A nonlinear computational model, based on solving the Navier-Stokes equation, is used to study the motion of a 5 MW spar buoy floating wind turbine in moderate and extreme sea states with irregular waves. The main advantages of using the current model are that there is no limitation on the platform motion, the hydrodynamic loads do not rely on experimental data, and nonlinear hydrodynamic loads can be predicted. The current work extends a previously developed Navier-Stokes model for regular periodic waves on a tension leg platform floating wind turbine. Free decay tests are performed, and pitch, heave, and surge natural frequencies are determined. The responses of the spar buoy to operating conditions with significant wave height of 8 m and mean period of 10 s, and an extreme sea states including waves over 17 m height are studied. For the extreme sea state, a nonlinear model is required, since the platform response amplitudes are not small with respect to the spar buoy diameter. Effects not included in linear models, such as platform pitch angles higher than 10°, complete submergence of the platform tank and tether slacking are captured. Finally, a design study on spar buoy aspect ratio is performed for one sea state and it is shown that higher aspect ratio spars generally lead to lower mean pitch and surge responses as expected, but also may lead to a nonlinear trend in the standard deviations in pitch and heave, probably due to the increase in wind and wave moments on the spar.

1.
R. F.
Dominguez
, “
Analysis of a two-point mooring for a spar buoy
,” Ph.D. thesis (
Oregon State University
,
1969
).
2.
H. C.
Graber
,
E. A.
Terray
,
M. A.
Donelan
,
W. M.
Drennan
,
J. C.
Van Leer
, and
D. B.
Peters
, “
Asis-a new air-sea interaction spar buoy: Design and performance at sea
,”
J. Atmos. Oceanic Technol.
17
,
708
720
(
2000
).
3.
A. K.
Jha
,
P.
De Jong
, and
S. R.
Winterstein
, “
Motions of a spar buoy in random seas: Comparing predictions and model test results
,” in Proceeding of Behaviour of Offshore Structures Conference, Delft, The Netherlands (
1997
).
4.
M.
Karimirad
and
T.
Moan
, “
Extreme dynamic structural response analysis of catenary moored spar wind turbine in harsh environmental conditions
,”
J. Offshore Mech. Arct. Eng.
133
,
041103
(
2011
).
5.
J.
Jonkman
, “
Dynamics modeling and loads analysis of an offshore floating wind turbine
,” Technical Report No. NREL/TP-500-41958,
2007
.
6.
J. M.
Jonkman
, “
Dynamics of offshore floating wind turbines. Model development and verification
,”
Wind Energy
12
(
5
),
459
492
(
2009
).
7.
F. G.
Nielsen
,
T. D.
Hanson
, and
B.
Skaare
, “
Integrated dynamic analysis of floating offshore wind turbines
,” in 25th International Conference on Offshore Mechanics and Arctic Engineering, Humburg (
2006
).
8.
P.
Sclavounos
,
C.
Tracy
, and
S.
Lee
, “
Floating offshore wind turbines: Responses in a seastate, pareto optimal designs and economic assessment
,” in 27th International Conference on Offshore Mechanics and Arctic Engineering, Estoril, Portugal (
2008
).
9.
T.
Utsunomiya
,
E.
Nishida
, and
I.
Sato
, “
Wave response experiment on spar-type floating bodies for offshore wind turbine
,” in Proceedings of the 19th International Offshore and Polar Engineering Conference, Osaka (
2009
).
10.
L.
Sethuraman
and
V.
Venugopal
, “
Hydrodynamic response of a stepped-spar floating wind turbine: Numerical modelling and tank testing
,”
Renewable Energy
52
,
160
174
(
2013
).
11.
J.
Jonkman
and
D.
Matha
, “
Dynamics of offshore floating wind turbines-analysis of three concepts
,”
Wind Energy
14
,
557
569
(
2011
).
12.
M. J.
Muliawan
,
M.
Karimirad
, and
T.
Moan
, “
Dynamic response and power performance of a combined spar-type floating wind turbine and coaxial floating wave energy converter
,”
Renewable Energy
50
,
47
57
(
2013
).
13.
F.
Beyer
,
M.
Arnold
, and
P. W.
Cheng
, “
Analysis of floating offshore wind turbine hydrodynamics using coupled CFD and multibody methods
,” in Proceedings of the 23rd International Offshore and Polar Engineering Conference, Anchorage, Alaska, USA, 30 June–5 July
2013
.
14.
A.
Nematbakhsh
,
D. J.
Olinger
, and
G.
Tryggvason
, “
A nonlinear computational model for floating wind turbines
,”
J. Fluids Eng.
135
,
121103
(
2013
).
15.
A.
Nematbakhsh
, “
A nonlinear computational model of floating wind turbines
,” Ph.D. thesis (
Worcester Polytechnic Institute
,
2013
).
16.
A. C.
Baldwin
and
J.
Edmond
, “
Hypre
,” Center for Applied Scientific Computing (CASC), Lawrence Livermore National Laboratory, Livermore, CA (
2011
).
17.
S.
Osher
and
J.
Sethian
, “
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
,”
J. Comput. Phys.
79
,
12
49
(
1988
).
18.
R.
Fedkiw
,
T.
Aslam
,
B.
Merriman
, and
S.
Osher
, “
A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method)
,”
J. Comput. Phys.
152
(
2
),
457
492
(
1999
).
19.
M.
Sussman
and
E.
Fatemi
, “
An efficient interface-preserving level set redistancing algorithm and its application to interfacial incompressible fluid flow
,”
SIAM J. Sci. Comput.
20
(
4
),
1165
1191
(
1999
).
20.
T.
Yabe
,
F.
Xiao
, and
T.
Utsumi
, “
The constrained interpolation profile method for multiphase analysis
,”
J. Comput. Phys.
169
(
2
),
556
593
(
2001
).
21.
N.
Patankar
and
N.
Sharma
, “
A fast projection scheme for the direct numerical simulation of rigid particulate flows
,”
Commun. Numer. Methods Eng.
21
(
8
),
419
432
(
2005
).
22.
O.
Faltinsen
,
Sea Loads on Ships and Offshore Structures
(
Cambridge University Press
,
1993
).
23.
E.
Wayman
,
P.
Sclavounos
,
S.
Butterfield
,
J.
Jonkman
, and
W.
Musial
, “
Coupled dynamic modeling of floating wind turbine systems
,” in Offshore Technology Conference, Houston, TX, 1–4 May
2006
.
24.
S.
Liao
and
R.
Yeung
, “
Investigation of the mathieu instability of roll motion by a time-domain viscous-fluid method
,” in Proceedings of 16th International Workshop on Water Waves and Floating Bodies, Hiroshima, 22–25 April
2001
.
25.
B.
Koo
,
M.
Kim
, and
R.
Randall
, “
Mathieu instability of a spar platform with mooring and risers
,”
Ocean Eng.
31
,
2175
2208
(
2004
).
26.
E. E.
Bachynski
and
T.
Moan
, “
Design considerations for tension leg platform wind turbines
,”
Mar. Struct.
29
,
89
114
(
2012
).
You do not currently have access to this content.