ECN publication
Modelling the effect of wind farming on mesoscale flow - Part 2: Modification of the velocity profile
Published by: Publication date:
ECN Wind Energy 15-8-2008
ECN report number: Document type:
ECN-M--08-048 Conference Paper
Number of pages: Full text:
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Presented at: European Wind Energy Conference 2008, Brussels, Belgium, 31 maart 2008-3 april 2008.

This paper presents a new method for determining the interaction between a wind farm and the prevailing wind for wind energy siting studies plus first insights on the modification of the wind profile as obtained with this method. It is shown that neutral planetary boundary layer flow with wind farming essentially is steady and two-dimensional; and that the convective forces, the Coriolis forces and the vertical and spanwise gradients of the turbulent momentum fluxes all have the same order of magnitude. A numerical representation in the form of backward differences allows for an implicit solution of the two horizontal velocity components in vertical direction, iterating on the turbulent viscosity, in combination with a marching solution in the horizontal directions. The continuity equation is sat-isfied by employing the Lagrange multiplier method to the velocity components that satisfy the continuity equation. Resolved profiles show how most of the wind speed change occurs in the lower part of the boundary layer whereas most of the wind direction change occurs in the upper part, and that the thinner the boundary layer or the larger the surface roughness, the larger the wind direction change. Near a 5 MW wind turbine with a rotor diameter of 100 m operating at full load the ve-locity deficit is of the order of 5%, the wind direction change is increased with 1 ... 2 deg, and the velocity recovery distance is 20 rotor diameters. For a wind farm with 22 of these turbines these numbers are 15%, 2 ... 3 deg, and 2 wind farm length scales.

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