J. Meteor. Res.  2019, Vol. 33 Issue (5): 895-904   PDF    
The Chinese Meteorological Society

Article Information

WANG, Binglan, Zhiqiang HE, Lili SONG, et al., 2019.
Improved Calculation of Turbulence Parameters Based on Six Tropical Cyclone Cases: Implication to Wind Turbine Design in Typhoon-Prone Areas. 2019.
J. Meteor. Res., 33(5): 895-904

Article History

Received November 16, 2018
in final form June 16, 2019
Improved Calculation of Turbulence Parameters Based on Six Tropical Cyclone Cases: Implication to Wind Turbine Design in Typhoon-Prone Areas
Binglan WANG1,2, Zhiqiang HE3, Lili SONG1,2, Wenchao CHEN4     
1. Beijing Jiutian Weather Technology Co., Ltd., Beijing 100081;
2. Public Meteorological Service Center, China Meteorological Administration, Beijing 100081;
3. North China Regional Meteorological Center, Civil Aviation Administration of China, Beijing 100621;
4. Guangdong Meteorological Disaster Prevention Technology Service Center, Guangzhou 510080
ABSTRACT: In view of the absence or insufficiency of tropical cyclone (TC) turbulence parameters in current design standards of wind turbines, in this paper, TC turbulence parameter models with roughness length involved are developed based on six landfall TCs observed from meteorological towers located on various underlying surfaces, so as to provide references for the wind turbine design under TC conditions. Firstly, the roughness length values are examined in order to reduce the effect on turbulence parameters of the various underlying surfaces. On this basis, the reference turbulence intensity is normalized by the roughness length. The related turbulence parameters are parameterized, including the turbulence standard deviation and the turbulence spectrum; and the turbulence parameters available under TC conditions for turbulence turbine design are presented finally. Comparisons of the wind parameter models presented in this paper with those used in current turbine design standards suggest that the former can represent TC characteristics more accurately. In order to withstand TCs, we suggest that the turbulence parameter models recommended in this paper be included in future wind turbine design standards under TC conditions.
Key words: tropical cyclone     turbulence parameter models     wind turbine    
1 Introduction

With a coastline of more than 18,000 km, China has abundant offshore wind power resources. The offshore wind energy reserves that can be exploited are three times that of onshore wind energy resources. In the 13th Five-Year Plan for Energy Technological Innovation issued by the State Energy Administration in January 2017, it was pointed out that the key technologies of offshore wind turbines should be focused on during the 13th Five-Year Plan to meet the needs of national offshore wind power development.

The coastal and offshore areas in southeastern China, however, are affected by tropical cyclones (TCs). TCs are important constraints to the development of offshore and coastal wind power, due to the damages caused by TCs to wind turbines and offshore wind farms. Previous studies have manifested that the combined action of TCs’ unique eddy circulation structure and complex underlying surface produces extremely strong, complex, and unsteady turbulent winds in the surface layer. Overall, this is the main factor leading to the damage of wind turbines, especially in rugged mountainous wind farms. Using hurricane data collected in the boundary layer, Zhang (2010) found that most of the energy is concentrated in the region with shorter wavelength, which highlights the uniqueness of the hurricane boundary layer. Song et al. (2016) found that the strong wind profiles closer to the typhoon eye-wall show a wake-like shape and deviate from the power law distribution. In addition, it has been demonstrated that wind characteristics in the typhoon eye-wall, eye area, and peripheral areas outside the eye-wall are significantly different. The typhoon eye-wall, where wind parameters (such as wind profile index, turbulence intensity, wind attack angle, etc.) increase significantly, is invariably considered as disaster-causing areas. Amirinia and Jung (2016) indicated that the unsteady high winds result in 4.9% decrease in fluctuating fore-aft base moment caused by buffeting forces and 3.5% decrease in buffeting fore-aft tower tip displacement. The turbulence parameter characteristics of typhoons and non-typhoons are significantly different. Even in the same typhoon, the parameters differ in different locations inside the typhoon, e.g., the parameters in the eye of typhoon are different from those in the eye-wall. Based on observed typhoon data, Li et al. (2015) parameterized turbulence spectra for different typhoon structures such as the eye-wall and outer region, proving that typhoon eye-walls contain more energy. Using airborne Doppler measurements, Lorsolo et al. (2010) revealed that the strongest turbulence is generally located in convective regions, such as the eye-wall.

In view of the unique wind characteristics of TCs, several investigators have examined the applicability of building structures codes (e.g., ASCE/SEI 7-10, 2010) under typhoon conditions (Li et al., 2015). In this paper, we focus on examining the turbulence parameters required for the wind turbine design in International Electro technical Commission (IEC) standard (GB/T 184511-2012, 2016) under TC conditions, as IEC is the most widely used standard for the wind turbine design at present. A brief introduction of some relevant turbulence parameters in IEC is presented in Section 2. Section 3 introduces the observed typhoon data used in this study and the method of data processing. Section 4 presents the experimental study to make new wind parameter models using observed typhoon data. Section 5 contains the conclusions and some ideas for further work.

2 Turbulence parameters in IEC

The IEC specifies essential design requirements to ensure the engineering integrity of wind turbines and has been widely used (Huang et al., 2015; Gong et al., 2019). In IEC, the wind turbine is classified according to the wind speed and turbulence parameters. Table 1 specifies the basic parameters for different wind turbine classes. It should be noted that the parameters defined for wind turbine classes I, II, and III do not contain TC conditions. TC conditions may require wind turbine class S design, whose values shall be chosen by the designer and shall reflect an environment at least as severe as is anticipated for the use of the wind turbine.

Table 1 Basic parameters for different wind turbine classes (IEC, 2005)
Wind turbine class/turbulence intensity class Ⅰ/A Ⅱ/B Ⅲ/C S
Vref (m s–1) 50.00 42.50 37.50 Values specified
 by the designer
Iref 0.16 0.14 0.12

In Table 1, Vref is the reference wind speed averaged over 10 min. The reference turbulence intensity Iref is the expected value of the turbulence intensity at 15 m s–1 and is defined as the mean value rather than a representative value. A, B, and C designate the categories for higher, medium, and lower turbulence intensity characteristics, respectively.

In addition, the turbulence standard deviation and turbulence integral length scale are recommended by IEC (see Table 2). In Table 2, k is the index referring to the velocity component direction (i.e., 1, 2, and 3 reperent longitudinal, lateral, and vertical; the same below), and σ1, given by the 90% quantile for the wind speed, is the representative value of the longitudinal turbulence standard deviation. This value is given as follows,

Table 2 Turbulence parameters for the wind turbine design (IEC, 2005)
Velocity component index (k)
1 (longitudinal) 2 (lateral) 3 (vertical)
Standard deviation σk σ1 0.8σ1 0.5σ1
Integral scale Lk 8.1Λ1 2.7Λ1 0.66Λ1
${\sigma _1} = {I_{\rm ref}}\left({0.75V + b} \right),\;\;{\rm{}}b = 5.6\;{\rm{m}}\;{{\rm{s}}^{ - 1}},$ (1)

where V is the wind speed. In Table 2, Λ1 is the longitudinal turbulence scale parameter, and Λ1 at height z is gi-ven by Eq. (2),

${\varLambda _1} = \left\{ {\begin{array}{*{20}{c}} {0.7z,\;\;\;z < 60 \; {\rm m}}\\ {42,\;\;\;z \geqslant 60 \;{\rm m}} \end{array}} \right. .$ (2)

In IEC, the component power spectral densities are given in non-dimensional form by Eq. (3),

$\frac{{f{S_k}\left(f \right)}}{{\sigma _k^2}} = \frac{{4f{L_k}/V}}{{{{\left({1 + 6f{L_k}/V} \right)}^{5/3}}}},$ (3)

where f is the frequency in Hz, Sk is the single-sided velocity component spectrum, σk is the velocity component standard deviation, and Lk is the turbulence integral scale.

As is pointed out by IEC, equations of turbulence parameters metioned above, including Iref, σk, Lk, and Sk, are neither applicable to offshore conditions nor to TC conditions. In the following sections, observed TC data are analyzed to derive TC turbulence parameters, which are then compared with those recommended by IEC under non-typhoon conditions. On this basis, we attempt to find out more accurate parametric formulas to describe the turbulence parameters under TC conditions, so as to provide references for the wind turbine design.

3 Data sources and processing 3.1 Introduction to wind measurement data of TCs

Data observed at six towers located near the paths of western Pacific typhoons are chosen. For each TC, both wind gradient data and three-dimensional (3-D) high frequency ultrasonic wind velocity data are gathered. The closest distances between TC centers and towers are all shorter than 35 km. The observed gradient wind data are used to calculate the terrain roughness length where the tower is located. The 3-D high frequency data observed from the ultrasonic anemometer are used to calculate the turbulence intensity, turbulence integral length scale, and turbulence spectrum of TCs as the wind turbine design parameters. Table 3 shows the selected TC information such as the observation site, time period, measurement location, nearest distance to the tower, and grades of TCs according to GB/T 19201-2006 (2006). The GPS coordinates of the sites and descriptions of these towers’ surrounding underlying surfaces are listed in Table 4.

Table 3 TC information
TC name Tower name Time period of TC data Closest distance between
TC eye and the tower (km)
Grade of TCs
Nuri Sanjiao Island tower 22–23 August 2008 32.0 TY (typhoon)
Hagupit Zhizai Island tower 23–24 September 2008 8.5 STY(severe typhoon)
Molave Shatian tower 16 July 2009 12.0 TS (tropical storm)
Nesat Xuwen tower 29 September 2011 18.0 STY(severe typhoon)
Rumbia Donghai Island tower 1–2 July 2013 18.0 STS (severe tropical storm)
Utor Yangxi tower 14 August 2013 19.7 Super TY
Table 4 Description of the towers’ surrounding underlying surfaces
Typhoon name Tower name GPS coordinate of tower The surrounding underlying surface
Nuri Sanjiao Island 22.1413°N,
The tower is located at Sanjiao Island. Sanjiao Island is a mountain island whose area is 0.62 km2. The island runs from east to west, and the underlying surface is covered by low grass and bushes. There are several islands around Sanjiao Island within 20 km.
Hagupit Zhizai Island 21.45°N,
The tower is located at Zhizai Island. This 90-m long and 40-m wide island, whose surface is covered by weeds, runs from northeast to southwest, and swells in the middle. The shortest distance between the island and the coastline is 4.5 km. At the top of the island, 10 m above sea level, there is the 100-m high gradient tower.
Molave Shatian 22.8539°N,
Shatian tower is an inland meteorological tower. The underlying surface is flat, surrounded by sparse pastures and low trees.
Nesat Xuwen 20.2408°N,
The tower is 30 m away from the coast, with dense eucalyptus, 7–8 m high, surrounding the tower.
Rumbia Donghai Island 21.013°N,
The tower is 1200 m away from the coast, with dense eucalyptus, 2–3 m high, surrounding the tower. In the southwest of the tower, there are 20-m high buildings, as well as low villa group.
Utor Yangxi 21.523°N,
The tower is 1300 m away from the coast, mainly surrounded by farm land.
3.2 Observation setting and specifications of anemometers

The meteorological towers, whose edge width is 1.0 m, are triangular steel structures with altitudes between 100 and 112 m. We name the meteorological towers after their locations. Every tower is equipped with a gradient wind measuring system and an ultrasonic anemometer. Here, the gradient wind refers to winds observed from different altitudes in the meteorological tower in the boundary layer. The gradient winds are measured by the system with wind-speed and wind-direction sensors, a data collector, a communication unit, an electrical source, and relevant software. The sensors of the gradient wind measuring system are NRG-#40 cup anemometers and NRG-#200p wind vanes made by American Renewable NRG Systems. The time step of the data collection is 2 s. The 10-min mean wind speed, maximum gust (2 s) wind speed, and wind speed standard deviation (STD) are recorded every 10 min. The sampling frequency of the ultrasonic anemometers (WindMasterTM Pro 3D; Gill Instruments Limited, 2016) is 10 Hz.

In order to ensure that the instrument performance meets the requirements for TC observation, a calibration is performed in the standard wind tunnel before installation of the anemometers. The height of the tower, the height above sea level, and the installation height of the anemometers are listed in Table 5. In addition, Table 6 shows specifications of the anemometers and wind direction vanes.

Table 5 Tower information and sensor settings
Tower name Tower height/height above sea level (m) Observation height of wind speed and wind direction Installation height of ultrasonic anemometer (m)
Sanjiao Island tower 100/98 10, 20, 40, 60 m 60
Zhizai Island tower 100/10 Observation height of wind speed: 10, 20, 40, 60, 80, 100 m;
Observation height of wind direction: 10, 60, 100 m
Shatian tower 100/8 10, 20, 40, 60, 80 m 75
Xuwen tower 112/4 10, 20, 40, 60, 90, 110 m 90
Donghai Island tower 100/22 30, 50, 70, 100 m 65
Yangxi tower 100/2 10, 20, 40, 70, 100 m 70
Table 6 Specifications of the anemometers and wind direction vanes
Performance parameter Cup anemometer Wind direction vane Ultrasonic anemometer
Threshold 0.78 m s–1
Sensor range 1–96 m s–1 0–359° ≤ 65 m s–1
Accuracy 0.1 m s–1 1% 0.1 m s–1
Resolution 0.1 m s–1 0.1 m s–1
Operating temperature range –55 to 60°C –55 to 60°C –40 to 70°C
Operating humidity range 0–100% RH 0–100% RH 0–100% RH
3.3 Data quality control and processing

IEC stipulates the time interval like this: wind data shall be the statistics of 10-min samples. Thus, all the turbulence parameters are calculated based on 10-min intervals.

Quality control was first carried out on the raw observation data of gradient wind according to the relevant specifications (GB/T 18710-2002, 2004; QX/T 74-2007, 2007), and the effective integrity rate of the annual data (Rei) was calculated according to Eq. (4) as below.

$ R_{\rm ei} = \frac {V_{\rm m} - V_{\rm u}-V_{\rm i}}{V_{\rm m}} \times 100 \text% ,$ (4)

whereVm, Vu, and Vi represent the measured data volume, unmeasured data volume, and invalid data volume, respectively. In Eq. (4), the data volume refers to the number of 10-min averaged wind speed recorded in the entire year.

From the gradient wind observation, the observation data of a meteorological tower for one year with an effective integrity rate ≥ 90% were selected as the basic data for the calculation of roughness length. For the observation data from 3-D ultrasonic anemometers, the accuracy and reliability of the collected TC data were determined. First, the invalid data in the samples were identified based on the invalid data discrimination function of the ultrasonic anemometer. Outlier selection and data interpolation were carried out on the sample data based on the method proposed by Wang et al. (2013). As data observed by ultrasonic anemometers were unreliable during TC rainfall, the samples whose effective rate was less than 90% were removed to avoid the impact to the statistical results. Numbers of valid samples are listed in Table 7.

Table 7 Number of valid samples for the six landfall TCs
TC name Hagupit Molave Nesat Rumbia Nuri Utor
Number of valid samples 131 143 144 134 137 113

Data obtained from the ultrasonic anemometers are north-facing and west-facing geographical coordinates (figure omitted). According to Song et al. (2012), the raw data have been processed, and the longitudinal wind speed (main wind direction) and the lateral wind speed (perpendicular to the main wind direction) have been obtained.

As this study is based on the comparison between wind turbine design parameters from measured data and the recommended values in IEC, a major idea from IEC is used during the data analysis: when confirming representative values of parameters, mean values are not used, but the values at the 90% quantile are used for the determination. On the other hand, we can see from Table 3 that besides TC Nesat, the installation heights of ultrasonic anemometer are typically around 60–75 m, and they are not greatly different by height. The turbulence standard deviation, turbulence integral length scale, and wind speed spectrum do not change with height. This is also consistent with the IEC assumption.

4 Results and analysis 4.1 TC wind speed

Figure 1 shows temporal variations of the TC wind speed and distances between TC centers and meteorological towers. It can be seen that variations of the wind speed during the six TC processes are all distributed as an “M” shape with double-peak, which indicates that the wind data representing TC eye-wall has been observed (Chen, 2002). TC Hagupit, with the maximum wind speed of 45.9 m s–1, is the strongest TC observed in this study. Distances between the TC center and the meteorological tower decreases first and then increases, showing the process of the TC center approaching and moving away from the meteorological tower.

Figure 1 Temporal variations of the wind speed and distances between TC centers and meteorological towers: (a) Hagupit, (b) Molave, (c) Nesat, (d) Nuri, (e) Rumbia, and (f) Utor.
4.2 The roughness length

The observation data used in this study were basically derived from coastal or offshore meteorological towers with various underlying surfaces, which can affect turbulence parameter analyses. In order to reduce this impact, the roughness length was drawn into to normalize turbulence parameters. The various surfaces were firstly divided into sea or land exposures according to the incoming wind direction. Figure 2 shows the classification of various meteorological towers according to sea and land underlying surfaces, with TC tracks overlaid.

Figure 2 Exposure classifications of the towers. The land and sea surfaces are filled with left and right diagonals, respectively, and the yellow lines are TC tracks.

Song et al. (2016) provided a calculation method for the roughness length. At neutral stratification, the wind speed at height z can be expressed as follows according to the logarithmic law:

${u}(z) = \frac{1}{\kappa }{u_*}\ln \frac{z}{{{z_0}}},$ (5)

where k is the Karman constant, u* is the friction velocity, z0 is the roughness length, z is the height, and u(z) is the wind speed at height z. The observed data of gradient wind was collected from meteorological towers for one year. According to the wind direction, the data were classified into land or sea direction. The gradient data for 10 min were fitted based on Eq. (5). When the mean value of the fitted residual sum of squares ≤ 0.1 m2 s–2, the goodness of fit was considered to be high. The mean wind profiles of the samples with high goodness of fit are calculated and fitted by using Eq. (5), and then the roughness length ${z_0}$ is obtained based on the fitting coefficient. Table 8 shows the calculated roughness length of various anemometer towers on sea or land underlying surfaces.

Table 8 Classification of the exposures and the corresponding roughness lengths
TC name Tower name Exposure Roughness length (m) Range of wind speed of samples used to calculated z0 (m s–1)
Nuri Sanjiao Island tower Sea 0.0051 4.3–28.9
Hagupit Zhizai Island tower Sea 0.0004 4.4–39.7
Molave Shatian tower Land side 1.69 4.4–18.0
Sea side 0.6 4.3–20.1
Nesat Xuwen tower Land side 3.0 4.0–18.9
Sea side 0.06 6.3–22.3
Rumbia Donghai Island tower Land side 0.76 4.7–17.7
Utor Yangxi tower Land side 1.11 5.8–12.3
Sea side 0.04 6.4–19.5
4.3 The reference turbulence intensity

IEC defines the reference turbulence intensity as the mean value of sample turbulence intensity at the 10-min mean speed of 15 m s–1. Using the 6 TCs as examples, corresponding wind speed samples of different terrain roughness (sea or land) at 15 m s–1 were selected. As the measurement data samples of TCs are sparse, the samples with the 10-min mean wind speed of 15 m s–1 are even sparser. In order to ensure the accuracy of the reference turbulence intensity, when the number of samples with the 10-min mean wind speed of 15 m s–1 is greater than 2, the mean turbulence intensity is calculated as reference turbulence intensity. Figure 3 shows the reference turbulence intensity changing with the roughness length. Multiple functions (Song et al., 2016) were used for fitting of the roughness length and reference turbulence intensity, and a power-exponential function was found to accurately describe the relationship between Iref and z0. The fitting equation is expressed as follows:

Figure 3 Relationship between the reference turbulence intensity and roughness length. The black solid line is the fitting curve.
${I_{\rm ref}} = m \cdot {z_0^n},$ (6)

where z0 is the roughness length,Iref is the reference turbulence intensity, and m and n are the fitting parameters. The fitting curve is shown in Fig. 3 based on Eq. (7):

${I_{\rm ref}} = 0.16 \cdot {z_0^{0.06}}.$ (7)

Empirical formula (7) is used for the examination on the fitting results. The results show that the fitting correlation coefficient of the reference turbulence intensity and roughness length is 0.99, and the residual variation of the fitting curve is only 0.0023, indicating that this empirical formula has relatively high reliability. From the fitting formula, we can see that the reference turbulence intensity increases with roughness length, i.e., the rougher the terrain roughness is, the greater the reference turbulence intensity is, which is consistent with Li et al. (2015).

4.4 Turbulence standard deviations

Studies have shown that turbulence standard deviations will increase under TC conditions (Schroeder et al., 1998; Sharma and Richards, 1999; Xu and Zhan, 2001; Li et al., 2004). According to IEC, the turbulence standard deviations, including σ1, σ2, and σ3, are the corresponding standard deviation at the 90% quantile. For every TC, wind speeds are first grouped at the interval of 1 m s–1. The corresponding σ1 at the 90% quantile of each group of wind speed samples is found out as the standard deviation in this wind speed interval. Figure 4 shows the standard deviation of 6-TC measured longitudinal wind speeds changes with the 10-min mean wind speed. The stratifications of turbulence standard deviations among TCs observed from various surfaces are significant, indicating the roughness length analysis is necessary. The turbulence standard deviation σ1 recommended by IEC available for non-typhoon condition is also demonstrated in Fig. 4. It can be seen that for a single TC, the recommended values are either too large or too small.

Figure 4 Changes of σ1 with the 10-min mean wind speed. The solid, dashed, and dotted lines represent the wind turbine classes I, II, and III recommended by IEC, respectively.

According to the analyses of roughness length in Section 3.2, the turbulence standard deviations are normalized by the roughness length. Figure 5 shows variations of the normalized turbulence standard deviations with the wind speed. The best-fitting formulas of the normalized turbulence standard deviations acting on the wind speed are obtained as follows:

Figure 5 Relationship between the normalized σ1 and wind speed. The best fitting (solid), 90% envelope (dotted), and envelope (solid with black squares) curves are also shown
${\sigma _1} = {I_{\rm ref}}\left({0.94V + 1.56} \right).$ (8)

Fitting curves can be seen in Fig. 5. Owing to the involvement of roughness length, turbulence parameters are not invariant constants; they depend not only on the wind speed but also on various surfaces. That is to say, the model involving the roughness length can accurately describe the characteristics of TCs’ longitudinal turbulence standard deviation, which are observed on different underlying surfaces.

In IEC, the lateral and upward turbulence standard deviations σ2 and σ3 are estimated by σ1. Table 9 shows the ratios of σ2/σ1 and σ3/σ1 for every TC calculated by the observed data. It can be seen that the ratio σ2/σ1 ranges from 0.6 to 0.9, and the ratio σ3/σ1 ranges from 0.4 to 0.5. Taking the average ratio of the six TCs, the ratios of σ2/σ1 and σ3/σ1 are determind to be 0.8 and 0.5, respectively, which is consistent with IEC and Cao et al. (2009).

Table 9 Ratios of σ2/σ1 and σ3/σ1 under TC conditions
TC name ${\sigma _2}/{\sigma _1}$ ${\sigma _3}/{\sigma _1}$
Nuri 0.8 0.4
Hagupit 0.8 0.5
Molave 0.9 0.5
Nesat 0.7 0.5
Rumbia 0.6 0.5
Utor 0.7 0.5
Average of the six TCs (this study) 0.8 0.5
IEC 0.8 0.5
Cao et al. (2009) 0.5 0.5
4.5 Turbulence integral length scale

The turbulence integral length scale is calculated using the following equation.

${L_k} = V\mathop \smallint \nolimits_0^{{\tau _{0.05}}} {r_{{u_k}}}\left(\tau \right) {\rm d} \tau,$ (9)

where ${\tau _{0.05}}$ represents the corresponding delay time when the autocorrelation coefficient monotonically decreases from 1 to 0.05, and uk (k = 1, 2, 3) is the components of fluctuating wind speed in longitudinal, lateral, and upward directions. ${r_u}\left(\tau \right) = E\left[ {u\left(t \right)u\left({t + \tau } \right)} \right]$ is the autocorrelation function of uk relative to a time-lag value τ. In this function, E represents the mathematical expectation, and t is the time.

Imitating the determination method of σ1 recommended by IEC, and considering that the turbulence integral length scale increases with wind speed at the same time (Wang et al., 2011), wind speed is first divided into 1-m s–1 interval groups. Then the corresponding turbulence integral length scale value at the 90% quantile of each group is obtained as the representative values for the longitudinal, lateral, and upward turbulence integral length scales of each group in TCs. Figure 6 shows the representative values of integral scales for each-interval wind speed. Turbulence integral scales recommended by IEC and this study are also plotted in Fig. 6. It can be seen that turbulence integral scales recommended by IEC are indeed not available under TC conditions, especially for the lateral or upward direction.

Figure 6 Comparison of the representative values of TC turbulence integral scale recommended by this work (dotted line) and IEC (solid line). Black dots denote the turbulence integral scale calculated by using observed TC data.

The corresponding turbulence integral length scale at the 90% quantile of wind speed sequence at 1-m s–1 interval is taken as its representative value of TCs. The turbulence scale parameter ${\Lambda _1}$ is divided by the longitudinal turbulence integral length scale to obtain the coefficients of longitudinal, lateral, and vertical turbulence integral length scales of various TCs. These values are 10.6, 6.8, and 1.8, respectively (see the dotted line in Fig. 6).

Figure 7 shows the relationship between L1 and L2 and the relationship between L1 and L3. Linear fitting without intercept is carried out to obtain the ratios of L2/L1 and L3/L1, and they are 0.64 and 0.17, respectively. These values match the recommended coefficient ratios well. Table 10 demonstrates ratios among turbulence integral length scales examined by several researchers. It is clearly indicated that the lateral and upward turbulence scales recommended by this work are larger than those recommended by IEC, and the ratio L3/L1 is consistent with Cao et al. (2009).

Table 10 Turbulence integral length scales under TC conditions
L1 L2 L3 L2/L1 L3/L1
This study 10.6 ${\varLambda _1}$ 6.8 ${\varLambda _1}$ 1.8 ${\varLambda _1}$ 0.64 0.17
Cao et al. (2009) 0.41 0.18
IEC 8.1 ${\varLambda _1}$ 2.7 ${\varLambda _1}$ 0.66 ${\varLambda _1}$ 0.33 0.08
Figure 7 Relationships between longitudinal and lateral, as well as longitudinal and vertical turbulence integral scales. The lines in (a) and (b) represent L2/L1 and L3/L1 ratios averaged for all the paired data points, respectively. The correlation coefficient between L1 and L2 is 0.75, and that between L3 and L2 is 0.45.
4.6 Turbulence spectrum

Samples with wind speed greater than 10.8 m s–1 are selected and the mean turbulence spectra of these samples are analyzed. Table 10 shows the comparison between the measured wind speed spectrum and the IEC-recommended wind speed spectrum. It can be seen that left shifting of the corresponding frequency to the peak spectrum exists in the IEC-recommended wind speed spectrum, i.e., the corresponding frequency to the maximum value of the wind speed spectrum tends to be small. Furthermore, the longitudinal and lateral turbulence spectra are overestimated significantly (Class A and Class B), or overestimated in low frequency and underestimated in high frequency. The turbulence wind spectra are intended to be parameterized by three coefficients:

$\frac{{f{S_k}\left(f \right)}}{{\sigma _k^2}} = \frac{{{\alpha _k}f{L_k}/V}}{{{{\left({{\beta _k} + {\gamma _k}f{L_k}/V} \right)}^{5/3}}}},$ (10)

where σk is the turbulence standard deviation recommended by this study [Eq. (8) and Table 6],αk, βk, and γk are fitting cofficients, and Lk is the turbulence integral length scale recommended by this study (Table 9). The best fitting curves for longitudinal, lateral, and upward turbulence spectra are demonstrated in Fig. 8 and the best turbulence spectral coefficients are shown in Table 11.

Table 11 Turbulence spectral coefficients
Velocity component index (k)
1 (longitudinal) 2 (lateral) 3 (upward)
αk 0.4 0.4 1.2
βk 0.3 0.5 0.8
γk 0.9 0.8 1.8
Figure 8 Mean turbulence wind spectra of samples with the wind speed greater than 10.8 m s–1: (a) longitudinal, (b) lateral, and (c) upward.

The spectral model is commonly used in a class of turbulent-inflow simulators for the wind turbine design and load estimation. From this perspective, the accuracy of the model directly affects the design of wind turbine load. From Fig. 8, we can see that the frequency of the peaks from the power spectral models in this work are 0.3 and 0.08 Hz for the longitudinal and lateral components, and the corresponding values are 0.02 and 0.05 Hz in the spectral model in IEC. It seems that the peaks of the new models, which are more in line with the measured wind spectrum, are shifted to higher frequencies than the peaks from the spectral models recommended by IEC for non-typhoon conditions. This shift suggests that, under TC conditions the most dominant eddies in the flow have a smaller wavelength (higher frequency) than those in non-typhoon conditions (Worsnop et al., 2017).

Further, the new spectral curves with the roughness length involved can more accurately describe the wind spectrum characteristics of typhoons on different underlying surfaces; thus, the wind spectrum model can be determined more pertinently according to the underlying surfaces in the wind turbine design, rather than by simply and roughly using the existing specifications.

5 Conclusions

Based on the data of six TC cases obtained from coastal and offshore meteorological towers near Guangdong Province, China, turbulence parameters for the wind turbine design required by IEC have been analyzed. The effect of various underlying surfaces on turbulence parameters is now taken into consideration and parameterized by using the roughness length. The conclusions from this study are summarized as follows.

(1) The reference turbulence intensity under TC conditions varies with different underlying surfaces. The variations can be described by incorporating the roughness length. A power-exponential function can be better fitted to express the mathematical relationship between the reference turbulence intensity of typhoons and the roughness length.

(2) Normalized turbulence standard deviations under TC conditions still increase linearly with the wind speed, which is in accord with IEC.

(3) Based on the turbulence standard deviation and turbulence integral scale, the turbulence wind spectra are parameterized by using three coefficients, which can describe TC turbulence spectra more accurately.

Furthermore, owing to the involving of roughness length, the wind parameter models can be determined more pertinently according to the underlying surface in wind turbine design, rather than simply and roughly using the existing specifications. In order to withstand TCs, we suggest that the turbulence parameter models recommended in this paper be included in the future wind turbine design standards in typhoon-prone areas.

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