The sensitivities of idealized large-eddy simulations (LESs) to variations of model configuration and forcing parameters on quantities of interest to wind power applications are examined. Simulated wind speed, turbulent fluxes, spectra and cospectra are assessed in relation to variations in two physical factors, geostrophic wind speed and surface roughness length, and several model configuration choices, including mesh size and grid aspect ratio, turbulence model, and numerical discretization schemes, in three different code bases. Two case studies representing nearly steady neutral and convective atmospheric boundary layer (ABL) flow conditions over nearly flat and homogeneous terrain were used to force and assess idealized LESs, using periodic lateral boundary conditions. Comparison with fast-response velocity measurements at 10 heights within the lowest 100 m indicates that most model configurations performed similarly overall, with differences between observed and predicted wind speed generally smaller than measurement variability. Simulations of convective conditions produced turbulence quantities and spectra that matched the observations well, while those of neutral simulations produced good predictions of stress, but smaller than observed magnitudes of turbulence kinetic energy, likely due to tower wakes influencing the measurements. While sensitivities to model configuration choices and variability in forcing can be considerable, idealized LESs are shown to reliably reproduce quantities of interest to wind energy applications within the lower ABL during quasi-ideal, nearly steady neutral and convective conditions over nearly flat and homogeneous terrain.
Accurate characterization and prediction of the microscale wind flow environment plays an important role in many facets of wind power generation, including wind park siting, layout, operations, and the formulation of turbine design standards (e.g., Shaw et al., 2009). While wind power generation has grown tremendously over the last few decades, both turbine reliability and plant power generation frequently underperform projections based on existing turbine design standards and site assessments (e.g., Bailey, 2013). A key contributor to these underperformance issues is the disconnect between the data and models used in turbine and plant design and site assessment, and actual characteristics of the atmospheric boundary layer (ABL), and the in situ wind plant operating environment. Realistic ABL flows under routine atmospheric conditions often include much higher levels of atmospheric turbulence, shear, veer, and other important transient phenomena than are typically captured in measurements or design tools.
Characterization of the wind plant operating environment has historically relied chiefly on observations, typically utilizing a small number of slow-response instruments, augmented occasionally by fast-response instruments capable of accurately characterizing turbulence (Magnusson and Smedman, 1994; Barthelmie et al., 2010). While remote sensing instruments (e.g., Högström et al., 1988; Barthelmie et al., 2003; Nygaard, 2011; Hirth et al., 2012; Rhodes and Lundquist, 2013; Smalikho et al., 2013; Iungo et al., 2013) provide one pathway to improve site characterization, the absence of fast-response turbulence information and limited sampling volumes provided by many systems, coupled with long deployments required to sample long-term variability, constrain the utility of observations for many applications.
Compounding the inadequacies of many observational datasets are the generally lower-fidelity numerical simulation approaches used in conjunction with observations to inform various stages of turbine and plant design and operation. While higher-fidelity simulation techniques exist, their significant computational overhead has precluded widespread adoption due to the limited computational infrastructure generally available to industry (Sanderse et al., 2011; Troldborg et al., 2011).
The increasing availability of high-performance computing infrastructure is enabling more widespread use of high-fidelity numerical techniques, such as the turbulence-resolving large-eddy simulation (LES), to significantly improve understanding of the ABL and wind plant flows. While not yet considered as reliable as established observational and computational approaches, high-fidelity numerical simulations can potentially provide superior site characterization and design data to reduce costs, including (1) flow information over an entire wind farm across many levels within the turbine span, (2) simulation over a distribution of characteristic flow regimes in a short time period, and (3) estimates of flow parameters that are difficult or expensive to observe (e.g., turbulence).
While atmospheric LES is increasingly being utilized to simulate turbulent flows for wind energy applications (Sim et al., 2009; Lu and Porté-Agel, 2011; Bhaganagar and Debnath, 2014; Mehta et al., 2014; Mirocha et al., 2014a; Aitken et al., 2014), by focusing primarily on turbine wakes in quasi-ideal meteorological conditions, these studies have addressed only a limited range of atmospheric conditions and parameters of relevance to industry. Development of atmospheric LES for general meteorological and surface conditions is ongoing; however, this extension relies upon the development of novel forcing treatments both within the computational domain and at the lateral boundaries (e.g., Mirocha et al., 2014a; Muñoz-Esparza et al., 2014, 2015), where assumptions of periodicity and standard approaches for specifying turbulent inflow conditions, such as recycling methods (e.g., Lund et al., 1998; Mayor et al., 2002), precursor simulations (e.g., Churchfield et al., 2012; Mirocha et al., 2014b), or synthetic turbulence generators (e.g., Veers, 1988; Jonkman and Buhl, 2005; Xie and Castro, 2008) are not applicable.
Irrespective of the complexity of the setup, high-fidelity atmospheric LES will require both thorough validation of simulated quantities of interest, and formal assessment of uncertainties, prior to widespread adoption within the wind power industry. To satisfy these requirements, the Atmosphere to Electrons (A2e) initiative within the US Department of Energy's Wind Energy Technologies Office is supporting development and validation of next-generation computational approaches for wind energy applications. This is being undertaken via both assessment of existing simulation approaches, such as idealized LES, and development of new mesoscale–microscale coupling (MMC) methods, as required for extension to more general environments and forcing conditions.
The present study, conducted under the auspices of the A2e MMC project, examines the efficacy of idealized atmospheric LES using periodic lateral boundary conditions (LBCs), an approach commonly applied in fundamental and applied ABL studies (see e.g. Deardorff, 1970, 1980; Moeng, 1984; Kosović and Curry, 2000), to provide flow parameters of interest to wind energy applications. The present study is unique in its focus on the representation of the accuracy of the simulated flow, rather than on turbine interactions, including detailed comparison of simulated and observed turbulence information, including spectra and cospectra. Moreover, we investigate this capability using a computational framework that is both relatively mature and reasonably economical, in comparison with more general yet also more complicated and expensive methods, such as those incorporating time-varying mesoscale input via additional internal forcing terms (e.g. Sanz Rodrigo et al., 2017) or at the lateral domain boundaries (e.g. Muñoz-Esparza et al., 2017; Rai et al., 2017a, b). Finally, an examination of uncertainties provides a required basis for assessment of both existing idealized simulation capabilities, as well as of more sophisticated MMC techniques under development, to the wind energy arena. Section 2 describes the case studies, code bases, boundary conditions, turbulence models, and variations employed to assess uncertainty, Sect. 3 presents simulation results and uncertainty analysis, and Sect. 4 provides a summary and conclusions.
Rather than focusing on turbine response and wake characteristics, as most studies of atmospheric LES targeting wind energy applications have, we instead focus on the accuracy of the resolved atmospheric flow field itself, including profiles of wind speed and direction, turbulence kinetic energy (TKE), turbulent fluxes, and spectra and cospectra. Also included is assessment of simulation uncertainties, undertaken by varying common numerical methods, turbulence models, and setup approaches, using three simulation codes. The simulations are assessed against one another, theoretical expectations, and observations taken from two case studies featuring quasi-ideal ABL flow during nearly steady neutral and convective conditions over nearly flat and homogeneous terrain. The use of quasi-ideal conditions simplifies the attribution of sensitivities to changes of various configuration and forcing parameters representing common simulation setups.
The Sandia National Laboratories Scaled Wind Farm Technology (SWiFT) test
facility, located in the US Southern Great Plains, was selected for the
study, due to its nearly flat terrain and homogeneous surface cover,
permitting reasonable approximation in idealized computational setups. These setups
consist of flat terrain with uniform surface characteristics and forcing
conditions, as well as periodic LBCs. Data used to force and evaluate the
simulations were obtained from two instrument platforms, a 200 m
instrumented meteorological tower, and a radio acoustic sounding system
(RASS), each located at the neighboring Texas Tech University's National Wind
Institute. The tower provided fast-response data at 10 heights between 0.9
and 200 m from which turbulence and mean flow data were computed, while the
RASS data provided an assessment of the prevailing meteorology, as well as
estimates of a common parameter used to force atmospheric LES, the
geostrophic wind speed,
To satisfy conditions under which idealized forcing is appropriate, data were
examined for case studies encompassing canonical ABL regimes occurring during
convective, neutral, and stable conditions. Criteria for case selection
included nearly constant values of wind speed, wind direction, and
Several periods approximating quasi-canonical convective ABL conditions were found within the observational data, with the most ideal, occurring during the apex of solar heating during the early afternoon of the 4 July 2012, selected for the convective case study. In contrast, canonical neutral conditions occurred relatively infrequently, and for much shorter durations, during evening and morning transitions. As transitional boundary layers contain the imprint of preceding stable or convective forcing, many of the candidate neutral periods showed strong influence from prior states and thus were not considered. Furthermore, sonic anemometers on the meteorological tower are mounted on the booms pointing in the west-northwest direction while the dominant wind direction at the SWiFT tower is southerly. As such, most of the candidate neutral cases occurred during times at which the instruments were somewhat influenced by the tower wake. With respect to these constraints, the optimal neutral case study occurred during the evening transition of the 17 August 2012.
While stable conditions are of high importance for wind energy, the combination of difficulties in specifying proper forcing (to capture the correct evolution of the nocturnal low-level jet) and the high computational demands imposed by the fine mesh resolutions required to capture sustained turbulence during moderately stable nocturnal conditions precluded inclusion of a stable case study in the present study.
Three code bases representing standard approaches to ABL simulation are examined.
The Weather Research and Forecasting (WRF) model (Skamarock et al., 2008) is a community atmospheric simulation framework that supports applications ranging from global to micro scales, including LES, with several subfilter scale (SFS) models available. WRF uses finite differencing to solve the compressible Euler equations, using a split time stepping algorithm within the Runge–Kutta time integration scheme, and a filter for acoustic modes. Advective discretization options include second- through fifth-order in the horizontal and second- or third-order in the vertical.
The WRF model uses a Cartesian mesh, with variables specified on an Arakawa “C” grid. Vertical spacing is specified using a terrain-following pressure-based eta coordinate.
At the model top, WRF imposes free slip for
The Simulator fOr Wind Farm Applications (SOWFA) (Churchfield et al., 2012)
is a collection of flow solvers, turbulence SFS parameterizations, boundary
conditions, and utilities for computing wind plant flows. SOWFA is built upon
the Open-source Field Operations And Manipulations (OpenFOAM) CFD Toolbox
(OpenFOAM,
The High Gradient applications (HiGrad) model (Sauer et al., 2016) discretizes the fully compressible, nonhydrostatic Euler equations using the finite-volume technique, on an Arakawa “A” grid. A variety of even- and odd-order advection schemes (first- to fifth-order accurate), as well as two LES SFS models, are available. A third-order explicit Runge–Kutta time-marching method is used in the present study.
For all simulations, the surface boundary condition is
Four SFS parameterizations were used in the sensitivity analysis (more complete descriptions are available in the references).
The Smagorinsky closure (SMAG) (Smagorinsky, 1963; Lilly, 1967) parameterizes
the SFS stresses as
Scalar fluxes are given by
The Lilly model (Lilly) (Lilly, 1967) is similar to the Smagorinsky closure,
but uses
The nonlinear backscatter and anisotropy (NBA) model (Kosović, 1997)
includes both a linear eddy viscosity component, similar to SMAG and LILLY
(but with different values for the constants), and a second term containing
nonlinear products of strain rate and rotation rate tensors. The NBA model
can be formulated exclusively in terms of velocity gradients or also using
Simulations utilized domains of 2.4 km
While SOWFA and HiGrad use height as the vertical coordinate, WRF's use of a
pressure-based coordinate precludes exact specification of heights above the
surface; therefore, the heights of the pressure levels are initialized using
the hypsometric equation,
Each simulation utilized damping in the upper portion of the model domain to
prevent wave reflection at the model top. WRF utilized Rayleigh damping,
which nudges the horizontal wind components toward their geostrophic values,
with a coefficient value of 0.003 s
Simulations were initialized with thermodynamic variables approximating
observations during the two case studies described previously. Initial
horizontal wind components were
For these idealized simulations, which were based upon case studies with no precipitation, and little cloudiness or synoptic-scale weather variability, the simulations were initialized dry, and the only physical process parameterizations utilized were SFS turbulence fluxes, with surface sensible heat and stresses as described in Sect. 2.3.
Due to the initial flow field being nonturbulent and not in balance with the
applied geostrophic forcing, a spin-up period was required for the flow
statistics to approach nearly steady values. During neutral conditions, the
spin-up period is longer, due to the weak turbulence forcing, and the existence
of an inertial oscillation with a period of several hours (at the specified
latitude of 33.5
For the convective case study, which requires much shorter spin-up due to strong buoyant forcing dominating turbulence and ABL characteristics, the model solutions were compared after 1 h.
Comparisons of instantaneous horizontal wind speed [m s
Sensitivities of the simulations to variability in model forcing, numerical
methods, configuration, and turbulence SFS models were obtained from a suite
of simulations using different values of relevant parameters. Sensitivity to
forcing was examined by varying
While forcing and configuration parameters could be varied within all code
bases, not all codes supported multiple options for all parameters. The
sensitivity experiments therefore involved changes both across and within the
different codes. Due to the large number of parameters, assessing the impacts
of each independently was infeasible. Instead, forcing, configuration,
numerics, and SFS turbulence options were combined into a large yet feasible
suite of simulations listed in Tables 1–2 (the
Forcing and configuration parameters for the neutral-case sensitivity studies, using WRF (W), SOWFA (S), and HiGrad (H), as described in the text.
Forcing and configuration parameters for the convective-case sensitivity studies, using WRF (W), SOWFA (S), and HiGrad (H), as described in the text.
Comparisons of instantaneous horizontal wind speed [m s
First, high-level results from the sensitivity simulations are shown to indicate some key differences between the case studies and solvers. A more detailed comparison of various flow parameters from the simulations is provided in Sect. 3.2.
Figure 1 shows instantaneous horizontal wind speed in both
Comparisons of instantaneous potential temperature [K] from the
unstable case study, at 100 m above the surface
While differences among the solutions are apparent, all three solvers show similar characteristic turbulence structures, namely the elongated low-speed streamwise structures, a range of sizes of turbulence structures, diminishing with increasing proximity to the surface, and similar ABL heights, due to the capping inversion.
Figure 2 shows the impacts of increasing both the grid resolution and the
accuracy of the advective operators within the same solver, in this case
HiGrad, on instantaneous wind speed, in the same two planes as Fig. 1. The
grid spacing was decreased by a factor of two in all directions, while
Comparison of instantaneous potential temperature in the convective
case at 100 m above the surface
Figure 3 shows instantaneous cross sections of potential temperature in both
the
Inspection of Fig. 3 reveals qualitative similarities in resolved flow characteristics, including the shapes and sizes of the turbulent structures in both cross sections. However, the WRF simulations exhibit less fine-scale structure than the others, despite the use of higher resolution in the vertical direction, and higher-order advection operators, indicating that horizontal resolution is the dominant factor influencing the size distribution of resolved scales, within the examined range of parameter values. The slightly higher temperatures within the WRF ABL (Fig. 3) are most likely artifacts of the Rayleigh damping imposed above the ABL, which relaxes temperature back to its initial value beginning at the ABL top. WRF also generates a slightly deeper ABL, likely due to a combination of higher vertical resolution and a warmer ABL, the latter slightly reducing the relative strength of the capping inversion. HiGrad produces the shallowest ABL, despite using the same resolution as SOWFA, likely due to its use of an odd-order advection operator, which being more dispersive than SOWFA's even-order operator, slightly reduces TKE (see Fig. 16a).
Figure 4 isolates the impact of changing only the mesh resolution (by a factor of three in each direction) within the same solver (WRF) while leaving all other settings constant. Instantaneous cross sections in the same two planes as shown in Fig. 4, from the coarse-resolution (left) and fine-resolution (right) simulations, show that while both resolutions capture the same morphological characteristic, most notably quasi-cellular convective cells of similar sizes and magnitudes, an increased range of scales of motion are captured with the finer-resolution LES.
Simulated profiles of time-averaged wind speed plotted against
observations
The ABLs and simulations thereof comprising this study are approximately horizontally homogeneous; therefore averaging over horizontal planes could be applied for assessment. However, considering that future planned studies will involve heterogeneous boundary layers under time-varying forcing, temporal averaging and spectral analysis in the frequency domain is instead utilized. Simulation results therefore consist of a single vertical profile located near the center of the computational domain, which is output every second (1 Hz) during the time window of analysis.
As described in Sect. 2.1, the evening transition of the 17 August 2012 provided the best approximation to canonical near neutral ABL conditions within the observational dataset; however, subsequent detailed analysis of TKE measured with sonic anemometers at the SWiFT tower showed that the instruments were partially in the wake of the tower. This resulted in larger measured TKE values than what would be expected in unobstructed flow under the same conditions. As the tower cross section and lattice structure comprise length scales much smaller than the characteristic production scales of turbulence for the considered ABL types, most of the covariance, arising primarily from the largest eddies, is hypothesized to have been only minimally impacted by the tower. Therefore, while preventing a detailed comparison of TKE, other parameters not strongly impacted by the quasi-random perturbations created by tower interactions, such as turbulent stresses and velocity spectra and cospectra, were compared qualitatively. Mean wind speed and direction profiles, which showed no evidence of tower wake influence, were compared quantitatively.
Figure 5 shows time-averaged profiles of wind speed from simulations using
all three solver bases, compared against both measurements at the SWiFT tower
(left), and to the theoretical logarithmic profiles in the surface layer
(right). Measurement variability is shown as “uncertainty” bars that
signify one standard deviation from a mean value computed as a 90 min time
average. All simulations use the Lilly SFS model and the highest-order
advection option available. Two different grid setups were used, with
horizontal and vertical grid sizes of 25 and 7.5 m for WRF, resulting in
Despite the use of different numerical and grid specifications, all simulations produced generally good agreement with measurements, falling within measurement variability. The measured wind speed profile does not increase monotonically with height, as would be expected in canonical ABL flow, indicating the presence of height-dependent transient processes and forcings. Considering that such processes cannot be captured with idealized forcing and simulation setups, the agreement between the model output and the data can be considered to be quite good. The logarithmic profile in the surface layer is also captured well, despite the known tendency of the Lilly SFS parameterization to overpredict nondimensional shear relative to a logarithmic profile in the surface layer of a neutral ABL (Brasseur and Wei, 2010; Mirocha et al., 2010).
Impacts of different solvers, all using isotropic grids of 15 m in
each direction, on simulated profiles of time-averaged wind speed plotted
against observations
Impacts of different advection schemes within the HiGrad model, on
simulated profiles of time-averaged wind speed plotted against observations
Figure 6 compares simulated wind speed profiles using the three models, all with isotropic grid formulations, while also showing the impact of using two different SFS parameterizations in WRF, Lilly, and NBA-TKE. Again, results are generally similar, with HiGrad showing slightly slower wind speeds above 50 m, slightly closer to the mean of the observations, than SOWFA and WRF. All models reproduce logarithmic near-surface shear profiles reasonably well (Fig. 6b).
The impact of different advection operators was also analyzed. Here, only
results from HiGrad and WRF are presented, as SOWFA includes only one
advection option. Figure 7 shows results from HiGrad with
The relative performances of various configurations are assessed quantitatively using the mean absolute error (MAE), root mean square error (RMSE), and vertical shear, computed across two different depths. Tower MAE and RMSE were computed across all heights on the tower spanned by the model mesh (no extrapolation to tower values below the lowest model height), by interpolating model values to the sensor heights using cubic splines. Rotor MAE and shear were computed analogously over a depth of 40 to 140 m, corresponding to the swept area of a representative modern utility-scale wind turbine with a 100 m rotor diameter and a hub height of 90 m. Wind profile characteristics within and across the rotor swept area are relevant to both power production and fatigue loading.
Impacts of varying advection schemes and SFS models in WRF, on
simulated profiles of time-averaged wind speed plotted against observations
Table 3 shows the impact of varying the order of the advective operators within the HiGrad model on each of the above statistics, indicating that changes to this configuration choice result in generally small changes in velocity profile characteristics across both the tower and the rotor, with neither the higher- nor lower-order results notably superior overall.
Analysis of HiGrad performance using different advection schemes with the Lilly SFS parameterization.
Similar analysis was performed using the WRF model varying the order of the
advection scheme and the SFS parameterizations, as summarized in Tables 4 and
5. Here,
Impacts of varying surface roughness length and geostrophic wind
speed using HiGrad
As numerical simulations of homogeneous boundary layers generally represent ideal conditions, more realistic simulations may include significant spatial gradients associated with, for example, microfronts. For such applications, odd-order upwind schemes would likely be advantageous. The analysis of WRF results indicates that the choice of the advection scheme could be as important as the choice of a SFS parameterization and that the best performance is obtained with specific combinations of SFS parameterizations and advection schemes (also see Fig. 8).
Analysis of WRF LES performance using different advection schemes with the Lilly SFS parameterization.
Assessment of sensitivity to two key boundary conditions and forcing
parameters,
The effects of varying
Observed and simulated wind speed and direction, from the neutral
case study, using higher resolution, with each solver using its optimal
aspect ratio and the Lilly SFS model. Top panels show each models' mean wind
speeds against observed variability
Differences in response to varying surface boundary conditions among the models can likely be attributed to differences in implementation of surface boundary conditions. Considering the infeasibility of resolving the viscous sublayer of a high-Reynolds-number ABL flow, due to both extreme computational demands and uncertainties in details of terrain and surface cover, LES of ABLs generally rely on approximate surface boundary conditions that are in some form based upon the assumption of a developed logarithmic surface layer profile, modified by atmospheric stability (e.g., Moeng, 1984).
The preceding analysis of sensitivity to model configuration and forcing
parameters utilized simulations conducted with moderately fine grid
resolutions. A more detailed assessment of model performance based on
higher-resolution simulations of the baseline case of
A comparison of simulated and observed time-averaged wind speed profiles is
shown in Fig. 10a. Excellent agreement is observed between SOWFA and WRF
model results, each predicting slightly higher magnitudes than HiGrad, with
all simulations falling within the range of observed variability. Each
simulation also produced good agreement with the logarithmic profile in the
surface layer (Fig. 10b). Temporal variability of the 10 min average wind
speed for each simulation is shown in Fig. 10c, d, and e, denoted as “error”
bars, representing one standard deviation from the mean across all 10 min
averages. All three models result in similar temporal variability, all
markedly lower than that of measured profiles. The difference between
simulated and measured variability could be attributed to the fact that
idealized simulations forced with constant and uniform
For completeness, comparison between measured and simulated wind direction is shown in Fig. 10f. Excellent agreement is observed except for a small difference at the lowest levels that could be potentially attributed to the effects of small terrain heterogeneities not represented within the simulations.
Analysis of WRF LES performance using different advection schemes with the NBA and NBA-TKE SFS parameterization.
Quantitative MAE and RMSE values from the high-resolution simulations are presented in Table 6. While all the models perform well, the HiGrad simulations produce the lowest values of wind speed MAE and RMSE across the tower depth, as well as the lowest value of wind speed MAE across the rotor heights. The SOWFA simulations achieve the lowest shear MAE across the rotor disk. It is noted that configurations used for the high-resolution simulations may not have been optimal for each model. As discussed earlier, using model configurations with different combinations of SFS models and advection schemes may yield better performance. In addition, uncertainty in the forcing conditions and the unsteadiness of the evening transition may have contributed to these errors. Finally, WRF's relatively lower scores are likely partially attributable to the use of a factor of two coarser horizontal resolution (relative to the other models), a key modulator of resolved turbulence scales.
Analysis of high-resolution LES performance using different models with the Lilly SFS parameterization for the neutrally stratified ABL observed on 17 August 2012.
Simulated and measured turbulent stress
Simulated and measured spectra of the streamwise
In addition to wind speed and direction, time-averaged profiles of vertical
turbulent stresses,
Figure 11 shows time-averaged turbulent stresses (left) and TKE (right) from
both simulations and observations. All quantities were computed over a
90 min period using 15 min running mean values. In addition to the 17 August
case, observations here include an additional near-neutral period
occurring during the morning of the 10 July 2012, which featured similar but
slightly greater wind speeds (by approximately 1 m s
Simulated and measured spectra and cospectra, as in Fig. 12, from another neutral case study occurring 10 July 2012, exhibiting no tower wake effects.
Measured and simulated wind speed
An explanation for the large differences between measured and observed TKE values, despite similar stress values, is that tower wake effects likely contributed small, uncorrelated perturbations, enhancing the variances contributing to TKE while not strongly impacting the covariances that determine the stress. The larger observed TKE values during the unwaked 10 July case are likely due to greater vertical wind shear occurring within the stable conditions preceding the near neutral morning transition period. Observed TKE values during the 17 August case also could have been influenced by residual turbulence from the previous afternoon's convection. These factors highlight difficulties inherent in comparing observations taken during near-neutral periods within a diurnal cycle, to idealized neutral simulations forced with no diurnal variability. Despite the omission of diurnal variability (and other simplifications) in the idealized setups used herein, the stress values, which are critical factors in turbine fatigue loading, were captured well.
Figure 12 shows power spectra of streamwise (top left) and vertical velocity
(top right) components, as well as cospectra of two turbulent stress
components:
The spectra shown in Fig. 12 (top) suggest that the primary cause of the larger measured than simulated TKE values is increased variability in the observed horizontal velocity components relative to the simulations, likely due to tower wake effects. In contrast, the cospectra (bottom) show much better agreement between simulations and observations due to their dependence upon correlated structures produced by nonlinear dynamics, rather than the generally uncorrelated structures produced by the lattice tower.
Spectra and cospectra computed from model output display a high-wave-number drop-off characteristic of finite difference and finite volume discretization schemes. A numerical scheme without full spectral resolution acts as a low-pass filter with a width that depends on the type and order of the numerical scheme (Kosović et al., 2002; Skamarock, 2004). As can be seen from Fig. 12, all three models exhibit similar high-wave-number drop-off characteristics, as expected, with the SOWFA results producing slightly wider inertial subranges due to the use of an even-order, centered scheme.
Figure 13 shows velocity spectra and cospectra, as in Fig. 12, from the unwaked 10 July case. As with the 17 August case, observed and simulated cospectra and vertical velocity spectra again agree well with each other. However, the absence of spurious, tower-induced horizontal velocity perturbations greatly improves agreement between the measured and simulated horizontal velocity spectra.
Comparison of variability in observed and simulated wind speed
profiles using all three solvers, HiGrad
Simulations during convective conditions were assessed using many of the same
criteria applied to the neutral simulations, again evaluated using each
solver's optimal
Figure 14 shows wind speed (left) and direction (right) profiles, again with “measurement variability” bars on the wind speeds indicating one standard deviation about the mean of the 10 min average values from the observations, from each solver. During convective conditions, the WRF results show the closest agreement with the mean values of the observed wind speed, with SOWFA and HiGrad producing slightly slower values. All predictions were within the range of the observed values.
Simulated and measured TKE
Simulated and measured spectra of streamwise velocity
Figure 15 plots variability of the 10 min average wind speed values from each simulation, with the measurement variability bars signifying one standard deviation from the mean value across all 2 h of the simulation. All three models capture a similar range of wind speed variability as was observed, in contrast to the neutral case described in Sect. 3.2.1, with good agreement for the convective case attributed to the models' ability to accurately capture convective turbulent structures including updrafts and downdrafts, relatively steady geostrophic wind and surface flux forcing, and an absence of tower wake contamination given the more southerly mean wind direction.
Analysis of high-resolution LES performance using different models with the Lilly SFS parameterization for the convective ABL observed on 17 August 2012.
Simulated and measured cospectra of vertical and streamwise velocity
Quantitative MAE and RMSE scores from the convective simulations are provided in Table 7. Computed values of MAE and RMSE across all tower levels or across the turbine rotor disk confirm our previous observation of excellent agreement between the WRF simulation results and measurements. Due to a well-mixed layer characteristic of convective ABLs, the shear over the rotor of a wind turbine is nearly zero and this is captured well by the models.
Assessment of turbulent quantities including TKE, stresses, and the sensible
heat flux, was again carried out as described for the neutral conditions,
here over a slightly longer 2 h period. Figure 16 shows measured versus
simulated (resolved
Similar to the neutral case, spectra and cospectra are again computed, here
by dividing 2 h time series into overlapping 20 min intervals (overlapping
over 10 min) and averaging the resulting 11 spectra. Figure 17 shows
observed and simulated spectra of the streamwise velocity (top left),
vertical velocity (top right), as well as observed
Figure 18 shows cospectra of the vertical velocity with the streamwise (upper
left) and spanwise (upper right) components, as for the neutral case, along
with those of the measured vertical velocity and
With a view toward assessing the utility of idealized LES to provide turbulent flow quantities of interest to wind power applications, three different LES solvers were utilized to simulate quasi-steady neutral and convective ABL flow regimes. Simulations were compared against observations over nearly flat and homogeneous surface cover, for two case studies featuring nearly steady near-neutral and convective conditions, permitting use of idealized geostrophic forcing, uniform surface conditions, and periodic LBCs. The three solvers, encompassing a range of common numerical formulations and turbulence SFS models, were subject to a series of sensitivity experiments to assess the impacts of variations of model configuration and forcing parameters on quantities of interest, including wind speed, turbulent stresses and fluxes, TKE, spectra, and cospectra.
A unique aspect of this study was computation of model turbulence statistics, spectra and cospectra, in the frequency domain, enabling direct comparison with observed values. Spectral characteristics from all simulations displayed expected qualitative characteristics, including peak energy at low wave numbers, an inertial cascade, and attenuation of power with increasing frequency. The narrower inertial subranges exhibited by the simulated versus the observed flows were due in part to lower sampling rates of the simulations, and in part to the implicit model filter imposed by the mesh and numerical discretization, the latter evidenced by the slightly wider inertial subranges from the SOWFA simulations.
Comparison with observations reveals generally good performance of all models, under a typical range of configuration and forcing variations. This supports the use of idealized LES to produce useful flow and turbulence parameters during appropriate quasi-canonical flow conditions. The convective simulations provided generally better agreement with the observations, especially in quantities expressing variability, with superior performance attributed primarily to buoyancy-generated turbulence dominating other forcing. While it is difficult to attribute the sources of discrepancies to features of the forcing versus generic limitations of the models, given the limitations of the data and simplicity of the model setups and forcing, sensitivity to different advection schemes, SFS parameterizations, and forcing was evident. An important conclusion is that the choice of advection discretization can be as important as the SFS parameterization.
Given the generally good performance of the idealized LES evaluated herein
for simulating canonical, quasi-ideal cases, future efforts will focus on
further identifying sources of the discrepancies between the simulations and
the observations. This includes further isolation of the impacts of choices of
numerical methods, domain configuration, and physical forcing parameter
values on various quantities of interest. One approach will be to conduct
mesoscale simulations of quasi-ideal case studies such as those examined here
to obtain better estimates of various forcing parameters not available from
the observations, or representable using constant values, such as changes of
The following datasets are available at mmc/microscale.anl.wrfles.convective.ttu ( mmc/microscale.anl.wrfles.neutral.ttu ( mmc/microscale.lanl.higrad.convective.ttu ( mmc/microscale.lanl.higrad.neutral.ttu ( mmc/microscale.lanl.wrfles.convective.ttu ( mmc/microscale.lanl.wrfles.neutral.ttu ( mmc/microscale.llnl.wrfles.neutral.ttu ( mmc/microscale.nrel.sowfa.neutral.ttu ( mmc/microscale.pnnl.wrfles.convective.ttu ( mmc/mesoscale.nrel.hrrr.wfip2.d01 ( mmc/mesoscale.nrel.wrf.ttutower.d03 ( mmc/mesoscale.pnnl.wrf.ttutower.d03 ( mmc/tower.z01.a0 ( mmc/tower.z01.00 ( mmc/microscale.snl.sonic.convective.ttu ( mmc/radar.z01.00 (
The authors declare that they have no conflict of interest.
This work was performed under the auspices of the US Department of Energy (DOE) by Lawrence Livermore National Laboratory, the National Renewable Energy Laboratory, Los Alamos National Laboratory, Pacific Northwest National, Argonne National Laboratory, and Sandia National Laboratories, under contracts DE-AC52-07NA27344, DE-AC36-08GO28308, DE-AC52-06NA25396, DE-A06-76RLO 1830, DE-AC02-06CH11357 and DE-AC04-94AL85000, respectively. Ramesh Balakrishnan used resources of the Argonne Leadership Computing Facility, which is a DOE Office of Science User Facility supported under Contract DE-AC02-06CH11357. All participants were supported by the US DOE Office of Energy Efficiency and Renewable Energy. The US Government retains and the publisher, by accepting the article for publication, acknowledges that the US Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for US Government purposes. Edited by: Joachim Peinke Reviewed by: two anonymous referees