Verification of the 3-Component IEC-3 Kaimal Turbulence Model

A verification study was conducted for the Kaimal model and will be reported in the present article. Both spectra and coherence will be evaluated according to the procedure described in the data processing method. To assess the quality of the results, theoretical quantities of the Kaimal model in terms of the spectra and coherence are used as comparisons. The turbulent wind files were generated using Bladed version 4.16. The tests have been conducted for varying grid sizes and separation distances, see again the data processing method. Input parameters for the turbulence generation using the Kaimal model are given in the Table 1.

Table 1: Parameters used for testing the Kaimal turbulence model.

Parameter	Value
Decay Constant	12
Scale Parameter	340.2
Length Scales (\(^xL_u\), \(^xL_v\), \(^xL_w\))	340.2, 113.2, 27.72

Spectra

Figure 1 and Figure 2 illustrate comparisons of the theoretical Kaimal spectra with spectra extracted from Bladed 4.16. The calculations were done using two different grid resolutions, one being a squared grid (equispace) while the other is a non-squared grid. It can be seen from the figures that Bladed shows a good match with theoretical spectra and change of the grid size does not show a significant effect on the results. The spectra are captured from low to high frequency range, allowing the small scale turbulent eddies to be modelled appropriately. This shows that the Kaimal turbulence model in Bladed is a good representation of the turbulent flow field according to the Kaimal model with respect to spectra.

Figure 1: Comparison of the theoretical spectra of the Kaimal turbulence model against the spectra extracted from Bladed simulations. The calculations were done with a turbulence box having 51x51 grid points in lateral and vertical directions, respectively. Left: \(u\), middle: \(v\) and right: \(w\).

Figure 2: Comparison of the theoretical spectra of the Kaimal turbulence model against the spectra extracted from Bladed simulations. The calculations were done with a turbulence box having 51x26 grid points in lateral and vertical directions, respectively. Left: \(u\), middle: \(v\) and right: \(w\).

Coherence

Figure 3, Figure 4 and Figure 5 show comparisons of the theoretical Kaimal coherence with coherence extracted from Bladed 4.16. The calculations were done using two different grid resolutions, one being a squared grid (equispace) while the other is a non-squared grid. It is evident from Figure 3 to Figure 5 that Bladed demonstrates a good match with theoretical coherence. The separation distance has increased from 1 to 3 grid steps (see again the data processing method) between Figure 3 and Figure 5, yet this change does not impact the accuracy of the turbulent field to match the theoretical coherence. In a similar fashion, the grid resolution (51x51 in Figure 3 and 51x26 in Figure 4) also hardly affects the accurate representation of the theoretical quantity. This shows that the Kaimal turbulence model in Bladed is a good representation of the turbulent flow field according to the Kaimal model with respect to coherence.

Figure 3: Comparison of the theoretical coherence of the Kaimal turbulence model against the coherence extracted from Bladed simulations. The calculations were done with a turbulence box having 51x51 grid points in lateral and vertical directions, respectively. Separation distance \(r\) is equal to the adjacent grid point distance. Left: \(u\), middle: \(v\) and right: \(w\).

Figure 4: Comparison of the theoretical coherence of the Kaimal turbulence model against the coherence extracted from Bladed simulations. The calculations were done with a turbulence box having 51x51 grid points in lateral and vertical directions, respectively. Separation distance \(r\) is equal to three time the distance between adjacent grid points. Left: \(u\), middle: \(v\) and right: \(w\).

Figure 5: Comparison of the theoretical coherence of the Kaimal turbulence model against the coherence extracted from Bladed simulations. The calculations were done with a turbulence box having 51x26 grid points in lateral and vertical directions, respectively. Separation distance \(r\) is equal to the adjacent grid point distance (based on the vertical dimension with 26 grid points). Left: \(u\), middle: \(v\) and right: \(w\).

Last updated 17-07-2024