Verification of the Mann Uniform Shear Turbulence Model

A verification study was conducted for the Mann 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 Mann 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 Mann model are given in the Table 1.

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

Parameter	Value
Shear parameter	3.9
Scale length	33.6
Maximum wavelength (lateral & vertical)	214.2
FFT points	128, 64 and 32

Spectra

Figure 1 and Figure 2 illustrate comparisons of the theoretical Mann 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. Overall, Bladed exhibits a strong agreement with theoretical results. However, in terms of the spectra, it becomes apparent that the turbulent model encounters some challenges in capturing higher frequency components. This is caused by the decay of the turbulence and is physically correct as the general behaviour of the Mann turbulence model, see again Mann. The higher frequency range capture depends strongly upon the FFT points being used in the calculations. Nonetheless, adjusting the grid size has minimal impact on the degree of alignment as demonstrated in Figure 1 and Figure 2. This shows that the Mann turbulence model in Bladed is a good representation of the turbulent flow field according to the theoretical Mann model with respect to spectra.

Figure 1: Comparison of the theoretical spectra of the Mann 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, and the FFT points were set to 128. Left: \(u\), middle: \(v\) and right: \(w\).

Figure 1: Comparison of the theoretical spectra of the Mann 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, and the FFT points were set to 128. Left: \(u\), middle: \(v\) and right: \(w\).

Coherence

Figure 3, Figure 4 and Figure 5 illustrate comparisons of the theoretical Mann 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. The separation distance has increased from 1 to 3 grid steps (see again the data processing method) between Figure 3 and Figure 4, 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 5) also hardly affects the accurate representation of the theoretical quantity. However, this depends on the FFT points being used in the calculations in relation with the determination of the grid number for the Mann uniform shear turbulence model. Overall, using the settings given in Table 1, Bladed results show that the theoretical coherence model according to Mann is well represented.

Figure 3: Comparison of the theoretical coherence of the Mann 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 distance between adjacent grid points. Left: \(u\), middle: \(v\) and right: \(w\).

Figure 4: Comparison of the theoretical coherence of the Mann 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 Mann 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 distance between adjacent grid points. Left: \(u\), middle: \(v\) and right: \(w\).

Last updated 17-07-2024