient becomes negative and will contributepositively to hydrodynamic damping. This feature is illustratedin Figure 4.

    VIVANA applies a set of lift coefficient curves where eachcurve is defined by three points as can be seen in Figure 4. The

    0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2 0.210

    0.2

    0.4

    0.6

    0.8

    1

    1.2

    1.4

    Non dim. freq.

    Lift coefficient model for crossflow VIV.

    (A/D)CL=0

    (A/D)CL,max

    CL,maxCL,0

    0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.20

    0.05

    0.1

    0.15

    0.2

    0.25

    0.3

    0.35

    Non dim. freq.

    Lift coefficient model for inline VIV.

    (A/D)CL=0

    CL,max

    Figure 5. LIFT COEFFICIENT PARAMETERS FOR VIVANA.

    points depend upon f as is shown in the upper window of Fig-ure 5. The curves are established based on empirical data fromGopalkrishnan [12] and Vikestad [13].

    In-line VIV in VIVANAThe VIVANA program has been extended to take in-line

    VIV into account using a simple model, based on the in-line re-sponse model recommended by DNV [14].

    An important difference between the well-established cross-flow VIV model in VIVANA and the new in-line VIV model, isthe method by which the response frequencies are established.Whereas the cross-flow response frequencies are consistent witha frequency dependent added mass, it is not possible to achievethis for the in-line response frequencies at the present time. Thereason is that the relationship between frequency and added massis not known for oscillations in-line with the current flow. In oursimple in-line VIV model we therefore make the assumption thatthe response frequencies are identical to the natural frequenciesin still water for the in-line modes. Any in-line frequency, givinga non-dimensional frequency, f , between 0.25 and 1.0 anywherealong the pipe, is considered to be a possible in-line VIV re-sponse frequency. Excitation zones and damping zones along thepipe are defined in the same way as for cross-flow VIV. The sameself-limiting mechanism, which comes into effect when the re-sponse amplitude exceeds a certain limit, as is used in the cross-flow VIV model is also at work in our new in-line VIV model.

    A set of curves defining the relationship between reducedvelocity, UR, maximum in-line response, (A/D)max, and a stabil-ity parameter, KSD, is given in DNVs Recommended Practicefor free spanning pipelines, [14]. The reduced velocity is defined

    4 Copyright c 2003 by ASME

  • by

    UR =U

    fosc,IL D

    where fosc,IL is the natural frequency for a given in-line mode.The stability parameter represents the damping for a given modalshape. We use the curve corresponding to KSD = 0 (zero damp-ing) in our simple model for in-line VIV. Structural- and hydro-dynamical damping for in-line VIV is included in VIVANA inthe same way as in the traditional cross-flow VIV model. Trans-forming the curve for KSD = 0 so that it is given as a functionof f = fosc,ILDU , which is the form used by VIVANA, we obtainthe curve drawn with a solid line in the lower window of Figure5. This curve has the same significance for prediction of in-lineVIV as the solid-line curve in the upper window of Figure 5 hasfor prediction of cross-flow VIV. Our lift coefficient model for in-line VIV is similar to that for cross-flow VIV. We apply a set oflift coefficient curves where each curve is defined by two pointsas can be seen in Figure 4. The points depend upon f as can beseen in the lower window of Figure 5. The curve for CL,max inthe lower window of Figure 5 is tentatively drawn due to the lackof relevant empirical data. The lift coefficient corresponding toA/D = 0 is set to zero in our in-line VIV model, and we use

    (A/D)CL,max = 0.5 (A/D)CL=0

    for all values of f .

    Response calculationThe VIV-response is calculated by the frequency response

    method. However, an iteration is necessary, and the reason forthis is that the load depends upon the response (see Figure 4), andso does the hydrodynamic damping. The iteration, if successful,yields response amplitudes at the element nodes consistent withthe loading. The frequency response method is not able to takeinto account all the nonlinearities that occur in connection withfree spans, see Larsen et al. [14]. The focus in the present paper,however, is on the effect of directional distribution of the cur-rent speed and reduced lift from inclined flow. A linear responsemodel is deemed sufficient for investigating these properties.

    It is assumed that the pipe responds to all possible in-lineVIV response frequencies simultaneously, irrespective of thepresence of any cross flow response. The fatigue damage is thuscalculated by adding the contributions from all possible in-linefrequencies and from any cross flow frequencies that are alsopresent.

    Pipeline

    -

    Towing directionF

    Figure 6. MODEL TESTS WITH INCLINED FLOW.

    EFFECT OF INCLINED FLOW ON VIVMost of the lift coefficient data shown in Figures 4 and 5 are

    obtained from experimental data. The exception is the curve forCL,max as a function of f for in-line VIV, this curve is tentativelydrawn due to lack of relevant empirical data. Most experimen-tal data of VIV response is valid only when the current flow isperpendicular to the longitudinal axis of the pipe. An extensiveseries of model tests of free span pipelines have been carried outat the Ocan Basin Laboratory facilities in Norway, Huse [15].Some of the tests were performed with an inclined flow onto thepipeline, as is illustrated in Figure 6. The length of the span dur-ing the inclined flow tests was 11.413 meters in model scale. Thiscorresponds to 194.6 meters in full scale (the linear model scaleduring the tests was 1:17.05). Three flow directions were tested,F = 90, 60 and 30 degrees. The bending stiffness of the pipewas 300 106 Nm2 (full scale) and the diameter was 0.556 me-ters (full scale). The pretension was set to 344.5 kN (full scale)for the tests with F = 90 degrees, and 346.5 kN for the testswith F = 60 and 30 degrees. Time traces of the measured pipecurvature was logged at 10 locations along the length of the pipefor a number of different towing speeds. Mo and Solaas [16]processed these data to obtain estimates of the pipe displacementby the method of modal decomposition. The relationship be-tween f and the maximum cross-flow displacement of the pipecan be seen in Figure 7. Unfortunately, no measurements of thelift force are available, and we shall have to rely on the data inFigure 7 for establishing the effect of inclined flow on the VIV.The two windows in Figure 7 contain exactly the same infor-mation, the only difference is the way that the non-dimensionalfrequency is calculated. Our data, which are very sparse, indi-cate that the maximum response as a function of f is the samefor all F if the flow direction is included in the calculation of f .This indicates that inclined flow is sufficiently accounted for byusing the component of the flow that is perpendicular to the pipein the VIV analysis. This means that a larger flow speed is re-

    5 Copyright c 2003 by ASME

  • 0.05 0.1 0.15 0.2 0.25 0.3 0.350

    0.2

    0.4

    0.6

    0.8

    190 degrees60 degrees30 degrees

    0.05 0.1 0.15 0.2 0.25 0.3 0.350

    0.2

    0.4

    0.6

    0.8

    190 degrees60 degrees30 degrees

    f = foscDU

    f = foscDU sin(F )

    A/D

    A/D

    Figure 7. MAXIMUM DISPLACEMENT AS A FUNCTION OF f .

    quired for the oscillation amplitude to reach a certain level, for agiven response frequency, when the flow is increasingly inclinedto the longitudinal axis of the pipe. The method by which weaccount for inclined flow is therefore simply to use the compo-nent of the flow velocity vector that is perpendicular to the pipein the analysis, otherwise the VIV analysis is unchanged. By thismethod the flow is always applied normal to the pipe. The staticsolution and the natural frequencies will therefore not be exactlythe same as they would if the true current direction was used. Amore refined method would be to use the static solution for thetrue current direction, and thereafter to include F in the calcu-lations of f throughout the remaining part of the analysis. Inthis paper, however, we use the perpendicular flow component-method. Even though we have considered cross-flow responseonly in reaching this conclusion, we use the same method for in-line VIV as for cross-flow VIV when calculating lift coefficientsdue to inclined flow.

    CASE STUDIESIn this section we apply the data for the near-bed current flow

    and the findings from the model tests. These results are used forestimating the fatigue life of a typical free span pipeline. Weestimate the annual fatigue damage by two different methods asoutlined in the following. The fatigue life is the inverse of theannual fatigue damage.

    The effect of the directional distibution of the current on theestimated fatigue damage due to VIV is studied by running thefatigue analyses for different global orientations of the free span.The length of the free span is also varied.

    Method 1 - Not accounting for the directional distribu-tion of the current flow or the pipeline orientation.

    Using this method, we disregard the directional distributionof the current and use only the statistical distribution for the flowspeed when calculating the fatigue damage. The orientation ofthe pipeline in the global coordinate system is irrelevant for thismethod because all flow is considered to be directed perpendic-ular to the longitudinal axis of the pipe. The total annual fatiguedamage is found from

    D1 = 0.5

    0D(v) p(v)dv (3)

    where D(v) is the resulting annual fatigue damage from a VIV-analysis using a flow speed of v. The probability density functionfor the current speed, p(v), is defined in equation (2).

    Method 2 - Accounting for the directional distributionof the current flow and the pipeline orientation.

    Using this method, we take the available statistical distribu-tion of the current speed and direction into account when calcu-lating the fatigue damage. We define the following variables (seeFigure 8),

    CG - positive clockwise.Current direction in the global coordinate system. Thedirectional distribution, p(), refers to this parameter.

    R - positive clockwise.The orientation of the free span in the global coordi-nate system.

    CR - positive counter-clockwise.Current flow direction relative to a local coordinatesystem (XV , YV , ZV ) used by the computer program VI-VANA.

    From Figure 8, we can establish the following expression for CR(note that angles are defined differently in the global and the localcoordinate system),

    CR = 360+RCG

    The total annual fatigue damage for a given span direction (R)is found from

    DR,2 = 0.5

    0

    3600

    D2(v,CG) p(v,CG)dCG dv (4)

    where D2(v,CG) is the resulting annual fatigue damage froma VIV-analysis using a flow speed of, VCF = v sinCR. The2D probability density function for current speed and direction,p(v,), is defined in equation (1).

    6 Copyright c 2003 by ASME

  • 6-XG90o

    YG, 0o/360o

    1

    BBBBBBBM XV , 0

    oYV , 90o

    R

    Current flow

    CG

    CR

    Figure 8. DEFINITION OF CG, R, AND CR.

    Structural model of the free spanAn idealized model of a free span was used for the case stud-

    ies. In this model, the pipe is pinned in both ends. Translationaldegrees of freedom are all fixed in one end. At the other end thevertical degree of freedom and the horizontal degree of freedomnormal to the longitudinal axis of the pipe is fixed, but the hori-zontal degree of freedom along the longitudinal axis of the pipeis free. A pretension, T , is applied in this degree of freedom. Atotal of 150 3D beam elements were used for modelling the freespan. Mechanical and geometrical properties for the structuralmodel of the pipeline can be found in Table 1. Natural frequen-cies in still water for all span lengths considered are listed inTable 2.

    RESULTSResults from the analyses are compiled in Tables 3 and 4.

    Estimated fatigue damage along the pipe, calculated by method1, is shown in Figures 9 and 10. Estimated fatigue damagealong the pipe, calculated by method 2, is shown in Figures 11-16, and it is clearly seen that the orientation of the free span,relative to the prevailing flow directions, is an important param-eter when estimating the fatigue life of free span pipelines. Themaximum estimated fatigue damage due to cross-flow VIV andin-line VIV is shown in Figures 17 and 18, respectively. As onewould expect, the accumulated fatigue damage is significantlyreduced when the directional distribution of the current flow is

    Table 1. MECHANICAL AND GEOMETRICAL PROPERTIES OF THESTRUCTURAL MODEL.

    Property Symbol Unit Numerical value

    Outer diameter D m 0.55

    Inner diameter Di m 0.50

    Wall thickness t m 0.025

    Modulus of elasticity E kN/m2 2.07108Mass per unit length M kg/m 324

    Submerged weight W kN/m 0.786

    Steel area Ast m2 0.041

    Section modulus Wst m3 0.0518

    Pretension T kN 200

    Table 2. NATURAL FREQUENCIES IN STILL WATER.Span length Mode1 Mode2 Mode3

    (m) (Hz) (Hz) (Hz)50 0.49 1.85 4.17

    80 0.21 0.75 1.63

    100 0.15 0.49 1.05

    125 0.10 0.33 0.69

    150 0.08 0.24 0.49

    180 0.06 0.17 0.35

    taken into account.

    CONCLUSION AND RECOMMENDATIONSModel tests of free span

    Results from model tests of a free span in inclined currentflow have been studied. The results suggest that the direction ofthe current relative to the pipe can be taken into account by usingthe component of the flow velocity vector that is perpendicularto the longitudinal axis of the pipe when estimating the VIV-amplitudes. The data from the model tests are somewhat sparse,we only have a few data points for three different directions. Wetherefore recommend that systematic model tests be carried outin order to establish a firm basis for determining the effect ofinclined current flow on the VIV of free span pipelines.

    7 Copyright c 2003 by ASME

  • Table 3. RESULTS FROM THE CALCULATIONS BY METHOD 1.Length of Minimum estimated fatigue life (years) andfree span location of worst damage (m from end 1)

    Cross flow In line

    (m) (years) (m) (years) (m)50 2.4108 24.8 8664 24.880 1324 39.7 15858 39.7

    100 2606 49.7 7104 49.7

    125 2203 62.1 3984 62.1

    150 618 111.5 2916 111.5

    180 863 133.8 1775 133.8

    In-line VIV modelThe new in-line VIV model, described and used in this pa-

    per, is based on assumptions and qualified guessing. It is rec-ommended that systematic experiments be carried out in order toreduce the uncertainties, and establish a consistent in-line VIVmodel similar to what is now used in the cross-flow VIV model.These experiments should be aimed at finding the relationshipbetween non-dimensional frequency and in-line added mass. Abetter model for the lift coefficients (frequency dependent) couldalso be established through systematic experiments.

    VIV induced damage in free spansResults from calculations of VIV-induced fatigue damage in

    an idealized model of a free spanning pipeline have been pre-sented.

    When the length of the free span is decreased, the damagefrom cross flow VIV, calculated by method 1, first increases, thenit decreases until L=100m, and then it increases again (L=80m),see Figure 17. The large damage at L=180m and L=150m iscaused by the presence of the second mode in the response(see Figure 9). Only first mode response is observed for theshorter span lengths. The accumulated damage is governed bythe stresses that are caused by the VIV and by how often theyappear. If the span length is reduced, the flow speed that is re-quired to create VIV increases, and the number of occurrences ofVIV (for a given distribution of the flow speed) decreases. At thesame time, the stresses that occur, if VIV is created, increase. Inconlusion, a reduction of the span length affects the parametersthat govern the fatigue damage differently. It is therefore difficultto say something beforehand on whether the fatigue damage willgo up or down if the span length is changed. Detailed analyses,using a model of the actual pipe, is necessary. This feature is notseen as clearly for in-line VIV or when method 2 is applied. This

    Table 4. RESULTS FROM THE CALCULATIONS BY METHOD 2.

    Length of R Minimum estimated fatigue life (years) andfree span location of worst damage (m from end 1)

    Cross flow In line

    (m) (deg.) (years) (m) (years) (m)50 0.0 2.381018 24.8 41309 24.8

    45.0 1.301018 24.8 21025 24.890.0 1.101019 24.8 1.37105 24.8

    135.0 - - - -

    80 0.0 4.501015 39.7 53758 39.745.0 2.261015 39.7 41704 39.790.0 6.621015 39.7 58988 39.7135.0 1.681018 39.7 5.78105 39.7

    100 0.0 4048 49.7 37721 25.7

    45.0 4170 49.7 19744 27.1

    90.0 20020 49.7 1.06105 29.6135.0 7.231016 49.7 4.91105 62.1

    125 0.0 10177 62.1 19895 26.3

    45.0 3940 62.1 11165 27.1

    90.0 21417 62.1 42002 29.6

    135.0 2.371016 62.1 1.25106 62.1150 0.0 8725 73.5 13207 27.5

    45.0 7625 73.5 6785 27.5

    90.0 9735 73.5 27276 30.5

    135.0 5.961016 75.5 6.81105 30.5180 0.0 6890 132.6 9070 27.0

    45.0 3573 133.8 5007 27.0

    90.0 23729 87.0 17210 30.6

    135.0 64486 87.0 3.92105 46.2

    does not mean, however, that it is not present for these cases. It isentirely possible that a different current distribution would bringit out.

    The damage from in-line VIV is generally lower than thedamage from cross flow VIV for all but the shortest span lengths,

    8 Copyright c 2003 by ASME

  • the exception is the damage calculated for R = 45 degrees forthe span length of 150 meters. In this case the cross flow damageand the in-line damage are comparable.

    From Figures 9 - 16 it can be seen that the in-line responseoften contains higher modes than the cross flow response. Thereason for this is that the excitation zone for in-line VIV extendsover the non-dimensional frequency range 0.2 to 1.0, whereasthe excitation zone for cross flow VIV is between 0.125 and 0.2.Reference is made to Larsen et al. [1] for details on the cross flowVIV excitation zone.

    ACKNOWLEDGMENTThe current flow data and the model test results used in this

    paper were collected by Norsk Hydro as part of the developmentof the Ormen Lange Gas field.

    REFERENCES[1] Larsen, C.M., Vikestad, K., Yttervik, R. and Passano, E.,

    Empirical model for analysis of vortex-induced vibrations- theoretical background and case studies, Proceedings ofthe 20th International Conference on Offshore Mechanicsand Arctic Engineering, Rio de Janeiro, Brazil, June 2001.

    [2] Bjerke, P.E., Moshagen, H., Red, L.P. , Eidnes, G. andMcClimans, T., Troll Oil Pipeline: Current measurementsand modelling. Data basis for pipeline free span design.,Proceedings of the 14th International Conference on Off-shore Mechanics and Arctic Engineering, Vol. V, PipelineTechnology, pp 29-36, 1995.

    [3] Marchesani, F., Gianfelici, F. Bruschi, R and Bryndum,M.B., Response of very long and multi-span pipelines inturbulent flows - experimental results., Proceedings of the14th International Conference on Offshore Mechanics andArctic Engineering, Vol. V, Pipeline Technology, pp 487-498, 1995.

    [4] Bryndum, M.B., Trum, A., Vitali, L. and Verley, R., TheMultispan Project, Laboratory tests on in-line VIV of pipessubjected to current loads., Proceedings of the 16th Inter-national Conference on Offshore Mechanics and Arctic En-gineering, Vol. V, Pipeline Technology, pp 7-15, 1997.

    [5] Det Norske Veritas, Free spanning pipelines., GuidelinesNo. 14, Det Norske Veritas, Hvik, Norway.

    [6] Vandiver, J. K. and Li, L., SHEAR7 Program Theoreti-cal Manual., Massachusetts Institute of Technology (MIT),July, 1995.

    [7] Larsen, C.M., Vikestad, K., Yttervik, R. and Passano,E., VIVANA Theory Manual., MARINTEK Report, Trond-heim, Norway.

    [8] Triantafyllou, M., Vortex-Induced Vibration Analysis Ma-rine Riser Software. Users Manual. DOS Version 3.2, David

    Tein Consulting Engineers, Ltd., Houston, TX, USA, April,2000.

    [9] Furnes, G.K. and Berntsen, J., On the response of a freespan pipeline subjected to ocean currents., Ocean Engi-neering (in press).

    [10] Mathiesen, M., Current data for the design of multispan-ning pipelines., Proceedings of the 15th International Con-ference on Offshore Mechanics and Arctic Engineering,Florence, Italy, Vol. V, Pipeline Technology, pp 451-457,1996.

    [11] Mathiesen, M., Hansen, E. A., Andersen, O. J. and Bruschi,R., The Multispan Project, Near Seabed Flow in Macro-Roughness Areas., Proceedings of the 16th InternationalConference on Offshore Mechanics and Arctic Engineer-ing, Yokohama, Japan, Vol. V, Pipeline Technology, pp 17-22, 1997.

    [12] Gopalkrishnan, R., Vortex-Induced Forces on OscillatingBluff Cylinders., Sc.D. Thesis, Department of Ocean En-gineering, MIT, and Department of Applied Ocean Phys.and Eng., WHOI, USA.

    [13] Vikestad, K., Multi-frequency response of a cylinder sub-jected to vortex shedding and support motions., Ph.D. The-sis, Faculty of Marine Technology, Norwegian Universityof Science and Technology, Trondheim, Norway, 1998.

    [14] Larsen, C.M., Koushan, K. and Passano, E., Frequency andtime domain analysis of vortex induced vibrations for freespan pipelines, Proceedings of the 21st International Con-ference on Offshore Mechanics and Arctic Engineering,Oslo, Norway, June 2002.

    [14] Det Norske Veritas, Free spanning pipelines., Recom-mended practice DNV-RP-F105, Det Norske Veritas,Hvik, Norway.

    [15] Huse, E., Ormen Lange 3D Phase II Model Tests. Main Re-port., MARINTEK Report 512352.00.01, Trondheim, Nor-way.

    [16] Mo, K. and Solaas, F., Ormen Lange 3D Phase II ModalAnalysis., MARINTEK Report 512352.00.02, Trondheim,Norway.

    9 Copyright c 2003 by ASME

  • 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

    0.2

    0.4

    0.6

    0.8

    1

    1.2

    1.4

    1.6

    1.8x 103 Cross flow damage computed by method 1.

    Length along pipe / L ()

    Dam

    age

    (1/ye

    ar)

    L=150 m

    L=180 m

    L=80 m

    L=50 m

    L=125 m

    L=100 m

    Figure 9. DISTRIBUTION OF FATIGUE DAMAGE DUE TO CROSSFLOW VIV CALCULATED BY METHOD 1. THE DENOMINATION ONTHE X-AXIS IS NON-DIMENSIONAL LENGTH ALONG THE LONGITU-DINAL AXIS OF THE PIPE.

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

    2

    4

    6x 104 In line damage computed by method 1.

    Length along pipe / L ()

    Dam

    age

    (1/ye

    ar)

    L=180 m

    L=150 m

    L=125 m

    L=100 m

    L=80 m L=50 m

    Figure 10. DISTRIBUTION OF FATIGUE DAMAGE DUE TO IN LINEVIV CALCULATED BY METHOD 1. THE DENOMINATION ON THE X-AXIS IS NON-DIMENSIONAL LENGTH ALONG THE LONGITUDINALAXIS OF THE PIPE.

    0 5 10 15 20 25 30 35 40 45 500

    2

    4

    6

    8x 1019 Distribution of damage computed by method 2.

    CF D

    amag

    e (1/

    year)

    0 5 10 15 20 25 30 35 40 45 500

    1

    2

    3

    4

    5x 105

    Length along pipe (m)IL

    Dam

    age

    (1/ye

    ar)

    R=45

    R=45

    R=135

    R=135

    R=0

    R=0R=90

    R=90

    Figure 11. DISTRIBUTION OF ESTIMATED FATIGUE DAMAGE. CAL-CULATED BY METHOD 2. SPAN LENGTH IS 50 METERS. CROSSFLOW (TOP) AND IN-LINE (BOTTOM) DAMAGE IS SHOWN.

    0 10 20 30 40 50 60 70 800

    1

    2

    3

    4

    5

    6x 1016 Distribution of damage computed by method 2.

    CF D

    amag

    e (1/

    year)

    0 10 20 30 40 50 60 70 800

    0.5

    1

    1.5

    2

    2.5x 105

    Length along pipe (m)

    IL D

    amag

    e (1/

    year)

    R=0R=135

    R=135

    R=0

    R=45

    R=45

    R=90

    R=90

    Figure 12. DISTRIBUTION OF ESTIMATED FATIGUE DAMAGE. CAL-CULATED BY METHOD 2. SPAN LENGTH IS 80 METERS. CROSSFLOW (TOP) AND IN-LINE (BOTTOM) DAMAGE IS SHOWN.

    10 Copyright c 2003 by ASME

  • 0 10 20 30 40 50 60 70 80 90 1000

    0.5

    1

    1.5

    2

    2.5

    3x 104 Distribution of damage computed by method 2.

    CF D

    amag

    e (1/

    year)

    0 10 20 30 40 50 60 70 80 90 1000

    1

    2

    3

    4

    5

    6x 105

    Length along pipe (m)

    IL D

    amag

    e (1/

    year)

    R=90

    R=90

    R=0

    R=0

    R=135

    R=135

    R=45

    R=45

    Figure 13. DISTRIBUTION OF ESTIMATED FATIGUE DAMAGE. CAL-CULATED BY METHOD 2. SPAN LENGTH IS 100 METERS. CROSSFLOW (TOP) AND IN-LINE (BOTTOM) DAMAGE IS SHOWN.

    0 20 40 60 80 100 120 1400

    0.5

    1

    1.5

    2

    2.5

    3x 104 Distribution of damage computed by method 2.

    CF D

    amag

    e (1/

    year)

    0 20 40 60 80 100 120 1400

    0.2

    0.4

    0.6

    0.8

    1x 104

    Length along pipe (m)

    IL D

    amag

    e (1/

    year)

    R=0

    R=0

    R=45

    R=45

    R=135

    R=135

    R=90

    R=90

    Figure 14. DISTRIBUTION OF ESTIMATED FATIGUE DAMAGE. CAL-CULATED BY METHOD 2. SPAN LENGTH IS 125 METERS. CROSSFLOW (TOP) AND IN-LINE (BOTTOM) DAMAGE IS SHOWN.

    0 50 100 1500

    0.2

    0.4

    0.6

    0.8

    1

    1.2

    1.4x 104 Distribution of damage computed by method 2.

    CF D

    amag

    e (1/

    year)

    0 50 100 1500

    0.5

    1

    1.5x 104

    Length along pipe (m)

    IL D

    amag

    e (1/

    year)

    R=45R=0

    R=90R=135

    R=45

    R=0

    R=90

    R=135

    Figure 15. DISTRIBUTION OF ESTIMATED FATIGUE DAMAGE. CAL-CULATED BY METHOD 2. SPAN LENGTH IS 150 METERS. CROSSFLOW (TOP) AND IN-LINE (BOTTOM) DAMAGE IS SHOWN.

    0 20 40 60 80 100 120 140 160 1800

    0.5

    1

    1.5

    2

    2.5

    3x 104 Distribution of damage computed by method 2.

    CF D

    amag

    e (1/

    year)

    0 20 40 60 80 100 120 140 160 1800

    0.5

    1

    1.5

    2x 104

    Length along pipe (m)

    IL D

    amag

    e (1/

    year)

    R=45

    R=0 R=90

    R=135

    R=45

    R=90R=0 R=135

    Figure 16. DISTRIBUTION OF ESTIMATED FATIGUE DAMAGE. CAL-CULATED BY METHOD 2. SPAN LENGTH IS 180 METERS. CROSSFLOW (TOP) AND IN-LINE (BOTTOM) DAMAGE IS SHOWN.

    11 Copyright c 2003 by ASME

  • 40 60 80 100 120 140 160 180 2002

    0

    2

    4

    6

    8

    10

    12

    14

    16

    18x 104 Cross flow VIV.

    Length of span (m)

    Dam

    age

    (1/ye

    ar)

    Meth.1Meth.2, R=0Meth.2, R=45Meth.2, R=90Meth.2, R=135

    Figure 17. MAXIMUM ESTIMATED DAMAGE DUE TO CROSS FLOWVIV.

    40 60 80 100 120 140 160 180 2002

    1

    0

    1

    2

    3

    4

    5

    x 104 In line VIV.

    Length of span (m)

    Dam

    age

    (1/ye

    ar)

    Meth.1Meth.2, R=0Meth.2, R=45Meth.2, R=90Meth.2, R=135

    Figure 18. MAXIMUM ESTIMATED DAMAGE DUE TO IN LINE VIV.

    12 Copyright c 2003 by ASME