Hydrodynamic Response of Alternative Floating Substructures for

The 2012 World Congress on
Advances in Civil, Environmental, and Materials Research (ACEM’ 12)
Seoul, Korea, August 26-30, 2012
Hydrodynamic Response of Alternative Floating Substructures for
Spar-Type Offshore Wind Turbines
*
B.W. Wang2), E.J. Choi2), S. Jung2), S. Park1)
1), 2)
School of Mechanical Engineering, Pusan National University, GeumJeong-Gu,
Busan 609-735, Korea
1)
[email protected]
ABSTRACT
The severe working environment that floating offshore wind turbines experience
underscores the need to understand their hydrodynamic behavior when evaluating
and optimizing the substructures. In this study, two types of substructure, namely
classic-spar and truss-spar, were considered for the purpose of structure optimization.
These two spar substructures were treated as rigid bodies with multi-DOFs and
attached to the seabed by mooring lines. The wave force was calculated using
Morison Equation and diffraction theory. A coupled analysis method is required
because the presence of mooring lines introduces a nonlinear restoring force. For this
reason, a widely used FE method was adopted to analyze the coupled hydrodynamic
responses of the two floating substructures and obtain the response analysis results
of the various DOFs in the frequency domain. Finally, a comparison of the
hydrodynamic response performances was carried out to determine the differences
between the two configurations. From the comparison results, an alternative
configuration of the floating substructure with better hydrodynamic performance for
wind turbines is recommended.
1. INTRODUCTION
Wind energy offshore has become one of the most promising renewable energy
resources because of the advantages of offshore wind, such as higher wind speed,
lower land cost, as well as less visual pollution and enormous potential (Leung 2012;
Tavner 2008; Snyder 2009). According to the water depth, different concepts have
1)
2)
Professor
Graduate Student
been proposed to help build wind turbines in an offshore area (Breton 2009; Byrne
2003). Among these concepts, many floating-base configurations (tension leg platform,
semi-submersibles, and spar-type floating structures) for wind turbines are
recommended to explore wind energy in deeper water (Hua 2011; Moe 2010).
Regarding a spar-type floating structure, there are three configurations of spars in the
offshore Oil and Gas (O&G) industry, classic-spar, truss-spar and cell-spar (John
2003). The truss-spar platform has been reported to be a favorable configuration
because of its lower cost and better performance in some degrees of freedom (DOF)
(Andreas 2000). In the wind energy industry, however, only the classic-spar platform
has been introduced to deep water offshore prototypes, such as the Hywind and Sway
prototypes (Angela 2008).
Fig. 1 Configurations of two kinds of spars
Therefore, this study compared the hydrodynamic performance of the classic-spar
and truss-spar in the frequency domain using a finite element (FE) method. The
specifications of the two spars (Fig. 1) are based on the Hywind prototype (Hywind
brochure 2011) with minor modifications. Their specifications and loading conditions
were adjusted to be similar (Table 1) to make the comparison reasonable.
2. METHODOLOGY
2.1 Assumption
Only the wave loads were considered in this study because they are the main parts
of the environmental load encountered by offshore platforms. For simplicity, the
dynamic effects caused by wind and current were not taken into consideration. The
water was assumed to be an ideal fluid, non-rotational and incompressible with small
wave elevation (ANSYS AQWATM-Line Manual).
2.2 Definition of motions
The spar-type floating platform is a compliant platform moored with mooring lines.
The entire system undergoes rigid body motions in six DOFs (Agarwal 2003). The
coordinate system used in this study is a right handed system with its origin at the
mean water level (MWL). The positive z axis is vertically upwards. The system
motions are described by six DOFs (Fig. 2a): the surge, sway and heave (translational
motions), and the roll, pitch and yaw (rotational motions). The wave directions are
defined as the angles between the wave front and positive x axis measured
anticlockwise (Fig. 2b).
a
b
Fig.2 Definition of motions and incident wave directions
Table 1 Specifications of the two spar platforms
Items
Classic-spar
Truss-spar
8 (Hull)
Hull diameter [m]
8
0.50 (Pillar)
0.45 (Truss)
Submerged depth (Total draft) [m]
100
100
Actual volumetric displacement [m³]
4994.30
3610.90
Total mass [tons]
4.99e3
3.61e3
Center of gravity (Centerline) [m]
-69
-57
Moment of inertial, Ixx [kg.m²]
1.01e10
9.54e9
Moment of inertial, Iyy [kg.m²]
1.01e10
9.54e9
Moment of inertial, Izz [kg.m²]
4.40e7
3.36e7
Sea water density [kg/ m³]
1025
1025
Water depth (MWL to sea bed) [m]
400
400
2.3 Calculations of the wave loads
For structures with a hull diameter (D) to wave length (λ) ratio > 0.2, linear diffraction
theory in potential flow was applied to calculate the inertia force and diffraction force
acting on the main bodies of the structure. The wave drag force acting on the truss
section of truss-spar was calculated using the Morison Equation. The coupled motion
equations of the spars were discretized and solved using the boundary element
methods (Green’s Function) (James 2003). The Governing Equation for the velocity
potential is
v
Ñ 2f = 0(V = Ñf ).
(1)
Linearized free surface condition becomes
¶f w 2
f ?= ,
¶z g
(2)
where w is the wave frequency and f is the velocity potential.
Sea bed boundary conditions are
Ñf = 0 when z → ∞ for deep water,
¶f
= 0 at z = -d (sea bed) for shallow water.
¶z
By the linearized assumption, the velocity potential can be decomposed into the
incident wave velocity potential, diffracted wave velocity potential and radiated wave
potential in the six DOFs. A linear superposition of the velocity components was
applied to obtain the total velocity potential due to unit amplitude incident wave, and
the total velocity potential becomes
f = je
- iwt
6
é
ù
= ê(j I + jdi ) + åj j × x j ú e - iwt ,
j =1
ë
û
(3)
where subscripts I, di and j = 1,2,…6 are velocity potential for incident wave, the
diffracted wave and the radiated wave in six DOFs, respectively, and xj is the structure
motion for the unit wave amplitude. The incident wave velocity potential for a finite
water depth d, can be defined as follows:
jI e
- iwt
-igz cosh éë k ( z + d ) ùû eik ( x cosq + y sin q +a ) e - iwt
=
?
w cosh ( kd )
(4)
where d is the water depth, θ is the wave direction, ζ is wave elevation, and k is the
wave number defined by
w 2 = gk tanh ( kd ) .
(5)
After the velocity potentials of the incident and diffracted wave are determined, the
hydrodynamic pressure acting on the surface of the structure can be calculated using
the Bernoulli equation as follows (James 2003):
P ?= - r
¶f
¶t
(6)
where P is the hydrodynamic pressure and r is the water density. The various fluid
forces can be calculated by integrating the hydrodynamic pressure over the wetted
surface of the body. For Morison structures (D/λ < 0.2), the wave force can be
calculated using the Morison equation:
&& + 1 r C DV V ,
F =rWaw + r Ca Waw - r Ca WX
(7)
d
2
where Ca and Cd are the added mass and drag coefficients of the element,
respectively (James 2003), Ω is the volume of the element per unit length, D is the
element diameter, aw is instantaneous flow acceleration, V is the relative velocity
between the flow and structure, and ̈ is the structure acceleration due to oscillation.
2.4 Wave frequency motions
The external loads acting on the spars can be calculated if the velocity potentials of
the incident, diffracted and radiated wave are available. The added mass and added
damping can be calculated based on diffraction theory. In general, the linear coupled
equation of motion can be written using the following matrix forms (Andreas 2000)
( M s + M a ) X&& + CX& + KX = F0e-iwt ,
(8)
where MS is the mass matrix of the structure, Ma is the added mass (6×6 matrix) by
frequency, C is the linear damping (6×6 matrix) by frequency, K is the restoring
stiffness (6×6 matrix), and F0 is the total external force.
The solution was assumed to be harmonic by
X = X 0 e - iwt
(9)
,
where is the complex amplitude vector. Substituting Eq. (9) into Eq. (8) yields the
following:
éë -w 2 ( M s + M a (w ) ) - iwC (w ) + K ùû X (w ) = F0 e - iwt .
(10)
The solution has the following form:
-1
X 0 = éë -w 2 ( M S + M a ( ω ) ) - iwC (w ) + K ùû F0 .
The response amplitudes are given in complex notation as follows:
(11)
Re
Im
é X 1 ù é X 1 + iX 1 ù
ú
ê X ú ê Re
X 2 + iX 2Im ú
2ú
ê
ê
X0 =
=
,
ú
ê M ú ê
M
ú
ê ú ê Re
Im
ë X 3 û êë X n + iX n úû
(12)
where the magnitude is
Xi =
Re 2
i
Im 2
i
(X ) +(X ) .
(13)
The response amplitude operator, RAO, is defined as the response divided by the
wave amplitude:
RAOi =
xi
1
Hw
2
=
Re 2
i
Im 2
i
(X ) +(X )
1
Hw
2
,
(14)
1
2
where H w is wave amplitude.
In hydrodynamic response analysis, the RAOs are normally used to evaluate the
performance of the structure in the frequency domain. Fig. 3 summarizes the process
for determining the calculation-related terms in Eq. (11).
Fig. 3 Process of wave force calculation in ANSYS AQWATM
3. MODEL DESCRIPTIONS
The classic-spar hull was assumed to be hermetically sealed (Sarpkaya 1981). The
truss-spar has a similar configuration except the middle section replaced by truss
elements. The effects of the mooring system were considered by giving the specified
pretension stiffness on the specified loading points on the hull of the spars (Wang
2008).
The FE method was applied to predict the hydrodynamic response using ANSYS
AQWATM software (version 13.0). Fig. 4 shows the FE model created in ANSYS. The
classic-spar contained 2797 nodes and 2780 elements in the diffracted bodies, and
the total number of nodes and elements are 4239 and 4243, respectively. Owing to the
presence of the truss section in the truss-spar platform, the total number of nodes and
elements were smaller than that of the classic-spar; 3336 and 3347, respectively.
Both spars were symmetric about the x and y axis. The incident wave angle could
be chosen from 0 to 180° with an interval of 45°. The RAOs of 0°, 45° and 90° for the
classic-spar and truss-spar were determined. The wave frequency ranged from 0
rad/s to 2.5 rad/s during the calculation. In this frequency domain, the RAOs in the
different DOFs and wave direction were obtained from the simulation results.
Fig. 4 FE models (Surface element) for analysis
4. RESULTS AND DISCUSSION
4.1 Hydrostatic results
A floating structure will experience external forces (i.e. wave force in this study)
trying to turn it over. The structure must be able to resist these forces through what is
termed hydrostatic stability. The metacentric heights are the key parameters needed
to evaluate the stability of the two spars. Table 2 lists the hydrostatic results for the
spars. As listed in the table, both metacentric heights of the spars were positive and
similar: a positive metacentric height makes the structure stable (Jochen 2009).
4.2 Frequency domain analysis of RAOs
Figs. 5 and 6 show the RAOs for the chosen incident wave directions. The RAOs of
some DOFs in certain directions are not shown in the figures because the magnitudes
were approximately 0. The magnitudes of the surge and sway motions of both spars
were similar. There was only one single curve in the graph of the heave RAOs, which
is because the heave motion is independent of the incident wave angle for both spars.
Figs. 5 and 6 also show that the maximum heave RAO of the classic-spar is much
larger than that of the truss-spar, which means that replacing the middle section of the
classic-spar with a truss is beneficial to the heave motion.
Surge RAOs for classic spar
Sway RAOs for classic spar
3.5
2.0
90°
45°
0°
3.0
1.0
45°
0
Sway, m/m
Surge, m/m
2.5
2.0
1.5
4.0
3.0
1.0
2.0
0.5
1.0
0
0
0.5
1.0
1.5
ω, rad/s
2.0
0
0
2.5
0.5
Heave RAOs for classic spar
1.0
1.5
ω, rad/s
2.0
2.5
Roll RAOs for classic spar
3.0
2.5
0°，45°，90°
45°
90°
2.5
2.0
Roll, °/m
Heave, m/m
2.0
1.5
1.5
1.0
1.0
0.5
0.5
0
0
0.5
1.0
1.5
ω, rad/s
2.0
0
0
2.5
Pitch RAOs for classic spar
0.5
2.5
x 10
2.0
2
1.5
1.5
Yaw, °/m
Pitch, °/m
2.5
0°，45°，90°
0°
90°
1.0
0.5
0
0
2.0
Yaw RAOs for classic spar
-3
2.5
1.0
1.5
ω, rad/s
1
0.5
0.5
1.0
1.5
ω, rad/s
2.0
2.5
0
0
0.5
1.0
1.5
ω, rad/s
Fig. 5 Response amplitude operators of classic-spar
2.0
2.5
Surge RAOs for truss spar
Sway RAOs for truss spar
3.5
2.0
0°
45°
3.0
45°
1.0
0
Sway, m/m
Surge,m/m
2.5
2.0
1.5
4.0
3.0
1.0
2.0
0.5
1.0
0
0
90°
0.5
1.0
1.5
ω, rad/s
2.0
0
0
2.5
0.5
Heave RAOs for truss spar
1.0
1.5
ω, rad/s
2.0
2.5
Roll RAOs for truss spar
2.0
0.8
0°，45°，90°
1.8
45°
90°
0.7
1.6
0.6
0.5
1.2
Roll, °/m
Heave, m/m
1.4
1.0
0.8
0.4
0.3
0.6
0.2
0.4
0.1
0.2
0
0
0.5
1.0
1.5
ω, rad/s
2.0
0
0
2.5
0.5
Pitch RAOs for truss spar
2.0
2.5
Yaw RAOs for truss spar
0.8
0.014
0°，45°，90°
0°
45°
0.7
0.012
0.6
0.010
0.5
Yaw, °/m
Pitch, °/m
1.0
1.5
ω, rad/s
0.4
0.008
0.006
0.3
0.004
0.2
0.002
0.1
0
0
0.5
1.0
1.5
ω, rad/s
2.0
2.5
0
0
0.5
1.0
1.5
ω, rad/s
2.0
2.5
Fig. 6 Response amplitude operators of truss-spar
For both spars, the roll and pitch were symmetrical with regard to the incident wave
angle, like the surge and sway. In addition, the magnitudes of the roll and pitch for the
truss-spar were smaller than that of the classic-spar.
The yaw motions of both spars were negligible and approximately zero at all
incident wave angles and frequencies examined. Table 3 lists the maximum RAOs in
the multi DOFs for both spars.
Table 2 Hydrostatic properties of the two spars
Items
Classic-spar
Center of Buoyancy (Centerline) [m]
Cutter water area [m²]
COG TO GOB [m]
Metacentric Heights, GMX [m]
Metacentric Heights, GMY [m]
-50
49.5
-19
19
19
Truss-spar
-41.6
49.5
-15
15.5
15.5
Table 3 Maximum values of RAOs for classic-spar and truss-spar
Items
Surge
Sway
Heave
Roll
Pitch
Yaw
Classic-spar
3.21
3.21
2.65
1.99
1.99
2.27e-03
Truss-spar
3.21
3.21
1.82
0.74
0.74
4.06e-02
CONCLUSIONS
In this study, the coupled hydrodynamic performance of both spars was calculated
and analyzed in the frequency domain. The hydrostatic stability of the two types of
spar was similar. The roll, pitch and heave motions of the truss-spar was improved,
and the surge and sway motions remained the same. Future studies will conduct time
domain analysis to evaluate the truss-spar further.
ACKNOWLEDGMENTS
This work was supported by the New & Renewable Energy of the Korea Institute of
Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea
government Ministry of Knowledge Economy (No.20113020020010).
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