Verification of theoretically computed spectra for a point rotating in a vertical plane

Abstract

The ability to generate a model tubulent wind as it is seen by a rotating blade, independent of measurement, is important in wind turbine design and testing. A theoretical model of the spectrum of rotationally sampled wind speed developed at the Pacific Northwest Laboratory is tested against corresponding measured wind spectra. The measured spectra were selected from a number of cases measured with a vertical plane array of anemometers. The array was set up to correspond to the tip circle of a nearby MOD-OA wind turbine rotor blade. For purposes of testing and of illuminating the process, the turbulence and mean wind shear were treated separately. In each case the test was based on two criteria, each involving comparison of results from the theoretical model and results from real data analysis. These criteria were the rotational spectra and the integration of the spectra within each harmonic band into energy. Particularly the latter criterion was used. The measured spectra were selected to represent different atmospheric stability conditions. The theory is shown to achieve respectable accuracy readily except when applied to the stable atmosphere case. Recommendations are made for selection of the values of atmospheric parameters to be used for computing the theoretical result. The importance of the length of time of a measured turbulence record that is to be used in estimating several parameters for input to the theoretical model applied to real wind conditions at a selected turbine site is discussed. The VAX 11/780 computer time required to generate a model spectrum is usually less than one minute.