The objectives of this work are multi-fold: first, to estimate the difference be- tween spatially- and temporally-disjunct wind speed measurements sampled by a ground-based pulsed LiDAR, an instantaneous snapshot of the flow and the temporal means over the time it takes to complete the 3D scan; second, to quantify how these differences affect wake characterization; finally, to apply wake characterization metrics [35] to LiDAR measurements. To our knowledge, this is the first work to provide a quantitative estimate of the uncertainty arising from these temporal limitations inherent in LiDAR measurements when large atmospheric volumes are probed. A simulated scanning LiDAR within an LES is used as the basis for this analysis, and we additionally provide a detailed methodology to derive cross-stream planes of wind turbine wakes at several
distances downstream from a stack of sector scans.
All of the analyses are based on transverse-vertical planes of horizontal wind at discrete distances downstream of a turbine and under single-wake condi- tions. Based on LES output, we determine that wind speeds sampled with the synthetic LiDAR are within ∼10% of the actual mean values and that the disjunct nature of the scan does not compromise the spatial variation of wind speed within the planes. The sampled points deviate more from the instanta- neous values closer to the turbine, with rms differences ∼13% when averaged over 80 sector scan stacks. Based on the LES synthetic scans, we show the scan- ning geometry coverage is very important to characterization of the wake cen- ter, orientation and length scales. Because of the radial symmetry in the mean vdfield, ample coverage of points is not required to obtain good estimates of the vd mean and standard deviation for which scanning geometry density is more important.
When the wake characterization metrics are applied to 59 3D scans obtained with a pulsed scanning LiDAR during a field experiment, the methods produce a consistent estimate of the wake center starting at 4 D, and the estimates for vertical and horizontal wake trajectory are robust between 4 and 7 D. Due to the scanning geometry limitations for this experiment, the wake length scales (i.e., width and height) are not well diagnosed and do not show a clear expan- sion with downstream distance. The characterization metrics can be applied to estimate the mean and standard deviation of the vd and, therefore, to quantify wake recovery. The consideration of the proposed indices to quantify scanning geometry density and coverage is recommended when planning a measurement campaign with a scanning LiDAR with the objective of characterizing wind tur-
bine wakes. Limiting the number of range gates and ensuring a good coverage of points in the vertical and horizontal directions is important to estimate wake length scales. Alternatively, higher density retrievals are necessary to estimate vd statistics. When focusing on the wake center, a compromise between cov- erage and density can be reached, and measurements can be made at a higher temporal frequency with a lower number of retrieved points. Finally, we recom- mend including periodic free stream measurements in the scanning geometry in order to minimize the uncertainty in vd quantification.
CHAPTER 6
ANALYSIS OF DIFFERENT GRAY ZONE TREATMENTS IN WRF-LES REAL CASE SIMULATIONS
6.1
Introduction
Recent advances in computational resources and atmospheric models have been driving the wind energy research community away from the Reynolds- Averaged Navier Stokes (RANS) approach, which does not permit a study of turbulence at the high Reynolds numbers that characterize flow within wind farms. Instead, research is increasingly based on Large-Eddy Simulations (LES) in which the horizontal grid size (∆xy) is reduced to a point where Navier Stokes
can be assumed to resolve all of the turbulence scales relevant to the problem at hand [102].
Due to their relatively high computational cost compared to RANS-based codes, LES have traditionally been used to examine ideal cases where a large number of assumptions simplify the problem sufficiently for computational tractability and physical understanding (e.g., [150, 44]). Thus far, real case (i.e., non-idealized) LES focusing on atmospheric phenomena at scales O102− 101
m have typically employed models that run un-coupled from the larger (meso and macro) scales (e.g., [151]) and for a time period on the order of hours (e.g., [152]) to days (e.g., [153]).
Recently, advances in computational resources have started to allow for cou- pling between meso and micro scale (i.e., LES-scale) models, and therefore for LES of the atmosphere under real-world scenarios. As a consequence, two
important questions have emerged. Firstly, how best to prescribe initial and boundary conditions to the LES and whether to allow feedback between the scales. Secondly, how best to treat the transition from meso to micro scales within numerical models [45]. The concept of “gray zone” (GZ) resolutions (i.e., O(102− 103)m) or “terra incognita” was coined to describe the spatial scales at
which NS is able to resolve a significant fraction of the kinetic energy in the atmospheric boundary layer (ABL), while still needing to model the remaining part with physical parameterizations [54], which are mathematical formulations derived from empirical data or from simplifications in theoretical concepts and included in global and mesoscale numerical models to account for SGS pro- cesses [56]. In other words, the GZ lies in between two extremes: the fully parameterized meso scale and the non-parameterized micro scale.
A lot of the recent work in meso-micro scale coupling has focused on the Weather Research and Forecasting (WRF) model [154], which is a widely used framework for idealized and real case mesoscale atmospheric simulations that can be run in LES mode by scaling∆xydown to the micro scale (i.e., O(102− 101)
m) and switching off several parameterizations. For example, [155] and [156] used ideal WRF-LES as benchmarks and developed scale-aware capabilities within existing ABL parameterizations (ABLP) to regulate their role at GZ res- olutions. So far, these and other ABLPs expanded to accommodate GZ resolu- tions are limited to convective boundary layers (CBLs) and have mostly been verified against reference idealized LES (e.g., [157, 156, 158, 159]).
Very little work has been done to understand the behavior of ABLPs at GZ resolutions under real case LES. [160] applied aircraft observations to evaluate simulations of stratocumulus formation under the proposed scale-aware modi-
fications to the Met Office Unified Model, while nesting domains from 4 km to 100 m and considering a period of 2 days. They found that the performance of the scale-aware ABLP at the gray zone matched the performance of the well- established one-dimensional large-scale ABLP used for coarser grids, and that of the three-dimensional small-scale parameterization typically used for micro scale grid sizes. Another study by [155] proposed a scale-aware ABLP in WRF and verified it for real cases considering 24 hours of data focusing on the de- velopment of a convective roll at ∆xy = 333 m. They found that the newly
proposed scheme enhanced the simulation of vertical motions under convec- tive conditions but highlighted the need for further improvements which will cover a wider range of simulation scenarios. A more comprehensive study was performed by [150], where the effect of modifications to the GALES model was assessed by comparing one year of simulation data at∆xy = 100 m to observa-
tions from a single meteorological mast. They found that the best agreement of simulations with observations occurred for ABL parameters that are explic- itly resolved (i.e., instead of parameterized) thus further highlighting the need for long-term real case LES and for further research in meso-micro scale model coupling.
The research presented herein adds to this limited body of work by evalu- ating different approaches for treating GZ resolutions in full-physics LES of the atmosphere that are coupled to the mesoscale. While focusing on flow param- eters of relevance to wind engineering, we quantify differences between three simulations in which the GZ is treated differently by being run with a well- established ABLP, its scale-aware version, and no ABLP at all (Section 6.4) and compare the simulation output to observational data collected during the Prince Edward Island Wind Energy Experiment [34] (Section 6.5). This specific loca-
tion was selected for our analysis because the terrain complexity and roughness changes warrant the use of LES. Moreover, the analysis considers a 15-day pe- riod which enables an assessment of the simulations performance under a wide range of atmospheric conditions.