NUMERICAL INVESTIGATION ON THE HYDRODYNAMIC PERFORMANCES OF A NEW SPAR CONCEPT
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473 Ser.B, 2007,19(4):473-481 NUMERICAL INVESTIGATION ON THE HYDRODYNAMIC PERFORMANCES OF A NEW SPAR CONCEPT* ZHANG Fan, YANG Jian-min, LI Run-pei, CHEN Gang State Key Laboratory of Ocean Engineering, Shanghai Jiaotong University, Shanghai 200030, China, E-mail: firstname.lastname@example.org (Received August 22, 2006; Revised September 28, 2006) ABSTRACT: Recently, the spar platform concept develops Main feature of the classic spar is its quickly in the offshore oil and gas exploitations, especially in deep-draft vertical cylinder hull, which presents deep and ultra-deep water, owing to its benign motion excellent motion characteristics even in severe sea performance, excellent stability and adaptation to wide range of states. However, in some sea area, where the water depth. Many new spar concepts have been put forward ambient deep current becomes a major factor, the with the purpose of reducing fabrication difficulty and cost, while meeting the requirements of exploitation in the meantime. drag on the large cylindrical shape can be Based on the aims mentioned above, a new spar concept was significant. In such a case, a truss spar is an presented in this article and its hydrodynamics both in attractive alternative[5, 6]. The truss spar is also more operating and survival conditions was studied by means of structurally efficient when substantial crude storage numerical simulation. Basic model tests were also conducted to is not required. It consists of a top hard tank and a calibrate the numerical approach. Following aspects are bottom soft tank separated by a truss mid-section. highlighted: (1) new spar concept, (2) global performance of Horizontal steel plates are fitted across the truss the spar concept and (3) mooring line analysis. bays to reduce heave motion by increasing both the added mass and damping for the structure. In KEY WORDS: spar platform, time-domain coupled analysis, addition, it has a much lower drag area than the hydrodynamic performances classic spar mid-section so that the current and associated mooring loads are reduced [7,8]. The cell spar is a new design that has several physical 1. INTRODUCTION characteristics that are different from those of the Since the installation of Neptune production classic and truss spars. Its upper portion is spar platform in the Gulf Of Mexico (GOM) by composed of six out cells surrounding a center cell Kerr-McGee in 1996, spar technology has been to provide the buoyancy, while the lower portion is developed quickly in recent years[1,2]. As a deep sea formed by extending three of the outer cells down oil and gas exploitation facility, the spar platform to the keel. This concept was put forward basically has aroused broad attentions, due to its adaptation in consideration of the reduction of fabrication of wide range of water depth and benign motion difficulty and cost, as the standard rolling technique characteristics. From the first generation of classic could be taken in. spar, spar platform has evolved into the second Based on the spar characteristics mentioned generation of truss spar. A new configuration of above, this article presents a new spar configuration spar platform - the cell spar is presently used in worked out by the State Key Laboratory of Ocean Texas[3,4]. * Project supported by the Major Fundamental Research Program of Science and Technology Commission of Shanghai Municipality (Grant No. 05DJ14001) and the National High Technology Research and Development Program of China (863 Program, Grant No. 2006AA09A107). Biography: ZHANG Fan (1981-),Male, Ph. D. Student
474 Engineering (SKLOE) in Shanghai Jiaotong The cell-truss spar is moored in place by 9 University, intending to take advantage of both the chain-wire-chain formed mooing lines, separated typical truss spar and cell spar. A nonlinear into 3 groups, as shown in Fig.2. Total vertical time-domain dynamic coupled analysis program, pretension of the mooring system is approximately named SESAM (developed by DNV software), is in 1.0×107 N. application to the investigation of the global performance and mooring factor of the new spar Table 1 Main particulars of cell-truss spar concept concept. Basic experiment with a 1:100 scale model Summary of key figures In-place is also conducted in the water basin of SKLOE to Height from keel to top (m) 170 calibrate the numerical approach. Draft (m) 160 Free board (m) 10 2. NEW SPAR CONCEPT Diameter (m) 20 A variation of spar is designed as a concept for Length of hard tank (m) 85 the study without any commercial purpose. Features Length of truss section (m) 80 of truss spar and cell spar are both taken into account in the design of the new spar concept, Diameter of cells (m) 6.4 which is named as the cell-truss spar here, aiming Side length of heave plate (m) 10 to take advantage of the heave plate damping Displacement (t) 17903 feature of the truss spar to obtain satisfactory heave Center of gravity above keel (m) 86 motion performance, while reducing manufacture and installation difficulty by means of cell Center of buoyancy above keel (m) 107 concept[9,10]. Illustration of the cell-truss spar concept is shown in Fig.1. Fig.2 Mooring system of cell-truss spar Fig.1 Illustration of cell-truss spar concept 3. HYDRODYNAMIC THEORY It is a tough work to include a complete The hard tank of the spar hull consists of 7 description of the numerical simulation method in cylinders (cells) with the same diameter and length, the short space of this article. Compared to the while the lower part is fitted with a truss section. traditional de-coupled approach, the coupling Each bay of the truss is spanned by a horizontal effects due to the mooring and riser system will hexagonal plate, as the hexagon shape results in typically tend to reduce the low frequency motion large added mass without extending the edges of of the spar platforms. Some details may be found in the plate outside the diameter of the hard tank and Ormberg et al. . Briefly, in the coupled approach lends itself to be supported efficiently on the truss mentioned here, the total loads (dynamics included) horizontal. Fixed ballast is set at the bottom of the from the “slender body models” of mooring lines hull in the soft tank to adjust the position of its and risers are transferred as a force into the “large gravity center. There is a strake around the outside body” model of the floater. Irregular Wave of hard tank to reduce Vortex-Induced-Vibration Frequency (WF) and Low Frequency (LF) (VIV). The design water depth is 1500 m. Its main environmental loading is required to give an particulars are shown in Table 1. adequate representation of the dynamic behavior of
475 the coupled vessel/slender structures system. systems work as spring mechanisms where the Dynamic equilibrium between the forces acting on displacement of the floater from a neutral the floater and slender structure response is satisfied equilibrium position causes a restoring force to at every time instant, and thus the assessment of the react to the applied loading. For the coupled low frequency damping from the slender structure approach the finite element model of mooring lines is not needed. consists of bar elements only, i.e., bending stiffness All the system components are described in a and torsional stiffness are neglected. The mass FEM-model. The governing dynamic equilibrium properties are modeled according to the reported equation of the spatially discretized system is measures. Hydrodynamic forces are modeled by expressed as means of the generalized Morison equation. The numerical model includes the spring and the bare R I ( r , r , t ) + R D ( r , r, t ) + R S ( r , t ) = R E ( r , r, t ) tendon and the bare riser body. (1) where R I , R D and R S represent the inertia, damping and internal reaction force vectors respectively, R E is the external load vector, r , r and r are the structural displacement, velocity and acceleration vectors respectively. The inertia force vector is expressed as R I ( r , r , t ) = M ( r ) r (2) where M is the system mass matrix that includes structural mass, mass accounting for internal fluid Fig.3 Panel FEM of cell-truss spar flow in pipes, and hydrodynamic mass. The damping force vector is expressed as Coupled analysis model for the spar and mooring system is shown in Fig. 4. R D ( r , r, t ) = C ( r ) r (3) where C is the system damping matrix that includes contributions from internal structural damping as well as hydrodynamic damping. The internal reaction force vector R ( r , r, t ) E is calculated based on the instantaneous state of stress in the elements. The external load vector accounts for the weight and buoyancy, forced Fig.4 Coupled analysis model (Depth = 1500 m) displacements, environmental forces and specific forces. 5. ENVIRONMENT CONDITIONS 4 environment conditions are selected to carry 4. NUMERICAL SIMULATION out the simulation, including: a storm condition 4.1 Hull panel happening once in 100 years, and a operation The hull panel is used for the calculation of condition in GOM, and a wave extreme condition 3-D velocity potential, as shown in Fig.3. Linear and a swell extreme condition in the West Africa. and quadratic hydrodynamic coefficients are Details are shown in Table 2. All sea states are obtained from the first- and second-order analysis. generated using the JONSWAP wave spectrum and 4.2 Mooring system modeling NPD wind spectrum for 3 h simulation. Wave and Mooring systems are compliant systems. They wind directions are set to be heading (180°). provide resistance to environmental loading by Dynamic waves and wind in time domain are deforming and activating reaction forces. Mooring
476 generated using random selected seeds. prevailing wave frequency range and thus heave motion is generally insignificant. This has been proven in the GOM where the long periods prevent 6. RESULTS AND DISCUSSIONS any serious occurrence of heave resonance, and The motion response of the spar platform, the thus induce very favorable heave response. heave mode of which is of special interest, should However, in some other sea areas, such as in the be adequately low to satisfy the installation of rigid West Africa, the spar platform may undergo large risers with dry-heads. The concept behind deep heave motions at resonance, up to 8-10 times of draft floaters is their ability to reduce the first-order incident wave amplitude, as in such areas, long heave excitation significantly. Typical natural swell condition may persist for a considerable periods of the spars deployed in the GOM case are portion of the year. 60 s for pitch and 28 s for heave. Figures 5-7 show both the numerical and experimental results of transfer functions with mooring lines for the surge, heave and pitch. Predicted RAOs are in excellent agreement with test measurements. Fig. 7 Pitch transfer function with mooring lines Spectral analysis results of motions and mooring line tension (Line 3) are shown in Table 3, where Hs is the significant value and Tz zero crossing period. Basically, global motion responses Fig. 5 Surge transfer function with mooring lines of the cell-truss spar platform are restrained in a satisfactory region, that the surge amplitude should be less 10% water depth, while heave and pitch amplitude should be within the range of –3 m-3 m and –10o-10o, respectively. On the other hand, though the significant wave height represents the energy contained in the waves, it may not have the simple effect of linearity on motions and mooring line tensions. From Table 3, it is known that the minimum significant values always appear in the operation condition in the GOM, inspiringly, which seems to reveal that the wave period is a more dominative factor in the relationship between incident wave and platform response. This is Fig. 6 Heave transfer function with mooring lines especially obvious in the heave motion. In view of the interests on the heave motion, For the cell-truss spar, the surge natural period Figs.8-11 show the power spectra of heave response is above 100 s, and the heave and pitch natural in the 4 environment conditions. Model tests periods are about 25 s and 31 s respectively. conducted in the 100 years storm in the GOM and Calculation results show that the cell-truss spar has wave extremes in the West Africa conditions are inherited the spar characteristics of long motion also presented. The predicted responses notably natural periods, which is considered one of the great capture the motion features of model tests. advantages of the spar concept. In most To indicate the relationship between the circumstances, this period is sufficiently outside the response and incident wave, wave spectrums are
477 Table 2 Ocean environment conditions Wave Wind Environment conditions Significant Peak γ Velocity (m/s) wave height (m) Spectrum Period (s) A 100 year storm in GOM 12.59 14.6 2 38.6 B Operation condition in GOM 3.96 9.0 2 38.6 C Wave extremes in West Africa 4.5 18.8 6 7.5 D Swell extremes in West Africa 1.7 25.0 6 7.1 Table 3 Spectral analysis results of motion and mooring line tension (Line 3) response Surge Heave Pitch Line 3 Hs (m) Tz (s) Hs (m) Tz (s) Hs (o) Tz (s) Hs (kN) Tz (s) A 15.0 39.4 1.32 29.3 5.17 31.9 345.3 17.2 B 2.65 20.5 0.016 12.9 1.33 25.9 50.6 6.1 C 7.71 56.7 2.52 39.1 3.32 54.0 195.5 33.1 D 3.75 72.9 2.92 49.1 3.1 86.2 147.7 46.2 plotted with imaginary lines in each figure as well. molecule. In most sea areas, such as the GOM, this The largest heave motion occurs in the swell could be easily satisfied as the waves there only extremes in the West Africa, as shown in Table 3, cause the motion of water molecule in a though the significant wave height is the lowest comparatively thin surface layer. However, in some among the 4 environment conditions. However, its long swell conditions, large wave length may period is the closest one to the heave natural period, arouse the water molecule in quit deep water. and Fig. 11 shows a notable coherence between the Instead of a relative motion, the molecule motion excitation and response. Comparatively, waves in even transfers the wave energy directly to the heave Fig. 9 barely arouse any heave response. plates, thus cause large amplitude of heave resonance. Fig.8 Heave spectrum in 100 years Storm in GOM From a hydrodynamic point of view, the heave plates entrap large amount of water to move with Fig.9 Heave spectrum in operation condition in GOM them, resulting in the increase of added mass and In the following discussions, the mean, potential damping, while the precondition is the standard deviation (Std) and extreme values of the relative motion between the plates and water
478 motion and mooring line tension response are which may indicate that, the resonant heave concerned. Because there are resonant frequencies response in long-period swell condition needs in the low frequency region, it is essential to filter adequate attention. the responses to further explore the coupled effects To predict the mooring line tensions, total in different frequency regions as shown in Table standard deviation is no longer than an adequate 4. value. Complete time-domain simulation is an essential process to obtain some important data, such as extreme values, which is valuable in the structural verification and other post-analysis. Fig.10 Heave spectrum in Wave Extremes in West Africa Fig.12 Statistical analysis of surge Fig.11 Heave spectrum in Swell Extremes in West Africa Fig.13 Statistical analysis of heave Table 4 Frequency region Frequency ω(rad/s) T (s) Low Frequency (LF) ≤0.2 ≥31.4 Wave Frequency (WF) 0.2-1.5 4.2-31.4 The results of statistical analysis for cell-truss spar motions and mooring line tensions are shown in Tables 5-8, in which the units are m and rad for motions and kN for tensions. As mentioned above, for the spar platforms, natural periods of horizontal motions are designed Fig.14 Statistical analysis of pitch far from the wave frequency in order to reduce first-order wave excitation, and thus the To indicate the effect of wave height and second-order wave becomes more dominant. This is period on the motions and mooring ling tensions, especially obvious in the surge and pitch motion, as the results of statistical analysis are plotted as bar the LF Std in always bigger than the WF Std. Heave chart maps in Figs.12-15, in which Abs Max stands motions seems to behave more like the WF motion, for the absolute maximum values.
479 Table 5 Statistical analysis of spar motions and line tensions in 100 years in GOM Extreme Mean LF Std WF Std Total Std Max Min Surge -12.32 3.036 2.260 3.784 2.305 -27.459 Heave 0.377 0.029 0.329 0.330 1.651 -0.777 Pitch -0.434 1.061 0.772 1.312 4.048 -5.009 Line 3 1274.0 28.7 81.5 86.4 1731.2 869.6 Line 8 1074.2 24.8 70.8 75.0 1660.1 729.8 Table 6 Statistical analysis of spar motions and line tensions in operation condition in GOM Extreme Mean LF Std WF Std Total Std Max Min Surge -1.237 0.559 0.375 0.673 1.086 -3.749 Heave 0.434 0.001 0.004 0.004 0.417 0.447 Pitch -0.047 0.306 0.150 0.340 1.000 -1.057 Line 3 1188.2 3.2 13.0 13.4 1237.0 1132.7 Line 8 1167.1 5.2 21.3 22.0 1259.2 1187.0 Table 7 Statistical analysis of spar motions and line tensions in wave extremes in West Africa Extreme Mean LF Std WF Std Total Std Max Min Surge -0.493 1.502 1.229 1.941 11.489 -19.653 Heave 0.431 0.021 0.629 0.630 2.327 -1.509 Pitch -0.021 0.724 0.433 0.843 3.147 -3.077 Line 3 1184.3 12.4 47.3 48.9 1507.6 982.0 Line 8 1175.6 15.1 37.3 40.3 1377.8 926.3 Table 8 Statistical analysis of spar motions and line tensions in swell extremes in West Africa Extreme Mean LF Std WF Std Total Std Max Min Surge -0.336 0.784 0.527 0.946 2.797 -3.270 Heave 0.433 0.071 0.727 0.731 2.345 -1.532 Pitch -0.017 0.747 0.214 0.778 2.050 -2.240 Line 3 1182.8 4.3 36.6 36.9 1330.0 1046.1 Line 8 1176.7 4.5 21.4 21.9 1259.3 1105.1
480 For surge and pitch motions, and line tension, frequency motions and tensions, as in many response values in Conditions A and C is larger situations, this kind of responses have become the than those in Conditions B and D, which shows most significant factors. For the horizontal motions, coherence to the wave heights in Table 2. However, low frequency motion usually present a by investigating the differential values, it may be second-order drift motion, while in vertical concluded that, the response differences are not direction, it is often aroused by the resonance only the representation of wave height variation. As between heave motion and long swell. for surge motion, Abs Max value in Condition C is (3) Wave height and period both play 71.6% of that in Condition A, while the wave important roles in affecting the motion responses significant height ratio of the two conditions is just and mooring line tensions. However, the former 35.7%. seems more influential to the horizontal motion, while the latter to the vertical motion. (4) Complete time-domain analysis is a necessary method in the design process and response prediction of spars, while the lower frequency responses occupy a considerable part, and traditional spectrum analysis alone may not adequately handle such problems. REFERENCES  ZHANG Fan, YANG Jian-min, LI Run-pei et al. Experimental investigation on hydrodynamic behavior Fig.15 Statistical analysis of tension (Line 3) of the geometric spar platform[J]. China Ocean Engineering, 2006, 20(2): 213-224. Surge response in Condition C is large than  AGARWAL A. K. and JAIN A. K. Dynamic behavior that in Condition D, agreeing with the wave height, of offshore spar platforms under regular sea waves[J]. which reveals that, the significant wave height Ocean Engineering, 2003, 30: 487-516.  FINN L. D., MAHER J. V. and GUPTA H. The cell plays a remarkable role among the factors affecting spar and vortex induced vibrations[A]. 2003 Offshore the horizontal motion. For the pitch motion and line Technology Conference[C]. Texas, USA, OTC tension, the wave period becomes more effective, as 15244,2003. shown in Figs.14 and 15.  LIM S. J., RHO J. B. and CHOI H. S. An experimental study on motion characteristics of cell spar platform[C]. The results of heave motion exhibit a little Proceedings of the Fifteenth International Offshore difference. Though the significant wave height in and Polar Engineering Conference. Seoul, Korea, Condition D is only 13.5% of that in condition A, 2005, 233-237. heave Abs Max in D is even larger than that in A.  DATTA I., PRISLIN I., HALKYARD J. E. et al. In this situation, the wave period has the priority in Comparison of truss spar model test results with numerical predictions[C]. 18th International the design process and performance prediction of Conference on Offshore Mechanics and Arctic spar platforms. Engineering. Newfoundland, Canada, OMAE99/OFT-4231, 1999.  WANG J., BERG S., LUO Y. H. et al. Structural design of the truss spar – an overview[C]. Proceedings of the 7. CONCLUSIONS Eleventh International Offshore and Polar A new cell-truss spar concept has been put Engineering Conference. Stavanger, Norway, 2001, forward, and its global performance has been 354-361. studied by nonlinear time-domain dynamic coupled  DOWNIE M. J., GRAHAM J. M. R., HALL C. et al. An analysis. The relationship between incident wave experimental investigation of motion control devices for truss spars[J]. Marine Structures, 2000, 13: 75-90. and responses of motion and mooring line tensions  LU R. R., WANG J. J. and ERDAL E. Time domain has been investigated as well. The following strength and fatigue analysis of truss spar heave plate[C]. conclusions have been reached: Proceedings of the Thirteenth International Offshore (1) Basically, the new cell-truss spar concept and Polar Engineering Conference. Hawaii, USA, 2003, 272-279. has inherited the advantages of its former  GROVE M. A., CONCEIÇÄO C. A. L. and generations of spars. Its motion responses could be SCHACHTER R. D. A Concept design and availably restrained in a satisfactory region. hydrodynamic behavior of a spar platform[C]. 22nd (2) Enough attention should be paid to the low International Conference on Offshore Mechanics and
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