High Frequency Compensation - IEC Turbulence Simulator

[f.perrone2]

Hi everybody,

I would like to ask you what the high frequency compensation consists of, when I go generating wind fields with the Mann model.

I know that because of the discretization (especially in the L2 and L3 directions) there is a loss in the wind power spectrum in the area of high frequencies.

To recover this abrupt reduction, one way is to normalize the variance of each time series to 1 by means of a safety factor defined as the square root of the ratio between the target variance and the variance in the center of the simulation box. Then, this factor is to be applied to each of the time series.

Nevertheless, I was wondering is there is any other way to achieve a better track of the ideal power spectrum.

Any literary reference or hint will be welcome.

I thank you all in advance and look forward to hearing from you.

Best regards,
Francesco Perrone

[Morten]

Hi Francesco,


As you mention, the high-frequency variations of the simulated wind field are normally reduced by the dicretization filter. The purpose of the ‘high-frequency compensation’ is to avoid this effect. The help file section ‘WAsP Engineering modeling| turbulence| IEC turbulence simulator’ shows some spectra simulated with and without this option. High-frequency compensation is relevant if you prefer realistic variations at each node in the computational mesh. On the other hand, you should not use it if you prefer fluctuations averaged over each mesh cell.


High-frequency compensation will not normalize the spectra. In fact, most of the variance is associated with the energy at lower frequencies. The WEng simulations are like samples of a stochastic process. There will be random variations, but if you increase the duration of the sample or average multiple simulations you will approach the target spectral model. Normalization is often applied on wind fields fed to aeroelastic models. This is probably because the load simulations are done on relatively short time series.


The best reference to the simulation method is "Mann J. (1998), Wind field simulation, in Probabilistic Engineering Mechanics, Vol. 13 (4), page 269-282". In here, you can also find references to the spectral models by Kaimal, ESDU and Simiu & Scanlan.


Cheers,
Morten

[f.perrone2]

Hi Morten,

I thank you for the reference to Jakob Mann paper: I already read it more than once, but I did not find any hint on how to overcome or compensate for high frequency losses.

I was thinking of this method/procedure (which is physically meaningless): once you generate the time series, you estimate where the power spectrum certainly deviates from the ideal one; from that point you fit a polynomial curve through the simulated points and get the square root of the ratio spectrum_ideal/spectrum_sim. Applying this factor to the spetrum amplitudes, it should be possible to "stretch" the simulated spetrum in order to match the target one.

But maybe, in the IEC Turbulence Simulator, the high frequency loss are recovered by means of another method.

I was more interested on the compensating approach from a mathematical aspect.

I look forward to hearing from you again.

Kindet regards,
Francesco

[Morten]

Hi Francesco,


First I like to repeat that it is perfectly natural when spectra of simulated or measured times series derivate from those of the target process. This is a consequence of finite sampling time and time step.


There are alternative methods where you get exactly the spectra you prescribe. They operate with complex input variables of fixed amplitude and random phase, instead of the complex Gaussian variables used in the Mann model. The stretching correction you describe sounds a little like that. It would correct spectra and probably only slightly corrupt cross-spectra and probability distribution.


I don’t know exactly how the high frequency compensation is implemented. My guess is that Jacob Mann first analyze the smoothing effect theoretically, then apply a compensating correction to the target spectra, and finally simulate the wind field by the usual method.


With best regards,
Morten

[f.perrone2]

Hi Morten,

I warmly thank you for the support.

I was interested in understanding a bit more how the compensation works, and you fulfilled my need.

Kindest regards from Germany,
Francesco