Large-Eddy Simulation of Stably Stratified Atmospheric Boundary Layer Turbulence: A Scale-Dependent Dynamic Modeling Approach

A new tuning-free subgrid-scale model, termed `locally-averaged scale-dependent dynamic' (LASDD) model, is developed and implemented in large-eddy simulations (LESs) of stable boundary layers. The new model dynamically computes the Smagorinsky coefficient and the subgrid-scale Prandtl number based on the local dynamics of the resolved velocity and temperature fields. Overall, the agreement between the statistics of the LES-generated turbulence and some well-established empirical formulations and theoretical predictions (e.g., Nieuwstadt's local scaling hypothesis) is remarkable. The results show clear improvements over most of the traditional subgrid-scale models in the surface layer. Moreover, in contrast to previous large-eddy simulations of stable boundary layers that have strong dependence on grid resolution, the simulated statistics obtained with the LASDD model show relatively little resolution dependence for the range of grid sizes considered here. In essence, we show that the new LASDD model is a robust subgrid-scale parameterization for reliable, tuning-free simulations of stable boundary layers, even with relatively coarse resolutions

Effects of Thermal Stability and Incoming Boundary-Layer Flow Characteristics on Wind-Turbine Wakes: A Wind-Tunnel Study

Wind-tunnel experiments were carried out to study turbulence statistics in the wake of a model wind turbine placed in a boundary-layer flow under both neutral and stably stratified conditions. High-resolution velocity and temperature measurements, obtained using a customized triple wire (cross-wire and cold wire) anemometer, were used to characterize the mean velocity, turbulence intensity, turbulent fluxes, and spectra at different locations in the wake. The effect of the wake on the turbulence statistics is found to extend as far as 20 rotor diameters downwind of the turbine. The velocity deficit has a nearly axisymmetric shape, which can be approximated by a Gaussian distribution and a power-law decay with distance. This decay in the near-wake region is found to be faster in the stable case. Turbulence intensity distribution is clearly non-axisymmetric due to the non-uniform distribution of the incoming velocity in the boundary layer. In the neutral case, the maximum turbulence intensity is located above the hub height, around the rotor tip location and at a distance of about 4-5.5 rotor diameters, which are common separations between wind turbines in wind farms. The enhancement of turbulence intensity is associated with strong shear and turbulent kinetic energy production in that region. In the stable case, the stronger shear in the incoming flow leads to a slightly stronger and larger region of enhanced turbulence intensity, which extends between 3 and 6 rotor diameters downwind of the turbine location. Power spectra of the streamwise and vertical velocities show a strong signature of the turbine blade tip vortices at the top tip height up to a distance of about 1-2 rotor diameters. This spectral signature is stronger in the vertical velocity component. At longer downwind distances, tip vortices are not evident and the von Kármán formulation agrees well with the measured velocity spectr

Large-Eddy Simulation of Stably-Stratified Flow Over a Steep Hill

Large-eddy simulation (LES) is used to simulate stably-stratified turbulent boundary-layer flow over a steep two-dimensional hill. To parametrise the subgrid-scale (SGS) fluxes of heat and momentum, three different types of SGS models are tested: (a) the Smagorinsky model, (b) the Lagrangian dynamic model, and (c) the scale-dependent Lagrangian dynamic model (Stoll and Porté-Agel, Water Resour Res 2006, doi:10.1029/2005WR003989). Simulation results obtained with the different models are compared with data from wind-tunnel experiments conducted at the Environmental Flow Research Laboratory (EnFlo), University of Surrey, U.K. (Ross etal., Boundary-Layer Meteorol 113:427-459, 2004). It is found that, in this stably-stratified boundary-layer flow simulation, the scale-dependent Lagrangian dynamic model is able to account for the scale dependence of the eddy-viscosity and eddy-diffusivity model coefficients associated with flow anisotropy in flow regions with large mean shear and/or strong flow stratification. As a result, simulations using this tuning-free model lead to turbulence statistics that are more realistic than those obtained with the other two model

A Large-Eddy Simulation Study of Turbulent Flow Over Multiscale Topography

Most natural landscapes are characterized by multiscale (often multifractal) topography with well-known scale-invariance properties. For example, the spectral density of landscape elevation fields is often found to have a power-law scaling behaviour (with a −2 slope on a log-log scale) over a wide span of spatial scales, typically ranging from tens of kilometres down to a few metres. Even though the effect of topography on the atmospheric boundary layer (ABL) has been the subject of numerous studies, few have focussed on multiscale topography. In this study, large-eddy simulation (LES) is used to investigate boundary-layer flow over multiscale topography, and guide the development of parametrizations needed to represent the effects of subgrid-scale (SGS) topography in numerical models of ABL flow. Particular emphasis is placed on the formulation of an effective roughness used to account for the increased aerodynamic roughness associated with SGS topography. The LES code uses the scale-dependent Lagrangian dynamic SGS model for the turbulent stresses and a terrain-following coordinate transformation to explicitly resolve the effects of the topography at scales larger than the LES resolution. The terrain used in the simulations is generated using a restricted solid-on-solid landscape evolution model, and it is characterized by a −2 slope of the elevation power spectrum. Results from simulations performed using elevation fields band-pass filtered at different spatial resolutions indicate a clear linear relation between the square of the effective roughness and the variance of elevatio

Simulation of Turbulent Flow Inside and Above Wind Farms: Model Validation and Layout Effects

A recently-developed large-eddy simulation framework is validated and used to investigate turbulent flow within and above wind farms under neutral conditions. Two different layouts are considered, consisting of thirty wind turbines occupying the same total area and arranged in aligned and staggered configurations, respectively. The subgrid-scale (SGS) turbulent stress is parametrized using a tuning-free Lagrangian scale-dependent dynamic SGS model. The turbine-induced forces are modelled using two types of actuator-disk models: (a) the ‘standard' actuator-disk model (ADM-NR), which calculates only the thrust force based on one-dimensional momentum theory and distributes it uniformly over the rotor area; and (b) the actuator-disk model with rotation (ADM-R), which uses blade-element momentum theory to calculate the lift and drag forces (that produce both thrust and rotation), and distributes them over the rotor disk based on the local blade and flow characteristics. Validation is performed by comparing simulation results with turbulence measurements collected with hot-wire anemometry inside and above an aligned model wind farm placed in a boundary-layer wind tunnel. In general, the ADM-R model yields improved predictions compared with the ADM-NR in the wakes of all the wind turbines, where including turbine-induced flow rotation and accounting for the non-uniformity of the turbine-induced forces in the ADM-R appear to be important. Another advantage of the ADM-R model is that, unlike the ADM-NR, it does not require a priori specification of the thrust coefficient (which varies within a wind farm). Finally, comparison of simulations of flow through both aligned and staggered wind farms shows important effects of farm layout on the flow structure and wind-turbine performance. For the limited-size wind farms considered in this study, the lateral interaction between cumulated wakes is stronger in the staggered case, which results in a farm wake that is more homogeneous in the spanwise direction, thus resembling more an internal boundary layer. Inside the staggered farm, the relatively longer separation between consecutive downwind turbines allows the wakes to recover more, exposing the turbines to higher local wind speeds (leading to higher turbine efficiency) and lower turbulence intensity levels (leading to lower fatigue loads), compared with the aligned farm. Above the wind farms, the area-averaged velocity profile is found to be logarithmic, with an effective wind-farm aerodynamic roughness that is larger for the staggered cas

Large-Eddy Simulation of Wind-Turbine Wakes: Evaluation of Turbine Parametrisations

Large-eddy simulation (LES), coupled with a wind-turbine model, is used to investigate the characteristics of a wind-turbine wake in a neutral turbulent boundary-layer flow. The tuning-free Lagrangian scale-dependent dynamic subgrid-scale (SGS) model is used for the parametrisation of the SGS stresses. The turbine-induced forces (e.g., thrust, lift and drag) are parametrised using two models: (a) the ‘standard' actuator-disk model (ADM-NR), which calculates only the thrust force and distributes it uniformly over the rotor area; and (b) the actuator-disk model with rotation (ADM-R), which uses the blade-element theory to calculate the lift and drag forces (that produce both thrust and rotation), and distribute them over the rotor disk based on the local blade and flow characteristics. Simulation results are compared to high-resolution measurements collected with hot-wire anemometry in the wake of a miniature wind turbine at the St. Anthony Falls Laboratory atmospheric boundary-layer wind tunnel. In general, the characteristics of the wakes simulated with the proposed LES framework are in good agreement with the measurements in the far-wake region. The ADM-R yields improved predictions compared with the ADM-NR in the near-wake region, where including turbine-induced flow rotation and accounting for the non-uniformity of the turbine-induced forces appear to be important. Our results also show that the Lagrangian scale-dependent dynamic SGS model is able to account, without any tuning, for the effects of local shear and flow anisotropy on the distribution of the SGS model coefficien

An Analytical Model for the Effect of Vertical Wind Veer on Wind Turbine Wakes

In this study, an analytical wake model for predicting the mean velocity field downstream of a wind turbine under veering incoming wind is systematically derived and validated. The new model, which is an extended version of the one introduced by Bastankhah and Porté-Agel, is based upon the application of mass conservation and momentum theorem and considering a skewed Gaussian distribution for the wake velocity deficit. Particularly, using a skewed (instead of axisymmetric) Gaussian shape allows accounting for the lateral shear in the incoming wind induced by the Coriolis force. This analytical wake model requires only the wake expansion rate as an input parameter to predict the mean wake flow downstream. The performance of the proposed model is assessed using the large-eddy simulation (LES) data of a full-scale wind turbine wake under the stably stratified condition. The results show that the proposed model is capable of predicting the skewed structure of the wake downwind of the turbine, and its prediction for the wake velocity deficit is in good agreement with the high-fidelity simulation data

Near-wake flow structure downwind of a wind turbine in a turbulent boundary layer

Wind turbines operate in the surface layer of the atmospheric boundary layer, where they are subjected to strong wind shear and relatively high turbulence levels. These incoming boundary layer flow characteristics are expected to affect the structure of wind turbine wakes. The near-wake region is characterized by a complex coupled vortex system (including helicoidal tip vortices), unsteadiness and strong turbulence heterogeneity. Limited information about the spatial distribution of turbulence in the near wake, the vortex behavior and their influence on the downwind development of the far wake hinders our capability to predict wind turbine power production and fatigue loads in wind farms. This calls for a better understanding of the spatial distribution of the 3D flow and coherent turbulence structures in the near wake. Systematic wind-tunnel experiments were designed and carried out to characterize the structure of the near-wake flow downwind of a model wind turbine placed in a neutral boundary layer flow. A horizontal-axis, three-blade wind turbine model, with a rotor diameter of 13cm and the hub height at 10.5cm, occupied the lowest one-third of the boundary layer. High-resolution particle image velocimetry (PIV) was used to measure velocities in multiple vertical stream-wise planes (x-z) and vertical span-wise planes (y-z). In particular, we identified localized regions of strong vorticity and swirling strength, which are the signature of helicoidal tip vortices. These vortices are most pronounced at the top-tip level and persist up to a distance of two to three rotor diameters downwind. The measurements also reveal strong flow rotation and a highly non-axisymmetric distribution of the mean flow and turbulence structure in the near wake. The results provide new insight into the physical mechanisms that govern the development of the near wake of a wind turbine immersed in a neutral boundary layer. They also serve as important data for the development and validation of numerical model

Wind-Turbine Wakes in a Convective Boundary Layer: A Wind-Tunnel Study

Thermal stability changes the properties of the turbulent atmospheric boundary layer, and in turn affects the behaviour of wind-turbine wakes. To better understand the effects of thermal stability on the wind-turbine wake structure, wind-tunnel experiments were carried out with a simulated convective boundary layer (CBL) and a neutral boundary layer. The CBL was generated by cooling the airflow to 12-15°C and heating up the test section floor to 73-75°C. The freestream wind speed was set at about 2.5ms−1, resulting in a bulk Richardson number of −0.13. The wake of a horizontal-axis 3-blade wind-turbine model, whose height was within the lowest one third of the boundary layer, was studied using stereoscopic particle image velocimetry (S-PIV) and triple-wire (x-wire/cold-wire) anemometry. Data acquired with the S-PIV were analyzed to characterize the highly three-dimensional turbulent flow in the near wake (0.2-3.2 rotor diameters) as well as to visualize the shedding of tip vortices. Profiles of the mean flow, turbulence intensity, and turbulent momentum and heat fluxes were measured with the triple-wire anemometer at downwind locations from 2-20 rotor diameters in the centre plane of the wake. In comparison with the wake of the same wind turbine in a neutral boundary layer, a smaller velocity deficit (about 15% at the wake centre) is observed in the CBL, where an enhanced radial momentum transport leads to a more rapid momentum recovery, particularly in the lower part of the wake. The velocity deficit at the wake centre decays following a power law regardless of the thermal stability. While the peak turbulence intensity (and the maximum added turbulence) occurs at the top-tip height at a downwind distance of about three rotor diameters in both cases, the magnitude is about 20% higher in the CBL than in the neutral boundary layer. Correspondingly, the turbulent heat flux is also enhanced by approximately 25% in the lower part of the wake, compared to that in the undisturbed CBL inflow. This study represents the first controlled wind-tunnel experiment to study the effects of the CBL on wind-turbine wakes. The results on decreased velocity deficit and increased turbulence in wind-turbine wakes associated with atmospheric thermal stability are important to be taken into account in the design of wind farms, in order to reduce the impact of wakes on power output and fatigue loads on downwind wind turbine