windspectrum#

S, f = windspectrum(U10, Sigma, L, CalcMethod, fmin, fmax, dispout)

Description#

Calculate wind spectrum with 513 frequencies

Inputs#

U10

Wind velocity at 10 m above surface in (m/s)

Sigma

Wind velocity standard deviation

IEC 61400-1:: Sigma_u=Sigma

Sigma_v=0.8*Sigma

Sigma_w=0.5*Sigma

L

Wind velocity integral length scale

Suggestion to calculate L (wind velocity integral length scale):

For Kaimal (1972) suggested by DNV-RP-C205 (2010):: L=300*(z/300)^(0.46+0.074*log(z0))
For Kaimal (1972) suggested by DNV-RP-C205 (2010) based on IEC 61400-1:: L=3.33*z for 0<z<=60

L=200 for z>=60
For Kaimal (1972) suggested by IEC 61400-1:: Lambda=0.7*z for for z<=60

Lambda=42 m for for z>60

Lu=8.1*Lambda

Lv=2.7*Lambda

Lw=0.66*Lambda
For Davenport (1961):: Lu=1200 m
For Harris (1971):: The same as the one for Kaimal (1972) suggested by DNV-RP-C205 (2010)
z: Height from surface in (m)
z0: Surface roughness

CalcMethod=’kaimal_dnv’

Wind spectrum calculation method
‘dnv’: DNV-RP-C205 (2010)
‘kaimal_dnv’: Kaimal (1972) suggested by DNV-RP-C205 (2010)
‘kaimal_iec’: Kaimal (1972) suggested by IEC 61400-1
‘davenport’: Davenport (1961)
‘harris’: Harris (1971)

fmin=0.002

Lower boundary of spectrum in (Hz)

fmax=0.3

Upper boundary of spectrum in (Hz)

Kaimal is valid in range from 0.002 Hz to 0.3 Hz (from 7.5 to 1000 cycles/hour)

dispout=’no’

Define to display outputs or not (‘yes’: display, ‘no’: not display)

Outputs#

S: Wind spectrum in ((m/s)^2/Hz)
f: Frequency in (Hz)

Examples#

import scientimate as sm

U10=15
Sigma=1
z=30
L=3.33*z
[S, f] = sm.windspectrum(U10, Sigma, L, 'kaimal_dnv', 0, 1, 'yes')

U10=15
Sigma=1
z=30
Lambda=0.7*z
L==8.1*Lambda
[S, f] = sm.windspectrum(U10, Sigma, L, 'kaimal_iec', 0, 1, 'yes')

References#

Bhattacharya, S. (2019). Design of foundations for offshore wind turbines. Wiley.

Bec, J. (2010). Influence of wind spectrum formula choice on footbridge response. In 5th international symposium on computational wind engineering (pp. 23-27).

Branlard, E. (2010). Generation of time series from a spectrum. Technical University Denmark. National Laboratory for Sustainable Energy.

Davenport, A. G. (1961). The spectrum of horizontal gustiness near the ground in high winds. Quarterly Journal of the Royal Meteorological Society, 87(372), 194-211.

Harris, R. I. The Nature of Wind, Proc. of the ModernDesign of Wind Sensitive Structures, Construction, Industry Research and Information Association, 1971, London, U. K

Kaimal, J. C., Wyngaard, J. C. J., Izumi, Y., & Coté, O. R. (1972). Spectral characteristics of surface‐layer turbulence. Quarterly Journal of the Royal Meteorological Society, 98(417), 563-589.

Rose, S., & Apt, J. (2012). Generating wind time series as a hybrid of measured and simulated data. Wind Energy, 15(5), 699-715.

Udoh, I. E., & Zou, J. (2018). Wind spectral characteristics on strength design of floating offshore wind turbines. Ocean Systems Engineering, 8(3), 281-312.

VERITAS, D. N. (2010). ENVIRONMENTAL CONDITIONS AND ENVIRONMENTAL LOADS.

https://www.mathworks.com/help/aeroblks/wind.html

https://www.mathworks.com/help/aeroblks/vonkarmanwindturbulencemodelcontinuous.html

windspectrum

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