A Comparison of Standard Coherence Models for Inflow Turbulence With Estimates from Field Measurements

Abstract

The Long-term Inflow and Structural Test (LIST) program, managed by Sandia National Laboratories, Albuquerque, NM, is gathering inflow and structural response data on a modified version of the Micon 65/13 wind turbine at a site near Bushland, Texas. With the objective of establishing correlations between structural response and inflow, previous studies have employed regression and other dependency analyses to attempt to relate loads to various inflow parameters. With these inflow parameters that may be thought of as single-point-in-space statistics that ignore the spatial nature of the inflow, no significant correlation was identified between load levels and any single inflow parameter or even any set of such parameters, beyond the mean and standard deviation of the hub-height horizontal wind speed. Accordingly, here, we examine spatial statistics in the measured inflow of the LIST turbine by estimating the coherence for the three turbulence components (along-wind, across-wind, and vertical). We examine coherence spectra for both lateral and vertical separations and use the available ten-minute time series of the three components at several locations. The data obtained from spatial arrays on three main towers located upwind from the test turbine as well as on two additional towers on either side of the main towers consist of 291 ten-minute records. Details regarding estimation of the coherence functions from limited data are discussed. Comparisons with standard coherence models available in the literature and provided in the International Electrotechnical Commission (IEC) guidelines are also discussed. It is found that the Davenport exponential coherence model may not be appropriate especially for modeling the coherence of the vertical turbulence component since it fails to account for reductions in coherence at low frequencies and over large separations. Results also show that the Mann uniform shear turbulence model predicts coherence spectra for all turbulence components and for different lateral separations better than the isotropic von Ka´rma´n model. Finally, on studying the cross-coherence among pairs of turbulence components based on field data, it is found that the coherence observed between along-wind and vertical turbulence components is not predicted by the isotropic von Ka´rma´n model while the Mann model appears to overestimate this cross-coherence.