Steady current forces on tanker-based FPSOs

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Steady current forces on tanker-based FPSOs

by

RS. Mercier, OTRC, Texas A&M University, USA F.A. Huijs, Deift University of Technology, Ship

Hydro-mechanics Laboratory, The Netherlands

Report No. 1455-P 2005

Presented at the Fluid Structure Interaction and

Moving Boundary Probiems,ISBN 1-84564-027-6, Edited by: S. Chakrabartl, Transaction: Engineering

Sciences Volume 84, Published: 2005

Fluid Structure Interaction and Moving Boundary Problems

Transaction: Engineering Sciences volume 84 OnHne ISSN: 1743-3533

Print ISBN: 1-84564-027-6

Edited By: S. CHAKRABARTI, Offshore Structure Analysis Inc., USA, S. HERNAN DEZ, University of Coruna, Spain and C.A. BREBBIA, Wessex Institute of Technology, UK

Published: 2005 Pages: 720

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Fluid Structure Interaction and Moving Boundary P ro b le m s

Transaction: Engineering Sciences volume 84 Online ISSN: 1743-3533

Print ISBN: 1-84564-027-6

Edited By: S. CHAKRABARTI, Offshore Structure Anal USA, S. HERNANDEZ, University of Coruna, Spain and BREBBIA, Wessex Institute of Technology, UK

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Steady current forces on tankerbased

FPSOs

R. S. Mercier' & F. A.

Huijs2

'Offshore Technology Research Center, Texas A&M University, USA

2Delfi University of Technology, The Netherlands

Abstract

There is very little information available in the public domain on steady current forces on tanker-based Flòating Production, Storage and Offloading systems (FPSOs). The general lack of available data and unresolved issues related to

scale effects in model tests bring into question whether the level of uncertainty in modelling of current forces on FPSOs is sufficiently well understood, which has

implications for the design of FPSO station-keeping systems. This paper

presents the results of a test program to measure current forces on a tanker-based FPSO at various current speeds and relative current headings While the results

are in general agreement with the design curves published by OCIMF, there are some important differences associated with the effect of bilge keels and the

effect of lift forces generated by vortex shedding from the bow and stem. Keywords: current forces, tankers, FPSOs, scale model tests, bilge keels.

i

Introduction

Steady forces exerted by ocean currents on deepdraft, column-based structures such as tension leg platforms or spars are relatively'straight forward to estimate using textbook information on bluff body drag. In the case of tanker-based Floating Production, Storage and Offloading Systems (FPSOs), there is very

little public domain information on drag and lift forces in steady currents that can be used for routine design calculations.

:Remery and' Van Oortmerssen [I] presented a method to predict current forces on moored tankers based on several model tests conducted at the

Netherlands Ship Model' Basin (currently MARIN). Since the authors felt the

small löngitudinal forces were not measured with sufficient accuracy, they

proposed that the ITTC-1957 frictional' resistance formulà be used' to predict the

lóngitudinal force. For the transverse force and' yaw moment coefficients they

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proposed these to model the variation of each coefficient with relative curreht

heading. They reasoned that since a tanker is a blunt body for flow in the lateral direction and since the bilge radius is small, flow separation would always occur

at the bilge so that the lateral current force and yaw moment coefficient should

be independent of Reynolds number. The calibrated Fourier coefficients

provided in the paper are applicable to a vessel moored in deep water. A curve

was provided for adjusting the force coefficients for shallow water effects.

Edwards [2 claimed that, contrary to results reported in [1]: and [3], the influence of Reynolds number on the läteral current force and yaw moment is

significant, in particular due to changes in the nature ofthe vortex shedding from

the bow and stern and transitión from laminar to turbulent boundary layer flow. The conclusions were based on tow tests performed on a i :24 scale model of a drillship in deep water and current tests performed on a I :45.5 scale model of a tanker in very shallow water Since these changes appeared to occur in the Reynolds number range of I x I O tú 5 x i O (based on the beam), Edwards

recommended that a systematic series of tests should be conducted at high

Reynolds numbers using 6 to I O rn long ship models in order to óbtain more

reliable force coefficients foruse in design analysis.

The Oil Companies International Marine Forum (OCIMF) publication on prediction of wind and current loads on VLCCs [3, 4] has been a most useful reference for the past 25 years. The publication provides curves for the current force coefficients as a function ofangle of attack, vessel draft, bow shape, and

water depth to vessel draft ratio. The curves are based on four model test

programs performed by MARIN from 1968 to 1990 with tankers ranging from

190 to 540 kDWT and prototype current speeds ranging from I to 2.6 mIs. The test results were interpreted based on Froude scaling under the assumption that for current angles that are not too small the force and moment coefficients

should be independent of Reynolds number. The test data on which the curves are based are not presented' so it is not possible to gauge the variability in the resu1ts

Since there is very little information available from other sources, the

so-called OCIMF data and load calculation procedures are built into many common

software packages used to analyze the behavior of moored ships. According to OCIMF, the curves provided in reference [4 are valid for vessels geometrically similar to VLCCs with 'length to beam ratio from 6.3 to 6.5, beam to draft ratio

from 2.2 to 2.6, and for bilge radius to beam ratio from O to 0.07. An interesting

conclusion made by OCIMF 'is that, for the range of tankers tested, bilge keels

have no impact on the current force coefficients.

The general' lack of available data and unresolved issues related to scale effects bring 'into question whether the level of uncertainty in modeling of

current forces on FPSOs is sufficiently well understood, which has implications for the design of FPSO station-keeping systems. Edwards [2] concluded that the use of OCIMF coefficients willi result in conservative estimates of ship' response,

power requirements for dynamic positiöning, and' tensions in mooring systems. Nevertheless, understanding the viscous scale effect at model scale is important

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complex situations where current acts in combination with waves to generate

slow drift forces on a moored tanker.

This paper presents the results of_{a test program to measure current forces on} a tanker-based FPSO at various current speeds and relatiye current headings. Measured forces for the FPSO with and without bilge keels are compared with

available information in the literature and significant differences are highlighted.

2

_{Current force model}

The approach for modelling current forces on FPSOs adópted herein is identical

to that presented in reference [4]. Only the horizontal plane forces and yaw moment are addressed.

F

STERN _BOW

CURRENT

Figure 1: Sign convention.

The force and moment components are defined in a body-fixed coordinate

frame illustrated by Figure 1 and they are given by

F =

CFxpV2LBPT,

i;; =

!CPV2L

_(I)

M = -- CM. p V2

T.

where F is the longitudinal force, F is the lateral force, M is the yaw moment,

and the associated dimensionless force and moment coefficients are

C, CF

, CM ,.respectively. The remaining variables are the vessel draft T

and length between. perpendiculars Lßp, the current velòcity V and the fluid

density p.

WIT Transactions on The Built Environment, Vol 84, 02005 WIT Press www.witpress.com, ISSN 1743-3509 (on-line)

(16)

attack of the current O, the Froude and Reynolds numbers, the hull form, the vessel draft, and the water depth to vesse] draft ratio. For_{currents flowing past} moored FPSOs in deep water the associated Froude numbers are sufficiently

small that free surface effects are not significant.

3

Experimental setup

A 1:60 scale model of a 200 kDWT FPSO (Figure 2) was tested at the Offshore

Technology Research Center model basin. The basin is 30.5 m wide by 45.7 m

long with a 5.8 m water depth. _{Local current is generated using an internal}

circulation system with a total flow capacity of 136 m3/min. The flow is pumped through an array of 297 nozzles. For this experiment the nozzle array was set up

to produce a mildly sheared current profile throughout the depth of the basin (0.015 to 0.035 s_I vertical velocity gradient). A stronger current gradient of

0.15 to 0.20 s_I was observed near the free surface over the draft of the FPSO.

Figure 2: FPSO model.

The FPSO was mounted beneath a bridge spanning the width of the basin through a six-axis load cell (Figure 3). Table I summarizes the main particulars of the FPSO, which was equipped with detachable bilge keels. The bilge keels

extended from 79.4 m to 203.5 m aft of the forward perpendicular, full scale. Table 1: Main particulars of the FPSO.

I

Description Symbol Unit Prototype Model

Displacement kDWT 200

Length between perpendiculars LBP m 310 5.17

Beam B m 47.2 0.787

Draft T m 15.1 0.252

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Figure 3: FPSO mounting in basin and close-up of load cell.

The bottom of the load cell was fixed to the deck of the FPSO model at

midship. The top of the load cell was fixed to a pair of circular turning plates in

the center of which was a guide pin. The top plate was fixed to the bridge

through a vertical box beam. The FPSO heading was adjusted by releasing the clamps on the horizontal turning plates, rotating the model to the desired angle, then re-clamping the plates together. Following each change of heading the vertical alignment of the beam was checked and adjusted as necessary to ensure the FPSO was level on its draft mark, and the load cell was re-zeroed. The load cell rotated with the model so the force measurements were made directly in a

vessel-fixed frame of reference.

Current tests were performed for six angles of attack (180°, 165°, 1500, 135°,

120°, 90°) and four model scale current speeds (6.1, 13.3, 18.3, and 25.6 cm/s) with the FPSO at mid-draft, both with and without bilge keels. Based on the beam dimension, this corresponds to Reynolds numbers 0.48, 1.04, 1.44 and

2.0 1x105. To ensure steady state flow conditions, the current was allowed to run

for a period of I-hour prior to starting a test. Each test was 30 minutes in

duration. All data channels were analog filtered using 2-pole Butterworth filters

with 10 Hz cutoff frequency, then digitally sampled at 40 Hz.

The current force tests were preceded by an extensive series of current measurements to map the current velocities in the basin at different pump

settings. Velocity measurements were made over a square horizontal grid with 1.5 m spacing (model scale) and at two depths, 0.15 m and 0.45 m. Using these

results it was determined that the horizontal variability in the mean velocity over

the region of the basin occupied by the FPSO model was less than ±8%. The

temporal variability (or turbulence intensity) in the region occupied by the FPSO

model varied from 12% to 17%. For all but the lowest (0.47 mIs) current, the

speed at 0.45 m depth was 3% to 4% less than that at 0.15 m depth. For the 0.47

mis current the speed at 0.45 m depth was 11% less than that at 0.15 m depth. The current speed used in deriving the force coefficients was the average of the

speeds measured at 0.15 m and 0.45 m depth.

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4 Test results

It is instructive to step though the analysis of the data to obtain a sense for the various sources and magnitudes of variability underlying the fiiïal estimates of

the force coefficients. Figure 4 shows the time series' of normalized force from a

current test at, 1500 angle öf attack and] Reynolds' number Re = 1.44 x iø with' bilge keels mounted on the hull. The forces were normalized as indicated in

eqn (1).

Longitudinal Force

Figure 4: Typical measured force time series.

The force coefficient is the mean value of the time series, in this case 0.36 for the lateral force and -0.0119 for the longitudinal force. It is evident that there is substantial temporal variability in the force time series. The standard deviation of the lateral force is 33% of the mean while 'that of the longitudinal force is

129% ofthe mean.

Spectral analysis' ofthe time series indicates there are three primary sources

of temporal variability i' the force: high frequency (3 Hz) inertial' oscillätions of the FPSO model, turbulence in the incident flow, 'and vortex 'shedding/wake flow

interaction. The first two sources are artefacts of the experimental setup while

the third source is, of relevance to the prototype (although 'subject to viscoUs scale effects) The' 'inertial oscillations may be easily isolated and filtered out.

WIT Transactions on The Built Environment, Vol 84, 02005 WIT Press' www.witpresscôm, ISSN 174335O9 (on-line)

1800

1600

600 800 1000 1200

ModelScale Time (s)

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flow from the wake flow effects. Since the location of flow separation on a

FPSO is gçnerally independent of the incident flow, 'one can argue that the

turbulence has minimal1 impact on the mean force However the fluctuations in

the force associated with vortex shedding are of interest to designers' if they are

significant relatiye to' the mean value

For the case where the Reynolds number Re 1.44 x li0, FigUre 5 compares

the observed heading dependence of the longitudinal force coefficient With

predictions using the model proposed by Remery and Van Oortmerssen [i].

Trend lines are provided to facilitate interpretation of the data While the test

results are quite different than the model predictions, they are in reasonable

agreement with OCIMF [4] except for angles of attack near 1800 and 90°.

- - - Remery & Van Oortmerssen

s

Current test - w/o bilge keels

A Current 'test - with bilge' keels

/

---

__i

F80 I!65 i 50 135 120

Ai

s

,

ç

Current Ane of Attack (deees)

i05 90

-0.02

Figure 5: Longitudinal: force coefficient for 'Re = '1 .44 x F05.

As noted in [I], [2] and [4], and illustrated 'in Figure 5, there are inherent

inaccuracies in' determining the small mean longitudinal force coefficients,

consequently there is a 'noticeable lack of consistency in the variation with angle

of attack. This lack of consistency is particularly evident 'in the results for the FPSO without bilge keéls However,, given the' apparent uncertainty in the determinatiòn of the longitudinal force' coefficient5 it is' difficult to attribute a

significant difference' between the results for the two vessel configurations (with' and without bilge keels).

The longitudinal force near 180° and 90° angle of attack is' strongly dependent on the' details of the bow 'and' stem configuration so it shOuld not 'be surprising

that' there are differences in results from different sources. For example,

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longitudinal force is purely due to asymmetry in the wake flow near the bow relative to that near the stern The OCIMF curves indicate a longitudinal force tending to zero near 85° angle of attack, however on physical grounds it seems that there should be considerable variability n the force coefficient near this

limiting heading, as supported by the experimental resúlts presented herein.

Apart from a noticeable effect of current speed on the longitudiñal force

coefficient for angles of attack. near 1800, the test results do not indicate a strong

or consistent dependence of the force coefficients on Reynolds number. The force coefficients for Re > 1 x iO5 are iñ better agreement with the referenced

infonnation than those below that threshold., Figure, .6 compares the. measured

lateral force coefficient with the Fourier seriés model proposed by Remery and Van Oottmerssen' [1 j: for the case where the Reynolds number Re = 1.44 x l.0. Trend lines, are again provided to facilitate interpretation of the 'data. The test

results for the FPSO with bilge keels are fli very good agreement with the

Remery and Van Oortmerssen model.

- 'Remery & Van Oortmerssen

Current test - w/o bilge keels

A Current test- with biIgekeeIs

18OE 165 150 135 120 105 90

Current Angle of Attack (degrees)

Figure 6: Lateral force' coefficient for Re = 1.44 x l!0.

The test results for the FPSO without bilge keels presented in Figure 6 are in

good agreement with the OCIMF [4] curve for deep water. 'However, contrary to

OCFMF, the experimental results show a consistent effect of bilgç keels on the

lateral force coefficient. In particular, for angles of attack ranging from 9O' to

1500 the lateral 'force is increased by' at least 50% when bilge keels. are added.

This behaviour is consistent with the known performance of bilge keels in

providing additional damping to mitigate roll motions of monohull's [5].

The variation of yaw moment coefficient with angle of attack is illustrated in'

Figure 7. The test results for the FPSO Without bil'ge keels are in good

1.2 u 08 o L) '0.6 Q) o 0.4 0.2 0 o 0:2

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180 ¡65 150 135

for angles of attack ranging from 900

to 150° the experimental results consistently show that bilge keels increase the yaw moment.

- - 'Remery & Van Oortmerssen

Current test - w/o bilge keels A Current test - with bilgekeels

120 105

Curreñt Anglè ofAttack(degrees')

Figure 7: Yaw moment coefficient for Re l .44 x 1i0

5

Cónclusions

In measuring horizontal current forces on a tatiker model there are several

mechanismsthat result in dynamic force variations, including inertial. oscillátións of the model, turbulence in the iñcident flów, and vortex shedding from the hull.

While the first two mechanisms are experimental artefacts, dynamic force variatiOns due to vortex shedding are of iñterest to designers if they are of

significant magnitude relative to the mean value. Unfortunately there appears to

be little,, ifany, information on dynamic forces associated with vortex shedding from moored tankers. Although beyond the. scope of this paper, this is a topic

worthy of further study.

If the dynamic force oscillations are very large relátive to the mean valúe, as is generally the case for' the longitudinal current force, then there is potential for

loss of accuracy and inconsistencies in results reported from different sources.

'The longitudinal' force coefficients. presented herein are significantly larger than the predictions of a model proposed by Remery and' Van Oottmerssen [1].

For the 'lateral current force and the 'yaw moment the dynamic variability

relative to the mean is not so large and the' mean; force coefficient should not be

highly dependent on the Reynolds number'(at least for Re> I x l.0). While the

results presented are in reasonable agreement with those' from other sources,

there are some important differences. OCIMF [4]' specifically concluded that bilge, keels had no effect on the current forces for the range of tankers tested' This conclusión is inconsistent with the well' known effectivenessof bilge keels in mitigating vessel roll motions. The experimental results presented

consistently show a significant bilge keel efféct, resulting in larger lateral force

and yaw .ornent than' indicated by OCIMF [4' for' broadside 'angles of attack.

0.08 0.06 0.04 , o 0.02 E o O

\'90

>! -0.02 -0.04

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sections in generating lift forces near the limiting 90° and 270° angles of attack.

While OCIMF addresses the impact of different bow configurations, it appears that the range of the longitudinal force near 90° is larger than indicated in [4].

Acknowledgements

The authors wish to thank the Offshore Technology Research Center for

providing financial support through its Cooperative Agreement with the. Minerals

Management Service and through its Industry Consortium. The views and

conclusions contained in this document are those of the authors and should not

be interpreted as representing the opinions or policies of the U.S. Government.

References

Remery, G.F.M. and Van Oortmerssen, G., The mean wave, Wind and

current forces on offshore structures and their role in the design of mooring

systems. Offshore Technology Conference, OTC 1741, Houston, 1973.

Edwards, R.Y., Hydrodynamic forces on vessels stationed in a current.

Offshore Technology Conference, OTC 5032, Houston, 1985..

Oil Companies International Marine Forum, Prediction of Wind and Current Loads on VLCCs (J Ed.), 1977.

[4.] _{Oil Companies International Marine Forum, Prediction of Wind and Current}

Loads on VLCCs(2ndEd.),, Witherby and Co.: Londön, 1994.

[5] Yeung, R.W., Roddier, D., Alessandrini, B., Gentaz, L., and Liao, S.-W., On

roll hydrodynamics of cylinders fitted with bilge keels. Proc. Twenty-Third

Symposium on Naval Hydrodynamics, Val De Reuil, France, 2000.