A Wind-Tunnel Investigation of Wind-Turbine Wakes: Boundary-Layer Turbulence Effects

Wind-tunnel experiments were performed to study turbulence in the wake of a model wind turbine placed in a boundary layer developed over rough and smooth surfaces. Hot-wire anemometry was used to characterize the cross-sectional distribution of mean velocity, turbulence intensity and kinematic shear stress at different locations downwind of the turbine for both surface roughness cases. Special emphasis was placed on the spatial distribution of the velocity deficit and the turbulence intensity, which are important factors affecting turbine power generation and fatigue loads in wind energy parks. Non-axisymmetric behaviour of the wake is observed over both roughness types in response to the non-uniform incoming boundary-layer flow and the effect of the surface. Nonetheless, the velocity deficit with respect to the incoming velocity profile is nearly axisymmetric, except near the ground in the far wake where the wake interacts with the surface. It is found that the wind turbine induces a large enhancement of turbulence levels (positive added turbulence intensity) in the upper part of the wake. This is due to the effect of relatively large velocity fluctuations associated with helicoidal tip vortices near the wake edge, where the mean shear is strong. In the lower part of the wake, the mean shear and turbulence intensity are reduced with respect to the incoming flow. The non-axisymmetry of the turbulence intensity distribution of the wake is found to be stronger over the rough surface, where the incoming flow is less uniform at the turbine level. In the far wake the added turbulent intensity, its positive and negative contributions and its local maximum decay as a power law of downwind distance (with an exponent ranging from −0.3 to −0.5 for the rough surface, and with a wider variation for the smooth surface). Nevertheless, the effect of the turbine on the velocity defect and added turbulence intensity is not negligible even in the very far wake, at a distance of fifteen times the rotor diameter.     

Impact of the Diurnal Cycle of the Atmospheric Boundary Layer on Wind-Turbine Wakes: A Numerical Modelling Study

The wake characteristics of a wind turbine for different regimes occurring throughout the diurnal cycle are investigated systematically by means of large-eddy simulation. Idealized diurnal cycle simulations of the atmospheric boundary layer are performed with the geophysical flow solver EULAG over both homogeneous and heterogeneous terrain. Under homogeneous conditions, the diurnal cycle significantly affects the low-level wind shear and atmospheric turbulence. A strong vertical wind shear and veering with height occur in the nocturnal stable boundary layer and in the morning boundary layer, whereas atmospheric turbulence is much larger in the convective boundary layer and in the evening boundary layer. The increased shear under heterogeneous conditions changes these wind characteristics, counteracting the formation of the night-time Ekman spiral. The convective, stable, evening, and morning regimes of the atmospheric boundary layer over a homogeneous surface as well as the convective and stable regimes over a heterogeneous surface are used to study the flow in a wind-turbine wake. Synchronized turbulent inflow data from the idealized atmospheric boundary-layer simulations with periodic horizontal boundary conditions are applied to the wind-turbine simulations with open streamwise boundary conditions. The resulting wake is strongly influenced by the stability of the atmosphere. In both cases, the flow in the wake recovers more rapidly under convective conditions during the day than under stable conditions at night. The simulated wakes produced for the night-time situation completely differ between heterogeneous and homogeneous surface conditions. The wake characteristics of the transitional periods are influenced by the flow regime prior to the transition. Furthermore, there are different wake deflections over the height of the rotor, which reflect the incoming wind direction.     

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 spectra.     

A Numerical Study of Wind-Turbine Wakes for Three Atmospheric Stability Conditions

The effects of atmospheric stability on wind-turbine wakes are studied via large-eddy simulations. Three stability conditions are considered: stable, neutral, and unstable, with the same geostrophic wind speed aloft and the same Coriolis frequency. Both a single 5-MW turbine and a wind farm of five turbines are studied. The single-turbine wake is strongly correlated with stability, in terms of velocity deficit, turbulence kinetic energy (TKE) and temperature distribution. Because of the Coriolis effect, the wake shape deviates from a Gaussian distribution. For the wind-farm simulations, the separation of the core region and outer region is clear for the stable and neutral cases, but less distinct for the unstable case. The unstable case exhibits strong horizontal variations in wind speed. Local accelerations such as related to aisle jets are also observed, whose features depend on stability. The added TKE in the wind farm increases with stability. The highest power extraction and lowest power deficit are observed for the unstable case.     

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 2.5 m s^?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 turbines.     

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 coefficient.     

城市湍流边界层内汽车尾气扩散规律数值模拟研究

以纳维斯托克斯方程组、大气平流扩散方程、湍流动能及湍流动能耗散率方程组为基础．采用伪不定常方法,建立了一个数值模式．利用该模式列城市湍流边界层内流场结构及汽车排放污染物扩散规律进行了研究。结果表明：街谷内会形成一个涡旋型流场．汽车排放污染物浓度在地面及建筑物背风面产生堆积,且其沿高度方向的梯度变化在背风面大．迎风而小。随着街谷两侧建筑物屋顶风速的增大,峡谷内形成的涡旋流场的强度增大,污染物扩散速率增大：当屋顶来流与街道之间的夹角逐渐增大时．涡旋中心位置由街道中心偏向于背风面及更高层且污染物扩散速度加快。     

Impact of Boundary-Layer Processes on Near-Surface Turbulence Within the West African Monsoon

High frequency measurements of near-surface meteorological data acquired in north Benin during the 2006 West African monsoon seasonal cycle, in the context of the African Monsoon Multidisciplinary Analysis (AMMA) experiment, offer insight into the characteristics of surface turbulence in relation to planetary boundary-layer (PBL) processes. A wide range of conditions is encountered at the lower and upper limits of the PBL: (i) from water-stressed to well-fed vegetation, and (ii) from small to large humidity and temperature jumps at the PBL top inversion, due to the Saharan air layer overlying the monsoonal flow. As a result, buoyant convection at the surface and entrainment at the PBL top play very different roles according to the considered scalar. We show that, when the boundary-layer height reaches the shear level between the monsoonal and Harmattan flows, the temperature source and humidity sink at the boundary-layer top are sufficient to allow the entrainment to affect the entire boundary layer down to the surface. This situation occurs mainly during the drying and moistening periods of the monsoon cycle and affects the humidity statistics in particular. In this case, the humidity turbulent characteristics at the surface are no longer driven solely by buoyant convection, but also by entrainment at the boundary-layer top. Consequently, the Monin–Obukhov similarity theory appears to fail for the parameterisation of humidity-related moments.     

Modelling Boundary-Layer Clouds With a Statistical Cloud Scheme and a Second-Order Turbulence Closure

We present a second-order turbulence model for the cloudy planetary boundary layer (PBL), which includes a statistical scheme of the sub-grid scale condensation. The model contains prognostic equations for the turbulent kinetic energy, total water, and liquid water temperature, the latter two being assumed to be conservative variables. Using these conservative thermodynamic variables the condensation process is formulated as a function of the departure of the total water from saturation and its variance. The computation of the variance requires second moment correlations which are modelled through the parameterization of the third-order moments using a convective mass-flux formulation. The inclusion of these third moments and new assumptions on heat flux transport lead to a nonlocal turbulence scheme with counter-gradient effects. The final form for the heat flux turns out to be a linearized version of a previously established result. For the statistical cloud formulation, a linear combination of a Gaussian and a positively skewed distribution function is used with a modified liquid water flux expression to account fornon-Gaussian behaviour.The effect of the turbulence scheme on the boundary-layer cloud structure is discussed and the performance of the model is tested by comparing it against the large eddy simulation (LES) of the undisturbed period of the Atlantic Stratocumulus Transition Experiment (ASTEX). The model is able to produce both mean and turbulent quantities that are in reasonable agreement with the LES output of ASTEX.     

A Length Scale Defining Partially-Resolved Boundary-Layer Turbulence Simulations

Numerical weather prediction (NWP) model forecasts at horizontal grid lengths in the range of 100 m to 1 km are now possible. Within this range of grid lengths, the convective boundary layer (CBL) is partially resolved and thus in the so-called ‘grey zone’. For simulations in the grey zone, numerical dissipation sources from both the advection scheme and the subgrid model are likely to be significant. Until now, these effects have not been incorporated fully into our understanding of the grey zone. In order to quantify these effects, a dissipation length scale is defined based on the second moment of the turbulent kinetic energy (TKE) spectrum. An ensemble of simulations of a CBL are performed using a large-eddy model across the grey-zone resolutions and for a range of subgrid model, advection scheme and vertical grid configurations. The dissipation length scale distinguishes the effects of the different model configurations in the grey zone. In the middle of the boundary layer, the resolved TKE is strongly controlled by the numerical dissipation. This leads to a similarity law for the resolved TKE in the grey zone using the dissipation length scale. A new definition of the grey zone emerges where the inversion depth and dissipation length scale are the same size. This contrasts with the typical definition using the horizontal grid length. At the inversion, however, the variation of the dissipation length scale with grid length is less predictable, reflecting significant challenges for modelling entrainment in the grey zone. The dissipation length scale is thus a simple diagnostic to aid both NWP and large-eddy modellers in understanding the grey zone.     

大气边界层湍流多尺度分形特征的研究

运用离散正交小波变换将湍流信号分解为不同尺度，计算其分数维。考察其分数维的变化得出：随着分解层次得增加，提取湍流信号得低频部分趋于简单光滑，分数维不断减小，高频部分呈现复杂，分数维趋于定值，平均为1．70左右。说明大气边界层湍流信号在某些尺度上，存在明显的自相似性特征。     

Numerical Prediction of the Boundary-Layer Flow Over the Bolund Hill: Assessment of Turbulence Models and Advection Schemes

Boundary-Layer Meteorology - The WindStation software package is applied to simulate the wind field over the Bolund hill. The standard, ReNormalization Group (RNG), realizable, and limited-length...     

Stable Boundary-Layer Modelling: Established Approaches and Beyond

In the light of Large Eddy Simulation and other recent work, this paper discusses methods of stable boundary-layer modelling that are established in numerical weather prediction and potentially relevant to other applications, e.g., to dispersion. It is argued that classical scaling theory is best expressed in terms of the local Richardson numbers. The theory can then be extended to treat cases where classical assumptions break down. There are indications that Richardson number models with suitable boundary conditions can mimic, at least qualitatively, some features of the very stable boundary layer. Despite advances in research modelling, detailed observational validation remains essential.     

The Effect of Wind-Turbine Wakes on Summertime US Midwest Atmospheric Wind Profiles as Observed with Ground-Based Doppler Lidar

We examine the influence of a modern multi-megawatt wind turbine on wind and turbulence profiles three rotor diameters ( $D$ D ) downwind of the turbine. Light detection and ranging (lidar) wind-profile observations were collected during summer 2011 in an operating wind farm in central Iowa at 20-m vertical intervals from 40 to 220 m above the surface. After a calibration period during which two lidars were operated next to each other, one lidar was located approximately $2D$ 2 D directly south of a wind turbine; the other lidar was moved approximately $3D$ 3 D north of the same wind turbine. Data from the two lidars during southerly flow conditions enabled the simultaneous capture of inflow and wake conditions. The inflow wind and turbulence profiles exhibit strong variability with atmospheric stability: daytime profiles are well-mixed with little shear and strong turbulence, while nighttime profiles exhibit minimal turbulence and considerable shear across the rotor disk region and above. Consistent with the observations available from other studies and with wind-tunnel and large-eddy simulation studies, measurable reductions in wake wind-speeds occur at heights spanning the wind turbine rotor (43–117 m), and turbulent quantities increase in the wake. In generalizing these results as a function of inflow wind speed, we find the wind-speed deficit in the wake is largest at hub height or just above, and the maximum deficit occurs when wind speeds are below the rated speed for the turbine. Similarly, the maximum enhancement of turbulence kinetic energy and turbulence intensity occurs at hub height, although observations at the top of the rotor disk do not allow assessment of turbulence in that region. The wind shear below turbine hub height (quantified here with the power-law coefficient) is found to be a useful parameter to identify whether a downwind lidar observes turbine wake or free-flow conditions. These field observations provide data for validating turbine-wake models and wind-tunnel observations, and for guiding assessments of the impacts of wakes on surface turbulent fluxes or surface temperatures downwind of turbines.     

Numerical Modelling of Neutral Boundary-layer Flow Across a Forested Ridge

Boundary-Layer Meteorology - Forest canopies have been shown to alter the dynamics of flows over complex terrain. Deficiencies have been found when tall canopies are represented in numerical...     

On the Structure and Adjustment of Inversion-Capped Neutral Atmospheric Boundary-Layer Flows: Large-Eddy Simulation Study

A range of large-eddy simulations, with differing free atmosphere stratification and zero or slightly positive surface heat flux, is investigated to improve understanding of the neutral and near-neutral, inversion-capped, horizontally homogeneous, barotropic atmospheric boundary layer with emphasis on the upper region. We find that an adjustment time of at least 16 h is needed for the simulated flow to reach a quasi-steady state. The boundary layer continues to grow, but at a slow rate that changes little after 8 h of simulation time. A common feature of the neutral simulations is the development of a super-geostrophic jet near the top of the boundary layer. The analytical wind-shear models included do not account for such a jet, and the best agreement with simulated wind shear is seen in cases with weak stratification above the boundary layer. Increasing the surface heat flux decreases the magnitude and vertical extent of the jet and leads to better agreement between analytical and simulated wind-speed profiles. Over a range of different inversion strengths and surface heat fluxes, we also find good agreement between the performed simulations and models of the equilibrium boundary-layer height, and of the budget of turbulent kinetic energy integrated across the boundary layer.     

A Comprehensive Modelling Approach for the Neutral Atmospheric Boundary Layer: Consistent Inflow Conditions, Wall Function and Turbulence Model

We report on a novel approach for the Reynolds-averaged Navier-Stokes (RANS) modelling of the neutral atmospheric boundary layer (ABL), using the standard k-ek-{\varepsilon} turbulence model. A new inlet condition for turbulent kinetic energy is analytically derived from the solution of the k-ek-{\varepsilon} model transport equations, resulting in a consistent set of fully developed inlet conditions for the neutral ABL. A modification of the standard k-ek-{\varepsilon} model is also employed to ensure consistency between the inlet conditions and the turbulence model. In particular, the turbulence model constant C _μ is generalized as a location-dependent parameter, and a source term is introduced in the transport equation for the turbulent dissipation rate. The application of the proposed methodology to cases involving obstacles in the flow is made possible through the implementation of an algorithm, which automatically switches the turbulence model formulation when going from the region where the ABL is undisturbed to the region directly affected by the building. Finally, the model is completed with a slightly modified version of the Richards and Hoxey rough-wall boundary condition. The methodology is implemented and tested in the commercial code Ansys Fluent 12.1. Results are presented for a neutral boundary layer over flat terrain and for the flow around a single building immersed in an ABL.     

Second-Order Modelling of Turbulence in Katabatic Flows

A complete one-dimensional second-order closure model is used to simulate katabatic flows observed on glaciers and ice caps. The model is tested with two different closure assumptions for the viscous dissipation, one based on a prognostic equation for and the other on a diagnostic buoyant length scale. Both formulations give quite similar results. Model simulations are compared to observations made over sloping ice surfaces during periods dominated by katabatic flow. In general, good agreement is found for both mean wind and temperature profiles as well as eddy correlation measurements. It is also found that the turbulent transport terms play an important role in katabatic flows as opposed to the classical stable boundary layer where these terms are usually ignored. Even the turbulent transport of temperature variance, which leads to the well-known countergradient term in unstable boundary layers, is relatively important for modelling the observed temperature profiles. The effect of these terms on the flux-profile relationships, using observed and simulated profiles, is also discussed.