The Sandia method (also known as Veers method) is a method for generating a turbulent wind profile that can be used in aero-elastic software to evaluate the fatigue imparted on a turbine in a turbulent environment. That is, it generates time series of wind speeds at a set of points on a surface, say the plane of the rotor of a wind turbine. Analysis is performed initially in the frequency domain, where turbulence can be described quantitatively with more ease than the time domain. Then, the time series are obtained by inverse fast Fourier transforms. In its original form, the Sandia method only simulates the u-component of the wind; that is, the wind was modelled as propagating in a direction perpendicular to the plane of the rotor. Work carried out by NREL, specifically Kelley, suggested that a considerable amount of turbulent energy existed in the v-component (the v-component is parallel to both the plane of the rotor and the Earth). As such, the Sandia method was upgraded such that it included the v-component and w-component. Further upgrades have been performed such that the wind profile exhibits cross-axis correlation (turbulent fluctuations in one component being somehow connected to turbulent fluctuations in another). However, these are not considered in this article.
Point-wind speed spectra Although turbulence leads to unpredictable results in the time domain, it can, to some extent, be characterized in the frequency domain. Turbulent fluctuations are dominated by low frequency components, with higher frequency components having less influence. For further information, see Kolmogorov's theory on turbulence. Several models of frequency domain representations of point wind speeds have been developed: the von Kármán wind turbulence model and Dryden Wind Turbulence Model are examples of such.
Discretizing a spectrum A spectrum in its original form is a continuous function. However, computer programmes operate on discrete functions. Thus a modification to whatever type of spectrum, be it Kaimal, von Karman, or some other spectrum, is needed. This is given below:
S ( ω k ) = S ( ω = ω k ) Δ ω / 2 {\displaystyle S(\omega _{k})=S(\omega =\omega _{k})\Delta \omega /2}
where S ( ω k ) {\displaystyle S(\omega _{k})} is the discretized spectrum evaluated only at the discrete frequencies ω k {\displaystyle \omega _{k}} , S ( ω = ω k ) {\displaystyle S(\omega =\omega _{k})} is the continuous spectrum evaluated at ω = ω k {\displaystyle \omega =\omega _{k}} and Δ ω {\displaystyle \Delta \omega } is the size of the step between consecutive frequencies being considered.
Coherence When generating a time series of wind speeds for a set of points across a surface, coherence needs to be taken into account. That is, the instantaneous wind speed at some point, A, will bear some resemblance to the wind speed at some other point, B. Clearly, the resemblance is influenced by the separation of points A and B. That is, two points separated by a large distance will show less similarity to each other than two neighbouring points on the surface. In addition, one would expect low frequency components of the wind speeds at points A and B to show more correlation than high frequency components. As such, many coherence functions have been proposed: Davenport, Solari, etc. The Solari coherence spectrum is provided as an example:
C o h i j k = exp − 2 C Δ r i j ω k / ( u i + u j ) {\displaystyle Coh_{ijk}=\exp ^{-2C\Delta r_{ij}\omega _{k}/(u_{i}+u_{j})}}
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