Proceedings of The Fifteenth (5) International Offshore and Polar Engineering Conference Seoul, Korea, June 9 4, 5 Copyright 5 by The International Society of Offshore and Polar Engineers ISBN -885-4-8 (Set); ISSN 98-89 (Set) Viscous Damping of Vessels Moored in Close Proximity of Another Object Gerrit de Boer and Bas Buchner Maritime Research Institute Netherlands (MARIN) Wageningen, The Netherlands ABSTRACT The focus of the hydrodynamic research has been on deep water applications during the last decade. Recent experience with mooring in close proximity with another object has shown that interaction effects play a significant role in the prediction of the motions and mooring loads. In typical close proximity situations such as side-by-side mooring and Gravity Based Structure mooring, strong interaction effects can be noticed not only for the wave forces, added mass and damping, but also on the drift forces. Further the viscous damping of the motions of the vessel in close proximity of another structure and moored in shallow water is a complex issue. Finally there is a significant interaction effect in the wind and current forces. In this (experimental) paper the effect of the waterdepth and the distance between LNG carrier and GBS in calm water is studied. Modeltest data for two waterdepths (5 and 5 meter) and distances between the LNG carrier and the GBS are analysed. Finally the application of these results in a numerical time domain simulation model is discussed. Results presented in this paper show that the damping is sensitive to the actual waterdepth and the actual distance between LNG carrier and the GBS. KEYWORDS: Multiple-body simulations; damping; offloading; LNG; GBS. INTRODUCTION In a lot of situations floating structures are moored in close proximity of other structures, see Figure : - during side-by-side mooring along a moored or sailing vessel (lightering) - in the case of mooring along a Gravity Based Structure (GBS) - when a vessel is moored along a quay in a harbour Complex hydrodynamic effects play a role not only in the wave forces, added mass and damping, but also to the viscous damping. The small distance between the sides of the structures results in large velocities of the flow around the bilges. The same applies between the bottom of the moored vessel and the seabed in shallow water. This results in viscous damping effects too. Finally there is a significant interaction effect in the wind and current forces. Fig. : Examples of mooring in close proximity of other structures: Offshore lightering (left), mooring alongside a GBS (right) The objective of the study was to develop and validate a numerical simulation model for the reliable prediction of relative motions and mooring loads during mooring of a vessel in close proximity of another object. For this purpose dedicated modeltests were carried out, focussing on the situation of a moored LNG carrier along a GBS in shallow water. The damping in the surge, sway, yaw and roll motions of the LNG carrier in close proximity to another object was studied with detailed decay tests with different distances of the LNG carrier to the GBS. BACKGROUND Recent experience with close proximity mooring in shallow water has shown that one of the most important issues is the viscous damping of the low frequency motions due to the low frequency viscous reaction forces. Wichers (987) has developed a complex model for viscous 8
damping both the still water and in current using results of modeltests of tanker models in the horizontal plane. For a close proximity situation the situation is even more complex due to interaction between a moored vessel and the other object. This interaction is illustrated schematically in Figure for a LNG carrier moored alongside a GBS. Due to the small distance between the LNG carrier and the GBS water velocities will be high when the LNG carrier is moving. Around the sharp bilges of the LNG carrier, the high water velocities results in vortex shedding, giving an important contribution to viscous damping. The application of bilge keels will enhance this effect. Fig.. Illustration of damping effects High water velocities will occur not only due to the close proximity of the LNG carrier and the GBS but also due to shallow water conditions at the GBS. The complexity is increased by the fact that both effects will interact as well. These viscous effects are not incorporated in the damping model of Wichers. Results from a simulation model and dedicated modeltests have been presented by Buchner (4). The model has initially been developed for a waterdepth of 5 meters and a gap of meters between LNG carrier and the GBS. The results showed that viscous damping data derived from modeltests are indispensable for the correct prediction of the motion response. Furthermore the validity of the use of the viscous data is restricted to a certain waterdepth and distance to another object. GENERAL TIME DOMAIN SIMULATION MODEL The response of a floating structure to waves in the frequency domain is generally described by means of a mass-spring system. Assuming a linear system in degrees of freedom, such analysis represents the equations of motions as: (Mkj a kj )x j bkj x j ckj xj Fk j k,... k,j = subscripts of hydrodynamic property in the k-mode as a result of motion in the j mode M kj = mass of structure a kj = added mass matrix b kj = damping matrix c kj = hydrostatic restoring matrix F k = external force in the k-th mode. () By applying the impulse response theory (see Cummins, 9, Van Oortmerssen, 97 and Buchner ), the following equations of motion for six degrees of freedom can be derived: t (Mkj m kj )x j R kj(t )x j( )d Ckj xj F k (t) () j x j = motion in j-direction F k (t) = arbitrarily in time varying external force in the k-mode of motion: - first order wave forces - low frequency drift forces - wind forces - non-linear viscous damping forces - interaction forces between (three) rigid bodies - current forces - mooring line forces M kj = inertia matrix m kj = added inertia matrix C kj = matrix of hydrostatic restoring forces R kj = matrix of retardation functions k,j = mode of motion. Ogilvie (94) has derived the relationship between the time domain and frequency domain quantities: akj mkj R kj(t)sint dt () bkj R kj(t)cost dt a kj = frequency dependent added mass coefficient b kj = frequency dependent damping coefficient = circular frequency. The retardation functions and the coefficients of (frequency independent) added inertia can be derived from frequency dependent damping values and the added mass at one frequency. R kj(t) b kj( )cost d mkj a kj( ') R kj( )sin 't d ' Once the system of coupled differential equations is obtained, arbitrary in time varying loading such as wave excited forces, current forces, non-potential fluid reactive forces and non-linear mooring forces may be incorporated as external force contributions. By rearranging the non potential fluid reactive (viscous) forces the motion equation becomes: t (Mkj m kj )x j R kj(t )x j( )d j bnon pot x kj j(t) Ckj xj F k (t) (4) (5) 8
b non pot kj = non-potential fluid damping coefficient In the Figure 5 an overview of the spring lines is given. These non potential fluid damping coefficients are obtained from modeltests. INITIAL SET OF MODELTESTS An initial set of modeltests was carried out in the offshore basin at a model scale of :5. The basin measures 45 meter by meter. The waterdepthh is variable by means of a moveable floor. The main dimensions of the LNG carrier and the GBS are listed in the Table. Table. Main dimensions of GBS and LNG carrier Destination Unit LNG carrier GBS Length between perpendiculars (Lpp) [m] 74. 8.5 Beam (B) [m] 44. 7 Draft (T) [m]. 5 / 5 The vessel was moored alongside the GBS by means of a soft mooring system. Between the vessel and the GBS no fenders were applied. During the modeltests no contact between LNG carrier and GBS has been recorded. The stiffness of the soft mooring system were chosen carefully in such a way that the natural period did not interfere with the wave spectra of the irregular sea tests also carried out (see Buchner 4). The soft mooring system consisted of 4 transverse spring lines and longitudinal springs. These spring lines are attached to component force transducers placed near the bow and the stern of the LNG carrier (see photos). Fig. 5. Overview spring lines The LNG carrier was placed in the centre of the basin. Fig.. Test set-up Offshore basin The nominal stiffness of the transverse spring lines is kn/m. For the longitudinal spring lines a nominal stiffness of kn/m was used. These spring lines give a nominal stiffness in surge, sway and yaw direction of kn/m, 8 kn/m and 9 kn.m/rad. With the above described vessel and test set-up decay tests was carried out for the surge, sway, roll and yaw motion. The motions of the LNG carrier were measured by means of an optical device. The initial offset for these tests was applied manually. Each decay test has been repeated once. It was found that the decay tests could be reproduced accurately, see Figure 7. Fig.. Two-component force transducer system at the bow 4 Surge [m] - -4 - Fig. 4. Two-component force transducer system at the stern 4 5 Fig. 7. Two decay tests t [s] 8
SECOND SET OF MODELTESTS In the second series of modeltests the LNG-vessel, the GBS and the complete test set-up was brought to the shallow water basin. This basin measures meters long and 5.8 meters wide. For this basin the waterdepth was adjusted by letting water out of the basin. The GBS was placed perpendicular to the length axis of the basin (see Figure 8). Fig. 8. Test set up Shallow water basin The loading condition applied was similar to the condition used in the Offshore Basin. Prior to the modeltests a number of standard verification tests (e.g. GM check) was carried out. Also in this second set of modeltests the motions of the LNG carrier were measured by means of an optical device. In the next table the conditions of the initial and the second set of modeltests are given. Table. Test overview Basin WD Gap LNG GBS [m] [m] carrier Offshore basin 5 present not present Shallow Water Basin 5 9 present present Offshore basin 5 present present Shallow Water Basin 5 present present Shallow Water Basin 5 present not present Shallow Water Basin 5 9 present present Shallow Water Basin 5 present present Shallow Water Basin 5 present present This table shows that reference-tests were also carried out with the GBS not present. ESTIMATING MASS AND DAMPING COEFFICIENTS FROM A DECAY TIME TRACE The determination of the mass and damping coefficients is based on the next motion equation: M. x ( t) b. x linear ( t) c. x( t) () x = LNG carrier motion M = inertia including added inertia c = stiffness b linear = linear damping coefficient The stiffness C is obtained from the soft mooring system. The motion equation is solved for initial estimated mass and damping coefficients. The calculated time trace is compared with the measured time trace. An optimalization algorithm, which minimizes a penalty function (see below), gives the best estimates which can be found for the mass and damping coefficients. PenaltyFunction n samples ( xmeasured ( i) xcalculated ( i)) (7) i All decay tests were repeated once. The fit procedure as described above can be carried out for the two tests individually. In general this results in two different estimates of the mass and the damping coefficients. The average of these two estimates can be taken. Another approach is to carry the fit procedure for both tests simultaneously. nsamples PenaltyFunction ( x ( i ) x ( i )) x = LNG carrier motion test y = LNG carrier motion test i nsamples i measured calculated (y (i) y (i)) measured calculated Crucial input for the fit procedure is the stiffness of the mooring system. The stiffness can be computed from the nominal stiffness of the mooring system. Another option is to use the decay test results. In Figure 9 the total restoring force in longitudinal direction is plotted against the surge motion of the LNG-carrier for a surge decay modeltest. The recording gives a more or less straight line which allows a clean determination of the actual stiffness of the mooring system. Fx [kn] 4 - - - -4 - -4-4 X [m] Fig. 9. Longitudinal restoring force versus surge motion. In Table the stiffnesses applied in the fit procedure are given: Table. Stiffnesses Designation Sym Unit Stiffness bol Surge stiffness c-x kn/m 7 Sway stiffness c-y kn/m 8 Roll stiffness c-xx kn.m/rad 4.8e Yaw stiffness c-zz kn.m/rad 9 (8) 84
RESULTS The fit procedure described above has been applied for all conditions. The obtained values are given in the Tables 4, 5 and. Table 4. Natural periods Natural Period Surge Motion (s) WD 5 8. 8. 84.8 8. WD 5 77.7 78.5 78.9 79. Natural Period Sway Motion (s) WD 5.4 4.9 8.7 9.8 WD 5 97.9.5. 4. Natural Period Roll Motion (s) WD 5 7. 7. 7. 7. WD 5 5. 5.7 5.8 5.8 Natural Period Yaw Motion (s) WD 5 49.8 5. 5.8 5. WD 5 4. 44.5 44.8 45. Table. Derived equivalent linear damping coefficients Linear Equivalent Damping Coefficient Surge Motion (kn.s/m) WD 5.97E+5.997E+5 4.458E+5 4.87E+5 WD 5.9E+5.E+5.54E+5.E+5 Linear Equivalent Damping Coefficient Sway Motion (kn.s/m) WD 5.7E+.889E+.99E+.744E+ WD 5.44E+.49E+.7E+.9E+ Linear Equivalent Damping Coefficient Roll Motion (kn.m.s/rad) WD 5.89E+9.59E+9.858E+9.5E+9 WD 5 9.59E+8 8.57E+8 8.E+8 9.7E+8 Linear Equivalent Damping Coefficient Yaw Motion (kn.m.s/rad) WD 5 7.9E+7 8.8E+7 8.54E+7 7.89E+7 WD 5 5.44E+7.47E+7 4.8E+7 4.87E+7 In Figures, and the data is plotted against the (/gap distance) value. Table 5. Derived total mass Total Mass Surge Motion (t) WD 5 447. 9.7 47.4 49. WD 5 9. 9557. 9449.9 977. Total Mass Sway Motion (t) WD 5 744. 589.8 54. 44.7 WD 5 948. 48. 95.9 897. Total Mass Roll Motion (t.m^) WD 5 47. 44. 58. 559795. WD 5 8749. 974. 9944. 9479. Total Mass Yaw Motion (t.m^) WD 5 894. 7549. 84784. 78894. WD 5 5755. 548485. 5588. 578. Roll Surge 8 84 8 8 Nat.period(s) 78 7 7.5 7.5 5.5 Fig.. Natural period Sway Yaw Nat.period(s) 9 54 5 5 48 4 44 4 85
Surge Roll.5 x 8..5 Total Mass.95.9. x.4..8 Sway.5 x 8.5 Total Mass.5 Yaw 9 x 9 8 7 5 Both tests have been screened carefully and no irregularities have been found. Consequently the tests in the shallow water basin have been screened. Again no irregularities were found. In the shallow water basin the model is located perpendicular to the basin axis. This orientation means for the surge motion that the walls of the basin are relative nearby. Unfortunately no surge decay motion test was carried out both in the Offshore basin and the Shallow Water basin. Application The above presented data can not be used directly in the time domain simulation model. In the simulation model added mass and damping derived from diffraction is already included. Double counting effects must be avoided. Fig.. Total mass (including added mass) Surge 4.5 x 5 4.5 B lin equi.5.8 x 9 Sway.5 x.5 B lin equi 9 x 7 8 In first instance the time domain simulation is carried out with only the mass matrix and the retardation-function-matrix from a diffraction analysis. No additional mass or damping is yet included. The computed time traces are analysed in a similar fashion as for the modeltests results. By subtracting the computed from the measured results the non-potential contributions are derived. This data can be used as input for the simulation model. madd. mmt msim blinear add. blinear MT blinear SIM (9) Roll..4. Yaw 7 5 suffix MT means value derived from the decay modeltests suffix SIM means value derived from the initial simulation.8 4 With the above mentioned additional mass and damping coefficients the equation of motion (5) becomes: Fig.. Linear equivalent damping coefficient The effect of the waterdepth on the damping is clearly demonstrated in the graphs. In general the damping increases with a decreasing waterdepth. This effect is not only found for the LNG carrier moored alongside the GBS but also for the LNG carrier alone. The effect of the size of the gap between LNG carrier and the GBS is not so clear. A slight increase of the damping is found for the surge motion. For the sway motion the effect is opposite; a decrease of the damping value is found. The results for the roll and the yaw motion do not show a specific trend. The effect of the waterdepth on the natural period can be found for all 4 motions; a decrease of the waterdepth gives an increase in the natural period. Again this effect is also found for the LNG carrier alone. A similar effect if found for the effect of the size of the gap between LNG carrier and GBS. Decreasing the size of the gap gives an increase of natural period. A more or less consistent influence is found for all four motions, except for the surge motion where two conditions were suspicious. These two conditions are the LNG carrier alone and with a gap size of meters. Both two conditions were tested in the Offshore basin. t (Mkj mkj m add. )x kj j R kj(t )x j( )d j b linear _ add.x kj j(t) Ckj xj F k (t) With this approach an excellent agreement is found between the simulation model and modeltest as shown by Buchner (4). CONCLUSIONS AND RECOMMENDATIONS In the present study the results are presented for dedicated modeltests with systematic variation of waterdepth and gap between a LNG carrier and a Gravity Based Structure. The objective was to obtain data which can be used in an extended numerical model for time domain simulation. The results show that: - A strong and complex hydrodynamic interaction occurs when a floating body is moored in shallow water. - This complex hydrodynamic interaction also found when a floating body is moored in close proximity of another object. - Results from dedicated modeltests are indispensable for the correct numerical modelling and prediction of the low frequency (relative) motion response. () 8
The following further research is recommended: - The rectangular shape of the Gravity Based Structure is arbitrary chosen. The effect of the shape on the hydrodynamic interaction has not been investigated in this study. - This present study only considers still water conditions; the effect of current (interaction) is not taken into account. The complex hydrodynamic interaction might be influenced strongly by the current and waves. REFERENCES Buchner B., de Boer G. and de Wilde J.J. (), The Interaction Effects of Mooring in Close Proximity of Other Structures, ISOPE 4, Toulon. Buchner B., van Dijk A.W.V. and de Wilde J.J. (), Numerical multiple-body simulations of side-by-side mooring to an FPSO, Proc Int Offshore and Polar Eng Conf, ISOPE, Stavanger, ISOPE, Vol, pp 4-5. B. Buchner and G.E. Loots G.Z. Forristall and E.J van Iperen, Hydrodynamic Aspects Of Gravity Based Structures In Shallow Water, Proc Offshore Tech Conf, OTC paper 7, Houston Cummins, WE (9). "The Impulse Response Function and Ship Motions", DTMB Report, Washington D.C. Huijsmans, RHM (99), Mathematical Modelling of the Mean Wave Drift Force in Current. A Numerical and Experimental Study, PhD thesis Delft University of Technology. Huijsmans, RHM, Pinkster, JA and Wilde, JJ de (). Diffraction and Radiation of Waves Around Side-by-Side Moored Vessels, Proc Int Offshore and Polar Eng Conf, ISOPE, Stavanger, ISOPE, Vol, pp 4-4. Inoue, Y and Islam, M (999). Relative Motions of Multiple Floating Offshore Structures, Offshore Mech & Art Eng, St. Johns. Ogilvie, TF (94). "Recent Progress toward the Understanding and Prediction of Ship Motions", Fifth Symposium on Naval Hydrodynamics, Bergen. Oortmerssen, G van (97): "The Motions of a Moored Ship in Waves", NSMB Publication No. 5. Oortmerssen, G van (98): "Some Hydrodynamical Aspects of Multi-Body Systems", Int. Symp Hydrodynamics in Ocean Eng. Pinkster, JA (98). "Low Frequency Second Order Wave Exciting Forces on Floating Structures," PhD Thesis, Delft University of Technology. Teigen, P (). Numerical Aspects of Multiple Body Hydrodynamics, Proc Int Offshore and Polar Eng Conf, ISOPE, Seattle, ISOPE, Vol, pp 5-7. Wichers, JEW (987). A Simulation Model for a Single Point Moored Tanker, PhD thesis Delft University of Technology. 87