Quasi-static response of a bottom-fixed wind turbine subject to various incident wind fields

In the design of offshore wind farms the simulated dynamic response of the wind turbine structure includes loading from turbulent wind. The International Electrotechnical Commission (IEC) standard for wind turbine design recommends both the Mann spectral tensor model and the Kaimal spectral model combined with an exponential coherence formulation. These models give deviating wind loads. This study compares these two models to a large eddy simulations model and a model based on offshore wind measurements. The comparisons are performed for three situations, covering unstable, neutral and stable atmospheric conditions. The impact of the differences in the wind fields on the quasi-static response of a large bottom-fixed wind turbine is investigated. The findings are supported by an assessment of the impact of individual wind characteristics on the turbine responses. The wind model based on measurements causes high tower bottom and blade root flapwise bending moments due to a high wind load at very low frequencies. Low and negative horizontal coherence is obtained using the Mann spectral tensor model. This causes relatively large yaw moments as compared to the results using the other wind models. The largest differences in response are seen in the stable situation. We furthermore show that the quasi-static wind load has great impact on the total damage equivalent moments of the structure. From the results, we conclude that in the design of large offshore wind turbines one should carefully consider the structure of the turbulent wind. Further, longer simulations than recommended by the standards should be used to reduce uncertainty in estimated response.publishedVersio

Processing of sonic anemometer measurements for offshore wind turbine applications

Quality assured measurements from offshore masts may provide valuable information of the characteristics of the offshore wind field, which is of high relevance for simulations of offshore wind turbines' dynamic response. In order to obtain these high quality data sets, a processing procedure tailored to offshore wind turbine applications must be followed. In this study, existing quality control routines applied in literature are evaluated, and a complete procedure is developed for sonic anemometer measurements. This processing procedure is applied to measurements at three heights from 16 months of measurements at FINO1. The processing procedure results in a data set of more than 6 000 30-minute periods of high quality time series showing a large variety in terms of wind speed and turbulence intensity. Together with an assessment of the stationarity, this processed data set is ready for use in offshore wind turbine research.publishedVersio

Sensitivity of the dynamic response of a multimegawatt floating wind turbine to the choice of turbulence model

In the design of offshore wind turbines, it is important to make a realistic estimate of the wind load. This is particularly important for floating wind turbines, having natural frequencies in a frequency range where the wind loads are high and large turbulent structures exist. This study shows that turbulence modelling greatly impacts the response of a 15-MW floating wind turbine. The turbulence models recommended by the International Electrotechnical Commission (IEC) are challenged by considering two additional models: Large Eddy Simulations (LES) and an approach using input from offshore wind measurements (TIMESR). The two standard models, the Kaimal spectrum with IEC coherence model (Kaimal) and the Mann spectral tensor model (Mann), differ in their coherence formulation. This results in higher standard deviations for the surge and pitch motions, and lower for the yaw motion, when applying Kaimal in comparison to Mann. For the specific floater of this study, more damage is obtained in the mooring lines when applying Kaimal. Applying the more realistic models, LES and TIMESR, increases the range of response further, concluding that the two standard turbulence models may lead to incorrect estimations of the response of a floating wind turbine. LES and TIMESR take atmospheric stability into account, which is proven to alter the response significantly.publishedVersio

Analysis of turbulence models fitted to site, and their impact on the response of a bottom-fixed wind turbine

This study compares a wind field recommended by the wind turbine design standards to more realistic wind fields based on measurements. The widely used Mann spectral tensor model with inputs recommended by the standard, is compared to FitMann, the Mann model with inputs fitted to measurements and TIMESR; using measured time series combined with the Davenport coherence model. The Mann model produces too low energy levels at the lowest frequencies of the wind spectra, while the wind spectra generated by FitMann approaches the measured values. TIMESR reproduces the measured spectral values at all frequencies. The different models give similar vertical coherence, while the Mann and FitMann models give lower horizontal coherence than TIMESR. Investigating the wind loads on a bottom-fixed 10-MW wind turbine, the spectra for the tower bottom fore-aft and blade root flapwise bending moment follow the shape of the wind spectra closely at low frequencies. The low-frequency range is important for the blade root and in particular the tower bottom bending moment. Thus, the TIMESR model, followed by FitMann, is assumed to give the most accurate fatigue estimates. For the specific situation analysed in this study, the FitMann model gives only 18 and 5 % lower estimates than TIMESR of the tower bottom and blade root damage equivalent bending moments, while the Mann model gives 27 % and 12 % lower estimates. The tower top yaw and fore-aft bending moments depend on the wind coherence. For the specific situation analysed in this study, the FitMann model gives 9 and 5 % higher estimates of the tower top yaw and tower top damage equivalent (bending) moments compared to TIMESR, while the Mann model gives 23 % and 18 % higher estimates. Since only measurements of the vertical coherence are available, it is not clear which model is superior for the tower top moments. However, the importance of a proper coherence model is documented.publishedVersio

The influence of contact modelling on simulated wheel/rail interaction due to wheel flats

Most available wheel/rail interaction models for the prediction of impact forces caused by wheel flats use a Hertzian spring as contact model and do not account for the changes in contact stiffness due to the real three-dimensional wheel flat geometry. In the literature, only little information is available on how this common simplification influences the calculation results. The aim of this paper is to study the influence of contact modelling on simulated impact forces due to wheel flats in order to determine the errors introduced by simplified approaches. For this purpose, the dynamic wheel/rail interaction is investigated with a time-domain model including a three-dimensional (3D) non-Hertzian contact model based on Kalker's variational method. The simulation results are compared with results obtained using a two-dimensional (2D) non-Hertzian contact model consisting of a Winkler bedding of independent springs or alternatively a single non-linear Hertzian contact spring. The relative displacement input to the Hertzian model is either the wheel profile deviation due to the wheel flat or the pre-calculated vertical wheel centre trajectory. Both the 2D model and the Hertzian spring with the wheel centre trajectory as input give rather similar results to the 3D model, the former having the tendency to slightly underestimate the maximum impact force and the latter to slightly overestimate. The Hertzian model with the wheel profile deviation as input can however lead to large errors in the result. Leaving aside this contact model, the correct modelling of the longitudinal geometry of the wheel flat is actually seen to have a larger influence on the maximum impact force than the choice of contact model

Simulation of rail roughness growth on small radius curves using a non-Hertzian and non-steady wheel–rail contact model

A time-domain model for the prediction of long-term growth of rail roughness (corrugation) on small radius curves is presented. Both low-frequency vehicle dynamics due to curving and high-frequency vehicle–track dynamics excited by short-wavelength rail irregularities are accounted for. The influence of non-Hertzian and non-steady effects in the wheel–rail contact model on rail wear is studied. The model features a contact detection method that accounts for wheelset yaw angle as well as surface irregularities and structural flexibilities of wheelset and rail. The development of corrugation on a small radius curve is found to be highly influenced by the wheel–rail friction coefficient. For vehicle speed 25 km/h and friction coefficient 0.3, predictions of long-term roughness growth on the low rail show decreasing magnitudes in the entire studied wavelength interval. For friction coefficient 0.6, roughness growth is found at several wavelengths. The corresponding calculation for the high rail contact of the trailing wheelset indicates no roughness growth independent of friction coefficient. The importance of accounting for the phase between the calculated wear and the present rail irregularity is demonstrated

Wheel–rail impact loads and axle bending stress simulated for generic distributions and shapes of discrete wheel tread damage

Wheel–rail impact loads generated by discrete wheel tread irregularities may result in high dynamic bending stresses in the wheelset axle, leading to a decrease in component life and an elevated risk for fatigue failure. In this paper, a versatile and cost-efficient method to simulate the vertical dynamic interaction between a wheelset and railway track, accounting for generic distributions and shapes of wheel tread damage, is presented. The wheelset (comprising two wheels, axle and any attached equipment for braking and power transmission) and track with two discretely supported rails are described by three-dimensional finite element (FE) models. The coupling between the two wheel‒rail contacts (one on each wheel) via the wheelset axle and via the sleepers is considered. The simulation of dynamic vehicle–track interaction is carried out in the time domain using a convolution integral approach, while the non-linear wheel–rail normal contact is solved using Kalker’s variational method. Wheelset designs that are non-symmetric with respect to the centre of the axle, track support conditions that are non-symmetric with respect to the centre of the track, as well as non-symmetric distributions of tread damage on the two wheels (or irregularities on the two rails) can be studied. Time-variant stresses are computed for the locations in the wheelset axle which are prone to fatigue. Based on Green’s functions for stress established using the wheelset FE model, this is achieved in a post-processing step. An extensive parametric study has been performed where wheel–rail impact loads and axle stresses have been computed for different distributions and sizes of tread damage as well as for different train speeds