Journal of Physics: Conference Series

PAPER • OPEN ACCESS

Prediction of dynamic response of semi-submersible floating offshore
wind turbines by a novel hydrodynamic coefficient model
To cite this article: Yuliang Liu and Takeshi Ishihara 2019 J. Phys.: Conf. Ser. 1356 012035

View the article online for updates and enhancements.

This content was downloaded from IP address 158.46.149.123 on 25/10/2019 at 02:18

16th Deep Sea Offshore Wind R&D conference
IOP Conf. Series: Journal of Physics: Conf. Series 1356 (2019) 012035

IOP Publishingdoi:10.1088/1742-6596/1356/1/012035

Prediction of dynamic response of semi-submersible floating
offshore wind turbines by a novel hydrodynamic coefficientmodel
Yuliang Liu1 and Takeshi Ishihara1
1

Department of Civil Engineering, School of Engineering, The University of Tokyo,
Japan,7-3-1 Hongo, Bunkyo, 113-8656 Tokyo, Japan
E-mail: ishihara@bridge.t.u-tokyo.ac.jp
Abstract. A novel hydrodynamic coefficients model is proposed for the components offloating offshore wind turbine (FOWT). First, the formulas for evaluation of the added massand drag coefficient for the components of FOWT are proposed to consider the interaction
effects between columns as well as the frequency and amplitude dependencies. The global
matrices of hydrodynamic coefficients are then evaluated by the proposed formulas andvalidated by the experimental data from the forced oscillation test. The predicted dynamic
response of FOWT is also validated by the water tank test. Finally, the improvement ofdynamic behaviour of the platform by the skirts is investigated. The decrease of amplitude andthe increase of natural period for the heave motion of the platform with skirts are successfully
simulated by the proposed model.

1. Introduction
In recent years, diversified types of floating platform have been applied in floating offshore windturbines (FOWTs) and studied through experiments and numerical simulations. In Hywind project [1],the world’s first spar type FOWT was positioned in Norway. Three FOWTs with different types ofplatform were built off the coast of Fukushima in Japan [2]. The first one is a 2MW semi-submersible
FOWT and the others are a 5MW advanced spar FOWT and a 7MW V-shape semi-submersible
FOWT. In addition, a 3 MW FOWT was installed by IDEOL in 2018 [3]. These platforms consist of
several type of components, as such, circular and rectangular cylinders as well as heave plates which
are used to improve the performance of FOWT. In order to accurately evaluate the motions of FOWTs,
the hydrodynamic coefficients of these components in various ocean conditions are necessary. The
water tank test is a general method to obtain hydrodynamic coefficients of platforms oscillating indifferent amplitudes and periods, however it needs a lot of costs due to manufacture of models andarrangement of tests. Computational fluid dynamics (CFD) is another powerful tool for prediction ofhydrodynamic coefficients, which can provide accurate distribution of pressure. However, thenumerical simulation by CFD is time consuming if fine grids are used and a large number ofsimulations are required.
It is well known that added mass and drag coefficients, which represent hydrodynamic inertia force
and viscous drag force acting on the offshore structure [4], are two critical coefficients for predictionof hydrodynamic loading. These coefficients for an isolated cylinder depend on Reynolds number (Re),
Keulegan–Carpenter number ( KC ) and surface roughness [5]. To discuss the effect of frequency ofContent from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distributionof this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
Published under licence by IOP Publishing Ltd
1

16th Deep Sea Offshore Wind R&D conference
IOP Conf. Series: Journal of Physics: Conf. Series 1356 (2019) 012035

IOP Publishingdoi:10.1088/1742-6596/1356/1/012035

oscillation on the hydrodynamic coefficients, the frequency parameter β is also used for oscillatingflows. It is defined as the ratio of Reynolds number to KC number.
For a complex floating structure, such as a semi-submersible type of FOWT, the interaction
between columns affects the hydrodynamic force on each column [6], especially when the columns arearranged closely between each other. The hydrodynamic coefficients of cylinders are commonly
decided by the experimental data. However, a cylinder in the complex floating structure may interferewith flow field around another cylinder, which leads to variation of hydrodynamic coefficients. In
OC4, added mass and drag coefficients of three upper columns in DeepCwind semi-submersible
platform were defined as the same value based on the experiment of a single circular cylinder [7].
Benitz et al. [6] conducted CFD simulations for the same platform to evaluate drag coefficients of eachcolumn in the current condition with a constant velocity. They pointed out that the effect of interaction
between the multi-columns changes the drag coefficients greatly and it should be included in
prediction of hydrodynamic loading. Liang and Tao [8] demonstrated that the drag coefficient of rearcolumn was smaller than that of frontal ones. The influence of distance between cylinders onhydrodynamic forces was studied experimentally at a constant Reynolds number using four cylinders
with equal diameters arranged in the in-line square configuration [ 9 ]. The flow pattern andhydrodynamic coefficients were found to be strongly dependent on the distance between cylinders.
Numerous investigations have been dedicated to establishing dependency of KC , β and Re on
added mass and drag coefficients. Sarpkaya [10] measured the hydrodynamic coefficients of two
dimensional cylinders in the oscillating flow and found that drag coefficients decreased while added
mass coefficients increased as β increases. Both of them approached a constant value when Reynolds
number become quite high. Zhang and Ishihara [11] studied the added mass and drag coefficients ofheave plates for an advanced spar platform through the forced oscillation test by CFD. The formulas topredict hydrodynamic coefficients of heave plate considering effect of KC number, thickness anddiameter were proposed. A series of forced oscillation tests of a large-scale heave plate used in a semisubmersible FOWT were carried out by Carlos and Iglesias [ 12 ] for investigating variation ofhydrodynamic coefficients in different amplitudes and frequencies. Both added mass and dragcoefficients of heave plate were dominated by KC . Kamizawa et al. [13] compared the designed value
with observed motion response of an advanced spar platform in Fukushima FORWARD [2]. It was
found that the predicted sway motion was overestimated since a constant drag coefficient was applied.
In this study, a novel hydrodynamic coefficients model for various components of FOWT is
described in section 2. The effect of interaction between cylinders of FOWT is evaluated based on the
numerical simulations by CFD, and Re, β and KC dependencies are investigated based on previous
studies for single cylinder. In section 3, the proposed model is validated by the global matrices ofhydrodynamic coefficients from the forced oscillation test. The effect of skirts on the dynamic
response of the semi-submersible platform is investigated by the proposed model and validated by thewater tank test. Finally, the conclusions are given in section 4.
2. Hydrodynamic coefficient models
A 1:50 scale model of 2MW FOWT is firstly described in section 2.1. The hydrodynamic coefficientsfor each component of the platform is then defined in section 2.2. The correction factor representing
the effect of interaction of columns is introduced in section 2.3. Finally, influences of β and KC on
the hydrodynamic coefficients are investigated in section 2.4.
2.1. Model description
A 1:50 scale model of 2MW FOWT used in Fukushima FORWARD [2] is used for study ofhydrodynamic coefficients. As shown in Fig. 1, the platform comprises a central column linked withbase of the tower and three side columns that are connected to the central one through three pontoonsand braces. At the base of side column, three heave plates are set to shift natural period of heave out
range of wave energy and suppress motion of the platform in wave. Three heave plates and the central
column are connected by three rectangular pontoons with variable cross sections.

216th Deep Sea Offshore Wind R&D conference
IOP Conf. Series: Journal of Physics: Conf. Series 1356 (2019) 012035

IOP Publishingdoi:10.1088/1742-6596/1356/1/012035

SC-2

SC-1

CC
SC-3
Pn-1

Hp-1

Hp-2

Hp-c

Hp-3

(a) Bird view of the platform
Sway (y) Y

Heave (z)Z
Yaw (θz)

Pitch (θy)
Ø 280

X
Surge (x)

580

Ø 136

500

1005

Roll (θx)Ø 100

X
Surge (x)80

870(b) Top view of the platform(c) Side view of the platform(Unit: mm)(Unit: mm)
Figure. 1. Configuration of 1:50 scale model of the semi-submersible platform for a 2MW FOWT
Table 1. Dimension and hydrostatic properties of the semi-submersible platform
Elements
Dimension (m)Draft of the platform
0.38
Elevation of center column (CC) and side columns (SC) above SWL
0.2
Spacing between side columns
1.005
Height of center column and side columns
0.5
Diameter of center column
0.1
Diameter of side columns
0.136
Depth to top of heave plate (Hp) below SWL
0.3
Height of heave plate and pontoon (Pn)
0.08
Diameter of heave plate
0.28
Width of pontoon
0.06~0.12
Length of pontoon
0.39
Diameter of brace (Br)0.045
Height of deck
0.045
Width of deck
0.045
Center of gravity below SWL-0.166
Meta-centric height above SWL
0.086
Radius of gyration Kxx
0.41
Radius of gyration Kyy
0.41

3

16th Deep Sea Offshore Wind R&D conference
IOP Conf. Series: Journal of Physics: Conf. Series 1356 (2019) 012035

IOP Publishingdoi:10.1088/1742-6596/1356/1/012035

Origin of the coordinate is defined at the gravity center as presented in Fig.1. The degrees of
freedom (DOFs) for the platform involve translational surge, sway and heave motions and rotationalroll, pitch and yaw motions.
A summary of Dimension and hydrostatic properties of the platform is described in Table. 1.
Displaced water of the platform is 42.2kg including contribution from mooring lines.
2.2. Definition of hydrodynamic coefficients for each component of the platform
The Morison’s equation and the boundary element method (BEM) are widely used for assessing thehydrodynamic loads on the FOWT [14], [15]. BEM provides linear wave induced force and motion
induced force. However, viscous drag force on structure resulting from flow separation cannot be
predicted by BEM because of the basic assumption of inviscid flow. Morison’s equation is anempirical formula to calculate inertial and viscous drag forces on the slender structure. The KC
dependent added mass and drag coefficients of isolated cylinder obtained from the previous study areused. The frequency-dependent radiation damping force in the time domain is calculated by Cummins
equation.
The equation of motion for a FOWT in waves [15] is written as follows:Mx + Cx + K x = FG  + FB  + FH  + FM  + FR (1)

where M , C and K are mass, damping and stiffness matrices of the platform respectively. x , x
and x represent displacement, velocity and acceleration vector of the platform at a specified
reference point. FG  , FB  , FH  , FM  and FR  denote the gravitational, buoyancy,hydrodynamic, mooring line and restoring forces, respectively. The restoring force is calculated by thematrix of hydrostatic stiffness [16] as follows:
FR = K R  x

KR

0
0
0
0
0
0

0
0
0
0
0
0

0
0
w gAw
0
0
0

(2)

0
0
0
W GM X000
0
00
W GM Y
0

0
0
0
0
0
0

(3)

where W is the weight of the platform and Aw is the area of water plane. GM X and GMY represent themeta-centric heights of the platform about x and y axes respectively.
The hydrodynamic force can be written as sum of hydrodynamic inertia force, linear radiation
damping, incident wave excitation and fluid viscous effect as shown in Eq. (4). Higher orderhydrodynamic force is not considered in this study.
FH = Fm,a + Fm,d + Fw, F − K + Fw,d + Fdrag(4)

where Fm , a and Fm , d are the hydrodynamic inertia and linear radiation damping forces, Fw , F − K and
Fw, d indicate the Froude-Krylov (F-K) and diffraction forces, Fdrag is the viscous drag force that is
proportional to square of relative velocity. Fm , a and Fdrag are classified as the motion induced forces
due to the movement of platform and Fm , d , Fw , F − K and Fw, d are treated as wave induced forces. The
hydrodynamic inertia and drag forces of a cylinder in the local coordinate are estimated by equations
as:iFmn, a

i

Can

x

i i

i

n
Fdrag

4

1
2

i

Cdn Ain (uinxin ) uin

xin

(5)

16th Deep Sea Offshore Wind R&D conference
IOP Conf. Series: Journal of Physics: Conf. Series 1356 (2019) 012035

IOP Publishingdoi:10.1088/1742-6596/1356/1/012035

where i Can and i Cdn are the added mass and drag coefficients of the cylinder in the normal direction, and i indicate the density of water and the displaced volume of water, uin - xin represents the relative
velocity of the cylinder to water particle, Ain is the project area of the cylinder in the normal direction.
Both i Can and i Cdn are dependent on β and KC .
KC expresses the relative amplitude of fluid oscillation to characteristic length and is defined as:KC =uT 2 a=L
L

(6)

where u and T are the amplitude of velocity and period of oscillation. In a sinusoidal oscillation, uT
can be presented by 2 a where a is the amplitude of motion. The characteristic length L of the semisubmersible platform is the diameter of side column for the horizontal movement and the diameter ofside heave plate for the vertical oscillation.
Re is the ratio of inertia force to viscous force and defined as: uL uL 2 aL
=
=
(7)


T
where  and  are the dynamic and kinematic viscosities of fluid. In sinusoidal oscillation, u indicatesthe amplitude of velocity of object relative to fluid, thus Re relates the amplitude and period of
oscillation at the same time. In the oscillation flow, the frequency parameter  is widely used andexpressed by the ratio of Reynolds number to KC number as:
Re =

=

Re D2  D2==
KC T 2

(8)

BEM offers the added mass coefficients with the assumption that the motion of the platform issmall and can perform well at low KC . However, the added mass coefficients Ca at high KC may
be different from those at low KC due to the nonlinearity of fluid. The drag coefficient Cd varies
greatly with  and KC and plays an important role on the motion of the platform near the resonanceperiod. In this study,  and KC are used as independent variables and Re is calculated by the
product of  and KC .
The added mass and drag coefficients of a cylinder can be determined by  , KC , the surface
roughness k s and the correction factor of interaction effect  . The effect of surface roughness on thehydrodynamic coefficients is not discussed in this study since the surface of model in the water tanktests is smooth. The hydrodynamic coefficients for each component of the platform can be expressed
as a function of  , KC and  :i

Cak (  k , KC k , k ) = r Cak (  0k , KC0k )  r  ak  i ak(9)i

Cdk (  k , KC k , k ) = r Cdk (  0k , KC0k )  r  dk  i dk(10)where subscript i indicates the component i of the platform and superscript k represents the directionof hydrodynamic coefficients, which expresses the normal direction by n or the axial direction by t.
k
k
k
k
k
k
k
k
i Ca (  , KC , ) and i Cd (  , KC , ) express the added mass and drag coefficients of thekkcomponent i at  and KC with consideration of the correction factor of interaction effect  k in the
k direction. r Cak (  0k , KC0k ) and r Cdk (  0k , KC0k ) indicate the representative Ca and Cd for thekreferenced component r at  0 and KC0k in the k direction. iak and idk are the correction factors forkinteraction effect on the component i in the k direction, r  ak and r  d are the correction factors forfrequency and amplitude effects on the referenced component r in the k direction.
The correction factors iak and idk are defined as the ratio between the hydrodynamic coefficientsof the component i and the referenced component r as shown in Eq. (11):516th Deep Sea Offshore Wind R&D conference
IOP Conf. Series: Journal of Physics: Conf. Series 1356 (2019) 012035

Cak (  k , KC k )kkkr Ca (  , KC )IOP Publishingdoi:10.1088/1742-6596/1356/1/012035

Cdk (  k , KC k )kkkr Cd (  , KC )kii a =kii d =(11)

where i Cak (  k , KC k ) and i Cdk (Re k , KC k ) are the added mass and drag coefficients of component i at
 k and KC k in the k direction. The components, such as SC-2, Hp-2 without the interaction effectare chosen as the referenced components.
In addition, the correction factors considering the frequency and amplitude effects are defined as:

Cak (  k , KC k )kkkr Ca (  0 , KC0 )Cdk (  k , KC k )kkkr Cd (  0 , KC0 )

k
r
ra =

k
r
rd =

(12)

where r  ak and r  dk are the correction factors for frequency and amplitude effects on the referenced
component r in the k direction.
2.3. Correction factor for interaction effects
During the periodical motion of the platform, the motion of the component disturbs the flow filed andsubsequently changes the hydrodynamic loading on other components, especially when thecomponents are close to each other. CFD can consider the interaction effects on the added mass anddrag coefficients of components. In this study, the predicted added mass and drag coefficients ofcomponents by CFD as shown in Pan and Ishihara [17] is used to investigate the interaction effectbetween the columns of the platform.
Table 2. Hydrodynamic coefficients of each component at  0 and KC0
Components

i

C an

i

an

i

C dn

i

dn

Side column SC-1
0.88
0.83
0.53
0.60
Side column SC-2 *
1.06
1.00
0.95
1.00
Side column SC-3
1.06
1.00
0.95
1.00
Center column CC
0.90
1.00
1.05
1.00
Side heave plate Hp-1
0.37
0.75
0.85
0.60
Side heave plate Hp-2 *
0.49
1.00
1.43
1.00
Side heave plate Hp-3
0.49
1.00
1.43
1.00
Center heave plate Hp-c
0.39
1.00
1.06
1.00
Pontoon Pn-1-x
1.76
1.00
3.10
1.00
Pontoon Pn-2-x*
1.76
1.00
3.10
1.00
Pontoon Pn-3-x
1.76
1.00
3.10
1.00
Pontoon Pn-1-z
1.82
1.00
3.22
1.00
Pontoon Pn-2-z*
1.82
1.00
3.22
1.00
Pontoon Pn-3-z
1.82
1.00
3.22
1.00
Brace Br-1
0.54
0.34
0.65
0.16
Brace Br-2 *
1.36
1.00
1.77
1.00
Brace Br-3
1.36
1.00
1.77
1.00
Total value
0.73
1.21
The component marked by * is used as the referenced component

i

Cat

0
0
0
0
1.78
1.78
1.78
2.10
0
0
0
0
0
0
0
0
0
1.11

i

 at

0
0
0
0
1.00
1.00
1.00
1.00
0
0
0
0
0
0
0
0
0

i

Cdt

0
0
0
0
3.09
3.09
3.09
3.69
0
0
0
0
0
0
0
0
0
5.55

i

dt

0
0
0
0
1.00
1.00
1.00
1.00
0
0
0
0
0
0
0
0
0

Table 2 shows the added mass and drag coefficients of each component at  0k and KC0k , which are
4.72 103 and 4.62 in the surge direction, and are 1.99 104 and 0.9 in the heave direction,
respectively. The referenced components are marked by * in Table 2, such as SC-2. Since there are noreferenced components for the center column and center heave plate, the interaction correction factors
are defined as 1 for them. In Table 2, x and z for the pontoons represent the horizontal and verticaldirections because the width of the pontoons in these two directions are different. The total values ofhydrodynamic coefficients of the platform in the surge and heave directions are also shown in Table 2.

616th Deep Sea Offshore Wind R&D conference
IOP Conf. Series: Journal of Physics: Conf. Series 1356 (2019) 012035

IOP Publishingdoi:10.1088/1742-6596/1356/1/012035

Fig. 2 displays an example of interaction correction factors of SC-1 for Ca and Cd , which show
small variation for different  and KC . For simplicity, the correction factor for interaction effect oneach component is set as a constant.
22SC-1 CFD (KC=4.62)
SC-1 CFD (KC=9.24)
Cal.
n

1.5



i d



i a

n

1.5

SC-1 CFD (KC=4.62)
SC-1 CFD (KC=9.24)
Cal.

1

0.5

0.5

0

1

0

2E+4

4E+4

6E+4

8E+4

1E+5

Re

0

2E+4

4E+4 6E+4
Re

8E+4

1E+5

(a) Interaction correction factor for the added(b) Interaction correction factor for the dragmass coefficient
coefficient
Figure 2 . Interaction correction factors for the hydrodynamic coefficients of SC-1
2.4. Correction factor for frequency and amplitude effects
The hydrodynamic coefficients of circular cylinder obtained from CFD simulation by Pan andIshihara [17] and the previous study [18]are used to predict the correction factors for frequency andamplitude effects on the circular cylinders. For simplicity, the heave plates and columns above them
are considered as one component and their correction factors are assumed to be the same. The circularcylinders in the semi-submersible model are classified into 3 types, such as SC, CC, Br, according todifferent ratio of length to diameter. In this study, the hydrodynamic coefficients of circular cylinders
are assumed as a function of Re, which includes the effects of KC and β at the same time. The
formulas for the correction factors of each component are presented in Table 3. Ca and Cd of circularcylinders for SC-2 and Br-2 are calculated by the correction factors in Table 3 and reference data in
Table 2. As shown in Fig. 3, Ca of the circular cylinder decreases as Re =   KC increases andapproaches a constant value when Re exceeds a critical value. The lower limit for Cd of the circularcylinder is defined as 0.6, which is the same as the value of two dimensional circular cylinder at highReynolds number.
For the rectangular cylinder and heave plates, the hydrodynamic coefficients are predicted as afunction of KC since they are insensitive to the frequency due to the flow separation. KC for theheave motion is small since the diameter of heave plate is large. In this range, the drag coefficient ofheave plate is sensitive to KC , but is insensitive to the frequency. The correction factor for frequency
and amplitude effects on the pontoon shown in Table 3 are evaluated based on the experimental datafrom the forced oscillation test for a square cylinder at KC of 1~14 [18]. The hydrodynamic
coefficients obtained from the vertical oscillation test of a circular heave plate is used for the heave
plates [19]. The frequency effect on Ca and Cd of heave plate shown in the experiment is relatively
small. The hydrodynamic coefficients of heave plates out the range of KC in the experiment is
extrapolated by fitting the curve as shown in Fig. 4. Cd of the heave plate decreases rapidly at low KC ,while Ca increases slowly. Tables 3 and 4 list the correction factors for each component in the normal
and axial directions, respectively. As the axial coefficients of side columns and pontoons are
negligible, correction factors of these components are set as 0.

7

16th Deep Sea Offshore Wind R&D conference
IOP Conf. Series: Journal of Physics: Conf. Series 1356 (2019) 012035
2

IOP Publishingdoi:10.1088/1742-6596/1356/1/012035

4
CFD (KC=4.62)

CFD (KC=4.62)

CFD (KC=9.24)

CFD (KC=9.24)

3

Cal.

Cd of SC-2

Ca of SC-2

1.5

1

0.5

0

Cal.

2

1

0

2.5E+45E+4

7.5E+401E+5

0

2.5E+4(a) Ca of SC-2

1E+5

3
CFD (KC=14)
CFD (KC=28)
Cal.

CFD (KC=14)
CFD (KC=28)
Cal.

2

Cd of Br-2

Ca of Br-2

7.5E+4(b) Cd of SC-2

3

1

0

5E+4

Re

Re

0

1E+4

2E+4

3E+4

4E+4

2

1

0

5E+4

0

1E+4

2E+4

Re

3E+4

4E+4

5E+4

Re

(c) Ca of Br-2(d) Cd of Br-2
Figure 3. Hydrodynamic coefficients of the circular cylinders in the normal direction.
6

3

Exp. [19]Cal.

Exp. [19]
Cal.

4




r a

t

r d

t

2

2

1

0

0
0

1

2

3

0

1

2

3

KC

KC

(a) Correction factor for Cat of Hp-1(b) Correction factor for Cdt of Hp-1

Figure 4. Correction factors of r  at and r  dt for the heave plate in the axial direction

8

16th Deep Sea Offshore Wind R&D conference
IOP Conf. Series: Journal of Physics: Conf. Series 1356 (2019) 012035

IOP Publishingdoi:10.1088/1742-6596/1356/1/012035

Table 3. Correction factors of frequency and amplitude effects in the normal direction
Component
SC-2, Hp-2
[17]

CC, Hp-C
[17]

r

r

Pn-2 [18] an = max −0.15tanh(1.2 10−5  Re− 6) + 0.85 − 10−6  Re, 0.57
0.954
Re  2  104
−4
−6
1.2
max 1.7 tanh(0.4  10  Re− 1.52) + 2.38 − 2.6  (10  Re) , 0.63nrd = r

Br-2 [17] an and r  dn

Re > 2  104

 an = max −0.18tanh(1.2  10−4  Re− 6.0) + 0.86 − 10−6  Re, 0.58

r dn = max 0.4tanh(4 10−5  Re− 0.8) + 1.2 − 4  (10−6  Re)0.9 , 0.57

r an = −0.12 tanh(10 −3  Re − 26) + 0.86r

 dn = max −0.18tanh(10−3  Re− 15) + 0.9 − 5 10−5  Re, 0.34

r an = r dn = −0.45 ( KC + 1)

KC  1.0
0.770.3
0.34 ( KC + 1) + 0.35 KC  1.0
0.33+ 1.93

Table 4. Correction factors of frequency and amplitude effects in the axial direction
Component

r

 at

r

 dt

Hp-2 [19]r at = 2.26 tanh( KC + 1.3) − 1.21r dt = 0.56(1.5 KC + 0.44) −2.0 + 0.83

Hp-c [19]r at = 2.23tanh( KC + 1.3) − 1.19r

 dt = 0.58(1.5KC + 0.44) −2.0 + 0.86

SC-2, CC
Pn-2, Br-2r

 at =0r

 dt =0

3. Validation and application
In order to validate the accuracy of proposed model, the global matrices of hydrodynamic coefficients
calculated from the distributed Ca and Cd for each component are compared with those from theforced oscillation tests in section 3.1. The dynamic responses of the platform predicted by the
proposed model are then validated by the experimental data from the water tank test in section 3.2.
Finally, the effect of skirts on the dynamic responses of the platform is investigated in section 3.3
3.1. Global matrices of hydrodynamic coefficients
The hydrodynamic coefficients of the platform are studied by the forced oscillation test as shown in
Fig. 5. The model is sinusoidally oscillated in still water by an actuator connected at the top of theplatform. The hydrodynamic coefficients of the platform are calculated by the measured forces. To
evaluate hydrodynamic coefficients for various  and KC , the experiments are carried out in several
oscillation amplitudes and periods given in Table 5.

916th Deep Sea Offshore Wind R&D conference
IOP Conf. Series: Journal of Physics: Conf. Series 1356 (2019) 012035

IOP Publishingdoi:10.1088/1742-6596/1356/1/012035

Table 5. Parameters used for the forced oscillation tests
Parameters
Mass of platform (kg)
Hydrostatic stiffness (N/m)
Oscillating amplitude (m)KC number
Oscillating period (s)Characteristic area (m2)
Displaced volume of water (m3)

Symbol
M
KR
a
KC
T
A


Horizontal
42.2
0.1, 0.2
4.62, 9.24
1.6~3.0
0.32160.0422

Vertical
42.2
570.6
0.04, 0.08
0.9,1.8
1.6~3.0
0.185
0.0422

Figure 5. Forced oscillation test for a 1:50 scale model of semi-submersible platform
The global matrices of [Ca ] and [Cd ] of the model are described in Eq. (13). Diagonal terms of [Ca ]represent the added masses in the surge, sway and heave directions and the added moment of inertia in
the roll, pitch and yaw directions. The off-diagonal terms denote the coupling between the motions in
the relevant two degrees of freedom.
 Ca11 0.0
 0.0 Ca 22

 0.0 0.0
[Ca ] = 
 0.0 Ca 42
C0.0 a 51
 0.0 0.0

0.0 0.0
0.0 Ca 24
Ca 33 0.0
0.0 Ca 44
0.0 0.0
0.0 0.0

Ca15
0.0
0.0
0.0
Ca 55
0.0

0.0 
 Cd 11 0.0 0.0 0.0 Cd 15 0.0  0.0 C0.0 
0.0 Cd 24 0.0 0.0 
d 22

0.0 
 0.0 0.0 Cd 33 0.0 0.0 0.0  [Cd ] =  (13)0.0 
 0.0 Cd 42 0.0 Cd 44 0.0 0.0 
C
0.0 
0.0 0.0 0.0 Cd 55 0.0  d 51
Ca 66  0.0 0.0 0.0 0.0 0.0 Cd 66 

The non-zero terms in the global matrices can be calculated using the added mass and dragcoefficients of each element as shown in Eqs. (14) and (15) [15].
Ca11 =1 NW
 i Can in sin 2  x + i Cat in cos 2  x ; w i =1

Ca 55 =1 NW
  i Cat it cos2  z xi2 + i Can in sin 2  z xi2 + i Can in sin 2  x ( zi - zG )2 + i Cat it cos2  x ( zi - zG )2 ; wR 2 i =1 

Ca 66 =

1 NW n n 2
 i Ca i  xi + yi2 ; wR 2 i =1

Ca 22 = Ca11;

Ca 44 = Ca55 ;Ca 51 = Ca15 ;Ca 24 = −Ca15 ;Ca 51 =Ca 33 =1 NW
 i Cat in cos 2  z + i Can in sin 2  z ; w i =1

1 NW
  i Can in sin 2  x ( zi - zG ) + i Cat it cos2  x ( zi - zG ) ; wR i =1 

(14)

Ca 42 = Ca 24 .

10

16th Deep Sea Offshore Wind R&D conference
IOP Conf. Series: Journal of Physics: Conf. Series 1356 (2019) 012035

IOP Publishingdoi:10.1088/1742-6596/1356/1/012035

Cd 11 =1 NW
  i Cdn Ain sin 3  x + i Cdt Ait cos3  x ;
Ax i =1 

Cd 55 =

1 NW  t t
3
3
33
 i Cd Ai cos3  z xi + i Cdn Ain sin 3  z xi + i Cdn Ain sin 3  x zi - zG + i Cdt Ait cos3  z zi - zG ;
Ax R 3 i =1 

Cd 15 =1 NW
  i Cdn Ain sin 3  x zi - zG ( zi - zG ) + i Cdt Ait cos3  x zi - zG ( zi - zG );Ax R 2 i =1 

Cd 66 =

3/ 2
1 NW n n  2
 i Cd Ai ( xi + yi 2 ) ;Ax R 3 i =1

Cd 22 = Cd 11;

Cd 44 = Cd 55 ;Cd 51 = Cd 15 ;Cd 24 = −Cd 15 ;Cd 33 =1 NW
  i Cdt Ait cos3  z + i Cdn Ain sin 3  z ;
Az i =1 (15)

Cd 42 = Cd 24 .

where  x and  z are the angles between the axial direction of cylinder and the global x and z axes
respectively, N w represents the number of element in water, zG expresses the z-coordinate of center ofgravity, xi , yi and zi are the local coordinates of each element.
3

3Exp. (KC=4.62)
Exp. (KC=9.24)
Cal.

Exp. (KC=4.62)
Exp. (KC=9.24)
BEM
Cal.

2

C

C

d11

a11

2

1

1

0

0

2E+4

4E+4

6E+4

8E+4

0

1E+5

0

2E+4

4E+4

Re

(a) Added mass coefficients in the surge direction

Exp. (T=3.0)
Exp. (T=1.2)
Cal.

d33

15

1

C

a33

1E+5

20

1.5

C

8E+4

(b) Drag coefficients in the surge direction

2

Exp. (T=3.0)
Exp. (T=1.2)
BEM
Cal.

0.5

0

6E+4

Re

0

1

2

10

5

0

3

KC

(c) Added mass coefficients in the heave direction

0

1

KC

2

3

(d) Drag coefficients in the heave direction

Figure 6. Global hydrodynamic coefficients of the scale model
The global hydrodynamic coefficients of the scale model are predicted by the proposed model and
BEM. In Fig.6, the predicted global coefficients of Ca and Cd matches well with the experimental
results under different Re and KC . The hydrodynamic coefficients in the surge direction change withRe, while the hydrodynamic coefficients in the heave direction show the variation with KC only. It isfound that the alteration of Ca with Re in the surge direction is small, but the variation of Cd is
obvious. The hydrodynamic coefficients in the heave direction are sensitive to KC due to the flow
11

16th Deep Sea Offshore Wind R&D conference
IOP Conf. Series: Journal of Physics: Conf. Series 1356 (2019) 012035

IOP Publishingdoi:10.1088/1742-6596/1356/1/012035

separation as shown in Zhang and Ishihara [11]. The predicted added mass coefficients of the platformin the surge direction by AQWA [20]shows small difference with those by the proposed model, while
Ca 33 in the heave direction by AQWA is underestimated at large KC .
3.2. Dynamic response of the scale model in regular waves
The dynamic response of the scale model in regular waves is investigated by a water tank test. The
rotor-nacelle-assembly (RNA) is modelled as a lumped mass and the hydrostatic characters of thescale model, such as gravity center and inertia moment, are adjusted by the distributed mass.

(a) Overview of the semi-submersible model in the water tank test(b) Arrangement of mooring lines and sensors
Figure 7. Overview and configuration of the model used in the water tank test
Fig. 7 illustrates the configuration of the water tank test for dynamic response of the scale model.
The model is positioned by 4 catenary mooring lines with a length of 10.353m anchored on the bottomof the water tank at a depth of 2.5 m. Two mooring lines on the left side are connected with Hp-1 andanother two are connected with Hp-2 and Hp-3 respectively. The wave elevations during theexperiment are recorded by two wave height meters installed in front of the wave generator andbesides the model. The wave heights recorded by the meter A are used for simulations since the meter
B is close to the wall of the tank and may be affected by the reflected wave. Three ball shaped passivereflectors are mounted on the top of side columns for recording the motion of the platform. Threecases of experiments are carried out as shown in Table 6. Case 1 and Case2 are conducted to confirm
the initial tension of mooring lines and the natural periods of the model in the surge, heave and pitch
directions. Dynamic response of the platform in regular waves with different wave heights areinvestigated in Case 3.

1216th Deep Sea Offshore Wind R&D conference
IOP Conf. Series: Journal of Physics: Conf. Series 1356 (2019) 012035

IOP Publishingdoi:10.1088/1742-6596/1356/1/012035

Table 6. Definition of the cases in the water tank test
Cases
1
2
3

Condition
Still water
Still water
Regular wave

Description
Static equilibrium test
Free decay test
H=0.02m, 0.10m; T=1.4~2.8s in model scale
H=1m, 5m; T=9.9~19.8s in full scale

12

12
Exp.
Cal.

9

Natrual periods (s)Initial Tension (N)

Exp.
Cal.

6

3

0
ML1

ML2

ML3

9

6

3

0

ML4

Surge

(a) Initial tension of mooring lines for the model

Heave

Pitch

(b) Natural periods of the model

Figure 8. The predicted and measured initial tensions of mooring lines (Case 1) and natural
periods of the model (Case 2)
The dynamic response of the motion and mooring tension in regular waves are evaluated by
Orcaflex [21]. The hydrodynamic coefficients of each component are calculated by Eqs. (9) and (10).
In each simulation, the global matrix of added mass is predicted by the proposed model instead of thatobtained from BEM. The dynamic loading on the mooring lines are estimated by Morison’s equation,
where Ca and Cd in the normal direction are 1.0 and 1.8, respectively.
The predicted initial tensions of mooring lines and natural periods of the model show good
agreement with the experimental data as illustrated in Fig. 8. The surge motions are almost linear since
the natural period of surge is much longer than the peak wave period as shown in Fig. 9 (a). The
response amplitude operator (RAO) of pitch in different wave heights show little difference when the
wave period is large than 2s. The nonlinear drag force significantly contributes the response near the
resonance range, which results in different RAOs under different wave heights as shown in Fig. 9 (b).
The tension of mooring lines is nonlinear and increases as the wave height increases. The predicted
RAOs show some discrepancies with the experimental data when the wave period is longer than 2.5s.
It may be due to the limitation of wave generator since the wave height measured by the meter B islower than that measured by the meter A when the wave period is longer than 2.5s, while thisphenomenon does not be observed when the wave period is shorter than 2.5s.

1316th Deep Sea Offshore Wind R&D conference
IOP Conf. Series: Journal of Physics: Conf. Series 1356 (2019) 012035
3

3

Exp.(H=0.02m)
Cal. (H=0.02m)
Exp.(H=0.10m)
Cal. (H=0.10m)

Exp.(H=0.02m)
Cal. (H=0.02m)
Exp.(H=0.10m)
Cal. (H=0.10m)

2

Heave (m/m)

Surge (m/m)

IOP Publishingdoi:10.1088/1742-6596/1356/1/012035

2

1

1

0

0
1

1.5

2

2.5

3

7.07

10.61

14.14

17.68

21.21

1

1.5

7.07

10.61

2.5

3

14.14

17.68

21.21

Period (s)Period (s)(a) Surge RAO(b) Heave RAO
20

4

Tension of ML1 (N/m)

Exp.(H=0.02m)
Cal. (H=0.02m)
Exp.(H=0.10m)
Cal. (H=0.10m)

3
Pitch (rad/m)

2

Full scale

Full scale

2

1

0
1

1.5

2

2.5

15

10

5

0

3

Full scale
7.07

Exp.(H=0.02m)
Cal. (H=0.02m)
Exp.(H=0.10m)
Cal. (H=0.10m)

1

1.5

7.07

10.61

2

2.5

3

14.14

17.68

21.21

Full scale
10.61

14.14

17.68

21.21

Period (s)Period (s)(d) Tension RAO of ML1(c) Pitch RAO

Figure 9. The predicted and measured RAO of dynamic motion and tension in regular waves

3.3. Effect of skirts on dynamic response of the platform
A FOWT may experience resonant response when the natural period of motion is close to the peakwave period. The resonance increases the loading on the structure and affects the power production ofwind turbine. The skirts installed on the bottom of the platform are generally applied to reduce theamplitude of motion.

Figure 10. Overview of a semi-submersible platform with skirts
1416th Deep Sea Offshore Wind R&D conference
IOP Conf. Series: Journal of Physics: Conf. Series 1356 (2019) 012035

IOP Publishingdoi:10.1088/1742-6596/1356/1/012035

Table 7. Description of configuration for 1:50 and 1:60 scale models in full scale
1:50 scale model
5275
19
5
6.8
-8.3
20.5
20.5
125

3

Displaced volume of water (m )Draft (m)Diameter of center column (m)Diameter of side columns (m)Center of gravity below SWL (m)Radius of gyration Kxx (m)Radius of gyration Kyy (m)Water depth (m)1:60 scale model
4672
16
4.95
7.5
-4.1
22.2
22.4
120

The viscous damping and added mass effects of the skirts are investigated based on a 1:60 scalesemi-submersible model, in which the skirts are installed on the bottom of pontoons and heave plates
as shown in Fig. 10. Table 7 describes the configuration of 1:50 and 1:60 scale models in detail.
The added mass of plate is dependent on the shape, such as circular or rectangular, while the dragcoefficient significantly varies with the thickness of plates. A formula to predict Ca and Cd of plateswith consideration of shape, thickness ratio and KC number effect are proposed by Zhang andIshihara [11]. These formulas are modified and used to calculate the hydrodynamic coefficients of theskirts in the heave direction. The modification is conducted with consideration of the shape of skirt andits connection with pontoon and heave plates. The modified formulas are shown as:

1
Ca = k 3 − [3rd2 k 2 − rd2 + (k − k 2 − rd2 ) 2 (2k + k 2 − rd2 )]4(16)

k = k1  k 2(17)

k1 = 0.88 + 0.15KC

(18)

1.00

k2 = 0.95
0.75


Circular plate(19)

Octgnonal plate
Square plate

Cd = min 0.9rt −1/3.7 ( KC ) −2.0/ k3 , 20
2.5
k3 = 2.5
3.0


(20)

Circular plate
Octgnonal plate(21)

Square plate

where k1 represents the correction factor considering KC dependency for Ca . k 2 and k3 account for
the effect of geometry shape on Ca and Cd and the values corresponding to square plate are used forskirt. rd is the ratio of diameter of attached column to that of the plate and it is defined as 0 since theskirts are very thin. rt implies the ratio of thickness of skirt to its diameter or width. Since the flow
fields near the edge of pontoons are changed due to the skirts, the interaction factors a = 1.3 andd = 1.0 for pontoon and heave plates in the normal direction is considered based on a numericalsimulation by CFD.
The dynamic responses of motion and mooring tension of a 1:60 scale model without and withskirts are shown to in Fig. 11. The experimental data in Fig. 11 is obtained from the water tank test
using a 1:60 scale model with skirts in the regular wave with the wave height of 0.05m. The
15

16th Deep Sea Offshore Wind R&D conference
IOP Conf. Series: Journal of Physics: Conf. Series 1356 (2019) 012035

IOP Publishingdoi:10.1088/1742-6596/1356/1/012035

contribution of skirts on the surge motion is very limited because the hydrodynamic coefficients of theplatform in the horizontal direction is unchanged. The heave and pitch motions of the model withskirts are smaller than those without skirts as shown in Fig. 11(b) and (c) since the skirts significantly
increase viscous damping in the vertical direction. In addition, the natural period of heave for themodel with skirts shifts to the long period since the added mass obviously increases with the skirts in
the heave direction. The RAOs of the mooring tension of the model without and with skirt are close
because the tension is mainly determined by the surge motion, which does not change. In the wave
period from 2.2s to 2.7s, the RAO of the mooring tension for the platform with skirts is lower than thatwithout skirts because of the lower heave motion of the model with skirts as shown in Fig. 11(d). This
indicates that the installation of skirts is an effective method to avoid resonance of heave motion withwaves and supress the vertical motion of platform.
3

3
Cal.(w/o skirt)

Cal.(w/o skirt)

Exp.(with skirt)

Exp.(with skirt)
Cal.(with skirt)

Heave (m/m)

Surge (m/m)

Cal.(with skirt)

2

1

0

1

1.5

2

2.5

2

1

0

3

Full scale

1

1.5

2

2.5

3

7.75

11.62

15.49
Period (s)

19.36

23.24

Full scale

7.75

11.62

15.49
Period (s)

19.36

23.24

(a) Surge RAO(b) Heave RAO

6

20
Cal.(w/o skirt)

Cal.(w/o skirt)

Tension of ML4 (N/m)

Exp.(with skirt)

Pitch (rad/m)Cal.(with skirt)

4

2

0

1

1.5

2

2.5

Cal.(with skirt)

10

5

0

3

Full scale

7.75

Exp.(with skirt)

15

1

1.5

2

2.5

3

7.75

11.62

15.49
Period (s)

19.36

23.24

Full scale

11.62

15.49
Period (s)

19.36

23.24

(c) Pitch RAO(d) Tension RAO of ML4

Figure 11. Predicted and measured RAO for the motion and mooring tension of a 1:60 scale model inregular waves
4. Conclusions
A novel hydrodynamic coefficient model for various components of FOWT is proposed. The predicted
dynamic responses of the platform in regular waves are validated by the water tank tests. The
conclusions are obtained as follows:
1. A novel hydrodynamic coefficient model for various components based on the water tank tests
and numerical simulations is proposed to consider effects of interaction, frequency andamplitude on the hydrodynamic coefficients for various components of FOWT.
2. The predicted global matrices of hydrodynamic coefficients and dynamic response of FOWTs
by the proposed model show good agreement with those obtained from the water tank tests.
1616th Deep Sea Offshore Wind R&D conference
IOP Conf. Series: Journal of Physics: Conf. Series 1356 (2019) 012035

IOP Publishingdoi:10.1088/1742-6596/1356/1/012035

3. The effect of skirts located on the bottom of platform is successfully simulated by the proposedhydrodynamic coefficient model. The increase of natural period and decrease of amplitude forthe heave motion of FOWT can be explained by the increase of added mass and viscousdamping in the vertical direction.
Acknowledgments
This research is carried out as a part of the Fukushima floating offshore wind farm demonstration
project funded by the Ministry of Economy, Trade and Industry. The authors wish to express their
deepest gratitude to the concerned parties for their assistance during this study.
Reference
[1]
[2]
[3]
[4]
[5]
[6]

[7]

[8]
[9]
[10]
[11]

[12]

[13]
[14]

[15]

[16]

[17]

Hywind Demo: http://innovate.statoil.com/challenges/hywind/Pages/default.aspx
Fukushima FORWARD: http://www.fukushima-forward.jp/english/index.html
IDEOL’s second demonstrator: https://www.ideol-offshore.com/en/japanese-demonstrator
Faltinsen O. Sea loads on ships and offshore structures. Cambridge university press. 1993.
DNV-RP-C205: Environmental conditions and environmental loads. DNVGL, Oslo, Norway,
2014.
Benitz M A, Schmidt D P, Lackner M A, Stewart G M, Jonkman J, Robertson A. Validation ofhydrodynamic load models using CFD for the OC4-DeepCwind semisubmersible. In
International Conference on Ocean, Offshore and Arctic Engineering 2015, American
Society of Mechanical Engineers. 2015.
Robertson A, Jonkman J, Masciola M, Song H, Goupee A, Coulling A, Luan C. Definition of
the semisubmersible floating system for phase II of OC4. National Renewable Energy
Laboratory, 2014.
Liang Y, Tao L. Interaction of vortex shedding processes on flow over a deep-draft semisubmersible. Ocean Engineering. 2017; 141:427-449.
Wang X K, Tan S K. Flow around four circular cylinders in square configuration. In 18th
Australasian Fluid Mechanics Conference Launceston, Australia. 2012.
Sarpkaya T. In-line and transverse forces, On cylinders in oscillatory flow at high Reynolds
numbers. In Offshore Technology Conference. 1976.
Zhang S, Ishihara T. Numerical study of hydrodynamic coefficients of multiple heave plates bylarge eddy simulations with volume of fluid method. Ocean Engineering. 2018; 163:583598.
Lopez-Pavon C, Souto-Iglesias A. Hydrodynamic coefficients and pressure loads on heave
plates for semi-submersible floating offshore wind turbines: A comparative analysis usinglarge scale models. Renewable Energy. 2015; 81:864-881.
Kamizawa K, Yoshimoto H, Awashima Y. The validation of the wave frequency motion of
floating substation, GRE2018, Yokohama, Japan, 2018.
Robertson A, Jonkman J, Vorpahl F, Popko W, Qvist J, Frøyd L, Chen X, Azcona J, Uzunoglu
E, Soares CG, Luan C. Offshore code comparison collaboration continuation within IEA
wind task 30: phase II results regarding a floating semisubmersible wind system.
International Conference on Ocean, Offshore and Arctic Engineering 2014 American
Society of Mechanical Engineers. 2014.
Ishihara T, Zhang S. Prediction of dynamic response of semi-submersible floating offshore windturbine using augmented Morison's equation with frequency dependent hydrodynamic
coefficients. Renewable Energy. 2019; 131:1186-1207.
Waris M B, Ishihara T. Dynamic response analysis of floating offshore wind turbine withdifferent types of heave plates and mooring systems by using a fully nonlinear model.
Coupled systems mechanics. 2012; 1(3):247-268.
Pan J, Ishihara T. Numerical prediction of hydrodynamic coefficients for a semi-submersible
platform by using large eddy simulation with volume of fluid method and Richardson
extrapolation method. EERA DeepWind'2019, 2019.
17

16th Deep Sea Offshore Wind R&D conference
IOP Conf. Series: Journal of Physics: Conf. Series 1356 (2019) 012035

IOP Publishingdoi:10.1088/1742-6596/1356/1/012035[18] Tanaka N, Ikeda Y, Himeno Y, Fukutomi Y. Experimental study on hydrodynamic viscous
force acting on oscillating bluff body. Journal of the Society of Naval Architects of Japan.
1991;169:85-92. (In Japanese)[19] Tao L, Dray D. Hydrodynamic performance of solid and porous heave plates. Ocean
Engineering. 2008; 35(10):1006-1014.
[20] AQWA: https://www.ansys.com/products/structures/ansys-aqwa[21] OrcaFlex: https://www.orcina.com/SoftwareProducts/OrcaFlex/

18