Along-wind buffeting responses of wind turbines subjected to hurricanes considering unsteady aerodynamics of the tower

Engineering Structures 138 (2017) 337–350

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Along-wind buffeting responses of wind turbines subjected to hurricanes considering unsteady aerodynamics of the tower Gholamreza Amirinia, Sungmoon Jung ⇑ Department of Civil and Environmental Engineering, Florida A&M University – Florida State University College of Engineering, Tallahassee, FL 32310, USA

a r t i c l e

i n f o

Article history: Received 5 May 2016 Revised 10 January 2017 Accepted 8 February 2017

Keywords: Wind turbine Hurricane Buffeting Unsteady Along-wind response

a b s t r a c t Most of the studies on wind turbine subjected to high winds, consider quasi-steady formulation for wind turbine parts. The objective of this paper is to investigate the along wind responses of a parked wind turbine subjected to hurricane forces by considering, first, the tower unsteady aerodynamics, and second, the recent observations and proposed models for hurricanes. For this purpose, quasi-steady formulation of aerodynamic forces on a parked wind turbine was modified by addressing unsteady aerodynamic effects on the wind turbine tower. A time domain approach for addressing the unsteady aerodynamics of the tower was proposed by using aerodynamic admittance function. The frequency dependent aerodynamic admittance function was addressed in time domain using rational functions (RF). This procedure was implemented in NREL-FAST package and the model was verified. In order to investigate the structural responses subjected to hurricane, the recent observations of the hurricane boundary layer winds as well as the models presented for hurricane turbulence energy were discussed. The unsteady analysis of wind turbine structure subjected to various hurricane turbulence models, resulted in the range of 29% smaller to 4.9% larger responses than quasi-steady analysis of conventional spectrum models presented in past literature and carried out by NREL-FAST module. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction Many studies have been conducted on regular boundary layer winds (non-hurricane winds) and their effects on the structures which their results are used in the standards and codes [1–6]; however, hurricane winds and their effects on the structures still need more studies and observations. Thus in the last decade, much research has been conducted in order to clarify the nature and characteristics of hurricanes, their differences with regular high winds, and their effects on the structures [7–13]. Analysis of hurricane surface winds [8,12,14–16] revealed that turbulence spectrum of hurricane winds differs from that of nonhurricane surface winds [2,17]. Some recent observations and models [8,12,16] showed that hurricane spectrum has higher level of energy in low frequencies; however, Li et al. [15] and Caracoglia and Jones [14] showed that in the hurricane, the higher frequencies have higher level of turbulence energy. This differences in turbulence spectrum of hurricane boundary layer winds and their effects on the special structures such as wind turbines needs to be investigated precisely [18]. The main purpose for analyzing various

⇑ Corresponding author. E-mail address: [email protected] (S. Jung). http://dx.doi.org/10.1016/j.engstruct.2017.02.023 0141-0296/Ó 2017 Elsevier Ltd. All rights reserved.

spectrum models is to propose a more conservative approach for wind turbines design subjected to hurricanes. Analytical approaches of structural analysis usually use the frequency domain formulation for efficient computation and convenience in modelling of frequency dependent unsteady aerodynamic forces [4,19,20]; however, the frequency domain approach is limited to linear structural behavior subjected to stationary wind loads without aerodynamic nonlinearities [21]. In order to address aerodynamic and structural nonlinearities as well as specific cases such as control problems, time domain analysis is more appropriate. Also in specific structures such as wind turbines, coupled analysis of the parts such as tower, hub and blades, should be carried out in the time domain framework. On the other hand, most of the studies and available models neglect unsteady aerodynamic forces on a parked wind turbine during high winds [22,23]. Since the blade pitch angle in a parked wind turbine is usually about 90° [22,24], the drag coefficient on blade airfoils are very small therefore the along-wind aerodynamic forces on the blades are smaller than those on the tower. Hence, the tower in parked condition plays an important role in along-wind responses of the wind turbine. By knowing the role of the wind turbine tower in high-winds, a detailed and accurate analysis of tower is necessary for structural analysis of a parked wind turbine.

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where f ¼ nz=UðzÞ represents the normalized frequency, n is the frequency, Suu is the spectral density of the longitudinal velocity fluctuation at height z, and r is the standard deviation of longitudinal velocity fluctuation. On the other hand, hurricane field data observations during the last decade revealed that turbulence spectrum of the hurricane boundary layer winds is different from those of non-hurricane boundary layer high-winds. According to the data observed by Schroeder and Smith [12], Yu et al. [16], Jung and Masters [8], Caracoglia and Jones [14], and Li et al. [15] (hurricane Bonnie (1998), Lili (2002), Ivan (2004), Gordon (2000), Isidore (2002), and Ike (2008)) the spectral distribution of hurricane winds shows a large variability. Schroeder and Smith [12], Yu et al. [16], and Jung and Masters [8] showed that compared to non-hurricane spectral models, hurricane spectrums had higher energy content in low frequencies. Eq. (2) shows a formula derived for hurricane wind turbulence spectrum [16] with high amount of energy in low frequencies:

There are number of studies investigated the wind buffeting and self-excited forces on narrow structures such as traffic signal columns. Most of these studies [21,25,26] used time domain approach to address structural and aerodynamic nonlinearities as well as non-stationary wind fields; however, time domain requires much higher efforts than frequency domain. In time domain approach, there are two well-known methods to address the frequency dependent aerodynamic admittance functions: rational functions [21,25,27] and indicial functions [28–30]. In this paper similar to previous studies [21,25,27–31] the buffeting forces was addressed in time domain. The unsteady aerodynamic forces on the tower was considered using frequency dependent aerodynamic admittance function [32]. For addressing the frequency dependent admittance function in time domain, Caracoglia and Jones [28], Costa [29], and Chang et al. [31] used indicial functions; however, in this paper the frequency dependent aerodynamic admittance function was addressed by rational functions (RF) [21,25,29] and the aerodynamic coefficients from rational functions and indicial functions were compared. This method has been used previously for bridge aerodynamics [21,25,29]. Previous studies [3,4,6,8,10] considered along-wind and acrosswind forces and responses; however, in this paper, since one of the spectrum models (Model B) only presents formula for along-wind turbulence component, the analysis was carried out only for alongwind forces and responses and the across wind effects were not focused; however, since the across-wind forces affect the out of plane moments, the across-wind turbulence components, loads, and responses were analyzed in NREL-FAST [22] based on acrosswind turbulence components of Kaimal et al. [17] spectrum. In this case, further studies and field measurements are required for addressing across-wind spectra of spectrum Model B. In this paper, first, the characteristics of hurricane boundary layer winds and new findings on hurricane turbulence energy was discussed. Then in Section 3, the influence of wind turbine parts on the aerodynamic responses was investigated. Next, according to mentioned influences of different parts on the aerodynamic responses, a time domain approach was implemented to calculate the unsteady aerodynamic forces on the tower. At this step, aerodynamic admittance function was presented in terms of rational functions (RF). Finally, the NREL-FAST [22] code was modified and used for analysis of along-wind buffeting responses of the NREL 5MW [33] wind turbine subjected to hurricane boundary layer winds considering unsteady aerodynamic forces on the tower.

nSuu

r

2 u

2

¼

1 p1 f þ p2 f þ p3  b f 3 þ q1 f 2 þ q2 f þ q3

ð2Þ

pffiffiffi where b ¼ r=u is the turbulence ratio and u represents the friction velocity, and pi and qi are constants proposed by Yu et al. [16] as shown in Table 1. On the other hand, Li et al. [15] and Caracoglia and Jones [14] based on series of observations, presented an opposite results that higher frequencies contained larger amount of energy rather than low frequencies. Li et al. [15] provided four various spectrum models for Front Outer Vortex region (FOV), Front-Eye Wall region (FEW), Back Eye-Wall region (BEW), and Back Outer Vortex region (BOV). Four models are presented and compared in the Fig. 1. In this research since there was no preference in wind turbine location during the hurricane, it was intended to choose one of the models which represents an average model among all the models. In this way, the BEW model was chosen since it represents almost an average spectrum among four models. Eq. (3) is the spectrum model proposed for back-eye-wall (BEW) region of hurricanes [15]. Table 2 summarizes the spectrum models used in this paper according to previous observations and Fig. 2 shows the difference between these models and the spectrum introduced by Kaimal et al. [17].

2. Characteristics of hurricane boundary layer winds The wind turbulence spectrum represents the energy distribution in turbulent wind [15]. Much research investigated wind turbulence spectrums for non-hurricane winds [3,17,34,35]. Kaimal et al. [17], based on series of experiments, showed that all turbulence spectrums reduce to a limited family of curves which fit a single universal curve in inertial subrange but spread out in low frequencies. They proposed a formula for wind spectrum as shown in Eq. (1):

nSuu

r2u

¼

21:6f

ð1Þ

5=3

ð1 þ 33f Þ

Fig. 1. Comparison between Li et al. (2012) various hurricane models.

Table 1 Coefficients of Yu et al. (2008) spectrum. Spectra

p1

p2

p3

q1

q2

q3

10 m, Over land 10 m, Over sea

0.9999 0.00598

3.112 0.1544

1.159e-4 1.055e-5

18.64 0.4458

1.188 0.06486

3.35e-3 9.754e-5

G. Amirinia, S. Jung / Engineering Structures 138 (2017) 337–350 Table 2 Spectrum models summary.

3. Influence of tower and blades in structural responses in high winds

Model name

Proposed by

Similar observations

Model A

Yu et al. (2008)

Model B

Li et al. (2012)

Schroeder and Smith [12], Yu et al. [16], Jung and Masters [8] Caracoglia and Jones [14], Li et al. [15]

Fig. 2. Comparison of hurricane spectrum models (over sea) and Kaimal spectrum.

nSu ðnÞ

r2u

¼

16:66f 1:72 þ 237:24f

339

5=3

ð3Þ

While the large variation in hurricane spectra is not yet fully understood, some relevant discussion can be found in the meteorological and engineering literature. Since the low frequency range of spectrum depends on the atmospheric stability [16,17,34], for increased instability, the spectral peak shifts to the lower frequencies. On the other hand, as well-known knowledge, energy dissipation occurs in the high frequency range [36–38]. The anemometers used for observations can also affect the measurements, but their effects can be corrected so that different measurements are comparable [8,12,16].

During high-wind conditions, wind turbine blades will be parked where the blade pitch angles are set to 90°. The blades were put on feathered condition and High Speed Shaft (HSS) brakes were applied. The definition of blade directions is presented in Fig. 3. In this case, since the drag coefficient of blades are much smaller than drag coefficient of the tower, tower will play an important role in along-wind responses. To investigate the contribution of blades and tower under this condition, the NREL onshore 5MW baseline wind turbine [33] was selected for analysis. For the analysis of the parked wind turbine, the following modes were considered: first and second foreaft (FA) of the tower, first side to side (SS) of the tower, first and second flapwise (flap) of the blade, and first edgewise (edge) of the blade. In addition, since the analysis purpose was along-wind responses of the wind turbine, the yaw degree of freedom was fixed. In order to consider randomness of the wind field, 40 stationary wind field time series (each one 600 s) were generated by NREL-TurbSim [39] with frequency of 10 Hz based on Kaimal spectrum ([17]). The analysis of hurricane Ike by Jung and Masters [8] showed that the non-stationarity of the hurricane wind field was caused by change in wind direction. Hence, for the current study, it was assumed that change in wind direction was not occurred during the analysis and therefore the stationary wind field was a correct assumption. The mean wind speeds at 10 m height were equal to 30, 40, 50, and 60 m/s (each speed 10 time series). ASCE 7–10 vertical profile for exposure D was used for height extrapolation as Eq. (4):

UðzÞ ¼ b

 z a U 10 10

ð4Þ

where U 10 is the mean hourly wind speed at 10 m height, z is the height and a and b are constants depending on the terrain. For flat

terrain or sea surface a and b are 0.11 and 0.8 respectively. Turbulence intensity was equal to 13% at 10 m height which corresponds with observed data by Li et al. [15]. Fluctuation parts of wind speed are correlated. Different formulas are presented for wind fluctuation correlation [3,40–42]. Gener-

Fig. 3. Definition of airfoil orientation in (a) general condition, and (b) parked condition.

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ally, spatial coherence between two points i and j in the wind field can be defined as [39,41]:

jSij ðnÞj Cohij ðnÞ ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Sii ðnÞSjj ðnÞ

ð5Þ

where n is the frequency, Sii and Sjj are the power spectra of wind fluctuation and Sij is cross-spectra of wind fluctuations. Coherence function by considering famous models by Davenport [3] and Solari [41] can be expressed as:

0



r Cohij ðnÞ ¼ exp@a zm

c

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1  2 nr þ ðbrÞ2 A Um

ð6Þ

where a and b are spatial coherence decrement and offset parameter, respectively, r is the distance between point i and j, n is frequency, c is coefficient for spatial coherence function and zm and Um are the mean height and wind speed of points i and j, respectively. In this study, Eq. (6) was used to describe the spatial coherence of wind speed fluctuation. In this regard, the authors assumed c ¼ b ¼ 0 and a ¼ 7:7 which represents Davenport [3] general formula. The time series were implemented for structural analysis of the wind turbine and the analysis was carried out in 0.01 s time steps. After the simulations, in order to prevent capturing the model start up inaccuracy, the first 30 s of the simulations were omitted [22]. The analysis was carried out for three cases: case 1 where aerodynamic forces were applied on the both tower and blades, case 2 where aerodynamic forces were applied only on the blades, and case 3 where the aerodynamic forces were applied only on the tower. Fig. 4 presents the schematic view of three different cases.

Case 1

In order to analyze the contribution of tower and blades in the parked condition, the tower base moment was calculated. The analysis carried out on total tower base moment showed that tower and blades are affecting the wind turbine structure in a coupled fashion; however, in some frequency ranges, the influence of one part was higher than the other. The mean of maximum base moments in each case were calculated in various wind speeds to investigate the influence of wind turbine parts (Fig. 5). The mean of maximum base moments in case 1 where both blade and tower are contributing in wind turbine responses was the greatest among all the cases; however, maximum base moment in case 3, where there was no aerodynamic force on the blades was higher than case 2. By this analysis it was observed that, blades and tower have coupled effects on the along-wind responses of a parked wind turbine, but since blades pitch angle is about 90° and hence the drag coefficient was small, tower played more important role. Hence an accurate analysis of tower aerodynamics of a parked wind turbine during high winds is necessary. Fig. 6 shows the spectral analysis of the base moment for three cases in 60 m/s wind speed. In the low frequencies, since the spectrum of the total base moment for case 1 was close to that of case 3, the total tower base moment was depending more on the base moment caused by aerodynamic forces on the tower. In addition the first spectral peak (1st tower fore-aft) of case 3, was almost 2.3 and 4.3 times larger than those of case 1 and case 2 respectively which corresponded with higher effect of tower in this frequency range. On the other hand, in the mid-range frequencies, the difference between base moment in case 1 and case 2 was very small which corresponds to getting lower influence from tower aerodynamics. Hence, at this frequency range blades aerodynamics were playing more important role.

Case 2

Fig. 4. Definition of three different cases of aerodynamic loading.

Case 3

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G. Amirinia, S. Jung / Engineering Structures 138 (2017) 337–350

static forces can be expressed as Eq. (9) where q is the air density, U is the mean wind speed, D represents the tower diameter, and cD , cL and cT a are drag, lift and moment coefficients [43].

2

3
D C
f ¼ qU D 6
L 7 4 C 5 2
BC T 2

ð9Þ

a

The second term in right hand side of Eq. (7), denotes wind buffeting force. The along-wind component of buffeting forces can be expressed as Eq. (10):

Bf ðzÞv ðz;tÞ ¼

Fig. 5. Mean of maximum tower base moment of various cases (10 min – 10 m height).

qU 2 D


D uðtÞ þ ðC 0  C
L Þv wðtÞ ½2vDu C D Dw

2

ð10Þ

where vDu and vDw are the frequency dependent aerodynamic admittance functions in longitudinal and lateral directions respec
D =da, C 0 ¼ dC
L =da and C 0 ¼ dC
T =da in which a is tively, C 0D ¼ dC a L Ta the angle of attack. In the time domain, the along wind buffeting forces (for the unit length of the structure) due to the wind fluctuations u and w can be expressed as the convolution integrals (Eq. (11)) as:

Bf ðzÞv ðz;tÞ ¼

qU

Z

2

t

1

fIDu ðt  sÞuðsÞ þ IDw ðt  sÞwðsÞgds



ð11Þ

where IDu and IDw are the aerodynamic impulse functions in along wind and across wind directions respectively. The aerodynamic admittance function can be addressed in the time domain, by comparing Fourier transform of Eq. (10) and the Fourier transform of Eq. (11) [21,27] as Eq. (12):


Dv F ðIDu Þ ¼ 2DC Du


L Þv F ðIDw Þ ¼ DðC0D  C Dw

ð12Þ

in which F represents the Fourier transform. These functions can be estimated by rational functions (RF) [21,27]. Following the method given in Chen et al. [21], one can obtain the time-domain unsteady formulation for along wind buffeting forces for unit length of tower as Eqs. (13)(15): Fig. 6. Total tower base moment for different cases (60 m/s – 10 min – 10 m height).

4. Unsteady wind load on wind turbine structure The effect of unsteady forces on the operating wind turbine has been investigated before [23]; however, generally, the unsteady forces for parked wind turbine in high-winds is neglected and only the quasi-steady method was used [22]. After knowing the influence of the tower in along-wind responses of parked wind turbine, the unsteady effect of aerodynamic forces can be investigated for more accurate analysis. In this section, we proposed new formulations for the tower in order to properly model the unsteady aerodynamic forces on the tower. Fig. 7 shows a schematic view of aerodynamic forces on a wind turbine structure. Formulation of wind loading on the wind turbine tower is given in Eqs. (7) and (8) [43] where it is assumed that the main flow direction is perpendicular to the rotor plane and wind field is homogenous [43].

2

3 2 3
f D ðzÞ f D ðz; tÞ 6
7 6 7 Fwind ðz;tÞ ¼ 4 f L ðzÞ 5 þ 4 f L ðz; tÞ 5 ¼
f þ Bf v þ Cae r_ þ Kae r T a ðz; tÞ T
a ðzÞ

ð7Þ

v ðz; tÞ ¼ ½u=U w=UT

ð8Þ

T In above formulas,
f ¼ ½
f D ðzÞ;
f L ðzÞ; T
a ðzÞ are quasi-static forces, _ Bf v are buffeting forces, Cae r and Kae r are self-excited forces, u and w are longitudinal and lateral fluctuating parts of the wind, and r and r_ are structural position and velocity vectors. The quasi-

F Dj ðtÞ ¼

1 qU 2 2

(

m X aDj;n bDj;n i x þ bDj;n n¼1

aDj;0 

m X aDj;n

!

vj þ

n¼1

!

vj ¼

m X aDj;n bDj;n ix þ bDj;n n¼1

! )

vj

m X bDj;n uDj;n ðtÞ

ð13Þ

ð14Þ

n¼1

u_ Dj;n ðtÞ ¼ bDj;n uDj;n ðtÞ þ

m X aDj;n

!

vj

ð15Þ

n¼1

where F Dj is a function of time, and v j is scalar representation of wind fluctuation introduced in Eq. (8) that represents the longitudinal component if j ¼ u and the lateral component if j ¼ w. Also, aDj;n and bDj;n represent rational function (RF) coefficients. The second parenthesis in the right hand side of the Eq. (13) is frequency dependent parameter where this term can be approximated by using Eq. (14). The time dependent functions uij;n ðtÞ are new variables to express aerodynamic phase lag and should be defined in such a way that satisfies Eq. (15). 5. Effect of aerodynamic admittance function on various spectrum models Aerodynamic analysis and wind tunnel tests showed that in a line-like structure, the turbulence eddies hit the structure simultaneously [2,44]; however, when the size of the structure increases, the turbulence eddies may not hit the structure at the same time which corresponds to aerodynamic unsteady forces. The aerodynamic unsteady forces can be addressed by aerodynamic admit-

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Fig. 7. Aerodynamic forces on the wind turbine tower.

tance function [2]. The aerodynamic admittance function can be presented in terms of rational function (RF) which will be discussed in detail in Section 6. Fig. 8 illustrates the aerodynamic admittance function presented by Davenport [2] compared with 2 terms rational function (RF) approximation (m ¼ 1), measured rational function by Clobes and Peil [27], rectangular prism wind tunnel tests, and measured indicial functions by Chang et al. [31]. According to wind speed and structure size, aerodynamic admittance may filter various frequency ranges of turbulence spectrum. Fig. 9 presents the effect of aerodynamic admittance function on the different hurricane models introduced before where the

Fig. 8. Aerodynamic admittance function.

vertical isolines represents the energy level of the spectrum model in a certain frequency. Also, skewed isolines show the level of filtration by aerodynamic admittance where the aerodynamic admittance function was calculated using rational functions (RF) and the coefficients were calculated based on Davenport [2] results. In the current case, the bottom and top diameter (at hub height) of the tower were 6 m and 4.5 m respectively. Moreover, the wind speed varied from 30 m/s @ 10 m height (38.1 m/s @ hub height) to 60 m/s @ 10 m height (76.2 m/s @ hub height). Therefore the D/U ratio varied from 0.06 to 0.20. Hence, in high frequencies (1 Hz), the maximum aerodynamic admittance effect was almost 20% for Kaimal et al. [17] spectrum and spectrum model B and less than 10% for spectrum Model A. According to the Eqs. (5) and (6), the spatial coherence considered both lateral and vertical direction; however, the aerodynamic admittance similar to bridge aerodynamics is still sectional and the unsteadiness is only considered in lateral direction in each height. Hence the problem in vertical direction is still quasi-steady. The effect of aerodynamic admittance function for various tower width and wind speed ranges can influence different energy ranges in hurricane models. For Kaimal et al. [17] spectrum, the aerodynamic admittance function with high D/U values (lower wind speeds and/or large tower diameters) affect almost 25% of turbulence energy where vertical isoline labeled 0.04 is affected by skewed admittance function contours; however, since in model A, the most of the turbulence energy is in lower frequency ranges, the aerodynamic admittance function only influences almost 10% of the turbulence energy in high frequency ranges. For Model B, the aerodynamic admittance filters almost 20% of the turbulence

G. Amirinia, S. Jung / Engineering Structures 138 (2017) 337–350

343

Fig. 9. Effect of aerodynamic admittance function on hurricane turbulence spectrum.

energy. For lower values of D/U (higher wind speeds and/or smaller tower diameters) almost all the turbulence energy of the hurricanes are applied on the tower. In other words, at top of the tower the aerodynamic admittance filtration rate is very low and the unsteady analysis is very close to quasi-steady analysis. 6. Model verification and numerical example For unsteady analysis, the aerodynamic admittance function was introduced in terms of rational functions (RF) as Eq. (16):

vij ðxÞ ¼ aij;0 

m X aij;n ix b þ ix n¼1 ij;n

Fig. 10. Comparison of FAST quasi-steady analysis and implemented unsteady analysis.

ð16Þ

where aij;n and bij;n are frequency independent coefficients and m represents the level of accuracy. In Eq. (16), by using m ¼ 1 and according to experimental tests by Davenport [2] and previous studies [27] for along-wind drag force responses, the coefficients were chosen as aDu;0 ¼ aDu;1 ¼ bDu;1 ¼ 1; however, when aDu;0 ¼ 1 and aDu;n ¼ 0, it will corresponds to quasi-steady condition. The procedure presented in the previous and current section was implemented in NREL-FAST code in order to analyze unsteady forces on tower in parked condition. In order to verify the modified FAST code, unsteady forces were calculated for NREL onshore 5 MW baseline wind turbine. A sample base moment result is presented in Fig. 10 where the unsteady results with aDu;0 ¼ 1 and aDu;n ¼ 0 (quasi-steady) completely matched the FAST quasi-steady results; however, the unsteady results with aDu;0 ¼ aDu;1 ¼ bDu;1 ¼ 1 are less

than two other counterparts. In this case, the maximum base moment from unsteady analysis is almost 4% lower than that from quasi-steady analysis. Fig. 11 presents the comparison of the base moments spectra calculated using quasi-steady analysis and unsteady analysis for different hurricane models where unsteady analysis resulted in slightly smaller values than quasi-steady model. As an example, the unsteady base moment spectra in the first peak (1st tower FA) resulted in 40%, 46% and 41% lower values than base moment spectra of quasi-steady analysis of Kaimal et al. (1972) model, Model A, and Model B respectively. After the model verifications, in order to address the effects of different hurricane spectrum models on wind turbines as well as the effects of unsteady analysis of the wind turbine tower, the NREL onshore 5 MW baseline wind turbine was chosen for analysis. The FAST code was used for quasi-steady analysis and also

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G. Amirinia, S. Jung / Engineering Structures 138 (2017) 337–350

Fig. 11. Comparison of base moment quasi-steady analysis with unsteady analysis for different hurricane models (60 m/s – 10 min – 10 m height).

the modified FAST code with unsteady formulation on the tower was used for unsteady analysis. 40 time series were generated using NREL-TurbSim for wind speeds of 30, 40, 50, and 60 m/s for each spectrum models. The details about the time series and structural analysis are same as the details mentioned in the Section 3. 7. Results for hurricane effects on wind turbines 7.1. Effect of different hurricane models Buffeting responses were computed for various hurricane spectrum models as well as quasi-steady and unsteady conditions. Various hurricane models resulted in different buffeting responses. The introduced hurricane turbulence models contained different levels of energy in specific frequency ranges. This various energy levels affects the blade-tower coupled analysis of the wind turbine. The peak of turbulence energy in spectrum Model B was in higher frequencies and also this model had higher energy level in the peak frequency compared to other spectrum models. This high level of energy in higher frequencies in this model is close to the response peak frequency ranges of wind turbine structural components (blades and tower). On the other hand, in the spectrum Model A, the peak of turbulence energy was in lower frequency ranges and consequently far from turbine response peak frequency ranges. In addition the peak energy value of spectrum Model A was slightly lower than that of Model B. The conventional Kaimal et al. [17] model was located between two hurricane models. Fig. 12 presents the mean of maximum total buffeting base moments and blade induced buffeting base moments where spectrum Model B had the greatest base moment responses. In quasi-steady analysis of the total buffeting base moment (Fig. 12a), spectrum model B

resulted in average 10.4% larger and the spectrum Model A resulted in average 8.6% smaller values than the conventional Kaimal et al. [17] spectrum model. In unsteady analysis, the total buffeting base moment from spectrum Model B and Model A were respectively 9.1% larger and 11% smaller than the average values caused by conventional Kaimal et al. [17] model (Fig. 12b). The effect of various hurricane models was more pronounced on blade responses. Comparison of the effects of different spectrum models on the wind turbine structure showed that various hurricane models caused higher differences between the blade induced base moments rather than total buffeting base moments. The mean of maximum blade induced buffeting base moments (the summation of moment on the tower tip and moment produced by tower tip shear on the base) are plotted in Fig. 12c and d. In the quasisteady analysis, the spectrum Model B resulted in average 13% higher and spectrum model A resulted in average 20% lower values than conventional Kaimal et al. [17] spectrum model. Also in unsteady analysis, spectrum Model B had an average 12% larger blade induced base moment values than Kaimal et al. [17] model while spectrum Model A resulted in almost 21% lower values than Kaimal et al. [17] model. The tower tip buffeting displacement followed a similar trend where the spectrum Model B caused the highest responses. In both quasi-steady and unsteady analysis, spectrum Model B and spectrum Model A resulted in average 10% larger and 7% smaller tower tip buffeting displacements than Kaimal et al. [17] (Fig. 13a and b). The reason for these results can be expressed through a spectral analysis. Spectral analysis of the tower tip displacements (Fig. 14) showed that spectrum Model A had higher effects on the low frequency responses of the tower than other two spectrum models. By increasing the frequency, the effect of the spectrum Model A on the responses decreases. In the mid-range frequencies

G. Amirinia, S. Jung / Engineering Structures 138 (2017) 337–350

345

Fig. 12. Mean of maximum buffeting base moments (BM) and maximum buffeting blade induced base moments in quasi-steady (a, c) and unsteady (b, d) situation (10 min – 10 m height).

Fig. 13. Mean of maximum tower tip buffeting displacement in quasi-steady (a) and unsteady (b) situation (10 min – 10 m height)

which contain the tower 1st FA frequency, the amplitude of response spectrum of Model A was almost half of response amplitudes of other two spectrums; however, in higher frequencies the amplitude of spectrum model A was almost 12–15 times less than two other spectrum models and this model had very small effects on the tower responses compared to its other two counterparts. Also since the spectrum Model B in almost all frequency ranges resulted in 10%–20% higher response amplitudes than Kaimal et al. [17] model, it had the highest effect on the tower tip displacements. The spectral analysis of the blade out of plane (edgewise) displacements clearly addressed the differences between effects of various spectrum models on the blade responses. Fig. 15 shows

that blade buffeting responses was affected by tower displacements where the blade displacement spectra has spikes in tower 1st and 2nd FA responses; however, the effect of blade edgewise displacements was higher than the effect of tower fore-aft displacements. Similar to tower displacement analysis, the spectrum Model A in very low frequencies had higher effects on the blade responses; however, after frequency of 0.04 Hz, its effects decreased and the differences between this model and other two models increased. In the frequency range of blade 1st edgewise responses, the spectrum Model A had almost 13 times lower response amplitudes compared to other two spectrum models. At this frequency, spectrum Model B also had 5% higher response amplitudes compared to conventional Kaimal et al. [17] spectrum

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Fig. 14. Spectra of tower tip displacements in quasi-steady (a) and unsteady (b) situation (60 m/s – 10 min – 10 m height).

Fig. 15. Spectra of blade displacements in quasi-steady (a) and unsteady (b) situation (60 m/s – 10 min – 10 m height).

model. The mean of maximum blade tip buffeting displacement (Fig. 16) and mean of maximum blade root moment (Fig. 17) also reflected the huge difference between Model A and other two spectrum models. The mean of maximum blade buffeting displacements of spectrum Model B in both quasi-steady and unsteady was almost 3% higher than values resulted by conventional Kaimal et al. [17]; however, spectrum Model A resulted in average 65% lower blade displacements compared to Kaimal et al. [17]. In addition, spectrum Model B resulted in almost 5% larger values than Kaimal et al. [17] spectrum for blade root moment in both quasisteady and unsteady; whereas spectrum Model A resulted in almost 61% smaller values than Kaimal et al. [17] spectrum model. The main fluctuation frequency range of the blade displacements were in the mid-range frequencies (blade 1st edge) where

the spectrum Model A had the least energy among all three spectrum models; however since spectrum Model B and conventional Kaimal et al. [17] model had higher amount of energy in this frequency range, they affected blade responses more than spectrum Model A. Also the spectrum Model B had high energy content in high frequencies and also higher peak energy value compared to Kaimal et al. [17] model which caused in slightly higher effects on blades structural responses. In general, since the main response fluctuation frequencies of wind turbine components (blades and tower) were in mid to high frequency ranges, the spectrum Model A which had low amount of energy in high frequencies, had the least effects on the wind turbine structural responses. In this case the spectrum Model B and Kaimal et al. [17] model which had high amounts of energy in

Fig. 16. Mean of maximum blade displacement in quasi-steady (a) and unsteady (b) situation (10 min – 10 m height).

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Fig. 17. Mean of maximum blade root moment in quasi-steady (a) and unsteady (b) situation (10 min – 10 m height).

Fig. 18. Comparison of mean of maximum buffeting base moments (BM) (a, c, e) and fluctuating blade induced base moment (b, d, f) in quasi-steady and unsteady analysis (10 min – 10 m height).

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mid to high frequency ranges, affected the wind turbine responses more. The spectrum Model B because of great amount of energy in high frequency ranges and also higher peak energy value, affected both blades and tower slightly more than Kaimal et al. [17] model. 7.2. Effect of quasi-steady and unsteady analysis on the responses In the previous section, buffeting analysis showed that wind turbine responses were highly dependent on coupled blades and tower responses. Also the response analysis of the blades showed that tower displacements influenced the blades responses. In this regard, in order to address the effect of tower quasi-steady and unsteady analysis on the responses in each hurricane model, the comparison between quasi-steady and unsteady was carried out. Analysis of the maximum tower buffeting base moment showed that the unsteady analysis of the tower subjected to conventional Kaimal et al. [17] hurricane model resulted in average 4.8% lower responses than quasi-steady analysis. Also the unsteady analysis of the tower for spectrum model A and B resulted in average 7.4% and 6.0% lower buffeting total base moments than quasisteady analysis. The numbers showed that the unsteady analysis of the tower resulted in average 6% lower total buffeting base moments (Fig. 18a,c, and e). Although the unsteady analysis was only applied on tower aerodynamic forces, the blade induced base moment were also affected by tower unsteady analysis. Unsteady analysis of Kaimal et al. [17] spectrum model, spectrum Model A and B resulted in 3.5%, 4.5% and 4.8% lower values in blade induced base moments respectively. The numbers showed unsteady analysis of the tower aerodynamics caused in almost 4.2% lower blade induced buffeting base moments compared to quasi-steady (Fig. 18b, d, and f). The above results showed that the unsteady analysis of the tower had almost 2% greater effects on total buffeting base moment rather than blade induced base moment. After considering the effect of unsteady analysis of the tower on wind turbine base moment responses, it was expected that tower

unsteady analysis also affects the tower tip buffeting displacements caused by different spectrum models. Fig. 19 presents the difference between tower tip buffeting displacements in unsteady and quasi-steady analysis. The unsteady analysis of the tower subjected to Kaimal et al. [17] spectrum model resulted in average 4% smaller tower tip buffeting displacements than quasi-steady (Fig. 19a). Also unsteady analysis of the tower subjected to both spectrums model A and B resulted in 6% smaller tower tip buffeting displacements compared to quasi-steady analysis (Fig. 19b and Fig. 19c). In previous sections it was presented that the turbulence energy peak in hurricane spectrum model A was located in low frequencies; however in Kaimal et al. [17] model and spectrum Model B the peak of turbulence energy was in higher frequencies. On the other hand, discussions in Section 5 showed that the energy filtration by aerodynamic admittance occurred in higher frequencies. Hence the spectrum models with high level of energy in high frequencies were filtered more than those with high level of energy in lower frequencies. But the analysis showed that blade responses were very dependent on tower responses and also tower responses was affected by blade responses. This coupled procedure caused that in the unsteady analysis, the energy filtration of all spectrum models by aerodynamic admittance function were almost in the same range. The comparison of the conventional Kaimal et al. [17] spectrum model through a quasi-steady analysis (NREL-FAST package) with unsteady analysis of the various spectrum models is presented in Table 3. Considering the Kaimal et al. [17] spectrum with unsteady analysis showed almost 3% smaller responses than quasi-steady analysis of the same spectrum model. The unsteady analysis of the wind turbine subjected to spectrum model A resulted in almost 29% smaller responses than quasi-steady analysis of Kaimal et al. [17] spectrum model; however, unsteady analysis of the spectrum model B resulted in almost 5% larger responses than quasi-steady analysis of the Kaimal et al. [17] spectrum model. Hence for

Fig. 19. Comparison of mean of maximum tower tip buffeting displacement in quasi-steady and unsteady analysis (10 min – 10 m height).

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G. Amirinia, S. Jung / Engineering Structures 138 (2017) 337–350 Table 3 Comparison of unsteady analysis of various hurricane model with quasi-steady analysis of conventional Kaimal et al. [17] (FAST). Response components

Kaimal et al. [17] (FAST)

Kaimal et al. [17] (Unsteady)

Model A (Unsteady)

Model B (Unsteady)

Total Tower Buff. B.M. Bld. Ind. Buff. B.M. Tower Tip Buff. Disp. Bld. Root Moment Bld. Tip Disp.

0.0% 0.0% 0.0% 0.0% 0.0%

4.9% 3.5% 3.5% 0.0% 0.0%

15.3% 23.6% 12.0% 61.2 65.3%

3.8% 7.9% 4.9% 5.5% 3.0%

extreme condition, considering hurricane spectrum model B through an unsteady analysis of the tower will make the analysis and design more conservative and also efficient.

of the wind turbine subjected to spectrum model B represents extreme wind conditions more realistic than conventional quasi-steady analysis carried out by NREL-FAST.

8. Conclusions Acknowledgements This paper first reviewed the recent hurricane observations and spectrum models for hurricane turbulence energy. At the next step, the influence of wind turbine components on the total structural responses was addressed. A well-known time domain procedure for unsteady analysis was employed to consider unsteady aerodynamic forces on the wind turbine tower. The frequency dependent aerodynamic admittance function was addressed by rational functions (RF). The procedure was implemented in the NREL-FAST module for analysis of a wind turbine (NREL onshore 5 MW baseline wind turbine). After conducting the using the model for analysis, the following points were concluded: – The effect of recent hurricane observations and models on the wind turbine components were different from conventional wind spectrum model introduced by Kaimal et al. [17]. It was observed that if the frequency range of hurricane spectrum peak energy get close to the main frequency range of structural responses, it will affect responses more. This resulted in that spectrum models which had high level of energy in higher frequencies (spectrum Model B) resulted in larger responses (base moments and displacements) than the model introduced by Kaimal et al. [17]. On the other hand, the spectrum models which depicted high amount of energy in low frequency ranges (spectrum Model A) resulted in smaller buffeting responses than conventional Kaimal et al. [17] spectrum model. – The unsteady analysis was carried out only on the tower; however, the analysis showed that the wind turbine responses are blade-tower coupled. The unsteady analysis resulted in 4.8%– 7.4% smaller total buffeting base moments for various spectrum models. Because of the couple blade-tower response, the unsteady analysis also resulted in 3.5%–4.8% smaller blade induced buffeting base moments compared to conventional quasi-steady analysis. The tower tip buffeting displacements also were influenced by unsteady analysis of the tower. In this case, unsteady analysis of various hurricane spectrum models resulted in 4%–6% smaller tower tip buffeting displacements compared to quasi-steady analysis. – The results in this article showed that in order to safely analyze and design the wind turbine systems in extreme wind condition, hurricane spectrum Model B resulted in more conservative values; however, since the unsteady analysis considered the effect of structure size and turbulence eddy sizes, it makes the analysis and design process more efficient. In this regard, unsteady analysis of the Kaimal et al. [17] spectrum, spectrum model A and spectrum model B resulted in average 3% smaller, 29% smaller and 5% larger responses than quasi-steady analysis of conventional Kaimal et al. [17] spectrum model (FAST) respectively. Hence it can be concluded that unsteady analysis

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