Dynamic Modeling of Deepwater Offshore Wind Turbine Structures in Gulf of Mexico Storm Conditions
DYNAMIC MODELING OF DEEPWATER OFFSHORE WIND TURBINE STRUCTURES IN GULF OF
MEXICO STORM CONDITIONS
Thomas Zambrano
AeroVironment, Inc. Monrovia, California, USA
Tyler MacCready
AeroVironment, Inc.
Monrovia, California, USA
Taras Kiceniuk, Jr.
AeroVironment, Inc
Monrovia, California, USA
Dominique G. Roddier Marine Innovation & Technology Berkeley, California, USA
Christian A. Cermelli Marine Innovation & Technology Berkeley, California, USA
ABSTRACT
A Fourier spectrum based model of Gulf of Mexico storm conditions is applied to a 6 degree of freedom analytic simulation of a moored, floating offshore structure fitted with three rotary wind turbines. The resulting heave, surge, and sway motions are calculated using a Newtonian Runge-Kutta method. The angular motions of pitch, roll, and yaw are also calculated in this time-domain progression. The forces due to wind, waves, and mooring line tension are predicted as a function of time over a 4000 second interval. The WAMIT program is used to develop the wave forces on the platform. A constant force coefficient is used to estimate wind turbine loads. A TIMEFLOAT computer code calculates the motion of the system based on the various forces on the structure and the system’s inertia.
INTRODUCTION
Large wind turbines designed for the marine environment may soon become a major contributor towards the UK’s long-term targets for renewable generation. While most present interests are for transmitting the power to shore, our interest is applying such technology for on-site power resource supply/supplement for deepwater oil and gas fields far offshore in the Gulf of Mexico as well as in the North Sea.
To explore this topic, we contacted Marine Innovations & Technology of Berkeley CA, who is in the process of qualifying a MiniFloat platform (Cermelli, Roddier & Busso, 2004). Their floater design features column-stabilized units (semi-submersible) with water entrapment plates – large horizontal skirts extending radially from the base of the columns – to control the platform dynamic performance. We also contacted Halus Power Systems of San Jose, CA, an engineering firm specializing in tubular tower structures for large wind turbines. Halus was able to supply general specifications for several propeller type Danish wind turbines in the 250 kW to 350 kW size ranges, along with tower loads information. Together, the floater and wind turbine data were used to create the marine renewable platform concept shown in Figure 1.
Figure 1. Study Example – Three 27-m rotor diameter wind turbines atop 30-m towers on the deck of MiniFloat floater -total displacement 4800 tons, 2300-m water depth.
Calculations described in Cermelli and Roddier (2004) highlight the MiniFloat’s excellent motion characteristics in waves, which were validated by model tests described in Marine Innovation & Technology Report (2005). For this study the floater was resized to accept the payload from three wind turbines, and to provide ample deck space to limit blade interference.
Proceedings of OMAE2006
25th International Conference on Offshore Mechanics and Arctic Engineering
June 4-9, 2006, Hamburg, Germany
OMAE2006-92029
Table 1 summarizes the main dimensions. Two different wind turbines sizes were investigated for sensitivity study. These were the Vestas models V17 and V27. Table 2 summarizes the main characteristics of these wind turbines. Column dimensions 7.3 x 15.6 m
Column center to column center 33.5 m
Pontoon dimensions 3 x 4.6 m
Draft 13.7 m Air Gap 12.2 m Displacement 4813 metric ton Structure steel 2473 ton Deck equipment (Turbine, nacelle, generators, Marine systems) 826 ton Ballast & Mooring 1522 ton GM (Stability Criteria) with mooring 6.1 m
Table 1. Floater main characteristics
Vestas V17 Vestas V27 Blade Diameter 17 m 27 m
Swept Area
227 m 2
573 m 2 Number of Blades 3 3 Tower height 22.5 m 30 m Power output 90 KW 225 KW Tower Weight 5600 kg 12,000 kg Total Weight
11,980 kg 19,800 kg
Table 2. Wind Turbines characteristics
ANALYSIS PROCEDURE
The response of the floater described in this paper is obtained in the time-domain because significant non-linear effects are expected, which make a frequency-domain approach more uncertain. Both the large viscous effects on the water-entrapment plate and the wind load on the turbine have
significant non-linear terms. A time-domain motion analysis
solver is used to predict the platform motion in any sea-state. This solver (TIMEFLOAT) solves Newton equations of motion. The vessel, mooring and wind turbine responses are fully coupled through a time-marching scheme. Wave loads are modeled using a linear diffraction-radiation solver and viscous effects on the water-entrapment plate using a modified Morison equation model. More details on the numerical model are presented in the next sections. The wind and wave data for the different analyses performed are presented in Table 3. These metocean criteria are generic for the deepwater Gulf of Mexico (GOM). 1 Year Storm 10 year storm 10-year hurricane 25-year hurricane Hs (m) 4.3 6.1 7.6 9.4 Tp (sec) 9 10.7 11.9 12.8 γ
2 2 2.2 2.2 V wind (m/sec) 14.
3 19.5 23.2 28.8 Table 3. Metocean criteria
Diffraction-radiation solution Figure 2: (a) WAMIT Panel model of submerged section for
hydrodynamic calculations (b) Topside model for wind load estimation. Time-domain formulation Time-domain simulations of the floater subjected to external forces are performed using the TimeFloat software, which was developed by Marine Innovation & Technology and used on a variety of floating systems projects (small and large ships, turret- and spread-moored, semi-submersible, and buoys) and validated by comparison with published data and several model test campaigns, shown in Cermelli and Roddier (2004) and Marine Innovation and Technology Report (2005). TimeFloat solves the Newton’s equations of motion of the floaters in the time-domain using a fourth order Runge-Kutta
time-marching scheme. At each fractional time-step, the
various external forces (due to wind, waves, and the mooring lines) are updated based on the motion of the ship. The
mooring line configuration is determined using a finite-difference scheme described in Chatjigeorgiou and Mavrakos
(1998).
Drift force
Newton’s equation of motion applied to this floating system reads: F drift is the 6 DOF-drift force on the ship computed based on WAMIT mean drift frequency-dependent coefficients obtained with the pressure integration method, and the wave amplitude components. Newman’s approximation (1974) is used.
([M]+[Ma])d 2X/dt 2+[C]dX/dt+[K]X =F diff +F visc +F drift +F moor +F wind (1)
Mooring force
F moor is the 6-DOF force on the vessel resulting from all mooring lines. A two-dimensional finite difference scheme described in Chatjigeorgiou and Mavrakos (1998) is implemented to solve the mooring line equations using a cable dynamics model. The nonlinear ordinary differential equations are solved at every time step using a relaxation method. A friction model is implemented on the sea-bed. The mooring line configuration between the vessel fairlead and the touch-down point is solved iteratively, until bottom tension and touch-down location are converged. The top tension is calculated on each mooring line, and fed into the Newton’s equation of motion for the floater . This is a vectorial equation applied to the 6 degrees of freedom of floater. The left-hand side of the Newton’s equation of motion contains terms proportional to the acceleration, velocity and displacement of the vessel. The right-hand side includes the various exciting forces. A detailed description of all the terms in the equation is given below.
Mass matrix
[M] is the 6x6 mass matrix. It is based on an explicit design of the floater for offshore wind turbine applications and includes all the system associated with the turbine particulars
Added-mass matrix
Wind force
[Ma] is the 6x6 added-mass matrix. An alternate formulation of the equation of motion of a floater is used here which does not require computation of the retardation functions: the added-mass terms for horizontal motions (surge, sway, yaw) are taken as the low frequency limit, obtained from the WAMIT runs for large periods (T=50 sec). For vertical motions (heave, roll, pitch), the added-mass terms corresponding to the peak period of the wave spectrum are used. This formulation developed by Ueda (1984) assumes that the motion response is narrow-banded. F wind is the 6 DOF wind force, proportional to the square of the wind velocity, and to wind coefficients that are based on a Wind Block model. The block model computes forces on geometrical shapes (or blocks) which can be rectangular, cylindrical or spherical. The force on each block is based on a semi-empirical wake model representing shielding effects from upstream blocks, and on empirical drag coefficients from wind-tunnel tests (Canada National Building Code, 1961). This program was created to design architectural elements taking into account interference between buildings.
Radiation damping matrix
[C] is the 6x6 radiation damping matrix, due to outgoing waves generated by the moving floater. These terms are also computed by WAMIT, and similar frequency limits as the added-mass terms are used. A model representing the main components of the floater and the wind turbine was created (See Figure 2b), and wind coefficients were determined for various wind headings. A model of a unique turbine was generated first and the wind force and overturning moment at the base of the column were calibrated against data from the manufacturer (Vestas, 1995 and 1998).
Hydrostatic stiffness matrix
[K] is the 6x6 hydrostatic stiffness matrix computed by WAMIT.
Numerical algorithm
Motion
TimeFloat is a FORTRAN program which advances the solution of equation (1) in time. TimeFloat first solves an initial static phase, in which mean wind and current loads are applied as well as the mooring line pretension. This phase serves to reduce the transient phases, and quickly provides static information if needed. In this particular analysis, no current loading was prescribed. (X), (dX/dt) and (d 2X/dt 2) are vectors with the 6-DOF displacement, velocity and acceleration of the floater origin in the inertial frame. The values are computed at each time-step in the time-domain solution.
Wave-exciting force
F diff is the 6-DOF wave-exciting force determined by a Fourier series using WAMIT frequency-dependent wave-exciting force components and wave amplitude components representing the specified wave spectrum.
Then, the solution is advanced in time using a Runge-Kutta algorithm for the 6 DOF rigid body motion and velocities. At each of the 4 fractional steps used in this process, external forces are updated.
Viscous force
F visc is the 6-DOF viscous force resulting from drag effects on the MiniFloat plates. These are computed using a Morison equation model based on the relative velocity of special line members (“viscous” elements assumed rigidly connected along the plate edges), and the wave and current kinematics. All storm simulations consisted of a one-hour long sea-state. An initial seed is used to determine the random wave time-series. Some sensitivity tests were conducted to show the variability of extreme response to the seed.
RESULTS AND DISCUSSION
Response Amplitude Operators
Figure 3 shows the 4,800 ton MiniFloat platform motion response. These RAO have been obtained from the ratio of the motion rms in time domain to the rms of a regular wave train. We note that the viscous and non-linear mooring responses are included in this “RAO” formulation. The wind has no direct effect on the dynamics, since in frequency domain its only contribution is a static offset.
Figure 3: Motion RAOs for the MiniFloat floater.
Irregular Sea States
The exciting force individual components as described in equation (1) are shown in Figure 4 (a & b) for the V27 turbine when the system is subjected to a one-year storm.
4
D
i f f r a c t i o n Surge Force (kN)
-1000
1000
V
i s c o u s 4D
r i f t M
o o r i n g W
i n d Time (s)
Figure 4(a) Break down of exciting forces on surge motion
Each component is calculated independently and is affecting the motion response at every time step. The simulation is run for one hour but only 500 seconds are shown in the figure for clarity sake. Table 4 and Figure 5 show the response to Table 3 metocean states.
5
D
i f f r a c t i o n Pitch Moment (kN.m)
4V
i s c o u s 2000
40006000D
r i f t 4M
o o r i n g 1000200030004000W
i n d Time (s)
Figure 4(b) Break down of exciting moments on pitch motion
Surge (m)
No Wind Deck only V17 V27 1 year Storm
Mean 0.36 0.73 1.02 1.22 Min -0.81 -0.45 -0.19-0.19 Max 1.91 2.06 2.35 2.56 rms 0.43 0.41 0.42
0.42
10 year Storm
Mean 0.51 1.23 1.76 2.19 Min -0.68 -0.10 0.400.40 Max 2.56 3.24 3.84 4.34 rms 0.44 0.46 0.48
0.52
10 year Hurricane
Mean 0.56 1.67 2.32 3.01 Min -0.94 0.11 0.580.58 Max 3.69 4.55 5.25 6.03 rms 0.59 0.61 0.65
0.71
25 year Hurricane
Mean 0.74 2.52 3.61 4.77 Min -1.28 0.49 1.16 1.16 Max 4.94 6.63 7.768.90 rms
0.79 0.82 0.90
1.03
Table 4(a) MiniFloat Surge response in GOM conditions
W i n d
M o o r i n g
D r i f t V i s c o u s D i f f r a c t i o n
W i n d M o o r i n g
D r i f t V i s c o u s D i f f r a c t i o n
The wind and waves are assumed to come from the same direction, and the platform has one column heading into the waves. It was shown in in Cermelli and Roddier (2004) that this is one of the worst-case scenarios when the pitch response is of interest. Without clear understanding of the individual requirement of each system components, the platform was sized to have less than 5o of mean pitch and ±15o of dynamic amplitude. The surge offset was not considered a significant factor as long as the loads in the mooring lines stayed within half of the breaking strength. (Safety factor of 2 on the dynamic loads).
Pitch (deg)
No Wind Deck only V17 V27
1 year Storm
Mean -0.24 0.05 0.47 1.10
Min -5.79 -5.94 -5.37 -4.48
Max 5.11 6.27 6.52 6.89
rms 1.89 1.72 1.72 1.72
10 year Storm
Mean -0.43 0.10 0.89 2.07
Min -6.15 -6.47 -5.43 -4.03
Max 2.94 3.24 4.23 5.78
rms 1.24 1.21 1.23 1.30
10 year Hurricane
Mean -0.54 0.19 1.32 2.98
Min -10.18 -8.86 -7.39 -5.42
Max 3.52 4.03 5.27 7.37
rms 1.54 1.52 1.54 1.65
25 year Hurricane
Mean -0.77 0.37 2.14 4.71
Min -14.44 -11.44 -9.19 -6.70
Max 4.61 5.27 7.37 10.68
rms 2.02 1.98 2.03 2.24
Table 4(b) MiniFloat Pitch response in GOM conditions
Figure 5(a) Surge and Pitch response in 1-year storm Maximum Line Tension (kN)
No Wind Deck only V17 V27
1 year Storm
Mean 567.56 579.82 592.88 596.61
Min 520.44 529.34 541.35 543.57
Max 626.31 634.76 648.11 652.55
rms 18.01 17.05 17.31 17.62
10 year Storm
Mean 571.91 597.88 612.95 627.19
Min 521.33 542.68 555.58 565.37
Max 658.78 688.14 705.93 722.39
rms 17.42 18.34 19.31 20.83
10 year Hurricane
Mean 573.64 612.41 637.43 659.42
Min 513.32 545.35 567.15 580.05
Max 703.71 744.63 769.99 791.34
rms 24.85 25.99 27.60 30.19
25 year Hurricane
Mean 579.59 644.40 678.88 721.26
Min 493.31 558.70 580.49 604.96
Max 783.78 827.37 863.84 906.10
rms 34.81 36.69 39.83 45.58 Figure 5(b) Surge and Pitch response in 10-year storm conditions
In the 25-year hurricane, survivability of the system is maintained. The surge displacement is 1% of the water depth, the pitch mean offset is about 5 degrees and the maximum is 10 degrees. The maximum tension in the mooring lines is less than half the ultimate strength. CONCLUDING REMARKS
In the supporting numerical example, the mathematical
representation of the wind turbine is simplified to a quadratic
drag term. A better modeling of the wind force and induced moment on the platform will be part of the follow-on activities,
which will also include model testing to fully analyze the coupling between the wind turbines and the offshore platform. Results are expected by early 2008.
Figure 5(c) Surge and Pitch response in 10-year hurricane REFERENCES
Canada National Building Code, 1961, “Handbook of Pressure Coefficients”.
Cermelli, C.A., D.G. Roddier and C.C. Busso, 2004, “MiniFloat: A novel concept of minimal floating platform for marginal field development”, Proc. 14th Int. Offsh. & Polar Engrg. Conf., Toulon, France.
Cermelli, C.A. and D.G. Roddier, 2004, “The stabilizing efffects of a water entrapment plate on the motion of a small semi-submersible platform”, Proc. 24nd Offsh. Mech. Arctic Engrg. Conf., Halkidiki, Greece.
Chatjigeorgiou I.K. and S.A. Mavrakos, 1998. “Assessment of bottom-cable interaction effects on mooring line dynamics” , 17th Intl. Conf. Offsh. Mech. Arctic Engineering.
Marine Innovation & Technology proprietary report: MI&T-007-015-0, May 2005, “MINIFLOAT-IV model tests at the Ship Model Testing Facility of the University of California, Berkeley”.
Newman, J.N., 1974, “Second-order, slowly-varying forces on vessels in irregular waves”, Proc. Int. Symp. dynamics of marine vehicles and structures in waves.
Ueda, S., 1984, “Analytical Method of Ship Motions
Moored to Quay Walls and the Applications”, Technical Note
of the Port and Harbour Research Institute 504.
Vestas Wind System A/S, 1995 “V27/V29 standard
foundation for tower, GWL below + ground”, 941507.RO.
Vestas Wind System A/S, 1995, “Vestas V27-225 kW,
60Hz WindTurbine: General Specification”, 941130.
Vestas Wind System A/S, 1988 “Vestas V17-90 kW,
WindTurbine: General Specification”.
Figure 5(d) Surge and Pitch response in 25-year hurricane