7 1 1 Wind DIMAS-2 [Λειτουργία...

Operational Operational ProgrammeProgramme “Education and Lifelong Learning”“Education and Lifelong Learning”Continuing Education Programme for updating Knowledge of Continuing Education Programme for updating Knowledge of

University Graduates:University Graduates:“Modern Development in Offshore Structures”“Modern Development in Offshore Structures”

7 1 1 Wi d7 1 1 Wi d

AUThAUTh TUCTUC

7.1.1. Wind7.1.1. Wind

Athanassios A. DimasProfessor, Department of Civil Engineering, University of Patras

[email protected]

Administrator

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Το παρόν υλικό δημιουργήθηκε στα πλαίσια του Προγράμματος Δια Βίου Μάθησης ΑΕΙ για την Επικαιροποίηση Γνώσεων Αποφοίτων ΑΕΙ "Σύγχρονες Εξελίξεις στις Θαλάσσιες Κατασκευές" (Επιχειρησιακό Πρόγραμμα "Εκπαίδευση και Δια Βίου Μάθηση") για αποκλειστική χρήση από τους εκπαιδευόμενους του Προγράμματος. Τυχόν άλλη χρήση του υλικού ή/και αναπαραγωγή αυτού δεν επιτρέπεται, καθόσον αποτελεί πνευματικό δικαιώμα του εκάστοτε διδάσκοντος.

IntroductionIntroduction

7.1.1 Wind7.1.1 Wind

Role of wind in the design of offshore structures:Role of wind in the design of offshore structures:

•• Direct loadDirect load•• Wave generationWave generation

References:References:

•• DNV 2010. Environmental Conditions and Environmental Loads. DNVDNV 2010. Environmental Conditions and Environmental Loads. DNV‐‐RPRP‐‐C205 (RECOMMENDED PRACTICE), DET NORSKE VERITAS AS.C205 (RECOMMENDED PRACTICE), DET NORSKE VERITAS AS.

•• DNV 2011. Design of Offshore Wind Turbine Structures. DNVDNV 2011. Design of Offshore Wind Turbine Structures. DNV‐‐OSOS‐‐J101 J101 (OFFSHORE STANDARD), DET NORSKE VERITAS AS.(OFFSHORE STANDARD), DET NORSKE VERITAS AS.

•• IEC 2009. Wind Turbines IEC 2009. Wind Turbines ‐‐ Part 3: Design Requirements for Offshore Wind Part 3: Design Requirements for Offshore Wind Turbines. IEC (International Turbines. IEC (International ElectrotechnicalElectrotechnical Commission) & BS (British Commission) & BS (British Standards) EN 61400Standards) EN 61400‐‐3.3.

IntroductionIntroduction


Purpose of presentation:Purpose of presentation:

•• Methods of windMethods of windmeasurements analysismeasurements analysis

20

25

30

35

U (m

/s)

20 m/sec10 m/sec

0 100 200 300 400 500 600

0

5

10

15

Time (sec)

Velo

city

U

•• Identification of appropriate (Identification of appropriate (normal, severe and extremenormal, severe and extreme) values of wind ) values of wind speed to be used in speed to be used in combinationcombination with other loads (waves, currents, etc) with other loads (waves, currents, etc) for the design of offshore structuresfor the design of offshore structures

Wind Speed Wind Speed ParametrizationParametrization


•• Wind speed, related to the computation of environmental loads on Wind speed, related to the computation of environmental loads on offshore structures, varies with time and height.offshore structures, varies with time and height.

•• Commonly, wind speed is presented after averaging over 1 minute, 10 Commonly, wind speed is presented after averaging over 1 minute, 10 minutes and 1 hour.minutes and 1 hour.

•• Commonly, a reference height of 10m is used.Commonly, a reference height of 10m is used.

•• The 10The 10‐‐minute mean wind speed at 10m height: Uminute mean wind speed at 10m height: U1010•• The 10The 10‐‐minute standard deviation of wind speed at 10m height: minute standard deviation of wind speed at 10m height: σσUU•• Turbulence intensity: Turbulence intensity: σσUU / U/ U1010

•• The assumption of stationary wind conditions during the 10 minutes is not The assumption of stationary wind conditions during the 10 minutes is not always valid (for example, wind gusts induced by front passages and always valid (for example, wind gusts induced by front passages and unstable weather conditions, tropical storms, etc).unstable weather conditions, tropical storms, etc).

Wind Speed StatisticsWind Speed Statistics


•• For design, the wind climate database for computing For design, the wind climate database for computing UU10 10 and and σσUU should should preferably cover a 10preferably cover a 10‐‐year period or more of continuous data with a year period or more of continuous data with a sufficient time resolution.sufficient time resolution.

•• Wind speed measured at heights different than 10m should be converted Wind speed measured at heights different than 10m should be converted p g ffp g ffusing either local data if they exist or by means of fitting profiles (to be using either local data if they exist or by means of fitting profiles (to be presented later).presented later).

•• If wind data are scarce and uncertain, and wind velocity measurements can If wind data are scarce and uncertain, and wind velocity measurements can not be carried out, then a reliable not be carried out, then a reliable hindcasthindcast wind model should be validated wind model should be validated and used.and used.

Mean Wind SpeedMean Wind Speed


Mean wind speed is usually obtained by one of the following sampling Mean wind speed is usually obtained by one of the following sampling schemes:schemes:

•• A A UU10 10 value is computed for every 10value is computed for every 10‐‐minute period consecutively, i.e., six minute period consecutively, i.e., six (6) values are obtained every hour or 144 values per day.(6) values are obtained every hour or 144 values per day.

•• A A UU1010 value is computed for one 10value is computed for one 10‐‐minute period every hour, i.e., 24 values minute period every hour, i.e., 24 values 10 10 p fp f p y , ,p y , ,per day.per day.

•• A A UU10 10 value is computed for one 10value is computed for one 10‐‐minute period every three hours, i.e., 8 minute period every three hours, i.e., 8 values per day.values per day.

Regardless of the sampling method, the collected Regardless of the sampling method, the collected UU10 10 values, obtained over values, obtained over a time span of several years, are used to compute the cumulative a time span of several years, are used to compute the cumulative probability function probability function FFU10U10(U)(U)..

Mean Wind SpeedMean Wind Speed


•• Unless the data set of Unless the data set of UU10 10 values indicates otherwise, a values indicates otherwise, a WeibullWeibulldistribution can be assumed for the cumulative probability distribution can be assumed for the cumulative probability (πιθανότητα (πιθανότητα εμφάνισης) εμφάνισης) function at a given heightfunction at a given height

( )10 10 1 expk

UUF U UA

⎛ ⎞⎛ ⎞≤ = − −⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠•• where A is the scale parameter and k is the shape parameter, which are where A is the scale parameter and k is the shape parameter, which are

site and height dependent and are obtained by fitting of the data set site and height dependent and are obtained by fitting of the data set values.values.

( )10 10 pU A⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

•• Note that Note that ( )10 10 0.632UF U A≤ =

Mean Wind Speed: ExampleMean Wind Speed: Example


( )10 10 1 expk

UUF U UA

⎛ ⎞⎛ ⎞≤ = − −⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

Beaufort Speed

(m/s)

Frequency

(%)

Speed

(m/s)

Probability of exceedance

1-F

0 0 - 0.2 30.000 0.0 1.00000

1 0.3 - 1.5 8.286 0.3 0.70000A⎝ ⎠⎝ ⎠2 1.6 - 3.3 5.568 1.6 0.61714

3 3.4 -5.4 21.706 3.4 0.56146

4 5.5 - 7.9 17.259 5.5 0.34440

5 8.0 - 10.7 9.851 8.0 0.17181

6 10 8 -13 8 4.502 10.8 0.07330( )10 10 0.632UF U A≤ =

6 10.8 13.8 4.502 10.8 0.07330

7 13.9 - 17.1 1.959 13.9 0.02828

8 17.2 - 20.7 0.836 17.2 0.00869

9 20.8 - 24.4 0.033 20.8 0.00033

Mean Wind Speed: ExampleMean Wind Speed: Example


•• From the definition:From the definition: ( )10 10 0.632 5.272 m/sUF U A A≤ = ⇒ =

25

U10

(m/s

)

10

15

20

1 - FU10

10-4 10-3 10-2 10-1 1000

5

Datak=1.2k=1.3k=1.4

Extreme Mean Wind SpeedExtreme Mean Wind Speed


•• The distribution of the annual maximum 10The distribution of the annual maximum 10‐‐minute mean wind speed minute mean wind speed UU10,max 10,max can be approximated bycan be approximated by

( ) ( )( )10,max,1 10N

U yr UF U F U− =

where N=52560 is the number of 10where N=52560 is the number of 10‐‐minute periods in one year.minute periods in one year.

•• The above approximation gives good results for the prediction of rare The above approximation gives good results for the prediction of rare winds with return periods of 50 and 100 years, which are typical for the winds with return periods of 50 and 100 years, which are typical for the design of offshore wind turbines and platforms, respectively.design of offshore wind turbines and platforms, respectively.

•• The above approximation does not work for tropical storms where only The above approximation does not work for tropical storms where only actual storm data should be used.actual storm data should be used.

Extreme Mean Wind SpeedExtreme Mean Wind Speed•• For the prediction of rare winds, theFor the prediction of rare winds, the GumbelGumbel distributiondistribution


For the prediction of rare winds, the For the prediction of rare winds, the GumbelGumbel distributiondistribution

gives also good results and is more operational than the power law.gives also good results and is more operational than the power law.

( ) ( )( )( )10,max,1 exp expU yrF U a U b− = − − −

•• The 10The 10‐‐minute mean wind speed with a return period of Tminute mean wind speed with a return period of TRR in years isin years is

( )( ){

( ) ( )( )( )

10,max,1 10,

Gumbel

11

1 1

RU yr TR

F UT− = − ⇒

⎛ ⎞⎛ ⎞⎜ ⎟⎜ ⎟

i.e., it is the 10i.e., it is the 10‐‐minute mean wind speed whose probability of minute mean wind speed whose probability of exceedanceexceedance(πιθανότητα υπέρβασης) (πιθανότητα υπέρβασης) in one year is 1/ Tin one year is 1/ TRR ..

( ) ( )( )( )10,max,1 10, 10, 10,1 1exp exp ln ln 1

R R RU yr T T TR

F U a U b U ba T−

⎛ ⎞⎛ ⎞= − − − ⇒ = − − −⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

Extreme Mean Wind SpeedExtreme Mean Wind Speed•• The 50The 50‐‐year 10year 10‐‐minute mean wind speed isminute mean wind speed is


The 50The 50 year 10year 10 minute mean wind speed isminute mean wind speed is

•• The 100The 100‐‐year 10year 10‐‐minute mean wind speed isminute mean wind speed is

( )( )10,501 3.9ln ln 0.98yrU b ba a− = − − = +

yy pp

( )( )10,1001 4.6ln ln 0.99yrU b ba a− = − − = +

Extreme Mean Wind Speed: ExampleExtreme Mean Wind Speed: Example


•• From the definition:From the definition: ( ) ( )( )10,max,1 10N

U yr UF U F U− =

50( )110,50 10,max,1 0.98 41.9m/syr U yrU F −

− −= =

U10

(m/s

)

44

46

48

( )110,100 10,max,1 0.99 43.4m/syr U yrU F −

− −= =

FU10,max,1-yr

0.95 0.96 0.97 0.98 0.99 140

42

k=1.333.54m

G/s

0.4667umbel

ba=⎧

⎨ =⎩

Extreme Wind SpeedExtreme Wind Speed•• The 50The 50‐‐year extreme wind speed shall be calculated according to theyear extreme wind speed shall be calculated according to the


The 50The 50 year extreme wind speed shall be calculated according to the year extreme wind speed shall be calculated according to the Extreme Wind Model (EWM) of DNV (2010) asExtreme Wind Model (EWM) of DNV (2010) as

while the 1while the 1‐‐year (or annual) extreme wind speed shall be calculated asyear (or annual) extreme wind speed shall be calculated as

EWM,50 10,501.4yr yrU U− −= ⋅

y ( ) py ( ) p

•• Therefore, the annual 10Therefore, the annual 10‐‐minute mean wind speed shall be calculated asminute mean wind speed shall be calculated as

EWM,1 EWM,500.8yr yrU U− −= ⋅

10,1 10,500.8yr yrU U− −= ⋅

Extreme Wind Speed: ExampleExtreme Wind Speed: Example


m/s

100100‐‐year 10year 10‐‐minute mean wind speed minute mean wind speed U10,100-yr 43.40

5050‐‐year 10year 10‐‐minute mean wind speed minute mean wind speed U10 50-yr 41.90yy pp 10,50-yr

Annual 10Annual 10‐‐minute mean wind speed minute mean wind speed U10,1-yr 33.52

100100‐‐year extreme wind speedyear extreme wind speed UEWM,100-yr 60.76

5050‐‐year extreme wind speedyear extreme wind speed UEWM,50-yr 58.66

Annual extreme wind speed Annual extreme wind speed UEWM,1-yr 46.93

Wind Speed ProfilesWind Speed Profiles•• The most common wind speed profiles with respect to height above theThe most common wind speed profiles with respect to height above the


The most common wind speed profiles with respect to height above the The most common wind speed profiles with respect to height above the mean sea level (MSL) are the logarithmic, the power law and the mean sea level (MSL) are the logarithmic, the power law and the FrFroyaoyaprofiles.profiles.

•• The logarithmic profile isThe logarithmic profile is

where where κκ=0.40 is the von Karman constant, u* is the friction velocity, z=0.40 is the von Karman constant, u* is the friction velocity, z00 is the is the roughness height (0.0001m for open still sea and 0.01m for open sea or roughness height (0.0001m for open still sea and 0.01m for open sea or

( )0

* lnu zU zzκ

= ( )100

*ln /a a

a

u f U fH z

τ κρ

= = ⋅ ⇒ =

coastal area with waves), H=10m is the reference height, coastal area with waves), H=10m is the reference height, ττ is the shear is the shear stress on the sea surface, stress on the sea surface, ρραα=1.225 kg/m=1.225 kg/m33 is the air density and is the air density and ffaa is the is the friction coefficient.friction coefficient.

Wind Speed ProfilesWind Speed Profiles


•• The power law profile isThe power law profile is

( ) ( )azU z U H

H⎛ ⎞= ⎜ ⎟⎝ ⎠

where the exponent a=0.12where the exponent a=0.12‐‐0.14 for open seas with waves and H=10m is the 0.14 for open seas with waves and H=10m is the reference height.reference height.

Wind Speed ProfilesWind Speed Profiles


•• The The FroyaFroya wind profile (DNV 2010) iswind profile (DNV 2010) is

where Uwhere U00 is the 1is the 1‐‐hour mean wind speed, Thour mean wind speed, T00=1 hour, T<T=1 hour, T<T00,,

( ) ( )00

, 1 ln 1 0.41 lnUz TU T z U C I zH T

⎛ ⎞⎛ ⎞⎛ ⎞⎛ ⎞= + ⋅ − ⋅ ⋅⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠ ⎝ ⎠⎝ ⎠

00 p ,p , 00 ,, 00,,

( ) ( )

20

0.23

0

5.73 10 1 0.148

0.06 1 0.043U

C U

zI z UH

−

−

= ⋅ + ⋅

⎛ ⎞= ⋅ + ⋅ ⋅⎜ ⎟⎝ ⎠

•• The The FroyaFroya profile is recommended by DNV for extreme mean winds with profile is recommended by DNV for extreme mean winds with return periods of 50 years.return periods of 50 years.

•• It includes a gust factor, which allows for conversion between different It includes a gust factor, which allows for conversion between different averaging periods.averaging periods.

Wind TurbulenceWind Turbulence


•• Measurements indicate that Measurements indicate that σσUU is well represented by a standard is well represented by a standard Gaussian cumulative distribution function of the formGaussian cumulative distribution function of the form

( ) lnU

bFa

σσ

σ

σσ⎛ ⎞−

= Φ⎜ ⎟⎝ ⎠

where the coefficients awhere the coefficients aσσ andand bbσσ depend on Udepend on U1010 of the particular site.of the particular site.

σ⎝ ⎠

( ) 2 /212

xrx e dr

π−

−∞

Φ = ∫

•• Wind turbulence also depends strongly on surface roughness zWind turbulence also depends strongly on surface roughness z00..

Wind TurbulenceWind Turbulence


•• The following model is proposed (DNV 2010) for the mean value of The following model is proposed (DNV 2010) for the mean value of σσUUbased on the Gaussian cumulative distribution function and conditioned based on the Gaussian cumulative distribution function and conditioned on Uon U1010

( )2

10 01 1expU zb a U Aσ σσ κ⎛ ⎞= + =⎜ ⎟

⎝ ⎠

The mean lateral and vertical speeds are zero but the mean lateral and The mean lateral and vertical speeds are zero but the mean lateral and

( )10 00

p2 ln /U z z zσ σ⎜ ⎟

⎝ ⎠

0 0 02.4 or 4.5 0.856lnz zA A z≈ = −

vertical standard deviations of wind speed are not zero:vertical standard deviations of wind speed are not zero:•• Lateral = between Lateral = between 0.750.75σσUU and and 0.800.80σσUU•• Vertical = Vertical = 0.500.50σσUU

Wind Turbulence: ExampleWind Turbulence: Example


10⎧ ⎫0 10

0

10mFor 2.9 0.168

0.01m z U

zA U

zσ

=⎧ ⎫⇒ = ⇒ = ⋅⎨ ⎬=⎩ ⎭

m/s100100‐‐year 10year 10‐‐minute mean wind minute mean wind U10 100 yr 43.40yyspeed speed

10,100-yr

5050‐‐year 10year 10‐‐minute mean wind speed minute mean wind speed U10,50-yr 41.90Annual 10Annual 10‐‐minute mean wind speed minute mean wind speed U10,1-yr 33.52

σU,100-yr 7.29σU 50 7 04σU,50-yr 7.04σU,1-yr 5.63

Wind Speed SpectraWind Speed Spectra


•• Datasets of consecutive wind speed values are analyzed as timeDatasets of consecutive wind speed values are analyzed as time‐‐series series using a Fourier transform. using a Fourier transform.

•• Fourier transformFourier transform

( ) ( ) 2 ift∞

∫

where x(t) is the timewhere x(t) is the time‐‐series, X(f) is its Fourier transform, and f is the series, X(f) is its Fourier transform, and f is the frequency.frequency.

( ) ( ) 2 iftX f x t e dtπ−

−∞

= ∫

•• The power spectral density of the wind speed corresponds to the Fourier The power spectral density of the wind speed corresponds to the Fourier transform of the wind energy and it is called the wind spectrum.transform of the wind energy and it is called the wind spectrum.



•• Several model wind speed spectra exist based on the analysis of large Several model wind speed spectra exist based on the analysis of large datasets of wind speed time series. datasets of wind speed time series.

•• In the high frequency range, the spectrum should approach the followingIn the high frequency range, the spectrum should approach the following

2

where Lwhere LUU is the integral length scale of the wind speed process.is the integral length scale of the wind speed process.

( )2

532 3

10

0.14 UU U

LS f fU

σ−

−⎛ ⎞= ⋅ ⎜ ⎟

⎝ ⎠



•• The The KaimalKaimal spectrumspectrum

( ) 2 1053

6.868

1 10 32

U

U U

U

LUS fL f

σ=⎛ ⎞+⎜ ⎟

with low frequency bound of about 0.01 Hz, i.e., 2 minutes, and with low frequency bound of about 0.01 Hz, i.e., 2 minutes, and integral integral length scale length scale parameterparameter

10

1 10.32 fU

+⎜ ⎟⎝ ⎠

3.33 for 60mz zL

<⎧⎨

•• Nevertheless note that this is a spectrum based on studies over land.Nevertheless note that this is a spectrum based on studies over land.

200m for 60mULz

= ⎨ ≥⎩



•• The The KaimalKaimal spectrum forspectrum for

10

200m20m/s

ULU

=1.6

1.8

2

S(f)

0.6

0.8

1

1.2

1.4

f (Hz)10-4 10-3 10-2 10-1 100 1010

0.2

0.4

0.6



•• The The FroyaFroya spectrumspectrum

( )( )

2 0.450

53

10 103201

Un n

U z

S ff

⎛ ⎞ ⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠=

+( )

20.753

0

1

17210 10

f

U zf f−

+

⎛ ⎞ ⎛ ⎞= ⋅ ⋅ ⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

where n=0.468. where n=0.468.

•• Nevertheless note that this is a spectrum based on studies over water in Nevertheless note that this is a spectrum based on studies over water in the Norwegian Sea for neutral (i.e., not unstable) conditions.the Norwegian Sea for neutral (i.e., not unstable) conditions.

Extreme Operating GustExtreme Operating Gust


•• Especially for the design of wind turbines, the Extreme Operating Gust is Especially for the design of wind turbines, the Extreme Operating Gust is defined as defined as

( ) ,11 10 1

3.3min 1.35 , U yr

EWM h b h bV U Uσ −

⎧ ⎫⎪ ⎪⎪ ⎪= −⎨ ⎬

wherewhere•• ΛΛLL = L= LUU / 8.1 is the longitudinal scale of turbulence and is related to the / 8.1 is the longitudinal scale of turbulence and is related to the

integral scale parameter of the integral scale parameter of the KaimalKaimal spectral density.spectral density.

( ), ,1 10, ,1min 1.35 ,1 0.1

EWM hub yr hub yr

L

V U U D− −⎨ ⎬⎪ ⎪+

Λ⎪ ⎪⎩ ⎭

•• D is the rotor diameter.D is the rotor diameter.

7 1 1 Wind DIMAS-2 [Λειτουργία...

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