A 3D wind simulator for estimates of extreme- and fatigue loads

Furthermore, the project collected information on extreme event probabilities and the probability distribution of measured turbulence. Results: Observed non-Gaussian velocities: Cup anemoneter data from two Bites (Lammefjord and Oak Creek) was analysed in order to determine probability density functions of v(t) = (u(t) -u_1_0_m_i_n/ u_1_0_m_i_n, where u(t) is made from data by applying a filter. The data showed no significant dependence of v(t) on u_1_0_m_i_n, which enables pooling of the data, thereby improving estimates. For small v the pdfs were observed to be close to Gaussian, but the tails of the distributions are very different and much closer to (double sided) exponentials than Gaussians. The same trend is observed for distributions of velocity differences, where it is even more pronounced. Cascading events in an unfiltered process: Basic theory has been developed, enabling the rate of events generated by a Gaussian simulator to be determined. The investigation shows that the events may occur in cascades if the definition of the event does not involve a low pass filter of order three or higher. It is argued that exactly this type of filtering is representative for the response of a regulated wind turbine Non-Gaussian extreme events: Event rates for dimensionless wind speed and dimensionless wind speed jump, both defined from properly filtered data, were also determined from data. The results show marked deviations from the theoretical prediction based on the assumption that the wind speed is a Gaussian process. In particular very high jumps are considerably more frequent than predicted from Gaussian theory, where the discrepancy amounts to several orders of magnitude. The Gaussian theory is therefore totally inadequate for the prediction of recurrence times for rare, and potentially damaging, events. Rice's exceedence theory works with modification: The data shows that event rates for events that involve small time scales are the most non-Gaussian. At the same time these show a simple exponential behaviour which, nonetheless, enables an extrapolation to events more rare than covered by the data at hand. Furthermore, the event rates are in all cases very nearly equal to 1/2P(v) . This is consistent with Rice's exact theoretical prediction if the assumption is made that v and dv/dt statistically independent. In order to make the extrapolation it therefore suffices to determine the pdf P(v) and . The same result applies to the variable #DELTA#v. Fronts passages: Examples of persistent and simultaneous changes of speed and wind direction were extracted form the database www.winddata.com. These special events cannot be modelled by a stationary process. Fourier simulation: Standard turbulence models often describe velocity fluctuations as a Gaussian process. This assumption implies that Fourier modes of a spectral representation are Gaussian and offers a simulation method based on the efficient FFT algorithm. The method may be extended in several ways, e.g. to multiple correlated time series or 3D fields of all velocity components. In either approach the target correlation between individual series of velocity components is achieved by 'square-root' decomposition of cross-spectral matrices. This soon becomes a considerable numerical task in the case of multiple series and several computational tricks were discussed. Non-Gaussian simulation: A simple simulation method for non-Gaussian processes is to simulate auxiliary Gaussian time series and transform these by monotonic function designed for a match with the target probability distributions. This operation alters spectra and correlation functions, and to compensate for this effect, the auxiliary processes are specified by distorted correlation functions, which are related to transformation functions of individual processes. The computational work of this operation is much eased when the mapping functions are expanded by Hermite polynormals. The simples version of this technique is called Winterstein's transformation, in which the transformation to non-Gaussianity is specified by a third-order polynormal designed to match the skewness and kurtosis of the target process. Also series of non-Gaussian time increments could be simulate by this method and integrated into processes, which due to the central limit theorem will be asymptotically Gaussian. Non-stationary simulation: Simulation of non-stationary processes with time-dependent probability distribution and correlation is feasible by Bezier interpolation between a set stationary simulations, produced by the same random seeds. Examples of non-stationary processes are turbulence in a front passage, turbulence near an undulating internal boundary layer, or velocities behind a wind turbine, where the unsteady wind directions tend to sweep the wake past a fixed observer. Conditional simulation: nother extension of Fourier simulation is the simulation of multiple correlated series given the measurements of a subset of these. In this way fixed data, e.g. from a mast at a site with unexpected turbulence features, could be used for simulation of turbulence on a rotor plane. Extreme event simulation: A method for simulation of extreme events has been developed. This is obtained by solution of a variational problem, in which the most probable adjustment of a simulated stationary Gaussian process, subject to relevant event conditions, is found. The event conditions are formulated as linear combination of points in the realization of the process. The extreme event generator is quite versatile and will generate gusts, velocity jumps, specified averages over finite periods, extreme velocity shears, sudden changes of wind direction, or similar events. Furthermore, it is compatible with Fourier simulation. The extreme event generator is generalized in various ways, i.e.: 1. Extreme events in multiple correlated processes. This is useful, e.g. for simulation of an extreme velocity shear and wind direction change. 2. Extreme events with multiple conditions. An example with an extreme value where the time derivative was exactly equal to zero was presented. The extra condition did, however, not affect the simulation much. 3. Extreme events in 3D turbulent fields. This was implemented similar to Mann's (1998) turbulence generator for anisotropic turbulence including the correlated response of all velocity components. Extreme event in non-Gaussian processes The extreme event generator was generalized for non-Gaussian processes subject to relatively simple conditions, i.e. gusts and velocity jumps. An additional generalization for gusts in multiple correlated non-Gaussian processes was suggested. The critical gust shape: The method may be used to detect the gust shape max response of a dynamic system, e.g. a turbine blade with pitch control. Possible use in forecasts problems: The extreme event generator might be generalized for forecasts or other problems, in which part of the process could be considered a (complicated) condition. It is, however, not yet known whether this would be a practical approach. Wavelet analysis: Gusts of a specified shape, similar to the 'Extreme Operational Gust' in the IEC 61400-1 design code, were detected by wavelet analysis and make extreme analysis of their recurrence rate. Wavelets might have been used for simulation, but this project preferred Fourier simulation. Deviation from the project plan: 1. Load simulations by an aeroelastic model using new methods for turbulence and extreme event simulation (phase four of the project plan) were not performed. 2. The extreme event simulation was made by another method than originally planned. The new method is more general and compatible with the generator of fatigue-load turbulence. 3. Simulation non-stationary turbulence was not planned. A potential application of this extended method is simulation of intermittent turbulence downwind a wind turbine caused by large-scale ambient turbulence sweeping the wake sidewards