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One‐way nested mesoscale to microscale simulations of an onshore wind farm have been performed nesting the Weather Research and Forecasting (WRF) model and our in‐house high‐resolution large‐eddy simulation code (UTD‐WF). Each simulation contains five nested WRF domains, with the largest domain spanning the north Texas Panhandle region with a 4 km resolution, while the highest resolution (50 m) nest simulates microscale wind fluctuations and turbine wakes within a single wind farm. The finest WRF domain in turn drives the UTD‐WF LES higher‐resolution domain for a subset of six turbines at a resolution of ∼5 m. The wind speed, direction, and boundary layer profiles from WRF are compared against measurements obtained with a met‐tower and a scanning Doppler wind LiDAR located within the wind farm. Additionally, power production obtained from WRF and UTD‐WF are assessed against supervisory control and data acquisition (SCADA) system data. Numerical results agree well with the experimental measurements of the wind speed, direction, and power production of the turbines. UTD‐WF high‐resolution domain improves significantly the agreement of the turbulence intensity at the turbines location compared with that of WRF. Velocity spectra have been computed to assess how the nesting allows resolving a wide range of scales at a reasonable computational cost. A domain sensitivity analysis has been performed. Velocity spectra indicate that placing the inlet too close to the first row of turbines results in an unrealistic peak of energy at the rotational frequency of the turbines. Spectra of the power production of a single turbine and of the cumulative power of the array have been compared with analytical models.

 

Recent works on wall-bounded flows have corroborated the coexistence of wall-attached eddies, whose statistical features are predicted through Townsend's attached-eddy hypothesis (AEH), and very-large-scale motions (VLSMs). Furthermore, it has been shown that the presence of wall-attached eddies within the logarithmic layer is linked to the appearance of an inverse-power-law region in the streamwise velocity energy spectra, upon significant separation between outer and viscous scales. In this work, a near-neutral atmospheric surface layer is probed with wind light detection and ranging to investigate the contributions to the streamwise velocity energy associated with wall-attached eddies and VLSMs for a very-high-Reynolds-number boundary layer. Energy and linear coherence spectra (LCS) of the streamwise velocity are interrogated to identify the spectral boundaries associated with eddies of different typologies. Inspired by the AEH, an analytical model for the LCS associated with wall-attached eddies is formulated. The experimental results show that the identification of the wall-attached-eddy energy contribution through the analysis of the energy spectra leads to an underestimate of the associated spectral range, maximum height attained and turbulence intensity. This feature is due to the overlap of the energy associated with VLSMs obscuring the inverse-power-law region. The LCS analysis estimates wall-attached eddies with a streamwise/wall-normal ratio of about 14.3 attaining a height of about 30 % of the outer scale of turbulence.

 

Next-generation models of wind farm flows are increasingly needed to assist the design, operation, and performance diagnostic of modern wind power plants. Accuracy in the descriptions of the wind farm aerodynamics, including the effects of atmospheric stability, coalescing wakes, and the pressure field induced by the turbine rotors are necessary attributes for such tools as well as low computational costs. The Pseudo-2D RANS model is formulated to provide an efficient solution of the Navier–Stokes equations governing wind-farm flows installed in flat terrain and offshore. The turbulence closure and actuator disk model are calibrated based on wind light detection and ranging measurements of wind turbine wakes collected under different operative and atmospheric conditions. A shallow-water formulation is implemented to achieve a converged solution for the velocity and pressure fields across a farm with computational costs comparable to those of mid-fidelity engineering wake models. The theoretical foundations and numerical scheme of the Pseudo-2D RANS model are provided, together with a detailed description of the verification and validation processes. The model is assessed against a large dataset of power production for an onshore wind farm located in North Texas showing a normalized mean absolute error of 5.6% on the 10-min-averaged active power and 3% on the clustered wind farm efficiency, which represent 8% and 24%, respectively, improvements with respect to the best-performing engineering wake model tested in this work. 

Light detection and ranging (LiDAR) measurements of isolated wakes generated by wind turbines installed at an onshore wind farm are leveraged to characterize the variability of the wake mean velocity and turbulence intensity during typical operations, which encompass a breadth of atmospheric stability regimes and rotor thrust coefficients. The LiDAR measurements are clustered through the k-means algorithm, which enables identifying the most representative realizations of wind turbine wakes while avoiding the imposition of thresholds for the various wind and turbine parameters. Considering the large number of LiDAR samples collected to probe the wake velocity field, the dimensionality of the experimental dataset is reduced by projecting the LiDAR data on an intelligently truncated basis obtained with the proper orthogonal decomposition (POD). The coefficients of only five physics-informed POD modes are then injected in the k-means algorithm for clustering the LiDAR dataset. The analysis of the clustered LiDAR data and the associated supervisory control and data acquisition and meteorological data enables the study of the variability of the wake velocity deficit, wake extent, and wake-added turbulence intensity for different thrust coefficients of the turbine rotor and regimes of atmospheric stability. Furthermore, the cluster analysis of the LiDAR data allows for the identification of systematic off-design operations with a certain yaw misalignment of the turbine rotor with the mean wind direction. 

A LiDAR Statistical Barnes Objective Analysis (LiSBOA) for the optimal design of lidar scans and retrieval of the velocity statistical moments is proposed. LiSBOA represents an adaptation of the classical Barnes scheme for the statistical analysis of unstructured experimental data in N-dimensional space, and it is a suitable technique for the evaluation over a structured Cartesian grid of the statistics of scalar fields sampled through scanning lidars. LiSBOA is validated and characterized via a Monte Carlo approach applied to a synthetic velocity field. This revisited theoretical framework for the Barnes objective analysis enables the formulation of guidelines for the optimal design of lidar experiments and efficient application of LiSBOA for the postprocessing of lidar measurements. The optimal design of lidar scans is formulated as a two-cost-function optimization problem, including the minimization of the percentage of the measurement volume not sampled with adequate spatial resolution and the minimization of the error on the mean of the velocity field. The optimal design of the lidar scans also guides the selection of the smoothing parameter and the total number of iterations to use for the Barnes scheme. LiSBOA is assessed against a numerical data set generated using the virtual lidar technique applied to the data obtained from a large eddy simulation (LES). The optimal sampling parameters for a scanning Doppler pulsed wind lidar are retrieved through LiSBOA, and then the estimated statistics are compared with those of the original LES data set, showing a maximum error of about 4 % for both mean velocity and turbulence intensity. 

Continuous advancements in LiDAR technology have enabled compelling wind turbulence measurements within the atmospheric boundary layer with range gates shorter than 20 m and sampling frequency of the order of 10 Hz. However, estimates of the radial velocity from the back-scattered laser beam are inevitably affected by an averaging process within each range gate, generally modeled as a convolution between the actual velocity projected along the LiDAR line-of-sight and a weighting function representing the energy distribution of the laser pulse along the range gate. As a result, the spectral energy of the turbulent velocity fluctuations is damped within the inertial sub-range with respective reduction of the velocity variance, and, thus, not allowing to take advantage of the achieved spatio-temporal resolution of the LiDAR technology. In this article, we propose to correct this turbulent energy damping on the LiDAR measurements by reversing the effect of a low-pass filter, which can be estimated directly from the LiDAR measurements. LiDAR data acquired from three different field campaigns are analyzed to describe the proposed technique, investigate the variability of the filter parameters and, for one dataset, assess the procedure for spectral LiDAR correction against sonic anemometer data. It is found that the order of the low-pass filter used for modeling the energy damping on the LiDAR velocity measurements has negligible effects on the correction of the second-order statistics of the wind velocity. In contrast, its cutoff frequency plays a significant role in the spectral correction encompassing the smoothing effects connected with the LiDAR gate length. 

Wind turbine wakes are responsible for power losses and added fatigue loads of wind turbines. Providing capabilities to predict accurately wind-turbine wakes for different atmospheric conditions and turbine settings with low computational requirements is crucial for the optimization of wind-farm layout, and for improving wind-turbine controls aiming to increase annual energy production (AEP) and reduce the levelized cost of energy (LCOE) for wind power plants. In this work, wake measurements collected with a scanning Doppler wind Li- DAR for broad ranges of the atmospheric static stability regime and incoming wind speed are processed through K-means clustering. For computational feasibility, the cluster analysis is performed on a low-dimensional embedding of the collected data, which is obtained through proper orthogonal decomposition (POD). After data compression, we perform K-means of the POD modes to identify cluster centers and corresponding members from the LiDAR data. The different cluster centers allow us to visualize wake variability over ranges of atmospheric, wind, and turbine parameters. The results show that accurate mapping of the wake variability can be achieved with K-means clustering, which represents an initial step to develop data-driven wake models for accurate and low-computational-cost simulations of wind farms. 

Abstract. The LiDAR Statistical Barnes Objective Analysis (LiSBOA), presented in Letizia et al. (2021), is a procedure for the optimal design of lidar scans and calculations over a Cartesian grid of the statistical moments of the velocity field. Lidar data collected during a field campaign conducted at a wind farm in complex terrain are analyzed through LiSBOA for two different tests. For both case studies, LiSBOA is leveraged for the optimization of the azimuthal step of the lidar and the retrieval of the mean equivalent velocity and turbulence intensity fields. In the first case, the wake velocity statistics of four utility-scale turbines are reconstructed on a 3D grid, showing LiSBOA's ability to capture complex flow features, such as high-speed jets around the nacelle and the wake turbulent-shear layers. For the second case, the statistics of the wakes generated by four interacting turbines are calculated over a 2D Cartesian grid and compared to the measurements provided by the nacelle-mounted anemometers. Maximum discrepancies, as low as 3 % for the mean velocity (with respect to the free stream velocity) and turbulence intensity (in absolute terms), endorse the application of LiSBOA for lidar-based wind resource assessment and diagnostic surveys for wind farms.