Prediction of Wave Impact Loads on Ship-type Offshore Structures in Steep Fronted Waves

8/10/2019 Prediction of Wave Impact Loads on Ship-type Offshore Structures in Steep Fronted Waves

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Prediction of wave impact loads on Ship-type Offshore Structures in Steep Fronted Waves

Arjan VoogtanMA

Wagen in gen.

W ABSTRACT

Steep fronted waves can induce extremely large impact pressures on thehuil of moored ship-type offshore structures. Several incidentsconfirmed that these loads can result in significant damage to the bow.As part of the SAFE-FLOW Joint Industry Project these loads wercinvestigated with a dcdicatcd series of model tests. Dctailed analysis ofthe results gave important insight in the wave impact hydrodynamics, Itwas observed that the local steepness of the waves has a large influenceon the magnitude of the occurring bow slams and that the siammingcould be characterised as a wave crest phenomenon. Thercfore highpressures can be experieneed in the upper bow and forecastle. Thepaper first presents the test philosophy, set-up and dedicated

measurements. Then the developed prediction method and its resultswill be discussed in detail.

KEY WORDS: 21 order waves; steep waves; FPSO; bow slam;equivalent pressure; dynamic response; prediction

INTRODUCTION

Keveral incidents in recent years have revealed iat wave impact'oading is an important issue for moored floating production systems.Wave impact damage has been experieneed by both the Foinaven andSchiehallion FPSOs.

Impact loading differs from other types of wave loads by their veryshort rise time. The rise times, defined as the time from the applicationof the slamUUthe peak in the loading, are in the order of milliseconds.The pressures resulting from the large impact loads are often describedwith a slam cofficint times the fluid density and the velocity squared.Most of these slam coefficients are based on drop tests in which astructure is dropped in the water with a known velocity. Campbell andWeynberg (1980) derived these coefficients for a cylinder.

The magnitudes of the slam coefficients provided in literature differsignificant and for application for the wave loading problem the impactvelocities need to be known. Ochi and Tsai (1984) define this velocityproportional to ie phase speed of the wave. Highest loads can beexpected in breaking or broken waves and De Haas (1999) showed that

i Bas BuchnertINNetherlands

for these steep fronted waves the phase speed differs significantly fromlincar theory. To describe steep waves more accurately Kjeldscn (2000)provides a number of parameters that describe the local profile of thewaves, which influences the slam loads.

The present paper was developed withtn the SAFE-FLOW project(SAFE-Floang LOading by Waves), which is initiatcd in response toencouragement by the UK Health and Safety Executivc (HSE)following earlier joint research, such as the JIP 'F(P)SO Green WaterLoading'. completed in 1997 (Buchner, 2002). lts main objective wasto investigate water impact loading hazards in detail. The research teamincluded a number of specialist European-based companies in this field.Approximately 49% of the SAFE-FLOW research budget is provided

by the European Community under the 'Competitive and SustainabieGrowth' Program (1998-2002), while the oier 51% is provided byindustrial sponsors including oil companies, ship builders, classificationsocicties and consultants.

Based on model tests carried out for both a free floating FPSO and afixed schematic bow a prediction tooi (BowLab) is developed whichwill bc discussed in iis paper.

EXPERIMENTS

The effects of wave impact on extemal surfaces of an FPSO have beenevaluated. Measurements have been made of:

Impact pressures for local design of the shell. Pressures on large areas of panel. Forces or impulses for large components of ship structure.

As part of the project MARIN performed 2 series of model tests atscale 1:60 in deep water:

Model tests on free floating Schiehallion FPSO Model tests on a highly instrumented fixed simplified bow

The tests on free floating Schiehallion FPSO focussed on the motionsof the FPSO, the local relative wave motions at the bow and the localpressures and sectional loads at the bow. An example for a significantslam is shown in Figure 1.

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Figure 1: Bow impact event on free floating Schiehallion model

nn these tests in irrcgular seas the incident wave data. vessel motionsand resulting relative motions, bow pressures and stnictural responseare measurcd. The measurements are visualised in Figure 2 whichshows both the undisturbed and disturbed wave fronts and thedimensions of the instrumented bow segments.

Figure2:Visualisation of measured wave fronts

The tests showed that more detailed load measurements were necessary

and that an investigation was needed into the relation between theincoming waves and these loads. This resulted in the model tests on ahighly instrumented fixed simplified bow.

The bow was instrumented with a large array of pressure transducersand 3 force panels (Figure 3). The test program, also making use ofextensive video recordings, was designed such that it was possible todeterminc the correlation between undisturbed wave shape and theimpact pressure time traces. From these tests inegular sea incidentwave data and bow pressure results are available on a fixed schematicbow structure with varying rake and plan angles.

j j l l . _il tt_ ^JtXi. ^ZL __EI1.

0^ 0^ & 0^ 0^


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The rclation between the local wave characteristics and themagnitude (and other characteristics) of the wave impact, thelower line in the figure.

The position of the impact based on the related ship motions,the upper line in the figure.

The combination results in a localised impact with specific properlies,

resulting in the struciural response of a local structure with its specificstructural propcrties.

motion

RAOs

WF shipmotions

selectgeometry

emplrical

relations

location


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15

10

F" 5

-5

-10

measured-2"

d order

linear \

\

dffdt/ ' ' ' linear 6

2nd

order 10

measured 12

1165 1170time [s]

Figure 9: Measured. first order and second order wave time trac

It is observed that up to a certain vertical free surface velocity noimpacts occur. Above ths threshold level. the probability increaseslinearly with the vertical free surface velocity up to the probability of100%.

Wave Characteristics and the Relation with Slam Magnitude

Beside the slam probability. the slam magnitude is of vital importance.After analysis of all data, it was decided to relate the slam imputse (I).the area under the load time trac, to vertical free surface velocity(dC/dt).

Figurc 12 shows the measured impulses versus the correspondingvenical free surface velocities. For different velocity bins the mean andStandard deviation of the occurring impulses is added to the figure.resulting in straight lines.

10u

!10'

10

^N.measured

linear second order

\\

V*^S.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14wavevelocitv Cdz/dtl in m/s

Figurc 10: Probabilities of exceedance of vertical free surface velocity

It is clcar that the second order theory is not capable to describe theasymmetry in the measured non-linear wave. However within theaccuracy of Lhe present design tooi ths is not considered a critical

aspect and the distribution of the vertical free surface velocities domatch the measured non-linear distribution rcasonably well.

To estimate the probability of an impact at a certain vertical freesurface velocity, the percentage of impacts occurring were counted forbins of vertical free surface velocities (Guedes Soares, et al. 2004). Anexample is given in Figure 11.

Mtrin.403001-403005. gaug* RELM VI

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Figure 11: Probability of impact versus vertical free surface velocity(from Guedes Soares. et al., 2004)

0CA *. .Q.LUI * *** ^nt * ' ' ^ ^ *o 01LU

Maximu

*

Vertical free surface velocity

Figurc 12: The measured impulses versus the corresponding verticalfree surface velocities

The relation is independent of the sea state and holds for a schematicflat plate bow. Within the design method the mean fit is used as amaximum that can occur. For more realistic curved bow shapes theloads are reduced as describcd in the next sections. The spreadingaround this mean can be used as input to the derivation of the loadfactors in a first principles reliability approach.

Other wave impact characteristics. such as rise time, decay time, spatialextent and the effect of the bow shape are later applied to this localimpulse on a flat plate to determine the resulting structural response.

Position of Impact Related to Crest Height

Besides the probability of the impacts, the position of the impacts, theircharacteristics (magnitude, characteristics in time, spatial extent, effectof bow shape) and resulting structural responses are important. In the

SAFE-FLOW project a complete methodology has been developed toderive this (Voogt, 2004).

In the model an array of pressure transducers was installed. In total 5columns of each 8 sensors were availablc for the analysis. From therepeated wave tests it was found that large spreading can occur on thetime trac of the pressure in exactly reproduced waves. Therefore theimpulse of ie slam is calculated with an integration of the pressureover its duration. The magnitude of the impulses is plotted for a columnof transducers (Figure 13).

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i measured impulseson array of

pressure sensors

schematic bowFigure 13: Defmition of slam centre (H) with respect to cresl height (C)of incoming undisturbed wave

From this column of measured impulses the slam centre (H) can bedefined as the leve! above the free surface with the maximum impulse.This height can be compared with the crest height of the correspondingincoming wave (C). Figure 14 shows this comparison for the crestheights of the undisturbed waves compare to the slam centre.

Figure 14: Slam centre (H) on horizontal axis versus crest height (C)

Due to the adopted method the impact height above the waterline issampled with the distance between the rows of the transducers. Foreach impact with the slam centre at the third row from above ahistogram of corresponding crest heights is shown with a small inset tothe graph. It is clear that some spreading occurs but that most of the

fcrest heights do corrcspond to the slam centre. The comparison with theFvave heights of the incoming undisturbed waves show that most slamloads occur relatively close to the wave crest. This is consistent withthe observation that the maximum velocity occurs close to the crestfront of the incoming wave.

Position of Impact Related to Ship Motions

The previous section showed that the slam centre occur close to thecrest of the undisturbed non-linear wave. However for the design of abow panel in a floating structure, aiso the ship motions should be takeninto account. To check the assumption that these motions in steepwaves can still be described with linear diffraction theory, the modeltests reported with a floating model (Voogt, 2001) werc analysedfurther.

An iterative procedure has been developed that fits a linear wave and tssecond-order contributions to a measured wave train. The procedureworks as follows:

1. An estimatc of the linear part of the wave train is given. Inpractice, a good first guess is the measured wave trainitself.

2. With a Discrete Fourier Transform (DIT) the amplitudes andphases of the linear estimatc are determined.

3. The corresponding second-order sum- and differencefrequency wave is determined and added to give an estimateof the total wave.

4. The difference between the estimated wave and the measuredwave is determined. If this difference is larger than a certainpre-defined value, the difference is added to the linearestimate and the scheme is repeated from point 2 onwards.

The sum and difference-frequency waves are not determined for theentire, theoreiical frequency range. Boih are restricted to the frequencyrange |0, camax], where the cut-off frequency ojmax depends on thewave spectrum. A second-order fit is not rcalistic above the cut-offfrequency since iird- and higher order effects are bound to occur. Theexact formulation for the cut-off frequency (or cut-off wave number) istaken from Stansberg (1998).

After the scheme has converged, the linear amplitudes are known andthe response to this linear wave can be calculated. The table below

shows a comparison of the Standard deviations from the calculation andthe measurements for a head seas condition.

Table 1: Measured compared to calculated linear ship responseMeasurement Linear calculation

Wave [m| 3.63 3.62Surge [m| 1.00 0.96heave [m| 1.50 1.32pitch [degl 2.26 2.04

A good comparison between measurements and linear calculations isfound, which is confirmed in the time traces in Figure 15.

Ta 205001

1300

1190 1200 1390(*1

Figure 15: Time traces of measured vessel response compared tocalculated response assuming linear motion response

Even for these large differences between the linear wave and memeasured wave, the linear wave is sll capable to describe me majorpart of the ship response. Therefore the following procedure isimplemented to determine the location of the impact:

For a time trac of the linear wave the motions of the vesselare calculated.

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With this linear wave non-linear wave components can becalculated and added to the time traces.

Combining the time trac of the non-linear wave and thelinear ship motions gives a relative wave motion in front ofthe vessel.

From these relative motions the slam centre can bedetermined ifaslam occurs.

Figure 16 visualizes the procedure. The yellow ship is moving on theblue linear seas. While the red line indicates the second order wavewhich determines the impact size and location.

From fixed schematic bow model:

, Impact &jlocatioi*^ ^

^ i

"igure 16: The position of the wave impact on the bow is determinedby the linear motion response combined with the second order creslheight

Bow impact characteristics

So far the method focussed on the local impact pressures on the bowand on its position. However, to design the plating and stiffeners in thebow area iis is not always sufficint to deierminc an accurate response-with resulting stresses.-The monitoring on the. Schiehallion. bow(Hodgson, 2003) allows for this comparison between pressures andstresses. Bascd on these results the pressurc duration, immersionvelocity and spatial extent are considered critcal (Figure 17).

JJaia a_lrea(ly_dcscnbcd_ Impulse! Magnitude

Target type

Immersionj Velocity

SpatialExtent

Structural Response

Equivalent Press ure Slam type

Figure 17: Bow impact characteristics

Immersion velocity

From the measured array of pressure on the schematic bow the pressurefront or immersion velocity can be derived. This velocity is definedbased on exceedancc of half the maximum value for each transducer, asshown in the Figure 18. This choice of exceedance level makes thecomputer program capable of dealing with each slam and gives a betteresdmate then the exceedance of a threshold level. Sometimes thisthreshold level is exceeded due to the hydrostatic pressure onlyresulting in unrealistic small pressure front velocities.

Measuredpressures at

different heightsup the bow

ImmersionVelocity

time IslFigure 18: Derivation of pressure front or immersion velocity from themeasured array of pressure transducers on the schematic bow

For some impacts the pressure front travels upward over the plate,while oicrs occur more instantaneous ly. If we determine the timebetween the impacts over the height of the flat plate differences of 0.0to 0.3 seconds can be found for two adjacent transducers. Thiscorresponds to a velocity of 10 m/s and higher. For comparison thetime derivative of the water level against the plate is determined, whichhas a maximum of approximately 16 m/s. Up to immersion velocities of100 m/s the pressure time trac of the slam show the traditional shape(progressive slams), above this velocity only short sharp(instantaneous) slams occur.

Different immersion velocities tend to occur at comparable values ofvertical free surface velocity. Therefore the probability disiribution ofthe immersion velocities is determined. This disiribution is independentof the slam size. The average disiribution is shown in Figure 19. Thisfigure shows two types of slams:

The blue bars on the left result in slams that progress over Uiebow. The duration of the resulting load time tracs on a bowsegment are direct related to these velocities.

For velocities above 100 m/s (the red bar) an instantaneousslam occurs. The duration of the resulting load time trac isindependent off the target size and thus independent of theimmersion velocity.

10 20 30 ao so40 90 oo rolmmrakvtfKly{rr*l

Figure19:The probability disiribution of the immersion velocities

Spatial Extent

For the schematic bow with the large number of pressure transducersthe spatial extent is derived by integrating the bow pressures downwardfrom the maximum slam over increasing areas, with steps of 1.5 metre.For the instantaneous and progressive slams this resulted in thefollowing curves:

Instantaneous: The whole pressure time trac decreases wiihthe integral over the area. This type of impulse is recognizedas an instantaneous slam. The decrease of the pressuredepends on ie size of the pressure front and drops down fastduring integration (Figure 20).

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Progressive: The rise time increases while the pressureimpulse remains relatively constant. This second type ofimpulse progrcsscs along the structure. Due to the pressureintegration the rise time increases with the size of the areaand the impulse remains approximately the same (Figure 21).

T 1 1 r

2.6 2.7 2.8 2.0 3 3.1 3.2 3.3 3.4

Time (s)

Figure20:Time traces of instantaneous stam for increasing panel sizes

3.1 3. 3.3 3.4 3.5 3,8 3.7 3.5

Time [s]

Figure21:Time traces of progressive slam for increasing panel size

For each calculated impact die time traces for instantaneous andprogressive slanis "are scaled to represent die correct impulse andimmersion vclocity. Widi the resulting curves and the location of theslam centre the equivalent static pressure on a specified panel can be

determined.

The width and curvature of the panel can result in a reduction of theequivalent static pressure. For very small panel width die results can beconsidered two dimensional and multiplication of the pressure with thewidth of the panel gives the design load. For larger panels the curvatureof the bow becomes important. Even for a flat plate die averagepressure reduces with the width of the panel due to local wave effects.An empirical formula is Fitted through the measurements performcd in

Klasgow and documented in Barltrop and Xu (2004). Since one wouldexpect ie curved bow factor to be always less than die flat plate value,the pressure for a curved plate is limited to die fiat plate value. Theresulting factor between the local pressure and the pressure averageover the width of the plate is shown in Figure 22.

o ao

Figure22:Pressure reduction factors for curved panels

Dynamic response

The previous sections focussed on the bow impact loading. Howevcr,for the evaluation of ship-type offshore structures, die structuralresponse under this impact loading determines wheier a structure isable to survive a certain event. It is a characteristic of bow impactloads, particularly instantaneous slams, that pressure loads are applied

very quickly. Dynamic response of the structure is therefore iikely.requiring that dynamic amplification be included in any designcalculations,

The structural evaluation of bow slam loading and structural response isin principle a coupled hydra elastic problem. These coupled effects areIikely to be most important when die natural period is longer than twicethe duration of ie slam. The full coupled problem has not beeninvesiigated in die present project. Instead a simplified approach hasbeen used.

With the rise and decay time (and their characteristics) of the slam andthe natural frequency of the structure the dynamic response can becalculated with a single degrec of freedom mass spring system.Excluding hydro-elastic effects, the structural response can be

described with the equation of motion in which a constant damping,added mass and mass are assumed.

For a typical large local slam die rise and decay times are about 10 msand for a panel natural period of about 1/10 sec the DAF will be 0.96(Figure 23). This DAF smaller than 1occurs if the structure has a longperiod and does not have time to respond to me impact load before itstarts to reduce.

Pressun Pmax

Pmax/2

Figure23:Example ofaDAF smaller than 1

For each combination of rise time, decay time and natural period dieDAF can bc calculated. The result is summarised in the design diagramin Figure 24.

R I Mttme/ Natural period10'

Figure 24: Design diagram with example of DAF of 1.66

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An example isprovided inFigure 24 for a stiffened panel withanimmerscd natural frequency of 20 Hz and bowslam rise anddecaytimesof0.01 and 0.03 seconds. The rise time divided by thenaturalperiod is0.2, reading thegraph verticalto theinclined line withthecorrect ratio between the decay half time and the rise timeof3, resultsin a dynamic amplification factor of 1.66.

RESULTS

SUMMARY

Bow impact loadingon floating offshore structures isrelated tosteepwaves occurring in random seas. Although new numerical methodsdogive promising results, they still need significant further development,integration and validation before they canbeused topredict thebow

slam loads asawhole wilhina reasonable timeframe.

With ieBowLab program theposition anddimensions of the targetpanel canbe varied and the resulting pressures indifferent waves canbe compared.

Figure 25 shows the effect of the wave steepness on the slam loads. Theresults show the most probablc maximum equivalent pressures for apanel of 1mwide and 2 mhcight.The panel centre is located 8 mabove themean surface Ie vel.Up to a significant wave height of 5metres no slams occur on the specified panelasthe waves do nol reachthe panel. Above this value the loads increase with thewave heightwhen ie wave period iskept constant as the wave steepness increases.The figure shows boththe load and response representing respectivelythe static and dynamic pressure averaged over the panel.

MPM pressures in 30 hexas sto m shows the edecl of waw heighl

bcapeak periodof10s on small panel (hxb2x1m)8 m ab ow MSL

_ 20 00 1

Sijj lcanl wave height |m]

Figure25:Increase of equivalent pressures with wave height

The tooi can alsobeused tocheck the sensitivity of the loadson thepanel position. Figure 26showstheresults for a 2 mhigh, 1mwidestructural panel within a 30 m radius bow structure. In thesecalculations, an Hs = 12m,Tp = 10ssea state has been processed for apeakednessof1andadurationof3 hours, The centreofthis structureis shifted trom 1 to21m above MSL with steps of2m.

The results indicate that most probable maximum (MPM) equivalentfcaressures up to 1600 kPa (160 m head of sea water) can occur once ina" hour sea state, when the panel centreisclose to the significant wavehcight above the MSL (close to the maximum crest height in the wave).

25-,

0 500 1000 1500 2000 2500

Equi\ralent Pressure [kPa]

Figure 26: Effect panel position above Mean Surface Level (Hs=12m)

Therefore iniis paper a design evaluation method was proposed.topredict die bow slam loading problem from ie input (scatter diagram)to theoutput (predictcd load andresponse levels) based on acleardescription of the bow slam physics. The methodisbased upon secondorder wave meory describing the wave steepness and an empiricalrelation between the wave steepness and ie local impact. The positionof this impact follows from acoupled time domain analysisofthe shipmotions. The method assumes long crested waves which are considereda worst case scenario.

In future work theprediction of the wave steepness can beimprovedwith higher order wave models and the inclusion of wave spreading.

ACKNOWLEDGMENTS

The SAFE-FLOW project (SAFI-FLOating offshore stmctures underimpact loading of shipped green water andWaves) isfunded by theEuropean Community under the 'Competitive and Sustainable Growth'Programme (EUProject No.: GRDl -2000-25656)and agroupof 26industrial participants (oil companies, shipyards, engineeringcompanies, regulating bodies), The participants areacknowledgedfortheir interesting discussion of theresults during theproject and iepermission to publish the present paper. The authors are solclyresponsible fordie present paper andit does nbt represent the opinionof the European Community.

The authors thank Trevor Hodgson (Galbraii Consulting), CarlosGuedes Soares (IST), Ricardo Pascoal (IST), Tim Bunnik (MARIN),Nigel Barltrop (NAME of Glasgow and Strathclyde), Ed Ballard(PAFA) and Sandy Fyfe (PAI;A) for thecooperation in theSAFEFLOW project, resulting in the method presented in this paper, whichisin detail reported in Buchner, Hodgson, Voogt (editors, 2004).

REFERENCES

Buchner, B., 2002, "Green WateronShip-type Offshore Structures".PhD-thesis Delft University of Technology

Buchner, B., HodgsonT.,Voogt, A.J. (editors), Ballard,E.,Barltrop,N., Falkenberg, E-,Fyfe, S.,Guedes Soares,C , Iwanowski,B.,Kleefsman, T., 2004, "Summary report on design guidanceandassessment mcthodologies forwave slam and green water impactloading", MARIN Report No. 15874-1-OE, Wageningen, TheNetherlands.

Barltrop,Nand Xu,L.,2004, "Wave Slap LoadingonFPSO Bows'\Naval Architecture & Marine Engineering of Glasgow &Strathclyde Universities (NAME)

Campbell I.M.C and Weynberg P.A., 1980,"Measurements ofparameters affecting slamming", Wolfson Unit for MarineTechnologyReport No. 440

Guedes Soares,C ,Pascoal,R.,AntSo, E.M, Voogt, A.J.andBuchnerB. 2004, "An approach to calculate the probabilityofwave impacton an FPSO bow", Proceedings of the 23" International

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Prediction of Wave Impact Loads on Ship-type Offshore Structures in Steep Fronted Waves

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