Probabilistic estimation of the Dynamic Wake Meandering model parameters using SpinnerLidar-derived wake characteristics

As the major part of new wind turbines are installed in clusters or wind farms, there is a strong need for reliable and accurate tools for predicting the increased loadings due to wake operation and the associated reduced power production. The dynamic wake meandering (DWM) model has been developed on this background, and the basic physical mechanisms in the wake—i.e., the velocity deficit, the meandering of the deficit, and the added turbulence—are modeled as simply as possible in order to make fast computations. In the present paper, the DWM model is presented in a version suitable for full integration in an aeroelastic model. Calibration and validation of the different parts of the model is carried out by comparisons with actuator disk and actuator line (ACL) computations as well as with inflow measurements on a full-scale 2 MW turbine. It is shown that the load generating part of the increased turbulence in the wake is due almost exclusively to meandering of the velocity deficit, which causes “apparent” turbulence when measuring the flow in a fixed point in the wake. Added turbulence, originating mainly from breakdown of tip vortices and from the shear of the velocity deficit, has only a minor contribution to the total turbulence and with a small length scale in the range of 10–25% of the ambient turbulence length scale. Comparisons of the calibrated DWM model with ACL results for different downstream positions and ambient turbulence levels show good correlation for both wake deficits and turbulence levels. Finally, added turbulence characteristics are compared with correlation results from literature.

Abstract. The outlined analysis validates the dynamic wake meandering (DWM) model based on loads and power production measured at an onshore wind farm with small turbine distances. Special focus is given to the performance of a version of the DWM model that was previously recalibrated at the site. The recalibration is based on measurements from a turbine nacelle-mounted lidar system. The different versions of the DWM model are compared to the commonly used Frandsen wake-added turbulence model. The results of the recalibrated wake model agree very well with the measurements, whereas the Frandsen model overestimates the loads drastically for short turbine distances. Furthermore, lidar measurements of the wind speed deficit as well as the wake meandering are incorporated in the DWM model definition in order to decrease the uncertainties.

The work presented in this paper focuses on improving the description of wake evolution due to turbulent mixing in the dynamic wake meandering (DWM) model. From wake investigations performed with high-fidelity actuator line simulations carried out in ELLIPSYS3D, it is seen that the current DWM description, where the eddy viscosity is assumed to be constant in each cross-section of the wake, is insufficient. Instead, a two-dimensional eddy viscosity formulation is proposed to model the shear layer generated turbulence in the wake, based on the classical mixing length model. The performance of the modified DWM model is verified by comparing the mean wake velocity distribution with a set of ELLIPSYS3D actuator line calculations. The standard error (defined as the standard deviation of the difference between the mean velocity field of the DWM and the actuator line model), in the wake region extending from 3 to 12 diameters behind the rotor, is reduced by 27% by using the new eddy viscosity formulation.

Abstract. Light detection and ranging (lidar) systems have gained a great importance in today's wake characteristic measurements. The aim of this measurement campaign is to track the wake meandering and in a further step to validate the wind speed deficit in the meandering frame of reference (MFR) and in the fixed frame of reference using nacelle-mounted lidar measurements. Additionally, a comparison of the measured and the modeled wake degradation in the MFR was conducted. The simulations were done with two different versions of the dynamic wake meandering (DWM) model. These versions differ only in the description of the quasi-steady wake deficit. Based on the findings from the lidar measurements, the impact of the ambient turbulence intensity on the eddy viscosity definition in the quasi-steady deficit has been investigated and, subsequently, an improved correlation function has been determined, resulting in very good conformity between the new model and the measurements.

Most of the global dynamic response models used today for the design of wind turbines are based on the aero-hydro-servo-elastic analysis of one single turbine. However, research on bottom- fixed offshore wind turbines has shown that interactions among turbines in a farm influence both the power production and the structural loading. Furthermore, floating wind turbines (FWTs) are sensitive to low-frequency variations, and therefore to wake meandering perturbations. In the current work, we use the Dynamic Wake Meandering (DWM) model as implemented in DIWA and FAST.Farm, to study the low-frequency content of the meandering at a target turbine placed 8 diameters downstream. At frequencies in the range of the natural frequencies of rigid body motions of semisubmersible floaters, the two models yield different results. These differences are seen for every wind speed and wind turbine model, even though they decrease as the wind speed increases. The observed differences may affect low-frequency motions and consequently mooring system design.

<strong class="journal-contentHeaderColor">Abstract.</strong> With the increasing growth of wind farm installations, the impact of wake effects from wind turbines on power output, structural loads, and revenue has become a major concern. Hence, there is a need for precise simulation tools to facilitate efficient and cost-effective design and operation of wind farms. To address this need, we present HAWC2Farm, a dynamic and versatile aeroelastic wind farm simulation methodology that combines state-of-the-art engineering models to accurately capture the complex physical phenomena in wind farms. HAWC2Farm models each turbine in a wind farm using the aeroelastic turbine simulator, HAWC2, while sharing a large, high-resolution turbulence box to model atmospheric flow field effects at the farm level, and a modified Dynamic Wake Meandering (DWM) model for capturing wake interactions. The method is computationally efficient and provides valuable insights for wind farm design. It is validated using time series field measurements from the Lillgrund wind farm, including scenarios with yaw steering and a turbine shutdown. HAWC2Farm addresses the challenges of modelling the complex dynamics in wind farms, enabling more accurate, informed and cost-effective design and operation.

In the present paper, single-wake dynamics have been studied both experimentally and numerically. The use of pulsed lidar measurements allows for validation of basic dynamic wake meandering modeling assumptions. Wake center tracking is used to estimate the wake advection velocity experimentally and to obtain an estimate of the wake expansion in a fixed frame of reference. A comparison shows good agreement between the measured average expansion and the Computational Fluid Dynamics (CFD) large eddy simulation–actuator line computations. Frandsen's expansion model seems to predict the wake expansion fairly well in the far wake but lacks accuracy in the outer region of the near wake. An empirical relationship, relating maximum wake induction and wake advection velocity, is derived and linked to the characteristics of a spherical vortex structure. Furthermore, a new empirical model for single-wake expansion is proposed based on an initial wake expansion in the pressure-driven flow regime and a spatial gradient computed from the large-scale lateral velocities, and thus inspired by the basic assumption behind the dynamic wake meandering model. Copyright © 2014 John Wiley & Sons, Ltd.

The IEC standards describe how to measure the power performance of an isolated wake-free wind turbine. However, most wind turbines operate under waked conditions for a substantial amount of time, calling for the need of a new methodology for power performance evaluation. We define multivariate power curves in the form of multivariate polynomial regressions, whose input variables are several wind speed and turbulence measurements retrieved with nacelle lidars. We use a dataset of synthetic power performance tests including both waked and wake-free conditions. The dataset is generated through aeroelastic simulations combined with both virtual nacelle lidars and the dynamic wake meandering model. A feature-selection algorithm is used to select the input variables among the available measurements, showing that the optimal model includes four input variables: three correspondent to wind speed and one to turbulence measures. Additionally, we give insights on the optimal nacelle-lidar scanning geometry needed to implement the multivariate power curve. Results show that the multivariate power curves predict the power output with accuracy of the same order under both waked and wake-free operation. For the in-wake cases, the accuracy is much higher than that of the IEC standard power curve, with an error reduction of up to 88%.

FAST.Farm is a newly developed multiphysics, midfidelity engineering tool that can be used to predict turbine power and structural loads of wind turbines in a wind farm with minimal computational expense. Previous studies have shown similarities and differences in wind turbine performance between FAST.Farm and high-fidelity large-eddy simulations (LES) using both LES precursor-generated inflow and TurbSim-generated synthetic inflow. While conservative resolutions have been used to date, no formal spatial or temporal discretization study has been performed for the FAST.Farm model wind domains. This work aims to study the effects of varying the spatial and temporal discretization of the wind domains on wake meandering (low-resolution domain) and turbine structural response (high-resolution domains) and resulting wake and load calculations. The purpose of this study is to establish convergence criteria and recommendations for discretization values in terms of rotor diameter (D, expressed in meters) that will maximize computational efficiency. To ensure a percent error of ≤ 1% in standard deviation of wake center position relative to the finest included resolution, a low-resolution time step of 0.024D s, 0.016D s, and 0.0079D s and a low-resolution spatial discretization of 0.079D m, 0.16D m, and 0.24D m is recommended for 8 m/s, 12 m/s, and 18 m/s mean ambient wind speed at hub height, respectively. These guidelines are likely applicable to other implementations of the dynamic wake meandering model. To ensure a percent error of ≤ 1% in standard deviation of all considered structural response outputs, a high-resolution time step that captures the highest influential excitation and natural frequencies in the system and a high-resolution spatial discretization comparable to the maximum airfoil cord length is recommended. These guidelines are likely applicable to any aeroelastic analysis.

The aim of this paper is to verify that a modeling approach affordable at wind farm scale, in this case a fourth-order finite differences code combined with a rotating actuator disk, provides equivalent results in terms of wake meandering compared to a method with a higher fidelity level, i.e. a Vortex Particle-Mesh Method combined with immersed lifting lines. The analysis is performed on the wake centerlines obtained from Large Eddy Simulations of an isolated NREL 5-MW wind turbine subject to several synthetic turbulent inflows: 6%, 10%, and 15% turbulence intensity. A direct comparison of the wake centerlines reveals a good match between the two approaches up to five rotor diameters. Concerning the amplitude and wavelength of the wake meandering, the lower fidelity code leads to larger amplitudes and shorter wavelengths. Assuming that Taylor’s frozen turbulence hypothesis is applicable, the Strouhal number St is computed as the ratio between the rotor diameter and the wavelength. Obtained values are such that 0.22 ⩽ St ⩽ 0.4.

Multi-model predictive control for wind turbine operation under meandering wake of upstream turbines

A nacelle‐mounted lidar system pointing downstream has been used to measure wind turbine wake dynamics. The new measurement and data analysis techniques allow estimation of quasi‐instantaneous wind fields in planes perpendicular to the rotor axis. A newly developed wake tracking procedure delivers the instantaneous transversal wake position which is quantitatively compared with the prediction of the Dynamic Wake Meandering model. The results, shown for two 10‐min time series, suggest that the conjecture of the wake behaving as a passive tracer is a fair approximation; this corroborates and expands the results of one‐dimensional measurements already presented in the first part of this paper. Consequently, it is now possible to separate the deterministic and turbulent parts of the wake wind field, thus enabling capturing the wake in the meandering frame of reference. The results correspond, qualitatively and to some extent quantitatively, to the expectations from CFD simulations which are compared in the paper. Copyright © 2010 John Wiley &amp; Sons, Ltd.

Abstract. A new theoretical framework, based on an analysis in the moving and fixed frames of reference (MFOR and FFOR), is proposed to break down the velocity and turbulence fields in the wake of a wind turbine. This approach adds theoretical support to models based on the dynamic wake meandering (DWM) and opens the way for a fully analytical and physically based model of the wake that takes meandering and atmospheric stability into account, which is developed in the companion paper. The mean velocity and turbulence in the FFOR are broken down into different terms, which are functions of the velocity and turbulence in the MFOR. These terms can be regrouped as pure terms and cross terms. In the DWM, the former group is modelled, and the latter is implicitly neglected. The shape and relative importance of the different terms are estimated with the large-eddy-simulation solver Meso-NH coupled with an actuator line method. A single wind turbine wake is simulated on flat terrain, under three cases of stability: neutral, unstable and stable. In the velocity breakdown, the cross term is found to be relatively low. It is not the case for the turbulence breakdown equation where even though the cross terms are overall of lesser magnitude than the pure terms, they redistribute the turbulence and induce a non-negligible asymmetry. These findings underline the limitations of models that assume a steady velocity in the MFOR, such as the DWM or the model developed in the companion paper. It is also found that as atmospheric stability increases, the pure turbulence contribution becomes relatively larger and pure meandering relatively smaller.

Componentwise influence of upstream turbulence on the far-wake dynamics of wind turbines

This paper describes the development of a wind turbine (WT) component lifetime fatigue load variation map within an offshore wind farm. A case study on the offshore wind farm Horns Rev I is conducted with this purpose, by quantifying wake effects using the Dynamic Wake Meandering (DWM) method, which has previously been validated based on CFD, Lidar and full scale load measurements. Fully coupled aeroelastic load simulations using turbulent wind conditions are conducted for all wind directions and mean wind speeds between cut-in and cut-out using site specific turbulence level measurements. Based on the mean wind speed and direction distribution, the representative 20-year lifetime fatigue loads are calculated. It is found that the heaviest loaded WT is not the same when looking at blade root, tower top or tower base components. The blade loads are mainly dominated by the wake situations above rated wind speed and the highest loaded blades are in the easternmost row as the dominating wind direction is from West. Regarding the tower components, the highest loaded WTs are also located towards the eastern central location. The turbines with highest power production are, not surprisingly, the ones facing a free sector towards west and south. The power production results of few turbines are compared with SCADA data. The results of this paper are expected to have significance for operation and maintenance planning, where the schedules for inspection and service activities can be adjusted to the requirements arising from the varying fatigue levels. Furthermore, the results can be used in the context of remaining fatigue lifetime assessment and planning of decommissioning.