A Framework for Modeling Wind-Farm Wake Turbulence from a Database for Simulation and Analysis

This paper presents a mathematical framework for constructing interpretive autospectral models of wind-farm wake turbulence from a database; these models are in closed form, and the database refers to flow velocity points from experimental - wind-tunnel and full-scale, and computational fluid dynamics, investigations. The framework begins with a perturbation series expansion of the autocorrelations for all three velocity components; therein, the first term has a form of the von Karman longitudinal or lateral correlation function. These series are then transformed into equivalent series of autospectra, and the coefficients of the series are evaluated by satisfying the theoretical constraints and fitting a curve on a set of selected autospectral data points. The framework ensures that the developed models and the corresponding autospectral data points have the same time scale, mean square value (energy) and autospectral asymptotic decay according to the Kolmogorov -5/3 law. It is tested against a demanding database of wake turbulence inside a wind farm over a complex terrain, and the developed models are further tested as to their suitability for routine simulation through white-noise-driven filters. Generally, a two-term series is found to be adequate and the filter design is as routine as the currently used procedure for the von Karman models. The framework can be applied to any database, and this model development from a database represents a new and promising research avenue.