Analysis of Dynamic Positioning System Performance for a Semisubmersible Platform
Lei Wang, Liang Wang, and Shi-zhi Yang
State Key Laboratory of Ocean Engineering, Shanghai Jiaotong University
Shanghai, China
ABSTRACT
This paper is concerned with a dynamic positioning system for a state of the art, ultra-deep water misubmersible platform with 8 azimuth thrusters. The system meets the ABS class requirements for DPS-3. Hydrodynamic characteristics of the platform and the propulsion systems were measured at scale model and computer simulations were made. The correction factors to the open water thruster performance were developed from hull-thruster, thruster-thruster interactions, the forbidden zones were also provided for optimum thruster performance in the dynamic positioning control system. Thruster failure analysis is also covered and discusd. Numerical simulations were carried out for some specific examples.
mentioned
KEY WORDS: Dynamic positioning system; mi-submersible platform; numerical simulation; model ex
periment. INTRODUCTION
Semi-submersible platforms are widely ud in the exploration and development of ocean resources and many such platforms are now in operation. They are required to maintain a given position and to adjust this position under external forces of ocean current, wind and waves. With increasing depths, the conventional mooring positioned operation prents rious technical and economical limitations. A robust DP system can then improve position control ability, enhancing operational time schedule and making the operation economically feasible.
This works deals with the analysis of a Dynamic Positioning System (DPS) for a specific deepwater mi-submersible platform.
The Vesl is a four-column stabilized mi-submersible drilling vesl. The vesl is equipped with a fully redundant DPS-3 positioning system consisting of 8*4.6MW azimuth thrusters. In order to obtain accurate information of DP environmental loads, DP environmental loads on Semi are calculated and a 1:50 scaled model test was finished to prove the calculation; the wave drift force is mainly discusd, in which the calculation is bad on the theory of near field integration and a new suit of measurement system is designed to fit for mi-submersible platform. Also, the effective thrust of 8 azimuth thrusters was calculated taking into interactions of current, thruster-thruster and
thruster-hull, and it reflected in the model test versus thrusters’ rpm.
The thruster interaction result in forbidden zones of 27.2 deg width，
and the zone which the thruster dependence on is labeled.
DP Capability Polar Plot and dynamic simulation are developed;
calculation and result analysis are carried out in some specific examples.
Thruster failure analysis is also covered and discusd.
VESSEL DATA
The mi-submersible platform's ' main particulars are included in the
Table 1. The draft of the mi-submerged platform is 19m.
A large scale model (Figure.1) of the vesl is constructed including
pontoons, columns, braces, and upper hull per the original arrangement
drawings.
Table 1. The detail parameters of the mi-submerged platform
Designation Unit
Fully
Model Length over all m 110.4 2.208
Width over all m 78 1.56
Elevation of box bottom m 30 0.6
Elevation of upper deck m 38.5 0.77
Length of pontoon over all m 110.4 2.208
Beam of Pontoon m 18 0.36
Height of Pontoon m 10 0.2
Length of column on pontoon m 20 0.4
Width of column on pontoon m 17.6 0.352
Corner radius of column m 4 0.08
Outer diameter of each circular cylinder
芝加哥有什么大学bracing
m 2.0 0.029
Elevation of each bracing above ba line m 13.1 0.193全美音乐奖2010
Proceedings of the Nineteenth (2009) International Offshore and Polar Engineering Conference Osaka, Japan, June 21-26, 2009
Copyright © 2009 by The International Society of Offshore and Polar Engineers (ISOPE) ISBN 978-1-880653-53-1 (Set); ISSN 1098-618
Fig.1. Model of the mi-submerged platform
The operating a-state for drilling operation was defined as 0.99m/s current, 25.8m/s wind (10min average) speed and waves with 5.8m significant height and 10.8 conds zero up-crossing wave period.
THRUST SYSTEM
As already explained, the platform will be equipped with 8 azimuth ducted thrusters. For simulation purpos, a ries Ka propeller with a
19A nozzle, with 3.6m diameter has been ud (Table.2). The 8 azimuth thrusters model reprent units with 850kN effective thrust for
the situation without current (open water thrust). A review of the locations of the azimuth thrusters is given (Figure.2); also the nomenclature of the numbering of the propellers ud in this paper is shown.
Table 2. Main parameters of the ducted propeller
Propeller Ka4-70
radius 3.6m
pitch ratio 1.1
blade area ratio 0.7
Duct NO.19A
radius 3.65m tip clearance 0.025m The main requirement for the controller is the ability to keep the platform at a pre-t position during drilling or standby operation; moreover, the DPS must be able to maintain vesl positioning even in the ca of failure or maintenance of one or two thrusters during operation. Simultaneous inactivity due to failure or maintenance purpos is considered for pairs of thrusters, powered by the same power plant or controlled by the same switchboard ction, namely: pairs 1-8, 2-7, 3-6and 4-5.
The azimuth and RPM of each thruster are controlled individually. Diameter of the thruster nozzle is 7.2cm at model scale (Figure.3), which equals 3.6m at prototype scale.
Figure.3. The model of thruster
fun学网
The thrusters do not allow direct thrust or torque measurement; therefore the open water thrust of each thruster was measured versus RPM’s prior to installation into the model. This relation is ud by the DP-controller to steer each thruster.
Thrust and azimuth of each azimuth thruster is determined by the thruster allocation algorithm. The total thrust of all thrusters matches the required thrust and moment, unless thruster saturation occurs.
Each of the thrusters is steered on RPM, in order to produce the required thrust, the relation between RPM and thrust of the propeller has been known by model test, the result is shown in Figure.4.
200
400
600
800
1000
050010001500 t
h
r
食既
u
s
(
k
N
)
RPM(rad/s)
open water thrust vs RPM
maximum thrust …
The bollard pull thrust values have been corrected for the thrust degradation due to current inflow velocities (Figutre.5). The data were incorporated into the simulation.
0200400600800
10000
0.5
1
1.5
2
2.5
3
t h r u s t (k N )
surface current speed (m/s)
open water thruat vs surface current speed
maximumu thrust curve
Figure.5. Open water thrust to surface current speed relationship
Besides the thrust deductions current inflow velocities, it is noted that (Dang and Laheij, 2004) interactions among thrusters and thruster-hull are much more complicated for DPS than a normal sailing vesl or tugs. The thrusters clo to the bow of the vesl will generate a water jet into the thrusters at the stern, it effectively increas the entrant speed into the downstream thrusters, resulting in thrust and torque reductions. For dynamic positioning, the thrusters are able to generate transver thrust and also water jet in 360 deg. In many cas, there exist critical angles when the jet of one thruster will hit the other thruster with large influences. Mostly, this should be avoided. If not completely, this interaction should at least be known.
Due to the complexity of all iterations, there is still no good theory or calculation method available in order to predict the interactions accurately. In order to have an accurate prediction for interactions, model tests have been carried out. The results are shown in Figure.6.
1 &3
It is en that the largest thrust loss due to thruster-hull interaction occurs at the situation when the t
hrust jet hits the vertical wall of the other pontoon. It is also en from Figure.6 that when the water jet flows all the way from the bow to the stern under the hull bottom (at 0 deg) the thrust loss can be 18% due to mainly friction drag. When the jet is discharged clo to the edge of the hull (say at 180 deg), the interaction is the lowest with a thrust loss somewhat around 10%. The largest thrust loss occur at the situation when the jet hits the other pontoon at the angle of 90 deg.
The thruster-thruster interaction is especially important in DPS, thrust loss is over 30% at some specific angles in this model test. For example, if thrusters 1 and 3 are producing thrust to stern, the downstream thruster (#3, in this ca) would experience significant reduction off the beam direction, due to the wake of thruster #1 blowing into thruster #3.
In order to avoid thruster-thruster interaction, azimuth restrictions are impod, e Table. 3. The centre angles are tho of the force vectors. The ‘Thruster dep.’ (thruster dependency) column denotes the thruster on which the zone is dependent. If this particular thruster is not in u, the zone is neglected in the thruster allocation. The forbidden zones are calculated using a simple algorithm bad on the results (Lehn, 1985) and were validated in model test.
Table 3. Thruster azimuth forbidden zones.
Thruster No. Zone No.
standardcentre ψ
(deg) beam ψ(deg) Thruster dep. 1 1 -21.8 ±13.6 3 2 1 21.8 ±13.6 4 3 1 158.2 ±13.6 1 4 1 -158.2 ±13.6 2 5 1 21.8 ±13.6 7 6 1 -21.8 ±13.6 8 7 1 -158.2 ±13.6 5 8 1 158.2 ±13.6 6
ENVIRONMENTAL CONDITIONS
In order to obtain accurate information of environmental loads, environmental loads on the vesl are calculated and some tests are finished to prove the calculation.
Wind and current forces and moments associated with vesl yaw rotation were evaluated using an improved building block approach propod by Sahin and Aybar (1984) and Walree (1991). The structure is built up of standard components with known force characteristics. Interaction effects like shielding are taken into account.
Wind load coefficients C XV , C YV and C MV are defined in the standard way by,
111222
;;126222V V V F C V F C V F C V XV a YV a MV a
ρρρ=== (1) which are prented in fugure.7. F 1V and F 2V are surge and sway component of wind force, F 6V is the yaw moment, ρa is air density; V is the mean wind velocity.
Figure. 7. Wind load coefficient
Current load coefficients (Figure.8), defined in the same way as the wind load coefficients.
111222;;126222
C C C F C C F C C F C C XC w YC w MC w ρρρ=== (2)
F 1C and F 2C are surge and sway component of wind force, F 6C is the yaw moment, ρw is water density; C is the mean wind velocity.
Figure. 8 Current load coefficient
The wave drift force (F wd ) (Figure.9~11) is mainly discusd, in which the calculation is bad on the theory of near field integration (Pinkster, 1980; Huijsmans and van Walree, 1991) and a new suit of measurement system is designed to fit for the vesl.
Figure. 9 Wave-drift load confidents, surge
结汇英语Figure.10 Wave-drift load confidents, sway
Figure. 11 Wave-drift load confidents, yaw
To validate the results of numerical calculations of the cond order wave forces, the measurement of wave drift forces utilizing a passive
restricted system (Figure.12) propod by Pinkster(1980).
Fig. 12. Passive restricted system
Fig.13 prents an illustrative example of such coefficients for a 45 deg wave-heading angle, 5.8m significant height of wave. Second order slow drift forces were evaluated time domain and the results are compared with the results of model tests. In this condition, the mean wave drift forces are 802.2kN (calculation) and 842.8kN (model experiment), the error is 5.06%.
Figure. 13 Results of wave drift forces of calculations and experiments.
aventador什么意思
The Pipe drag (F cp ) is defined as the current force distribution along the pipe and buffer (F cp ), induced by the relative current velocity (V C(Z)), where the relative current velocity is the pipe element velocity (V S ) relative to the surface or subsurface current velocity profile (Brink and Chung, 1981). Among the force components for the given operational and environmental requirements, the F cp and F wd are the largest force components and are in the same order of magnitude for the stationkeeping mode with no choice of headings. For the given requirements, the F cp remains the same regardless of the ship heading. The F cp values vary along the pipe length as a function of V C(Z) and the vertical variation of the subsurface water properties. The assumed mining velocity range can place the pipe drag coefficients (C D ) along the pipe near the subcritical to critical Reynolds number (Re) range. In other words, the F cp values can be quite different at an instant between the top- and bottom-end sides of the lift pipe. Furthermore, steep slope and ambiguity of the C D versus Re curve in this Re range can po problems on accurately estimating the contribution of total pipe drag at different ship velocities to the ship thrust allocation (Figure. 2 for details) and possibly for the ship thruster control. The latter will be further discusd in conjunction with the control simulation results. If the top end of the lift pipe is connected to a point far from the sh
, the pipe drag vector can require significantly large restoring moment in the ship thrust allocation.
STATIONKEEPING CAPABILITY
Brink and Chung (1981) was the first one to introduce azimuthing thrusters to dynamic positioning as improvement over Glomar Explorer's fixed thruster efficiency, and the improvement of the Glomar thruster system and control logic was a guide of our work. In this paper the control mechanism of the simulation program is a feedback system using position data and includes a wind feed-forward system. Bad on the position signals the total required thrust vector is determined with a PID controller:
int int
int int int int
i
tx X
X c x b x
xdt X treq e tx tx wff T T
i ty Y Y c y b y ydt Y treq e ty ty wff T T
remark什么意思i t N
N c b dt req e t t wff T T ψψψψψψψ=−+Δ+Δ+Δ+∫=−+Δ+Δ+Δ+∫=−+Δ+Δ+Δ+∫&&& (3)
In which X e is the average environmental force vector, T int is the integration time and Δx, Δy, Δψ are the position deviations, e Figure. 14. X wff is the wind feed forward force vector. c t, b t and i t are
Fig. 14 Sketch map of DP control
Solving the allocation of required forces (equation (2)) is a non-linear problem due to the possible prence of forbidden ctors for azimuthing angles. Furthermore, the solution of the location should be optimal in the n of minimal fuel consumption. This is achieved by defining a penalty function which us the square of the thrusts.
Forces in x and y direction for each azimuthing thruster is ud to build a objective function:
[,,...,]
12x x x x N = (4)
where N is the number of azimuthing thrusters, x 2i-1 is the surge force of azimuthing thrusters, x 2i is the sway force of azimuthing thrusters.
And the azimuth of thruster is defined as:
2arctan(
21
x i i
x
i α=− (5)
The objective function which must be minimized is defined as:
22()()2121
N
f x x x i i
i =+∑−= (6)
The constraints can be divided in equality and inequality constrains.
The three equality equations are determined by the equilibrium of forces in the surge, sway and yaw directions, i.e. the forces of the allocation solution must be equal to the forces required by the controller:
bolshevism()0121
1()0221
1()0321,21,11
N
g x X x treq i i N g x Y
x treq i i N N
g x N x l x l treq i y i i x i
i i =−=∑−==−=∑−==−+=∑∑−−== (7) in which l yi and l xi are distances in x and y between thruster and rotation
center of the platform.
