Vertical wind extrapolation using the k-e turbulence model

Abstract

Vertical wind speed extrapolation is an important component of wind resource assessment where measured wind data at a reference height is extrapolated to hub height using the logarithmic or power law. Both models depend on roughness length but disregard information pertinent to topography. The log law results from the balance between turbulent kinetic energy (TKE) production and dissipation rate for fully developed flow over a horizontally homogeneous surface and is not generally valid. In search of a better extrapolation methodology, the k - E turbulence model is used to simulate measurements of boundary layer flows over hills and a step change in roughness accurately. By vertically integrating terms of the modeled TKE equation, a generalization of the log law was developed. The improved model includes a radius of curvature term and height for hills and a fetch length for the step change in roughness. It outperforms the log law for the cases tested.