of the Maritime University of Szczecin
Akademii Morskiej w Szczecinie
2020, 64 (136), 25–35ISSN 1733-8670 (Printed) Received: 16.09.2020
ISSN 2392-0378 (Online) Accepted: 11.12.2020
DOI: 10.17402/450 Published: 30.12.2020
Hydrodynamic performance analysis of a modified
sandglass--type FPSO in regular waves using boundary element method
Adeleh Graylee, Mahdi Yousefifard
Babol Noshirvani University of Technology
e-mail: a.graylee1365@gmail.com, yousefifard@nit.ac.ir
corresponding author
Keywords: sandglass FPSO, BEM, regular wave, roll damper, dynamic motions, ANSYS-AQWA Abstract
This paper presents a numerical investigation of the hydrodynamic performance of a modified sandglass-type FPSO (Floating Production, Storage and Offloading) with different geometrical parameters. The influence of the roll damping plate on heave and pitch motions of the FPSO was studied in regular waves. To estimate the hydrodynamic performance and utilize the results on the design stage of the FPSO, the boundary element method (BEM) was used. Furthermore, the hydrodynamic performance of two cylindrical and sandglass-type FPSOs under the same conditions was compared in different waves. Five sandglass-type FPSOs with dissimilar inclination angles were utilized with the constant draft. The effects of different inclination angles, including various radii of water-plane part of the floating object on hydrodynamic responses and wave forces applied to the FPSO, were investigated, and presented here. Numerical results were compared against published exper-imental data of a sandglass-type model, and good agreement was achieved. Based on the simulation results, a conclusion that a sandglass-type FPSO with the inclination angle of 35 degrees proposes proper hydrodynam-ic performance in both heave and pitch motions for all ranges of wave frequencies was reached. In addition, as it was predicted, the effect of heading sea on a sandglass-type FPSO was significant compared to other wave directions. Finally, by adding a damper plate to the floor of the platform, its hydrodynamic performance is improved. For numerical analysis of the modified FPSO, three different damper sizes are used to investigate its effect on the reduction of the pitch motion amplitude in waves.
Nomenclature
A Added mass matrix (kg) A33 Added mass matrix-heave (kg) A21 Added mass matrix-pitch (kg) B Stiffness matrix (N/m) B33 Stiffness matrix-heave (N/m) B21 Added mass matrix-pitch (kg) C Damping matrix (–)
C33 Damping matrix-heave (–) C21 Damping matrix-pitch (–) Fij Exciting force matrix (N) F0 Initial value matrix (N) F33 Exciting force-heave (N) g Gravity acceleration (m/s2) h Depth of water (m) Ms Structure mass matrix (kg)
Mij Exciting moment matrix (N·m) M21 Exciting moment-pitch (N·m) P Pressure (N/m2) S Body surface (m2) t Time (s) v Velocity (m/s) X Coordinate matrix (m) X0 Initial value matrix (m)
X Speed matrix (m/s) Acceleration matrix (m/s2) x Longitudinal coordinate (m) y Transverse coordinate (m) z Vertical coordinate (m) φ Velocity potential (m/s) η Free surface elevation (m) ρ Density of water (kg/m3) ω Angular velocity (rad/s)
Introduction
Floating Production, Storage and Offloading or FPSO is a floating vessel located near an oil plat-form where oil is processed and stored until it can be transferred to a tanker ship for transporting. The use of this type of platform in newly established offshore oil regions is increasing because it does not require a pipeline infrastructure. Furthermore, when the oil extraction operation is completed, the vessel can be moved to another location.
The first design of an FPSO was presented based on classical ship-shaped hull lines. However, its slender and non-axisymmetric shape created signifi-cant loads due to hogging and sagging in waves. The ship-shaped form was also less efficient in storage volume per plated area of the structure. To overcome these shortcomings associated with using the tradi-tional ship-shaped vessel for FPSO, the industry is now developing simpler shapes of them. These types of FPSOs are being designed to have similar dynam-ic characteristdynam-ics from all directions. Nevertheless, simple shapes like cylindrical form still have some motion problems. The heave natural frequency of a cylindrical floating body is in the bandwidth of high wave energy, and thus the heave motion response is very large. Furthermore, the floating model with cylindrical shape easily triggers vortex-induced vibration and has a relatively smaller deck area.
Many experimental and numerical studies have been carried out to examine the effects of FPSO’s hull form on hydrodynamic performance in regular and irregular waves. Wichers (Wichers, 1996) stud-ied a turret moored FPSO exposed to a combination of irregular waves with wind and current. Heurt-ier et al. (HeurtHeurt-ier et al., 2001) analyzed a moored FPSO with two methods of coupled and uncou-pled in harsh environments and concluded that the uncoupled analysis can be used properly in the early design of the mooring FPSO. Pascoal et al. (Pascoal et al., 2004) studied the hydrodynamic behavior of an FPSO with eight columns experimentally in regu-lar and irreguregu-lar waves. Kim et al. (Kim et al., 2005) developed a time-domain method to analyze the motions of a turret moored FPSO. Hong et al. (Hong et al., 2009) investigated the dynamic performance of an LNG-FPSO numerically. Chen, Sun and Zhang (Chen, Sun & Zhang, 2013) explored the dynamic response of a ship-shaped FPSO using SEFAM soft-ware in deep water considering the large amplitude of motion. Nishanth, John and Whyte (Nishanth, John & Whyte, 2016) performed an uncoupled hydrodynamic analysis to study the response of
ship-shaped FPSO under the action of unidirection-al random waves. Nam, Kim and Hong (Nam, Kim & Hong, 2016) worked out a comprehensive study on the berthing problem of an FPSO and a shuttle tanker in waves. Somayajula and Falzarona (Somay-ajula & Falzarona, 2017) investigated a ship-shaped FPSO in irregular waves. They used a time-domain simulation program to include the second-order dif-ference frequency forces and moments. In the same context, Roy and Banik (Roy & Banik, 2018) car-ried out a numerical examination on the response of a ship-shaped FPSO exposed to a combination of wave, wind, and current. They assumed that the FPSO was moored on the sloped seabed and that the wave was irregular. The numerical model and anal-ysis was completed using an AQWA-ANSYS code. In recent years, sandglass-type FPSOs have been presented as an attractive form for the improvement of hydrodynamics performance in rough seas. It not only has larger spaces of oil storage than tradition-al ocean platforms, it tradition-also has better hydrodynam-ic performance and adaptability to the extreme sea environment. A modern concept of the floating body with an innovative sandglass-type was presented by Vijayalakshmi and Panneerselvam (Vijayalakshmi & Panneerselvam, 2012). They investigated a sand-glass-type FPSO with a nine-sided cross section in the icy water numerically and experimentally. They also studied the effect of damping plate on motion response of the mentioned FPSO. Yao, Wang and Huang (Yao, Wang & Huang, 2014) investigated the equivalent issue and presented the results of heave and pitch motions of a sandglass-type FPSO using boundary element and spectrum analysis methods in the frequency domain. By comparing the results with what was obtained for the cylindrical and octag-onal floating bodies, it was observed that the design of the structure with sandglass shape can improve the stability and hydrodynamic characteristics of an FPSO. In the same context, Wang et al. (Wang et al., 2015) investigated a sandglass-type FDPSO (Floating, Drilling, Production, Storage and Offload-ing) to enhance the hydrodynamic performance of traditional ship-type and cylindrical FDPSO using a method based on the wave potential theory. They used potential flow theory and engineering estima-tion methods to theoretically and mathematically deduce the wave excitation force, added mass and corresponding frequency for the minimum RAO (Response Airway Operator) of heave motion for the new sandglass-type model. Besides, the correspond-ing frequency for the minimum RAO was chosen as a control variable to design shape parameters and
thus minimize heave motion response. Compared with FPSO, the FDPSO denotes the addition of drill-ing rigs and therefore, the relevant floatdrill-ing models have a cylindrical moon-pool structure with various radii. Accordingly, the heave motion characteristics of different FDPSOs were simulated by BEM. Final-ly, the heave motion of sandglass-type FDPSO was compared with ship-shaped and cylindrical ones. Wang et al. (Wang et al., 2016) studied the effects of shape parameters on motion performance of cylin-drical and sandglass-type FPSO in small amplitude regular waves and also the influence of second-order slowly varying loads on the occurrence of deck-wet-ness in FPSOs with simple geometries experimen-tally and numerically. The effects of four different cross sections on the hydrodynamic performance of sandglass-type FPSOs exposed to regular waves were presented by Graylee and Yousefifard (Graylee & Yousefifard, 2019). They concluded that polyhe-dral cross-sections provide similar characteristics compared with the traditional circular one. So, it is possible to use simple types of cross-sections for FPSOs because of fewer manufacturing construction costs.
Reducing the amplitude of heave and pitch motions of FPSOs with the addition of dampers has also been of interest to researchers. Van’t Veer, Fathi and Kherian (Van’t Veer, Fathi & Kherian, 2011) presented a study focused on the roll motion predic-tion of ship-shaped FPSOs. Their paper contributed to the understanding of roll damping physics through model test results, CFD simulations and potential flow predictions. Besides, a computational code was developed by Avalos and Wanderley (Avalos & Wan-derley, 2018) to simulate forced roll oscillation of a middle section of an FPSO with different types of bilge keels. Proposed bilge keel configurations improve the roll damping of FPSO. Peng et al. (Peng et al., 2018) had a comprehensive study on a novel design of an FPSO named Low-Motion FPSO. This consists of a box shape hull with a free hanging sol-id ballast tank located in further distance below the hull keel. The addition of solid ballat tank to the con-ventional FPSO increases natural periods of motions which significantly reduces the motions in the wave frequency range. Recently, Sathia and Vijayalaksh-mi (Sathia & VijayalakshVijayalaksh-mi, 2019) conducted exper-iments on the non-ship-shaped FPSO model with different sizes of damping plates attached to the keel to study its influence on the responses of the ves-sel. Based on their findings, a significant reduction in the heave and pitch motions of the FPSO can be observed with the provision of the keel plate.
In this study, a numerical simulation of sandg-lass-type FPSO is conducted regarding the effects of linear regular waves. To accomplish this task, the frequency-domain numerical simulation program, ANSYS-AQWA software, is used. Current numeri-cal results of heave and pitch motions in the case of the cylindrical FPSO are validated by experimental data of Wang et al. (Wang et al., 2016). The effects of hull form parameters on linear motions of the sand-glass-type model are studied, and optimized struc-ture parameters are presented. Besides, the effects of wave directions on the dynamic characteristics of sandglass-type FPSOs are studied. Finally, the effect of adding a simple damper to the platform floor on its hydrodynamic performance is evaluated.
Governing equations
Although there are different methods to analyze the dynamic behavior of a floating body in waves, it is possible to get acceptable results in some cases using the linear analysis. A linear method in moder-ate marine conditions provides an admissible answer in a short time for a floating body. While investigat-ing the response of the floatinvestigat-ing body in waves usinvestigat-ing Reynolds Averaged Navier-Stokes (RANS) meth-od, considering viscosity and real wave condition, provides a more proper response than the potential method, using this method to solve a problem on such a scale requires a great deal of time and cost. A potential method can be used to find an appro-priate and approximate response by using a series of assumptions and simplifications in the problem, such as considering the low-speed floating body and the small-amplitude wave. ANSYS-AQWA is a powerful, fast, and accurate software at zero or low speed, and it can be used for a floating object with simple geometry and in moderate marine conditions. ANSYS-AQWA solves the linear water wave bound-ary value problem. It uses the Boundbound-ary Element Method (BEM), also known as the panel method, to find diffraction and radiation velocity potentials. In general, the BEM applies source ore dipole func-tions on the surfaces of the submerged bodies and solves for their strength so that all boundary con-ditions are met. Once the diffraction and radiation velocity potential fields have been solved, excitation forces, added mess and damping matrices, as well as wave field pressure, velocity, and surface elevation can be found.
In this study, we can analyze the dynamic motions correctly by using the potential method based on ANSYS-AQWA software. Under the traditional
assumption, the fluid is inviscid and incompressible, the flow is considered to be irrotational, and all vis-cous shear forces are neglected, so the fluid domain is governed by the velocity potential satisfied by Laplace equation (Wang, Tang & Wu, 2015). These equations and boundary conditions are as follows:
Continuity equation in potential flow: 0 2 2 2 2 2 2 2 z y x (1)
kinematic free surface condition:
) , , ( , z x yt z t (2) dynamic free surface condition:
) , , ( , 2 1 2 t y x z g t (3)
zero water vertical velocity at seabed: h z z
0, (4)
Here ϕ is the velocity potential and η is the free surface elevation.
Applying the speed of movement of the object to the fluid around it:
n v n (5) where, nv n
is the velocity vector. In addition, a proper far-field condition should be implemented to avoid the unwanted wave reflection from the downstream end of the domain:
0, x (6)
Bernoulli equation is used to determine the pres-sure (P) on the body. The hydrodynamic forces (F) and moments (M) can sequentially be obtained by integrating the pressure over the wetted body surfaces. ) . 2 1 ( gz t P (7)
S ds n P F (8)
S ds n X P M ( ) (9) Computational modelFigure 1 shows the schematic of the sandg-lass-type FPSO subjected to regular small amplitude waves. The main principles of the sandglass-type FPSO are presented in Table 1. This basic form is used for numerical solution investigation and validation.
Table 1. Main dimensions of the sandglass-type FPSO
Description Symbol Value Unit
Water-plane radius RW 26.2 m Bottom radius RB 45.006 m Top-deck radius RT 32.575 m Full-load draft d 13.168 m Freeboard f 9.607 m Displacement volume VB 53,658.54 m3 Displacement Δ 55,000 ton Up angle β 5.15 deg
Down angle α 4.34 deg
CoG above base ZG 7.35 m
Radius of gyration R 18.11 m
In this paper, the effects of variations of some underwater parameters such as the inclination angle and the radius of the water-plane of the structure on hydrodynamic responses of the sandg-lass-type FPSO are studied. The variation of incli-nation angles is from 25 degrees to 45 degrees. The draft and the bottom radius are constant for all structures. RT RW RB β α f d
Numerical method
In the present study, the boundary element meth-od is utilized to solve the potential flow equation. The hydrodynamic behavior of the sandglass-type FPSO in regular waves is calculated here using com-mercial ANSYS-AQWA software, which is widely utilized in the offshore industry. ANSYS-AQWA software is used for computing hydrodynamic prop-erties, including heave and pitch motions in waves. Both utilize a 3-D panel method for wave loads, which is based on potential flow theory. Since the unsteady motions are supposed to be small, and the wave amplitude is also small compared to the wave-length, the linearized theory is applied for the pres-ent study.
ANSYS-AQWA solves a set of linear algebraic equations to obtain the harmonic response of the body in regular waves. These response characteris-tics are commonly referred to as Response Ampli-tude Operators (RAOs) and are proportional to the wave amplitude. The equation of motion describing the response of the flexible structure to external exci-tation mentioned presented in Eq. (10).
F X B X C X A Ms ] [ (10)
While the force and displacement due to it both have oscillating properties, the relationship between them can be presented in this way:
t i t i e F F e X X 0 0 (11) Here Ms, A, C and B are the structure mass, added mass, damping and stiffness matrices. F0 and X0 are the initial value matrices and ω is the angular velocity.
RAO which is the ratio between motions of FPSO and wave amplitudes can be driven for heave and pitch motions as Eqs (12)–(13):
33 33 33 2( )33 RAO Heave C B i A M F (12) 21 21 21 2( )21 RAO Pitch C B i A M M (13) Validation
In order to verify the present numerical method, the results published by Wang et al. (Wang et al., 2016) for a cylindrical FPSO is investigated here using ANSYS-AQWA software, and the achieve-ments are compared for accuracy. The model is shown in Figure 2, and the structure parameters are presented in Table 2. The dimensionless heave and pitch motions of the cylindrical FPSO are studied, and the results are presented in Figures 3(a)–(b).
Table 2. Main dimensions of cylindrical FPSO
Description Symbol Value Unit
Water-plane radius RW 30 m Bottom radius RB 32.575 m Top-deck radius RT 32.575 m Full-load draft d 18.2 m Freeboard f 8.8 m Displacement volume VB 53,658.54 m3 Displacement Δ 55,000 ton Up angle a 5.15 m Down angle h 4.34 m
CoG above base ZG 7.35 m
Radius of gyration R 17.55 m
According to Figures. 3(a)–(b), a comparison of the maximum amplitude of heave and the pitch motions obtained by the present numerical model with those obtained using the numerical and experi-mental ones show a good agreement. The variations of maximum amplitude of motions for three meth-ods are presented in Table 3.
RT RW RB f d a h
Table 3. Derivation of the results of heave and pitch motions for three methods
Method Heavemotion response (–) response (deg/m)Pitch motion Experimental (Wang et al., 2016) 2.30 3.959 Numerical (WAMIT) (Wang et al., 2016) 2.395 3.79 Numerical (AQWA) 2.476 3.65 Relative error +7.65% –7.8%
From Table 3, it can be observed that the dif-ferences of maximum values of heave and pitch motions between the present numerical method, and the published numerical and experimental methods are less than 10 percent, which satisfies the engineer-ing precision requirement and validates the accuracy of the numerical method. Therefore, it is reasonable to use the ANSYS-AQWA software to investigate the sandglass-type FPSO.
Numerical results and discussion
Comparison of the Hydrodynamic Performance of sandglass-type and cylindrical FPSOs
In this section, the hydrodynamic properties of cylindrical and sandglass-type FPSOs are compared. In addition, the current numerical solution results are compared with published experimental data. From this comparison, the numerical and experimental results are in good agreement. Figure 4a shows the RAO values of heave motion at different frequen-cies of the incident wave. Furthermore, in Figure 4b, RAO values of the pitch motion are seen. The comparison of the amplitude of heave and pitch RAOs between the cylindrical FPSO and the sand-glass-type FPSO represents the significant reduction in values for the sandglass type one. Additionally, the maximum amount of heave RAO occurs in the lower frequency.
(a) heave RAO (b) pitch RAO
Figure 3. Comparison of experimental and numerical motion results of the cylindrical FPSO
(a) heave RAO (b) pitch RAO
Figures 5(a)–(b) also show the values of the exciting force of the heave and pitch at each frequen-cy. As it is expected, the amplitude of heave force for cylindrical FPSO is significantly more than that for the sandglass-type one. In contrast, the pitch excit-ing moment of the sandglass-type FPSO, in some specific frequencies, shows a magnificent increase in amplitude in comparison to the cylindrical one, but it does not have any remarkable effect on the pitch motion of FPSO with sandglass shape.
The effect of the variation of geometrical parameters of the sandglass-type FPSO on heave and pitch motions
In this section, the draft of sandglass-type FPSO is constant and the inclination angle of the hull var-ies from 25 degrees to 45 degrees with increments of 5 degrees. The radius of the mid-water plane of
sandglass-type FPSO changes in each specific value of the inclination angle to keep the draft constant. All RAO diagrams of sandglass-type FPSO are calculat-ed for 6-DOF (Degrees of Frecalculat-edom), and the heave and pitch results in regular waves are presented in Figures 6(a)–(b). These are the prominent motions of sandglass-type FPSO floating in wave with the heading of 180 degrees.
It is quite evident that the smallest amplitude of maximum heave motion occurs in the angle of 30 degrees, which has the lowest dimensionless heave amplitude of about 1.2, and the degree of 40 has the highest of about 3.84 (see Figure 6a). Also, the maximum amplitude of heave motion for the angle of 300 occurs in a lower frequency (0.135 rad/s). Besides, a sandglass-type FPSO with the inclina-tion angle of 35 degrees has the second rank with a maximum amplitude of 1.488 in the frequency of 0.296 rad/s. On the other hand, pitch motion analysis
(a) heave RAO exciting force (b) pitch RAO exciting moment
Figure 5. The variation of normalized exciting force results of FPSO with cylindrical and sandglass shape
(a) heave RAO motion (b) pitch RAO motion
is a bit complex. In this paper, the pitch motion behavior of structures is divided into two parts of the first and second critical frequencies. In Figure 6b, it is obvious that the maximum amplitudes of the pitch motion in the second critical frequency decrease
with the reduction of the value of the inclination angle. In the first natural frequency, we can see that variations are significant and a sandglass-type FPSO with the inclination angle of 35 degrees shows the best response in small amplitude regular waves.
(a) surge RAO motion (b) sway RAO motion
(c) heave RAO motion (d) roll RAO motion
(e) pitch RAO motion (f) yaw RAO motion
In this paper, based on the current simulation results in both heave and pitch responses of struc-ture, an FPSO with an inclination angle of 35 degrees, and a mid-water radius of 26.2 m is chosen. In this angle, both heave and pitch motions have an optimum amplitude. Consequently, for this angle, the effect of different wave directions on 6-DOF motions was examined.
The effect of the wave direction on 6-DOF of the optimized sandglass-type FPSO
The effect of the wave direction on 6-DOF of FPSO with the inclination angle of 35 degrees, mid-part radius of 26.2 m, and bottom-mid-part radius of 45.006 m was examined, and the results are present-ed in Figures 7(a)–(f).
As it is shown, wave direction does not have any significant effect on vertical motions like heave and yaw. In addition, it can be deduced from the results that angular directions of waves like 45 and 135 degrees have smaller values of maximum amplitude in comparison to straight wave directions like zero, 90 and 180 degrees. In fact, the maximum ampli-tude of one motion is distributed into two motions in angular waves. In angular wave, both roll and pitch motions exist in smaller amplitudes, but in straight wave direction, one of them is maximum and the other is zero. In this paper, based on the current sim-ulation results in both heave and pitch responses of structure, an FPSO with an inclination angle of 35 degrees, and a mid-water radius of 26.2 m is cho-sen. In this angle, both heave and pitch motions have optimum amplitude. Consequently, for this angle, the effect of different wave directions on 6-DOF motions was examined.
The effect of horizontal damper plate on performance of sandglass-type FPSO
Although the dynamic behavior of the sandg-lass-type FPSO is better than the cylindrical one, the addition of a horizontal damper can still have a posi-tive effect on this dynamic behavior. For this reason, a circular horizontal plate is attached to the floor of the platform and its effects on the movements of the platform in a regular wave for three different damp-er diametdamp-ers wdamp-ere evaluated. The three-dimensional view of the plate added to the floor of the FPSO is shown in Figure 8.
Figure 8. Three-dimensional view of the plate added to the floor of the platform
The values presented as each damper mode are the same as the difference between the damper radi-us and the platform radiradi-us. Figure 9a shows the RAO graph of the heave motion of the FPSO in reg-ular waves. The plate used in the bottom of sand-glass-type FPSO reduces the amplitude of heave RAO motion. This value in the initial FPSO with no additional plate is 1.488, which reaches 1.33 in the FPSO with a damper plate of 0.5 m, with a fre-quency of about 0.296 rad/s. This figure changes to 1.13 and 1.19 for the FPSO with keel plates of 1 m
(a) Heave RAO motion (b) Pitch RAO motion
and 1.2 m respectively. Also, the frequency that the maximum heave of initial FPSO occurs decreases for the two later damper plates (0.296 rad/s reduces to 0.135 rad/s).
Another FPSO motion studied here is the pitch RAO motion, which is illustrated in Figure 9b. The differences in results for the pitch RAO motion are negligible for the size of the plate near 1m. After that, an increase in the value of the maximum pitch motion in the first frequency and a reduction of that in the second frequency were observed.
Figures 10a illustrates the changes in the heave RAO exciting force of sandglass-type FPSOs due to the varying size of the damper plate. The vari-ation of results for the heave exciting force shows an increase in amplitude in the frequency near 1 rad/s when damping plates are added to the sand-glass-type FPSO. However, it does not have any effect on the amplitude of heave motion in this frequency.
Figure 10b also shows the changes in the pitch RAO exciting moment of sandglass-type FPSOs due to the different size of the damper plate. It is obvious, there are some variations in peak values of pitch exciting moment when damper plates are added to sandglass type FPSO. In the frequency of 0.296 rad/s, the maximum amplitude decreases from 0.29 GN/m for the sandglass-type FPSO without damper plate to 0.24 GN/m for that with a damp-er plate of 1 m, about 17%. This figure is altdamp-ered in a frequency of 0.6 rad/s and increases by 7% for the sandglass-type FPSO with a plate of 1m in compar-ison to the initial one. The maximum values of the pitch moment for damper plate of 1.2 m are about 0.28 GN/m and 0.3 GN/m in frequencies of 0.239 and 0.7 rad/s respectively.
Conclusions
In this paper, first, a new type of vessel named FPSO and a new type of FPSO with the form of sandglass were described. For verifying the solu-tion method, the heave and pitch mosolu-tion of a cylin-drical FPSO were compared with published results obtained by the experimental method. The results determined that the present numerical method could conclude an appropriate response. Next, numerical simulations were carried out to study the hydrody-namic behavior of a novel sandglass-type FPSO sub-jected to different conditions. For this purpose, the motions of the floating structure under the influence of changing the inclination angle that changes the radius of the water-plane part were studied. It was observed that changing the inclination angle has the greatest effect on heave and pitch motions. By ana-lyzing both heave and pitch motions together, the best inclination angle was about 35 degrees. Also based on the results of the effect of wave direction on 6-DOF, it is surmised that vertical motions do not have significant variations.
This paper also compared the dynamic behav-ior of two cylindrical and sandglass-type FPSOs under the same conditions. The results of the study of the dynamic behavior of sandglass-type FPSO presented far better results than the cylindrical FPSO. To achieve better results, a horizontal damp-er was added to the platform floor in three diffdamp-erent sizes and dynamics of the FPSO were also exam-ined under these conditions. The addition of this damper had a profound effect on the control of the heave movement. Overall, it can be noted that the results obtained in this study are instrumental for only FPSOs that have these properties. FPSOs with
(a) Heave RAO exciting force (b) Pitch RAO exciting moment
a different displacement, draft, and center of mass may get different results.
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