Advances in the Hydrodynamics of Side-by-side Moored Vessels

Proceedings of the 26th International Conference on Offshore Mechanics and Arctic Engineering OMAE2007 June 10-15, 2007, San Diego, California, USA

OMAE2007-29374 ADVANCES IN THE HYDRODYNAMICS OF SIDE-BY-SIDE MOORED VESSELS Willemijn H. Pauw

René H.M.Huijsmans

Arjan Voogt

MARIN, Wageningen The Netherlands

Delft University of Technology, The Netherlands

MARIN, Wageningen The Netherlands

KEYWORDS Diffraction methods, interactions, multi-body dynamics, sideby-side moorings, model test experiments

Offshore floating LNG systems become a more and more viable economic solution. The need for an accurate assessment of the hydrodynamic performance of LNG offloading systems is an important issue. LNG production offshore give rise to the need for a remote offshore berthing location, without the benefit of coastal protection against wind, waves and current.

ABSTRACT In this paper a comparison between model basin experiments and results of diffraction computations on side-by-side moored LNG carriers is presented. The computations are based on a new lid method in diffraction codes to suppress non-realistic high wave elevations between the two floating objects. This lid method was originally formulated by Chen (2005). In this method a damping value is added to the free surface by means of a damping parameter. Since no theoretical solution can be found to establish the required value of the damping parameter, model basin experiments have been performed to determine this value. However from the results of the model basin experiments it is shown that it is difficult to obtain one unique value of the lid damping (for the 4m or small gap). The way of tuning the damping value of the lid is crucial. Tuning the damping based on first order results, like motions or wave height RAO’s will lead to a much larger variation in the estimate of the second order sway wave drift force transfer function.

INTRODUCTION LNG carriers are used to transport the cargo from the floating LNG-FP(S)O to the shore or from terminal to terminal.

Calculation of the wave elevations at the waterline of the two floating bodies is necessary to calculate the wave drift force quadratic transfer functions (QTF’s) using a pressure integration scheme. In the model test campaign the wave heights are measured at the centerline between the two vessels, effectively at the wall of the model test basin. Unrealistic wave heights at the centerline will obviously also indicate their effects at the waterline between the two vessels. Conventional near field calculations result in unrealistic free surface elevations in the gap. Far field estimates of the QTF’s do not apply on the individual bodies of a multi body diffraction calculation. The middle field equation technique, to avoid spurious effects in pressure integration techniques is described by Chen (2006). The complex hydrodynamics of two floating bodies in close proximity has been a research topic for over two decades. Two main issues are to be considered. 1.The resonance behavior of the waves in the gap between the two vessels tends to be overestimated using standard diffraction programs. E.g due to non-linear effects in the physics of the waves like breaking tend to reduce the extreme wave elevations. 2. Viscous effects, neglected in diffraction theory, may be more dominantly present at the bilges of the keel due to the resonant flow between the two floating bodies. In our approach we disregards also any viscous effects at the tank wall and the hull of the vessel. For the viscous flow effects the current set-up is not applicable, then a full representation of the two side-by-side

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Copyright © 2007 by ASME

vessels is necessary. However, again this was neglected in our study. Different methods to reduce spikes in the QTF’s due to resonance effects have been reported. A suppression method based on the damping of generalized wave modes was given by Newman (2003). A simplistic approach to suppress the unrealistic wave motions was presented by Huijsmans et al. (2001) where a rigid lid was applied to the free surface between the two vessels. The formulation of this rigid lid approach is similar to the formulation to suppress irregular frequencies. A first attempt in applying the new damping lid method on multi-body hydrodynamics (Chen, 2005) was presented by Fournier et al. (2006). These studies showed that the lid method was effective in reducing the relative wave elevation and consequently in reducing the wave drift forces at the resonance peaks. In this case of a gap between the bodies of 25.m, it led to unique value for the damping of the lid both for the first order quantities as well as the second order wave drift forces. Also it was shown that no rationale could be found in establishing an a priori guess for the damping value for the lid. DIFFRACTION MODEL THEORY The damping lid method is based on the implementation of a damping force at the meshed free surface in between the two floating bodies (figure 1). This method can be implemented in standard diffraction theory programs. The theory behind the damping lid method, originally formulated by Chen (2005) is described briefly.

From Bernoulli it follows that the wave elevation at the free surface is:

1 g

ζ = − Φt −

At the free surface lid the boundary condition modifies to:

∂φ ω2 − (1 − iε ) φ = 0 ∂z g in which ω is the wave frequency and the non dimensional parameter ε is related to the damping parameter µ by:

ε=

µ ω

The selection of a damping parameter, ε can be determined such that either the computed wave elevation and/or the wave drift force transfer function can be fitted to the measured ones. The free surface condition of the conventional approach, no-lid, the rigid lid and the damping lid, are summarized in table 1. From the adapted free surface condition it becomes clear that also a frequency dependent epsilon value could be chosen. This was not done in this study for practical reasons. Table 1: Free surface boundary equations

Figure 1: The Free surface domain has been divided into F0, at which no damping is applied, Fi, the inner surface at which to suppress irregular frequencies and Flid where the boundary equation of the lid applies In the fluid a rotational free damping force is applied in the whole fluid domain as:

1 1 ∇Φ∇Φ − µΦ 2g g

Conventional Undamped wave elevation

Rigid lid Rigid No wave elevation

Damping lid Semi permeable Damped/tuned wave elevation

∂φ ω 2 − φ =0 ∂z g

∂φ =0 ∂n

∂φ ω2 − (1 − iε ) φ = 0 ∂z g

In order to be able to validate the damping lid method, model basin experiments have been performed.

F = µ∇Φ As such the force can be resembled as a sort of a frictional force. Applying the rotation free properties leads to a formulation that only is affected by the free surface boundary condition. Here Φ is the velocity potential and µ is the damping parameter.

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MODEL BASIN SET-UP Dedicated model basin experiments on side-by-side mooring of two floating bodies were carried out with one LNG carrier model, representing a general design LNG (table 2). The LNG carrier was positioned parallel, close to the side wall of the basin. Table 2: Main particulars and stability data of the LNG carrier Main particulars and stability data of LNG carrier Designation

symbol

unit

Length between perpendiculars Beam Depth Draught Displacement weight

Lpp

m

274

B D T ∆

m m m ton

Centre of gravity above keel Centre of gravity forward of st 10 Transverse metacentric height Roll radius of gyration Pitch radius of gyration Yaw radius of gyration Waterdepth Modelscale

KG LCG

m m

44.2 25 11 9775 9 16.1 -1.1

GMt

m

5.0

kxx kyy kzz d -

m m m m -

16.3 70.1 70.0 37.5 1:50

Figure 2: Test set-up representing a two body set-up. ( • is wave probe) The wall represents the centerline of the gap between the two bodies. The close proximity can be recognized in figure 3, the mirror on the picture helps to explain the function of the quay.

The wall acts as a mirror to the hydrodynamics, simulating a LNG carrier with an alongside moored identical LNG carrier at twice the distance to the wall (figure 2).

Figure 3: Model basin set-up Free floating (decay) tests, tests with the model moored in a soft mooring system and tests with the model rigidly fixed to a six component frame have been performed. The soft mooring system represents spring and brest lines; no fenders were modelled. The waterdepth was 37,5m and the model scale 1:50. A set of nine wave probes were located over the length of the gap close to the wall, approximately at the gap centerline in the two body analogy. The parallel position of the LNG carrier model to the basin wall restricts to head wave conditions. In the rigidly fixed setup two white noise wave spectra (WN), in soft mooring five operational sea states (O1-O5) have been generated with peak periods covering a large interval (5-20s). Regular waves with

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frequencies around the anticipated resonance frequency have been selected.

Calculated Wave RAOs between the fixed vessels

Comparison of the results of the model basin experiments with the results of diffraction calculations in which the damping lid has been implemented, requires a numerical model set-up which resembles the set-up of the model basin experiments. A two body panel distribution of two identical LNG carriers with a 4 meter gap in between is composed. At the free surface of the parallel part in between the two floating bodies the lid has been introduced.

@ st.10 -50m

8 6 4 2 0

0

0.5

1

1.5

0

0.5

1

1.5

1

1.5

@ st. 10

8 6 4 2 0

@ st.10 + 50m

8

ε=0.02 ε=0.05

4 2 0

Figure 4: Panel distribution, including the mesh of the lid, used in diffraction computations

ε=0 ε=0.01

6

0

0.5 frequency [rad/s]

WAVE PATTERN ANALYSIS Wave heights in the gap have been measured during fixed model tests. Interesting observations have been made considering the wave RAO’s, since no vessel motions affect the wave motions in the gap. Different mechanisms of wave interaction seem to appear in the gap between the two bodies. Firstly superposition of the incoming and diffracted waves results in cancellation in nodes at certain frequencies. This cancellation is dependent on the ratio between the gap dimensions such as the width and the length and the wavelength. This can be clearly recognized in figure 5. There the calculated wave RAO is presented for a range of values of epsilon for captive vessels. It shows the effect of cancellation of the wave at frequencies between 0.5 and 0.8 radians per second.

Figure 5 Wave RAO in Gap for fixed Vessels

Secondly resonance peaks seem to appear. In figure 5 sharp peaks can be recognized at 0.8 to 1.2 rad/sec. Several sloshing modes might appear, the most basic modes are the transverse sloshing, longitudinal sloshing and piston mode. Using linear potential theory simple quasi analytical approximations that yield the natural frequencies of sloshing modes in moon pools have been derived by Molin (2001). These formulations are used to approximate the three possible modes in the gap. In these calculations the length of the parallel part, width of the gap and draft of the vessel are taken into account. Results are presented in table 3. Although very crude assumptions have been made, this overview gives an idea on the variety of possible modes in the gap and on the complexity of the wave pattern.

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DISCUSSION In order to get a more detailed insight into the influence of the gap on the choice of the epsilon parameter model test experiments for a free floating and a fixed vessel in waves have been conducted.

Table 3 Approximated resonance frequencies

Calculated Wave RAOs between the vessels

Approximated natural frequencies of sloshing modes [rad/s] 4m

8m

16m

32m

2D

0.78

0.71

0.62

0.54

3D

0.75

0.67

0.58

0.49

mode 1

2.78

1.96

1.39

1.00

mode 2

3.93

2.78

1.96

1.39

mode 3

4.81

3.40

2.40

1.70

mode 1

0.91

0.88

0.83

0.75

mode 2

0.96

0.95

0.93

0.91

10 @ st.10 -50m

Gap width Piston

5

0

0

0.5

1

1.5

0

0.5

1

1.5

1

1.5

Long., 3D

@ st. 10

10

Trans. 2D

5

0

10

0.99

0.99

0.98

0.97

@ st.10 +50m

mode 3

5

0

Measured and Calculated First order Wave Loads

ε=0 ε=0.01 ε=0.02 ε=0.05

0


4

Fy [kN/m]

6

x 10

Figure 7 Calculated Wave RAO for free floating vessel for various values of epsilon

4 2 0

0

0.5

1

1.5

4

Mx [kNm/m]

15

x 10

10 5 0

0

0.5

1

1.5

1

1.5

6

Mz [kNm/m]

3

x 10

WN 1m 2

ε=0 ε=0.01 ε=0.02 ε=0.05

1 0

0


Figure 6 Measured and Calculated First Order Loads

The RAO’s of the absolute wave elevation at the gap center line and the first order wave forces on the LNG carrier (only the asymmetric forces Fy,Mx,Mz are presented, because in head sea they should be zero for a single body case) are presented in figure 6 to figure 10 The results of computations for various values of epsilon and results of white noise wave tests and other operational irregular wave tests are plotted. From the results of the RAO of the absolute wave elevation at position amidships (station 10, 0. m) it may be concluded that a value of epsilon of approximately 0.01 will fit the measured values of the absolute wave RAO most accurately (see figure 8). However for the first order wave load RAO’s one may conclude that a value of epsilon of 0.02 is more appropriate when observing the sway excitation force (see figure 6). From this figure 6 one observes that the calculated resonance peaks observed in the wave force tests are not in line with the experimental observed ones. This

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might be due to the fact that in the experiments resonance effects are diminished by non-linear type of effects. Measured and Calculated Wave RAOs between the fixed vessels

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Measured and Calculated Motion RAOs

2 0

0

0.5

1

@ st. 10

6 4 2 0

0.2

1.5

Y CO G [m /m ]

@ st.10 -50m

6

From the absolute wave RAO at amidships (st 10, 0.m) it may be concluded that a value of epsilon of 0.02 fits the measured data best (figure 8and figure 9).

0

0.5

1

0.15 0.1 0.05 0

1.5

0

0.5

1

1.5

0

0.5

1

1.5

1

1.5

WN1

1.5

ε=0.02

4

Roll [deg/m ]

@ st.10 +50m

6

2 0

0

0.5

1

1.5

frequency [rad/s]

1 0.5 0

Figure 8 Best Fit on based Irregular Waves

Y aw [deg/m ]

0.1

The RAO’s of the absolute wave elevation at the gap center line and first order vessel motions of a free floating vessel are presented in figure 9 and figure 10. The results of computations for various values of epsilon and results of both, measured regular as well as irregular waves (01-05), wave tests are plotted.

Measured and Calculated Wave RAOs between the vessels

@ st.10 -50m

4 3

ε=0 ε=0.01 ε=0.02 ε=0.05

0.05

O1-O5 0

0


Figure 10 Effect of Epsilon on motion RAO.

In figure 10 the measured and computed motion response ( the asymmetric modes) is displayed. Similar observations as encountered for the first order wave loads, as stated before, can be seen here as well.

2 1 0

0

0.5

1

1.5

0

0.5

1

1.5

1

1.5

8 @ st. 10

6 4 2 0

@ st.10 +50m

4

ε=0.02 3

O1-O5

2 1 0

0


Figure 9 Best Fit Wave RAO’s free floating

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CONCLUSION Calculated Mean Wave Drift Loads

Fx [kN/m2]

0 -50 -100 -150 -200

0

0.5

1

1.5

Fy [kN/m2]

2000

It can be concluded that no unique value of epsilon does fully cover the comparison with measured results. However for larger gap distances of for example 25 meters as presented by Fournier et al. (2006) a unique value of epsilon can be determined. However the main conclusion of this study is that tuning the damping value of the lid should be done on the second order wave drift force and not on the first order quantities, like absolute wave height and motion RAO’s. This because the epsilon parameter has a much greater effect on the drift forces than on the first order quantities. REFERENCES

0

X.B.Chen, 2005, Hydrodynamic analysis for offshore LNG terminals Proceedings of the 2nd offshore hydrodynamics symposium, Rio de Janeiro

-2000 -4000 -6000

0

0.5

1

1.5

4

Mz [kNm/m2]

2

x 10

ε=0 ε=0.01 ε=0.02 ε=0.05

0 -2 -4

0

R.H.M.Huijsmans, J.A.Pinkster, J.J. de Wilde, 2001, Diffraction and radiation of waves around side by side moored vessels. Proceedings of the 2001 ISOPE conference, Oslo Norway. Newman, 2003, Application of generalized modes for the simulation of free surface patches in multi body hydrodynamics. 2003 WAMIT Consortium report.

0.5

1

1.5

frequency [rad/s]

Figure 11 Computed Wave Drift Force RAO for Various values of epsilon

The calculated wave drift force transfer function in surge, sway and yaw is presented in figure 11. Here a pronounced effect of applying the lid is visible at the resonance frequency. The sensitivity of the epsilon parameter is much more dominant than for the first order quantities, like the absolute wave RAO and the wave load RAO. This in turn means that for the gap distance studied here tuning the value of the damping for the lid must be done for the second order wave drift forces and not for the first order quantities. From the first order quantities we determine a range of epsilon values between 0.02 and 0.05. Taking these values into the wave drift force calculation it will lead to a variation of the drift forces of more than a factor 5 at the resonance frequency.

J.B.Fournier, M.Naciri, X.B.Chen, 2006, Hydrodynamics of two side-by-side vessels, experiments and numerical simulations. Proceedings of the ISOPE 2006 Conference, San Francisco X.B.Chen, 2006, Middle-field formulation for the computation of wave drift loads (2006). Submitted for publication to the Journal of Fluid Mechanics B. Buchner, A. van Dijk, J.J. de Wilde, Numerical MultipleBody Simulations of Side-by-Side Mooring to an FPSO, Proceedings of the ISOPE 2001 Conference, Oslo Norway. B.Molin, On the sloshing modes in moon pools, or the dispersion equation for progressive waves in a channel through the ice sheet, Fluid Mech. (2001), vol 430, pp27-50, Cambridge University Press B.Molin, On the piston and sloshing modes in moonpools, J. Fluid Mech. (2001), vol. 430, pp. 27{50.

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