Abstract. We show that the upscaling of wind turbines from rotor diameters of 15–20 m to presently large rotors of 150–200 m has changed the requirements for the aerodynamic blade element momentum (BEM) models in the aeroelastic codes. This is because the typical scales in the inflow turbulence are now comparable with the rotor diameter of the large turbines. Therefore, the spectrum of the incoming turbulence relative to the rotating blade has increased energy content on 1P, 2P, …, nP, and the annular mean induction approach in a classical BEM implementation might no longer be a good approximation for large rotors. We present a complete BEM implementation on a polar grid that models the induction response to the considerable 1P, 2P, …, nP inflow variations, including models for yawed inflow, dynamic inflow and radial induction. At each time step, in an aeroelastic simulation, the induction derived from a local BEM approach is updated at all the stationary grid points covering the swept area so the model can be characterized as an engineering actuator disk (AD) solution. The induction at each grid point varies slowly in time due to the dynamic inflow filter but the rotating blade now samples the induction field; as a result, the induction seen from the blade is highly unsteady and has a spectrum with distinct 1P, 2P, …, nP peaks. The load impact mechanism from this unsteady induction is analyzed and it is found that the load impact strongly depends on the turbine design and operating conditions. For operation at low to medium thrust coefficients (conventional turbines at above rated wind speed or low induction turbines in the whole operating range), it is found that the grid BEM gives typically 8 %–10 % lower 1 Hz blade root flapwise fatigue loads than the classical annular mean BEM approach. At high thrust coefficients that can occur at low wind speeds, the grid BEM can give slightly increased fatigue loads. In the paper, the implementation of the grid-based BEM is described in detail, and finally several validation cases are presented. Comparisons with blade loads from full rotor CFD, wind tunnel experiments and a field experiment show that the model can predict the aerodynamic forces in half-wake, yawed flow, dynamic inflow and turbulent inflow conditions.
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Abstract. This paper presents the integration of a near-wake model for trailing vorticity, which is based on a prescribed-wake lifting-line model proposed by Beddoes (1987), with a blade element momentum (BEM)-based far-wake model and a 2-D shed vorticity model. The resulting coupled aerodynamics model is validated against lifting-surface computations performed using a free-wake panel code. The focus of the description of the aerodynamics model is on the numerical stability, the computation speed and the accuracy of unsteady simulations. To stabilize the near-wake model, it has to be iterated to convergence, using a relaxation factor that has to be updated during the computation. Further, the effect of simplifying the exponential function approximation of the near-wake model to increase the computation speed is investigated in this work. A modification of the dynamic inflow weighting factors of the far-wake model is presented that ensures good induction modeling at slow timescales. Finally, the unsteady airfoil aerodynamics model is extended to provide the unsteady bound circulation for the near-wake model and to improve the modeling of the unsteady behavior of cambered airfoils. The model comparison with results from a free-wake panel code and a BEM model is centered around the NREL 5 MW reference turbine. The response to pitch steps at different pitching speeds is compared. By means of prescribed vibration cases, the effect of the aerodynamic model on the predictions of the aerodynamic work is investigated. The validation shows that a BEM model can be improved by adding near-wake trailed vorticity computation. For all prescribed vibration cases with high aerodynamic damping, results similar to those obtained by the free-wake model can be achieved in a small fraction of computation time with the proposed model. In the cases with low aerodynamic damping, the addition of trailed vorticity modeling shifts the results closer to those obtained by using the free-wake code, but differences remain.
Regional estimation of extreme precipitation from a high resolution rain gauge network in Denmark is considered. The applied extreme value model is based on the partial duration series (PDS) approach in which all events above a certain threshold level are modelled. For a preliminary assessment of regional homogeneity and identification of a proper regional distribution L-moment analysis is applied. To analyse the regional variability in more detail, a generalised least squares regression analysis is carried out that relates the PDS model parameters to climatic and physiographic characteristics. The analysis reveals that the mean annual number of extreme events varies significantly within the region, and a large part of this variability can be explained by the mean annual rainfall. The mean value of the exceedance magnitudes can be assumed constant for intensities with durations less than one hour. For larger durations a pronounced metropolitan effect is evident, the mean intensities in the Copenhagen area being significantly larger than found in the rest of the country. With respect to second and higher order moments the region can be considered homogeneous for intensities with durations less than 24 hours. A regional parent distribution is identified as the generalised Pareto distribution.
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