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First International Symposium on Flutter and its Application, 2016

EFFECTS OF MULTIDIRECTIONAL SEA STATES AND FLEXIBLEFOUNDATION ON DYNAMIC RESPONSE OF FLOATING OFFSHORE
WIND TURBINE SYSTEM
Shining Zhang+1 and Takeshi Ishihara+2+1,2Department of Civil Engineering, School of Engineering, The University of Tokyo, JapanOne reliable simulation tool was developed to be able to predict dynamic response of Floating
Offshore Wind Turbines (FOWTs) to various sea states. To represent real environmental
condition in field site, multidirectional wave simulation was carried out in this research toinvestigate effect of wave spreading on dynamic response of FOWT. On the other hand, effectof tower frequency change due to flexible foundation on fatigue load was studied. It was foundthat unidirectional assumption is conservative in terms of prediction of dynamic motion of
platform and multidirectional sea state should be employed to reach cost-effect design. In
addition, when wind turbine is supported by flexible foundation, the change of tower natural
frequency will result in significant increase of fatigue load. Therefore, Effect of flexible
foundation on tower frequency change needs to be taken into consideration in the design ofplatform and commercial wind turbine.

Keyword: Floating Offshore Wind Turbines, Simulation tool, Multidirectional sea state,
Mooring system, Morison equation
1. INTRODUCTION

Development of floating offshore wind turbines is gaining increasing interest because huge windpotential energy is available offshore and less environmental impact is expected. In the design of floating
foundation which supports commercial wind turbine, assessment of various load cases associating with sea
state are required for safe concern. In IEC-61400-31), unidirectional wave propagation is suggested if there isno measured directional information on targeted site. Basically, this unidirectional wave assumption will leadto conservative design since multidirectional wave spreading is expected to dissipate wave energy across wave
direction and result in decreased motion of floating platform in dominant wave direction. From economic
point of view, however, wave spreading is preferred to be taken into account for cost-effective design offloating platform.
Water tank experiment is thought to be one of popular and reliable ways to investigate performance of
platform under hydrodynamic load or to validate developed simulation tool2),3),4),5),6). Environmental conditionin the water tank test, however, is only limited to simple cases, like wind only, wave only (regular or irregularwave), current only and combinations of those individually environmental conditions. Whereas, much more
complex and more realistic environmental condition, such as multidirectional wave and misalignment between
wind and wave, however, is difficult to carry out in most of water tanks. In real site, wave energy is actually
not only function of wave frequency but also the function of angular wave direction. Figure 1 shows typicalwave energy distribution at location 20Km offshore from Fukushima, Japan on 17,Sept,2015. One can easily
notice that wave energy has a distribution across a specific wave frequency as well as wave direction. It is
usually thorny to replicate this kind of complicated environmental sea states in water tank test, simulation toolwith consideration of wave spreading function is one alternative way to study effect of multidirectional wave
on dynamic response of FOWT. Description of spreading functions can be found in the research byLonguet-Higgins7), Mitsuyasu H8), T. Duarte et al.9) and Kohlmeier M10).
+1zhang@bridge.t.u-tokyo.ac.jp, +2 ishihara@bridge.t.u-tokyo.ac.jp+1zhang@bridge.t.u-tokyo.ac.jp, +2ishihara@bridge.t.u-tokyo.ac.jp

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Another important attention needed to be paid during design of floating platform is elastic impact on
evaluation of natural frequency of wind turbine. Figure 2 exhibits variation of dynamic magnification factor
versus tower natural frequency11). It can be found that substantial dynamic magnification factor will be
experienced and provoke significant fatigue loads in case of the situation that wind turbine natural frequency
locates inside of upper and lower blade passing and rotational frequencies. Not like fixed foundation, floating
foundation is flexible and will inevitably change the mode shape of wind turbine, which indicates commercial
wind turbines might need to be made certain modification to employed in floating platform. Without any
modifications, wind turbine which is supported by flexible foundation might encounter significant fatigue load
and it might contribute to eventual damage within very short period.

Figure 1: Typical wave energy distribution in Fukushima, Japan on 17,Sept,2015 22:50-23:10

Figure 2: Variation of dynamic magnification factors with tower natural frequency for a two speed,
three-bladed
The outline of this paper is as follows. Mathematical model is described in section 2, encompassinghydrodynamic model, wave model and spreading function employed in this research. Section 3 mainly addresseffect of multidirectional sea states on dynamic response of FOWT. Section 4 aims to discuss impact ofchange of tower frequency on evaluation of fatigue load. Section 5 gives future work and the paper is finalizedwith conclusions in Section 6.

2. MATHEMATICAL MODEL

A finite element scheme with beam, truss and spring type elements is developed to calculate dynamic
response of full coupled wind turbine, support platform and mooring system. The time domain analysis

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First International Symposium on Flutter and its Application, 2016enables the FEM to efficiently capture nonlinear characteristics of system in sea states. Morison equation is
implemented to evaluate hydrodynamic load on platform. Nonlinear restoring load from mooring system offloating platform is estimated from either quasi-static model12).
(1) Hydrodynamic model
Modified Morison equation is utilized to predict hydrodynamic loads on floating structures. Detailed
discussion of improved Morison equation could be found in the research by Z. Shining. and T. Ishihara2).
Illustration of force acting on segment of slender cylinders and heave plate is shown in Figure 3.

Figure 3: Illustration of hydrodynamic force acting on segment of cylinder and heave platea) Normal to axial of segment
The improved Morison equation used in this paper is expressed as following relative form:
(1)
{F
H}

wu

 w (CM  1)u  w (CM  1)X  [CRdtn ] X  0.5wCd A(u  X ) u  X

Froude  Krylov force

Diffraction force

Radiation force

Viscousdrag force

Where, first term in right of Eq. (1) accounts for Froude-Krylov force due to undisturbed incident
wave and second term represents diffraction force resulting from pressure effects due to presence of structure.
The third terms indicates radiation force (hydrodynamic inertia force and radiation damping force) which is
caused by motion of structural components in an ideal fluid. Fourth term gives viscous drag force due to therelative velocity between water particle and structural components.  w is density of water; u and u are vector ofundisturbed fluid-particle velocity and acceleration respectively; { X } , { X } and { X } are vector of support
platform displacement and their time derivatives; [CRdtn ] is linear radiation damping;  is the displaced
volume of fluid by each segment when the support platform is in its undisplaced position; A is cross-sectional
area; CM and Cd are inertia and drag coefficient respectively which depends on Keulegan-Carpenter number
KC  umaxT / D , frequency parameter   D2 / T and surface roughness etc. umax is the maximum waterparticle velocity, T is incident wave period, D is diameter of cylinder and is the kinematic viscosity of water.
b) Axial of segment
In order to effectively increase the hydrodynamic damping in heave direction and reduce heave
response13),14), appendage such as a disk (heave plate) are usually added to the keel of a vertical cylinder suchas the disk chosen in WindFloat and heave plate employed in Fukushima MIRAI15). Ishihara et al.15) proposed
Morison like equation to evaluate hydrodynamic force on heave plate in axial direction. Hydrodynamic force
for a heave plate is formulated using modified Morison equation as given below(2){Fz } 0.25 Dh2 pbHp  0.25 ( Dh2  Dc2 ) ptHp   w (CMz  1)z w
Froude  Krylov force

Diffraction force  w (CMz  1) z X 3 + 0.5  wCdz AC ( w  X 3 ) w  X 3
Radiation force

Viscous drag force

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Where, CMz is the added mass coefficient in the heave direction,  z is volume of heave plate, w is
the vertical wave particle acceleration, X 3 is acceleration of the heave plate in heave direction, Cdz is thedrag coefficient in the heave direction, AC is the cross-sectional area of the heave plat, w is the verticalwave particle velocity, X 3 is velocity of the heave plate in heave direction, Dh is the diameter of the heave
plate, Dc is the diameter of the upper column (which is placed on top of the heave plate), and pbHp and ptHp
are the dynamic pressure acting on the bottom and top faces of the heave plate. Dynamic pressure at positionz in regular wave using Airy theory is expressed as follows
P gH cosh k ( z  d )cosh kd2(3)

cos(kx  t )Where, H is wave height (m),  is wave frequency(rad/s), k is wave number, d is water depth, z is
specified position.
To evaluate axial force on the other segments of elements (such as vertical columns, braces andpontoons), only Froude-Krylove force is taken into consideration by integrating dynamic pressure on member
ends as follows,(4){FF  K } 0.25 Dc2 ( pb  pt )Where, pb and pt are the dynamic pressure acting on the bottom and top faces of segment.

(2) Linear irregular wave theory
As for the dynamic response of FOWT to irregular wave in both unidirectional and multidirectionalsea state, JONSWAP wave spectra was used in both simulation tool and water tank experiment. The spectrum
is given asS ( f )  H T f
2 4
S P

 

5

exp 1.25(TP f )  4

 (T f 1)2 exp  P 2 
2





0.06240.230  0.0336  0.185 /(1.9   )

(5)
(6)

Where, f is wave frequency (Hz), H S is significant wave height, TP is peak wave period,  is peakfactor (  =2 is used in this paper) and  is shape factor (   0.07 for f  (1/ TP ) and   0.09 forf  (1/ TP ) ).
(3) Spreading function
The spreading function used in this research is frequency independent cos-2s type implemented in
WAFO16). Total wave spectrum can be defined as

S (, ) S ()  D( )(7)Where, S ( ) is the frequency spectrum, independent of the direction of the waves, and D( ) is the
directional spectrum.

D( )    p 
( s  1)
cos 2 s 
2  ( s  1 2)
 2 

(8)

Where,  is the gamma function.  is the spreading angle,  p is the energy peak direction and s is
the spreading parameter.
After spreading function D( ) is determined, equal-energy method9) is used to discretize the wave
direction. Then wave elevation can be written in following way

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


N



 An cos kn  x cos k   y sin k    nt   n
n 1

(9)



Where, An , k n , n ,  n and  k are discretized wave height, wave number, wave frequency, random phaseand wave direction.
Linear superposition can also be used to compose water particle velocity and acceleration required inMorison equation.

3. DYNAMIC RESPONSE OF FOWT IN MULTIDIRECTIONAL IRREGULAR SEA STATEIn this section, prototype of Fukushima MIRAI 2MW FOWT is established with FEM and dynamic
response of floating system is investigated in terms of multidirectional wave spreading effect. Figure 4 shows
image of prototype of Fukushima MIRAI and FEM model adoped in numerical simulation. It should be notedthat aerodynamic load is excluded in the simulation to classify the solo wave spreading effect. To represent
irregular wave, JONSWAP wave spectra with measured significant wave height 3.83m and peak period 8.3sec.
is used in this research. Figure 5 illustrates wave spreading function and resulting wave energy distribution
across wave frequency and wave direction. Spreading parameter s in Eq.(8) is 13 and dominant wave
direction is 0 degree (Y-axis faces to north and wave propagates from west to east). In Figure 5(a), spreading
function follows from Eq.(8), it can be concluded that discretized spreading wave direction could represent
well for targeted spreading function.

MWL

Y

X

(a) Prototype of Fukushima MARIA(b) FEM model

Figure 4: Image of prototype of (a) Fukushima MARIA and (b)FEM model

Spreading Function D(1.5

DISCRETETARGET

1

0.5

0

-3

-2

-1

0

1

Wave Direction (rad)2(a) Spreading function

3(b) Polar plot of wave energy distribution

Figure 5: Wave spreading function and total wave energy distribution

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JAXA Special Publication JAXA-SP-16-008E

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1.5

1.5

Uni-directional
Multi-directional

1

1

Heave (m)0-0.5

Uni-directional
Multi-directional

1

0.5

Sway (m)Surge (m)

0.5

1.5

Uni-directional
Multi-directional

0
-0.5

0.5
0
-0.5

-1

-1

-1

-1.5
300

-1.5
300

-1.5
300

350

400

450

Time (sec.)

500

550

600

(a) surge motion

500

550

600

-1
-2

350

400

450

Time (sec.)

500

550

550

600

1
0
-1
-2

-3
300

600

500

Uni-directional
Multi-directional

2

0

-2

450

Time (sec.)(c) heave motion

1

Pitch (deg)

-1

400

3

Uni-directional
Multi-directional

2

0

-3
300

350

(b) sway motion

1

Roll (deg)450Time (sec.)3

Uni-directional
Multi-directional

2400

Yaw (deg)

3350(d) roll motion

350

400

450

Time (sec.)

500

550

600

-3
300

350

(e) pitch motion

400

450

Time (sec.)

500

550

600

(f) yaw motion

Figure 6: Dynamic motion of platform in unidirectional and multidirectional irregular wave
2

2

-2

10

-4

10

-6

10

-8

10

Uni-directional
Multi-directional

-10

0

0.05

0.1

0.15

0

10

2

2

10

10

-2

10

-4

10

-6

10

-8

10

Uni-directional
Multi-directional

-10

0.2

Frequency (Hz)

0.25

10

0.3

0

(a) PSD of surge motion

0.1

0.15

0.25

-4

10

-6

10

-8

10

-10

0.1

0.15

0.2

Frequency (Hz)0.25(d) PSD of roll motion

Uni-directional
Multi-directional00.3

Uni-directional
Multi-directional

0

10

-2

10

-4

10

-6

10

-8

10
10

0.05

0.1

0.15

0.2

Frequency (Hz)

0.25

0.3

(c) PSD of heave motion

-10

0.05

-8

10

2

2

2

-2

10

0

-6

10

10

Power Spectrum-Yaw [rad s]

Uni-directional
Multi-directional

0

-4

10

10

0.3

2

10

-2

10

-10

0.2

Frequency (Hz)10Power Spectrum-Pitch [rad s]2Power Spectrum-Roll [rad s]

0.05

0

10

(b) PSD of sway motion

2

10

10

Power Spectrum-Heave [m s]

0

10

2

10

Power Spectrum-Sway [m s]2Power Spectrum-Surge [m s]10

Uni-directional
Multi-directional

0

10

-2

10

-4

10

-6

10

-8

10

-10

0

0.05

0.1

0.15

0.2

Frequency (Hz)0.25(e) PSD of pitch motion

0.3

10

0

0.05

0.1

0.15

0.2

Frequency (Hz)

0.25

0.3

(f) PSD of yaw motion

Figure 7: Power spectrum density of dynamic motion of platform in unidirectional and multidirectional
irregular wave
Figure 6 provides time history of dynamic motion of platform under unidirectional andmultidirectional wave condition within 5mins. It can be found that sway, roll and yaw motion in unidirectional
wave condition are almost zero since platform geometry is symmetric about XZ-plane. Significant motion inthese three modes, however, are excited in multidirectional sea state since wave is not propagate only in
X-axis any more. Dissipation of wave energy over certain angular direction would amplify the motion in sway,roll and pitch direction. At the same time, this wave energy dissipation will decrease surge, heave and pitch
motion as expected. Same conclusion can be derived from what shown in PSD of dynamic motion in Figure 7.
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period (0.12Hz) and the other one conforms with to natural period of floating system in each mode.
Figure 8 gives maximum of displacement in mentioned two sets of wave directional condition.
Maximum surge, heave and pitch motion decrease by 10.3%, 14.7% and 31.4% respectively when wave
spreading is taken into account. Considering the recommendation in IEC-61400-3 in terms of unidirectional
wave assumption, appropriate evaluation and consideration of wave spreading will bring about cost-effective
design.
3

3

Maximum displacement (m)

2.5

2

1.5

-10.3%-14.7%

1

Maximum displacement (deg)Uni-directional
Multi-directional

0.5

0Uni-directional
Multi-directional

2.5-31.4%

2

1.5

1

0.5

Surge

Heave

Sway

0

Roll

(a) Max translational motion

Pitch

Yaw

(b) Max rotational motion

Figure 8: Maximum of (a) translational displacement and (b) rotational motion in unidirectional andmultidirectional sea state

4. EFFECT OF FLEXIBLE FOUNDATION ON TOWER FATIGUE LOAD

In this section, one 2MW offshore wind turbine will be used to clarify the effect of natural frequencyof tower on fatigue load evaluation. One fixed foundation and flexible foundation will be investigated on
resulting fatigue load. General characteristics of rotor and turbine are listed in Table 1. Rotor speed is 18rpm
and 1P blade passing frequency is 0.3Hz. Information about time dependent wind field is summarized in Table
2. Six 10mins stochastic realizations are conducted to determine the equivalent fatigue load.
Table 1: General characteristics of rotor and turbine
Rotor diameter

80m

Number of blades3

Hub height

61.5

m

Tower height

60m

Aerodynamic control surfaces

Pitch

Fixed / Variable speed

Variable

Cut in wind speed

4m/s

Cut out wind speed

25

m/s

Rotor speed

18

rpm

Table 2: Time dependent wind field
Wind model type

Turbulent Wind

Mean wind speed for simulation

21.5

m/s

Wind direction from North

0deg

Longitudinal turbulence intensity

16.17

%

Lateral turbulence intensity

12.93

%

Vertical turbulence intensity

8.08

%

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3.0E+4Wind speed (m/s)

Tower base moment

Tower base moment (KNm)

35Wind speed (m/s)

30
25
20
15
10

2.0E+4

1.0E+4

5
0

0

100

200

300
400
Time (sec.)

500(a) time series of wind speed

600

0.0

0

100

200

300
400
Time (sec.)

500

600

(b) time series of tower base moment

Figure 9: Time series of (a) wind speed and (b) resulting tower base moment in one wind seed
Freq=0.43Hz

Freq=0.33Hz

Fixed

Fixed

(a) Fixed foundation(b) Flexible foundation

Figure 10: Mode shape of tower in fixed condition and flexible foundation
Figure 9 shows one of simulation results in term of turbulent wind and resulting tower base moment.
Rainflow cycle counting is used to deal with time history of tower base moment to determine damage
equivalent load which would produce the same fatigue damage as the original signal. The equivalent load
M eq is defined as follows,1  ni Sim  mM eq   i

Tf





(10)

Where, ni is the number of cycles in load range Si ; T is the duration of the original time history(10mins); m is inverse S-N slopes and f is frequency of equivalent sinusoidal load.
Two types of foundation are shown in Figure 10. One assumes that wind turbine is supported on rigid
foundation and natural frequency is 0.43Hz. The other one assumes foundation is flexible and natural
frequency is 0.33Hz as a result. It is noteworthy that rotor speed is 18rpm and 1P blade passing frequency is
0.3Hz. Tower natural frequency under condition of flexible foundation is close to this rotational frequency.
Consequently, larger dynamic magnification factor is expected when compared with the wind turbine with
fixed foundation.
Figure 11 depicts statistics of tower base moment and evaluated damage equivalent load. In figure (a),one can find maximum and standard deviation of tower base moment increase by 7.1% and 23.7 respectively

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in case of flexible foundation. Damage equivalent load in fixed and flexible foundation with respect to various
inverse S-N slope m is shown in Figure 11(b). One can conclude that equivalent load increase by at least
10.6% in case of flexible foundation with m=3.
4.0E+4Tower base moment (KNm)

3.5E+4+7.1 %

Fixed foundation
Flexible foundation

3.0E+4

3.0E+4

2.5E+4

2.5E+42.0E+4
1.5E+42.0E+4+1.3 %+10.6 %

+14.5 %

+16.7 %

1.5E+4+23.7 %

1.0E+4

1.0E+4
5.0E+3

5.0E+3
0.0

Fixed foundation
Flexible foundation

3.5E+4

Damage equivalent load (KNm)

4.0E+4

0.0

Mean

Max

Std.

(a) Tower base moment statistics

3

4

inverse S-N slope m5(b) Damage equivalent load

Figure 11: Statistics of tower base moment and damage equivalent load in fixed and flexible foundation

5. FUTURE WORKThe results provided in this research are all based on simulation data. Accurate evaluation in effect ofmultidirectional sea state and flexible tower frequency will be further validated by field measurement.

6. CONCLUSIONS

Effects of multidirectional sea state on dynamic motion of platform and impact of flexible foundation
on damage fatigue load are studied in this research. Main conclusions are as follows,(1). Recommendation of unidirectional sea state assumption in IEC-61400-3 will lead to conservative
design of platform. Multidirectional sea state employment can decrease the motion by 10.3%, 14.7% and31.4% in surge, heave and pitch respectively which indicate cost-effective design could be reached whenintroducing reasonable wave spreading function.
(2). Flexible foundation would impact tower natural frequency and could increase damage equivalentload consequently. It means natural frequency of commercial wind turbine should be re-determined when it is
supported on flexible platform and impact of flexible foundation on dynamic load on foundation needs to beinvestigated again. Otherwise, wind turbine will suffer significant fatigue load, which could shorten service
time.

ACKNOWLEDGMENT

This research is funded by Ministry of Economy, Trade and Industry, Japan. I wish to express mydeepest gratitude to the concerned parties for their assistances and contributions in this research.

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