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Atmospheric Turbulence Effects on Wind-Turbine Wakes: An LES Study
Abstract and Figures
A numerical study of atmospheric turbulence effects on wind-turbine wakes is presented. Large-eddy simulations of neutrally-stratified atmospheric boundary layer flows through stand-alone wind turbines were performed over homogeneous flat surfaces with four different aerodynamic roughness lengths. Emphasis is placed on the structure and characteristics of turbine wakes in the cases where the incident flows to the turbine have the same mean velocity at the hub height but different mean wind shears and turbulence intensity levels. The simulation results show that the different turbulence intensity levels of the incoming flow lead to considerable influence on the spatial distribution of the mean velocity deficit, turbulence intensity, and turbulent shear stress in the wake region. In particular, when the turbulence intensity level of the incoming flow is higher, the turbine-induced wake (velocity deficit) recovers faster, and the locations of the maximum turbulence intensity and turbulent stress are closer to the turbine. A detailed analysis of the turbulence kinetic energy budget in the wakes reveals also an important effect of the incoming flow turbulence level on the magnitude and spatial distribution of the shear production and transport terms.
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... Typically, the turbulence kinetic energy is contributed by the turbulent momentum fluxes and mean flow shear [61]. For a wind turbine wake in flat terrain, the spatial distribution of turbulence kinetic energy shows a horseshoe shape with a peak around the rotor top tip level. ...
... This is due to high mean flow shear and momentum fluxes around the rotor periphery at the top. Moreover, the maximum turbulence kinetic energy and related turbulent momentum fluxes are relatively higher in the turbine wake compared to the surrounding boundary-layer flow [61,62]. Figure 13 shows the contours of the normalized turbulence kinetic energy in the turbine wake on the cliff for different wind directions. ...
This work investigates the effect of wind direction on the flow over a cliff and its interaction with the wake of a wind turbine sited on the cliff. The cliff is modeled as a forward-facing step, and five wind directions are tested ( θ = 0 ∘ , 15 ∘ , 30 ∘ , 45 ∘ , and − 45 ∘ ) , where 0 ∘ represents a wind direction perpendicular to the cliff edge. The flow becomes increasingly three-dimensional with the increase in the wind direction magnitude and a cross-stream flow separation develops from the cliff leading edge. The turbulence kinetic energy decreases for wind directions higher than 15 ∘ , which is due to the absence of the streamwise flow separation for higher wind directions. The cross-stream flow development in the base flow affects the shape of the turbine wake. A two-dimensional Gaussian fit is performed on the wake velocity deficit, which shows a slight departure from self-similarity in the lateral direction. The wake recovery slows down for wind directions higher than 15 ∘ , which is consistent with the decrease in the wake growth rate for θ > 15 ∘ . The wake shows higher deflection and tilt angle for higher wind directions. Analysis of the streamwise momentum in the wake reveals that the advection terms play a role in slowing the wake recovery for higher wind directions.
Published by the American Physical Society 2024
... The profiles of ∆U are reported in Fig. 22 using similarity variables. For comparison purposes, data reported for experimental lab-scale (Chamorro & Porté-Agel 2010) and numerical (LES) real-scale (Wu & Porté-Agel 2012) wind turbines are represented by the grey shaded area in Fig. 22. The Gaussian profile model proposed by Bastankhah & Porté-Agel (2014) was in fact compared to these exact data sets and used as a validation criteria. ...
We report a comprehensive study of the wake of a porous disc, the design of which has been modified to incorporate a swirling motion at an inexpensive cost. The swirl intensity is passively controlled by varying the internal disc geometry, i.e. the pitch angle of the blades. A swirl number is introduced to characterise the competition between the linear (drag) and the azimuthal (swirl) momentums on the wake recovery. Assuming that swirl dominates the near wake and non-equilibrium turbulence theory applies, new scaling laws of the mean wake properties are derived. To assess these theoretical predictions, an in-depth analysis of the aerodynamics of these original porous discs has been conducted experimentally. It is found that at the early stage of wake recovery, the swirling motion induces a low-pressure core, which controls the mean velocity deficit properties. The measurements collected in the swirling wake of the porous discs support the new scaling laws proposed in this work. Finally, it is shown that, as far as swirl is injected in the wake, the characteristics of the mean velocity deficit profiles match very well those of both lab-scale and real-scale wind turbine data extracted from the literature. Overall, our results emphasise that by setting the initial conditions of the wake recovery, swirl is a key ingredient to be taken into account in order to faithfully replicate the mean wake of wind turbines.
... where R1x = 0), before decreasing on the approach to the next row. This is in agreement with prior studies observing peak turbulence intensity occurring a few rotor diameters downstream of an individual turbine (Wu & Porté-Agel 2012). In the wake of the farm, R1x quickly approaches zero as the turbulence decays to its background level. ...
This paper presents a new generation of fast-running physics-based models to predict the wake of a semi-infinite wind farm, extending infinitely in the lateral direction but with finite size in the streamwise direction. The assumption of a semi-infinite wind farm enables concurrent solving of the laterally averaged momentum equations in both streamwise and spanwise directions. The developed model captures important physical phenomena such as vertical top-down transport of energy into the farm, variable wake recovery rate due to the farm-generated turbulence and also wake deflection due to turbine yaw misalignment and Coriolis force. Of special note is the model's capability to predict and shed light on the counteracting effect of Coriolis force causing wake deflections in both positive and negative directions. Moreover, the impact of wind farm layout configuration on the flow distribution is modelled through a parameter called the local deficit coefficient. Model predictions were validated against large-eddy simulations extending up to 45 km downstream of wind farms. Detailed analyses were performed to study the impacts of various factors such as incoming turbulence, wind farm size, inter-turbine spacing and wind farm layout on the farm wake.
... The far-wake can be separated into a decay region and a fully developed far-wake when turbulence has reached a homogeneous-isotropic state (Pope 2000). The size of each region, the intensity of the recovery and the turbulence of the wake depend greatly on the type of inflow and the operating conditions of the turbine (Wu & Porté-Agel 2012;Iungo, Wu & Porté-Agel 2013;Neunaber et al. 2017;Gambuzza & Ganapathisubramani 2023). It is clear that the emergence of the far-wake is directly linked to the phenomena that happen closer to the rotor; however, in the far-wake, the detailed features of its turbulence appear to be universal (Ali et al. 2019). ...
An experimental study in a wind tunnel is presented to explore the wake of a floating wind turbine subjected to harmonic side-to-side and fore–aft motions under laminar inflow conditions. The wake recovery is analysed as a function of the frequency of motion fp, expressed by the rotor-based Strouhal number, St=fpD/U∞ ( D is the rotor diameter, U∞ the inflow wind speed). Our findings indicate that both directions of motion accelerate the transition to the far-wake compared with the fixed turbine. The experimental outcomes confirm the computational fluid dynamics results of Li et al. (J. Fluid Mech., vol. 934, 2022, p. A29) showing that sideways motions lead to faster wake recovery, especially for St∈[0.2,0.6]. Additionally, we find that fore–aft motions also lead to better recovery for St∈[0.3,0.9]. The recovery is closely linked to nonlinear spatiotemporal dynamics found in the shear layer region of the wake. For both directions of motion and St∈[0.2,0.55], the noisy wake dynamics lock in to the frequency of the motion. In this synchronised-like state, sideways motions result in large coherent structures of meandering, and fore–aft movements induce coherent pulsing of the wake. For fore–aft motion and St∈[0.55,0.9], the wake shows a more complex quasiperiodic dynamic, namely, a self-generated meandering mode emerges, which interacts nonlinearly with the excitation frequency St, as evidenced by the occurrence of mixing components. The coherent structures grow nonlinearly, enhance wake mixing and accelerate the transition to the far-wake, which, once reached, exhibits universal behaviour.
A wind turbine wake causes a decrease in wind speed and an increase in turbulence intensity. The wind turbine wake interaction is essential for predicting the power output of a wind farm consisting of many wind turbines. This research proposes a CFD method able to reproduce wake interactions and power outputs of multiple wind turbines with high speed and accuracy. Large eddy simulations with the lattice Boltzmann method are used for fluid calculations, specifically for large-scale CFD simulations. The wind turbines are represented using an actuator line model. Optimal power generation efficiency is achieved by controlling the rotor speed and blade pitch angle. Large-scale simulations of eight aligned wind turbines are conducted using 1.75 billion grid points and 40 GPUs. We compare two cases with and without control to investigate the effect of turbine control on wake and power output. Both the instantaneous and mean streamwise velocities confirm that the turbine control reduces the wake velocity deficit of the downwind wind turbine. High-speed inflow of wind to the downstream turbines augments their power output. With implementation of turbine control, the power outputs of the downstream turbines agree well with the observation data obtained in an earlier study. The results demonstrate the importance of controlling the rotational speed and pitch angle for actuator line simulations.
The aim of this study is to evaluate and quantify the effect of the incoming flow on the coherent structures characterizing the wake of two NREL reference wind turbines with different dimensions: the NREL 5-MW and the NREL 15-MW. The Dynamic Mode Decomposition (DMD) approach has been used to detect dynamically-relevant flow structures. We employ the Sparsity-Promoting version of the DMD (SPDMD) algorithm for ranking the most relevant modes, in order to extract a limited subset of relevant flow features that optimally approximate the original data sequence. The dataset on which the SPDMD is based consists of ordered snapshots obtained by Large Eddy Simulations (LES), where the Actuator Line Method (ALM) simulates the rotor and the Immersed Boundary Method (IBM) models the tower and nacelle. To ensure a realistic comparison, the two turbines are subjected to two turbulent inflows with the same mean Atmospheric Boundary Layer (ABL) obtained through a precursor simulation. The results reveal significant differences in the dependence of the absolute value of the DMD amplitudes on the angular frequency for the two turbines. However, the coherent structures appear to have the same shape for the main modes, although the tip vortex structures have a higher dynamic relevance for the NREL 15-MW turbine. This is due to the larger length scales imposed by the rotor and the lower turbulence intensity at the taller rotor height.
A Gaussian‐shaped, three‐dimensional (3DG‐k) wake model is proposed considering the shear wind effect. The model defines the wake radius rw to be equal to twice the Gaussian standard deviation σ and establishes a link with the expansion coefficient k of the physical wake boundary to describe the wake boundary. Garrad Hassan (GH) wind tunnel test data, Shiren wind farm measurement data, Nibe wind farm measurement data, and Vestas V80‐2MW wind turbine computational data by large eddy simulation method are used to validate the accuracy of the 3DG‐k, Jensen, 3D Gaussian (3DG), and 3D cosine (3D‐C) models. Results show that the 3DG‐k model exhibits higher accuracy for the four cases compared to other models. Due to its simplicity and universality, the model can be used for layout optimization and wake control of wind farms.
Modelling wind turbine wake using the standard k − ǫ atmospheric turbulence model gives a too fast wake dissipation compared to measurements and more advanced turbulence models. The problem is that the relevant scales of turbulence are different from the point of view of the wind turbines and from the point of view of the terrain. As the atmospheric turbulence model imposes the scale of turbulence, part of the influence of the wind turbine on the air-flow is happening at the turbulence level. It becomes therefore necessary to add terms in the turbulence equations to account for the wind turbine activity. In this context two dif-ferent models are compared together and with wind turbine wake measurements. With the proper parameterization, they are both able to produce similar results, in agreement with the measurements.
Field measurements of the wake flow produced from a 2-MW Enercon E-70 wind turbine were performed using three scanning Doppler wind lidars. A GPS-based technique was used to determine the position of the wind turbine and the wind lidar locations, as well as the direction of the laser beams. The lidars used in this study are characterized by a high spatial resolution of 18 m, which allows the detailed characterization of the wind turbine wake. Two-dimensional measurements of wind speed were carried out by scanning a single lidar over the vertical symmetry plane of the wake. The mean axial velocity field was then retrieved by averaging 2D scans performed consecutively. To investigate wake turbulence, single lidar measurements were performed by staring the laser beam at fixed directions and using the maximum sampling frequency. From these tests, peaks in the velocity variance are detected within the wake in correspondence of the turbine top tip height; this enhanced turbulence could represent a source of dangerous fatigue loads for downstream turbines. The spectral density of the measured velocity fluctuations shows a clear inertial-range scaling behavior. Then, simultaneous measurements with two lidars were performed in order to characterize both the axial and the vertical velocity components. For this setup, the two velocity components were retrieved only for measurement points for which the two laser beams crossed nearly at a right angle. Statistics were computed over the sample set for both velocity components, and they showed strong flow fluctuations in the near-wake region at turbine top tip height, with a turbulence intensity of about 30%.
Large-eddy simulations are performed to evaluate the performance of the surface boundary condition downwind of a rough-to-smooth surface transition. Two types of boundary conditions are tested: (1) The standard formulation based on local application of the Monin–Obukhov similarity theory, and (2) a new model based on the modification of the recently proposed model of Chamorro and Porté-Agel (L. Chamorro and F. Porté-Agel, Velocity and surface shear stress distributions behind a rough-to-smooth surface transition: A simple new model, Bound.-Layer Meteorol. 130 (2009), pp. 29–41). The new model assumes that the wind velocity downwind of a rough-to-smooth transition can be estimated as a weighted average of two logarithmic profiles. The first log-law is recovered above the internal boundary-layer height and corresponds to the upwind velocity profile. The second log-law is adjusted to the downwind aerodynamic roughness and is recovered near the surface in the equilibrium sublayer. Within that layer, the local log-law model can predict the surface shear stress well. The proposed nonlinear form of the weighting factor is equal to ln(z/δeq)/ln(δ i /δeq), where z, δ i and δeq are the height of the prediction location, the internal boundary-layer depth at that downwind distance, and the height of equilibrium sublayer, respectively. The performance of the new model is tested with available wind-tunnel measurements and shows improved predictions of surface shear stress and velocity distribution at different positions downwind of the transition. In addition, the prediction of the new model shows very small dependence on the height (i.e., grid size) at which it is applied.
The book is aimed at the beginning graduate level for students with an undergraduate background in meteorology. The chapter organization is: mean boundary layer characteristics; statistics; application of the governing equations to turbulent flow; prognostic equations for turbulent fluxes and variances; turbulent kinetic energy, stability, and scaling; turbulence closure techniques; boundary conditions and external forcings; time series; similarity theory; measurement and simulation techniques; convective mixed layer; stable boundary layer; boundary layer clouds; geographic effects. -after Author
Wind farm-atmosphere interaction is complicated by the effect of turbine array configuration on momentum, scalar and kinetic energy fluxes. Wind turbine arrays are often arranged in rectilinear grids and, depending on the prevailing wind direction, may be perfectly aligned or perfectly staggered. The two extreme configurations are end members with a spectrum of infinite possible layouts. A wind farm of finite length may be modeled as an added roughness or as a canopy in large-scale weather and climate models. However, it is not clear which analogy is physically more appropriate. Also, surface scalar flux, including heat, moisture and trace gas (e.g. CO2), are affected by wind farms, and need to be properly parameterized in large-scale models. Experiments involving model wind farms, in aligned and staggered configurations, were conducted in a thermally controlled boundary-layer wind tunnel. Measurements of the turbulent flow were made using a custom x-wire/cold-wire probe. Particular focus was placed on studying the effect of wind farm layout on flow adjustment, momentum and scalar fluxes, and turbulent kinetic energy distribution. The flow statistics exhibit similar turbulent transport properties to those of canopy flows, but retain some characteristic surface-layer properties in a limited region above the wind farms as well. The initial wake growth over columns of turbines is faster in the aligned wind farm. However, the overall wake adjusts within and grows more rapidly over the staggered farm. The flow equilibrates faster and the overall momentum absorption is higher for the staggered compared to the aligned farm, which is consistent with canopy scaling and leads to a larger effective roughness. Surface heat flux is found to be altered by the wind farms compared to the boundary-layer flow without turbines, with lower flux measured for the staggered wind farm.
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 case.
In recent years, there has been a rapid development of the wind farms in Japan. It becomes very important to investigate the
wind turbine arrangement in wind farm, in order that the wake of one wind turbine does not to interfere with the flow in other
wind turbines. In such a case, in order to achieve the highest possible efficiency from the wind, and to install as many as
possible wind turbines within a limited area, it becomes a necessity to study the mutual interference of the wake developed
by wind turbines. However, there is no report related to the effect of the turbulence intensity of the external flow on the
wake behind a wind turbine generated in the wind tunnel. In this paper, the measurement results of the averaged wind profile
and turbulence intensity profile in the wake in the wind tunnel are shown when the turbulence intensity of the external wind
was changed. The wind tunnel experiment is performed with 500mm-diameter two-bladed horizontal axis wind turbine and the wind
velocity in wake is measured by an I-type hot wire probe. As a result, it is clarified that high turbulence intensities enable
to the entrainment of the main flow and the wake and to recover quickly the velocity in the wake.