Tong W. Wind Power Generation and Wind Turbine Design

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Tower Design and Analysis 545

maximum tower tip displacement observed without the damper of about 0.4 m,

reduced to approximately 0.32 m when the damper was included.

5 Wind tunnel testing

Wind tunnel testing of scaled model in order to experimentally investigate aero-

elastic and aerodynamic phenomena associated with structures has proved to be a

Figure 8 : Transfer function for the coupled tower-nacelle and rotating blades model.

Figure 9: Simulated displacement response at the top of the tower.

546 Wind Power Generation and Wind Turbine Design

valuable approach for wind engineers. Ever since the ﬁ rst major building study in a

boundary layer wind tunnel was conducted by Cermak and Davenport in the 1960s,

engineers have been able to inexpensively investigate turbulence-induced pheno-

mena. The results provide vital information necessary to ensure the serviceability

and survivability of ﬂ exible structures like a wind turbine.

Considerable experimental literature now exists regarding wind tunnel testing of

structures in general. Aerodynamic studies are primarily focused on evaluation of

drag and lift coefﬁ cients, such as those by Carril et al. [ 56 ] and Gioffrè et al. [ 57 ].

Aeroelastic scale model studies, similar to those by Ruscheweyh [ 58 ] and Kim and

You [ 59 ], examine the link between structural geometrical form and aeroelastic phe-

nomena, such as vortex shedding. Passive and active dampers are also proving to be

valuable devices in the mitigation of wind-induced structural vibration, and the wind

tunnel provides an excellent means to develop and test control strategies [ 60 , 61 ].

While there is very limited literature available on wind tunnel testing of wind tur-

bines, this kind of testing can be very useful for system identiﬁ cation [ 62 ], design,

and analysis of wind turbines and associated vibration control systems.

Figure 10 shows a model assembly of wind turbine constructed at the Depart-

ment of Civil Engineering, Trinity College Dublin, Ireland being tested in the wind

tunnel facility at National University of Ireland, Galway [ 63 ]. The model assembly

was composed of three main components: the tower, the nacelle and motor, and the

rotor system. The model was designed so that the fundamental frequencies of the

rotor blades and the tower were close to each other, ensuring signiﬁ cant dynamic

coupling between the two subcomponents. The model was immersed in a turbulent

wind ﬂ ow and the responses were recorded. The recorded bending strain at the

base of the tower and the corresponding Fourier amplitude spectrum are shown in

Figs 11 and 12 for the case of a stationary wind turbine.

Figure 10 : Wind turbine tower model installed in test section of wind tunnel.

Tower Design and Analysis 547

6 Offshore towers

Recent expansion in the wind energy sector has seen an associated growth in

energy production from offshore wind farms. Hence, turbines are becoming larger

with taller towers and are being moved further out to sea. As a result the wind

0 1 2 3 4 5 6 7 8 9 10

-150

-100

-50

100

150

Time (s)

Fluctuating Micro-Strain

Figure 11 : Strain time-history recorded at the tower base point for rotational

speed of 0 rad/s .

0 2 4 6 8 10 12 14 16 18 20

Frequency (Hz)

Fourier Amplitude

Figure 12: Fourier amplitude of strain response at tower base point for rotational

speed of 0 rad/s.

548 Wind Power Generation and Wind Turbine Design

turbine towers are subjected to ever greater wind and wave forces. Thus, it is

necessary to analyse the dynamics and minimize the response of wind turbine

towers to simultaneous actions of joint wind and wave loadings, instead of just the

wind loading as in the onshore case.

6.1 Simple model for offshore towers

A model for analysis of an offshore wind turbine tower can in general be repre-

sented by a discrete MDOF system [ 64 ]. A simple schematic model of an off-

shore tower is shown in Fig. 13 [ 65 ]. The response of such an MDOF system

under joint wind and wave loading subjected at the nodes can be calculated by

a time-history integration using a standard technique like Runge-Kutta of suit-

able order. A fatigue analysis can be performed using the rainﬂ ow counting

Figure 13 : Structural model.

Tower Design and Analysis 549

method and Miner’s rule in accordance with [ 66 ] following Colwell and

Basu [ 65 ].

6.2 Wave loading

Following the collection of data and analysis carried out under the Joint North

Sea Wave Observation Project (JONSWAP) [ 67 ], it was found that the wave spec-

trum continues to develop through non-linear, wave–wave interactions even for

very long times and distances compared to the Pierson–Moskowitz spectrum. The

wave excitation for an offshore wind turbine tower can be modelled using the

JONSWAP spectrum which takes into account the higher peak of the energy spec-

trum in a storm. Also, for the same total energy as compared with the Pierson–

Moskowitz wave energy spectra, it takes into account the occurrence of frequency

shift of the spectra maximum. The spectrum takes the form

222

exp[( ) / 2 ]

S() exp

ww sw

−

⎡⎤

⎛⎞

=−

⎢⎥

⎜⎟

⎝⎠

⎢⎥

⎣⎦

(24 )

where h is the function of water surface elevation. Equation ( 24 ) deﬁ nes a station-

ary Gaussian process of standard deviation equal to 1. In eqn ( 24 ), g is the peak

enhancement factor (3.3 for the North sea), g is the acceleration of gravity and w is

the circular wave frequency. The wave data from the JONSWAP project was used

to calculate the values of the constants in eqn ( 24 ) as follows:

0.22

0.076

⎛⎞

⎜⎟

⎝⎠

(25 )

1/3

⎡⎤

⎢⎥

⎣⎦

(26 )

and

0.07,

0.09,

≤

⎧

⎨

⎩

(27 )

where U

is the mean wind speed 10 m from the sea surface, F (fetch) is the uninter-

rupted distance over which the wind blows (measured in the direction of the wind)

without a signiﬁ cant change of direction. The fetch varies in its non-dimensional

form as follows [ 68 ]:

10 10

−

(28 )

The wave force acting on the offshore wind turbine structure can be calculated by

using the linearized Morison equation [ 69 ] and from the wave surface elevation

time-history calculated based on the wave spectrum (for details see [ 65 ]).

550 Wind Power Generation and Wind Turbine Design

6.3 Joint distribution of wind and waves

The JONSWAP spectrum deﬁ ned in the previous section is a stationary Gaussian

process and can be mapped into the process of the sea state deﬁ ned by the sig-

niﬁ cant wave height and mean zero-crossing wave period ( H

, T

) by letting the

dimensionless time be t / T

and the dimensionless process be X/(l

)

1/2

= 4X/H

[ 68 ]. The wind speed at 10 m, U

, and the signiﬁ cant wave height, H

, from the

JONSWAP spectrum can be related through the integral of eqn ( 24 ):

(

)

lww

∞

∫

(29 )

where (l

)

1/2

is the standard deviation of surface displacement. If a sea contains a

narrow range of wave frequencies, H

is related to the standard deviation of the sea

surface displacement [ 70 ]:

4H l=

( 30 )

The time-histories used for analysis in the joint distribution of wave period and height

are approximated by the linear combination of trigonometric polynomials [ 71 ].

Simulated wave surface elevation time-history for ‘moderate’ wave excitation

with target and simulated PSD have been presented for the purpose of illustration in

Figs 14 and 15 which have been taken from the investigation carried out by [ 65 ]. The

wave surface elevation time-history has been simulated with a joint dependence on

Figure 14 : Time-series for the ‘moderate’ wave excitation.

Tower Design and Analysis 551

a wind loading with mean wind speed of 18 m/s at a level of 10 m. Also, shown in

Fig. 16 is the wave force time-history at node 3 of the structural model in Fig. 13

for ‘moderate’ wave excitation [ 71 ].

6.4 Vibration control of offshore towers

As in the case with onshore wind turbine towers several structural vibration con-

trol strategies could be adopted. The use of passive control devices such as TMD,

Figure 15: PSD function of ‘moderate’ wave elevation.

0 10 20 30 40 50 60 70 80 90 100

-4

-3

-2

-1

Time (s)

Nodal Drag Force (10

Figure 16: Wave force at node 3 for ‘moderate’ wave excitation.

552 Wind Power Generation and Wind Turbine Design

TLD or tuned liquid column damper (TLCD) can be useful to suppress undesirable

structural vibrations. The use of a TLCD for the vibration control of offshore

towers has been investigated by Colwell and Basu [ 65 ]. The simple model in the

previous section was used to analyse the dynamic response of the system under

joint wind and wave loading. The assumed wind velocity at a height of 10 m was

18 m/s. The blades were 60 m in length and individually weighed 9.5 tonnes.

The blades rotated at a frequency equal to the fundamental natural frequency

of the MDOF system. The system was subjected to joint wind and wave loading

with the wind turbulence simulated from Kaimal spectra and the wave excitation

simulated from JONSWAP spectra. The details on the damper parameters are avail-

able in [ 65 ]. Figure 17 compares the total displacement response at the top of the

tower with and without the TLCD. It has been concluded that the passive damper

has a signiﬁ cant beneﬁ cial impact in suppressing the structural vibrations by about

60%. The maximum design bending moment for the theoretical simulation at the

base of the structure is reduced from 6.2607 × 10

to 4.0101 × 10

kNm.

7 Conclusions

Several aspects of dynamic analysis and design of wind turbine towers have been

discussed in this chapter. With the increase in rotor diameter and the height of the

towers, the analysis of wind turbine towers becomes crucial and needs special

attention particularly in the view of tower–rotor coupling. The important physi-

cal behaviour and phenomena to be accounted for are centrifugal stiffening of

blades, gravity effects, rotationally sampled turbulence and the tower–blade cou-

pled dynamic interaction. Numerical results have indicated that responses of the

0 5 10 15 20 25 30 35 40 45 50

-0.2

-0.1

0.1

0.2

0.3

0.4

0.5

Time (s)

Total Response (m)

MDOF with TLCD

MDOF without TLCD

Figure 17 : Time-history response of a rotating offshore turbine under wind and

‘moderate’ wave excitation with and without TLCD.

Tower Design and Analysis 553

tower may be severely underestimated if the tower–blade coupling is not taken

into consideration properly. A simpliﬁ ed gust factor approach for calculating the

response of wind turbine towers has been discussed. Two gust factors based on dis-

placement and bending moment response of the tower have been presented. They

have again highlighted the importance of tower–rotor coupling with the need for

response speciﬁ c gust factors. The importance of wind tunnel testing has been dis-

cussed and emphasized. Since vibration poses a critical challenge in wind turbine

towers, vibration control strategies with TMD and other passive dampers have

been discussed. Mathematical models have been presented for both onshore and

offshore wind turbine towers. Joint wind and wave loading have been modelled for

analyzing the offshore towers. It has been observed that vibration control damp-

ers signiﬁ cantly reduce the motions in a wind turbine tower with possible design,

maintenance and operational beneﬁ ts.

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