Wind Turbine Array Boundary Layer Research Articles

Velocity data in a fully developed experimental wind turbine array boundary layer

AbstractExperimental data are reported for a wind turbine array boundary layer (WTABL) in a model wind farm. An array of 95 model wind turbines consisting of 5 streamwise columns by 19 spanwise rows was studied in a high Reynolds number boundary layer in the Flow Physics Facility (FPF) at the University of New Hampshire. The wind turbine array was constructed of porous disks of 0.25 m diameter, which were drag (thrust) matched to typical offshore wind turbine operating conditions. The turbine spacing was 8 diameters in the streamwise and 4 diameters in the spanwise directions. Spires were used to thicken the boundary layer and achieve a boundary layer thickness on the order of 1 m at the first row of the wind turbine array, which is located 33 m downstream from the test section inlet, thus placing the turbines in the bottom 1/3 of the boundary layer. Velocity profiles were measured with a pitot tube in the center column of the array. To within experimental uncertainty, a fully developed WTABL condition is observed in the mean velocity, for defined inlet conditions and spacings, from row 12 on. The wind turbine array acts as a sparse displaced roughness: it creates an internal layer whose origin (in the wall‐normal direction) remains fixed in space, while the turbulent boundary layer the array was placed in continues to grow. Careful consideration was given to an expanded uncertainty analysis, which elucidates the need for long measurement times in large facilities. Porous disk turbine models are the experimental equivalent of numerical actuator disks; therefore, this publicly available data set is expected to be useful for numerical model validation.

Wind Farms and Humidity

Several investigations have shown that enhanced mixing brought about by wind turbines alters near-surface meteorological conditions within and downstream of a wind farm. When scalar meteorological parameters have been considered, the focus has most often centered on temperature changes. A subset of these works has also considered humidity to various extents. These limited investigations are complemented by just a few studies dedicated to analyzing humidity changes. With onshore wind turbines often sited in agricultural areas, any changes to the microclimate surrounding a turbine can impact plant health and the length of the growing season; any changes to the environment around an offshore wind farm can change cloud and fog formation and dissipation, among other impacts. This article provides a review of observational field campaigns and numerical investigations examining changes to humidity within wind turbine array boundary layers. Across the range of empirical observations and numerical simulations, changes to humidity were observed in stably stratified conditions. In addition to the role of atmospheric stability, this review reveals that the nature of the change depends on the upstream moisture profile; robustness of the mixing; turbine array layout; distance from the turbine, in all three directions; and vertical temperature profile.

Data-driven modeling of the wake behind a wind turbine array

The wake flow in a wind turbine array boundary layer is described using the Koopman operator. Dynamics of the flow are decomposed into the linear and forcing terms, and the low-energy delay coordinates are revealed. The rare events show the non-Gaussian long tails that capture the switching and bursting phenomena. The near-wake region shows the incoherent phase space region, where the dynamics are strongly nonlinear. The far-wake region is marked with the small non-Gaussian forcing term, and the dynamics are largely governed by linear dynamics. The data-driven predictive model is built based on the Hankel-based dynamic mode decomposition and treats the nonlinear state of forcing term as external actuation. The model forecasts the evolution of the flow field for short-term timescales. The mean relative errors between the predictive and test fluctuating velocities are approximately 15%.

Turbulence kinetic energy budget and conditional sampling of momentum, scalar, and intermittency fluxes in thermally stratified wind farms

ABSTRACTA description of the turbulence kinetic energy budget is investigated to understand the dynamics and turbulence energy transfer between the atmospheric boundary layer and large wind farms. The turbulence kinetic energy budget terms are a dominant factor in explaining the energy supply process in wind farms. Large eddy simulations are used to generate the thermally stratified wind turbine array boundary layer, where stable and unstable conditions are considered. The wakes represent a sink of mean kinetic energy, and turbulence transport redistributes energy in the wake region. The energy balance between the budget terms is dependent on the physical location in the wind farm. During the unstable scenario, turbulence is driven by the production, transport, and buoyancy terms. Further, the contribution of the turbulence kinetic energy budget terms is reduced with increasing atmospheric stability, especially above the shear layer, where the mechanical production is the dominant term. Pressure diffusion redistributes the turbulent energy from the streamwise direction into the other components of the normal Reynolds stresses. This distinctive feature of the changing thermal stratification is presented through the quadrant analysis. The momentum ejection and sweep frequencies are both comparable and dominant. The scalar flux shows an increase in the contribution of the negative correlation in the quadrants. The quadrant analysis is extended to account for intermittency based on the pointwise Hölder exponents. Positive correlations are dominant in the wake and in higher layers of the domain for both considered cases.

Analysis of near‐surface relative humidity in a wind turbine array boundary layer using an instrumented unmanned aerial system and large‐eddy simulation

AbstractSimulation and modeling have shown that wind farms have an impact on the near‐surface atmospheric boundary layer as turbulent wakes generated by the turbines enhance vertical mixing. While a few observational data sets that focus on near‐surface temperature changes exist, these studies lack high spatial resolution and neglect the combined effect of these temperature changes with an altered humidity profile. With a large portion of wind farms hosted within an agricultural context, changes to relative humidity can potentially have secondary impacts, such as to the productivity of crops. The goal of this study is to gather high‐resolution in situ field measurements in the wake of a single wind turbine in order to differentially map downstream changes to relative humidity. These measurements, obtained by an instrumented unmanned aerial system, are complemented by numerical experiments conducted using large‐eddy simulation. Observations and numerical results are in good general agreement around a single wind turbine and show that downstream relative humidity is differentially altered in all directions, specifically decreased below the turbine hub height. Large‐eddy simulation is then used to determine the effect of a large 7 × 4 turbine array on the relative humidity distribution in compounding wakes. It is found that the region of relative humidity decrease below the turbine hub height and the region of increase above the hub height both intensify, differentially extend in the lateral directions, and move slightly upward with downstream distance.

Assessing spacing impact on coherent features in a wind turbine array boundary layer

Abstract. As wind farms become larger, the spacing between turbines becomes a significant design consideration that can impose serious economic constraints. To investigate the turbulent flow structures in a 4 × 3 Cartesian wind turbine array boundary layer (WTABL), a wind tunnel experiment was carried out parameterizing the streamwise and spanwise wind turbine spacing. Four cases are chosen spacing turbines by 6 or 3D in the streamwise direction, and 3 or 1.5D in the spanwise direction, where D = 12 cm is the rotor diameter. Data are obtained experimentally using stereo particle image velocimetry. Mean streamwise velocity showed maximum values upstream of the turbine with the spacing of 6 and 3D in the streamwise and spanwise direction, respectively. Fixing the spanwise turbine spacing to 3D, variations in the streamwise spacing influence the turbulent flow structure and the power available to following wind turbines. Quantitative comparisons are made through spatial averaging, shifting measurement data and interpolating to account for the full range between devices to obtain data independent of array spacing. The largest averaged Reynolds stress is seen in cases with spacing of 3D × 3D. Snapshot proper orthogonal decomposition (POD) was employed to identify the flow structures based on the turbulence kinetic energy content. The maximum turbulence kinetic energy content in the first POD mode is seen for turbine spacing of 6D × 1.5D. The flow upstream of each wind turbine converges faster than the flow downstream according to accumulation of turbulence kinetic energy by POD modes, regardless of spacing. The streamwise-averaged profile of the Reynolds stress is reconstructed using a specific number of modes for each case; the case of 6D × 1.5D spacing shows the fastest reconstruction to compare the rate of reconstruction of statistical profiles. Intermediate modes are also used to reconstruct the averaged profile and show that the intermediate scales are responsible for features seen in the original profile. The variation in streamwise and spanwise spacing leads to changes in the background structure of the turbulence, where the color map based on barycentric map and Reynolds stress anisotropy tensor provides an alternate perspective on the nature of the perturbations within the wind turbine array. The impact of the streamwise and spanwise spacings on power produced is quantified, where the maximum production corresponds with the case of greatest turbine spacing.

Anisotropy stress invariants of thermally stratified wind turbine array boundary layers using large eddy simulations

In the interest of understanding the dynamics and energy transfer between the atmospheric boundary layer and large wind turbine arrays, a description of the turbulence anisotropy in the wake region of wind turbines is necessary. Flux of high momentum flow into the wind turbine array by anisotropic turbulence is a dominant factor of mean kinetic energy resupply for the wind farm. Under thermal stratification, the behavior of the turbulence field, and the energy flux, is significantly altered. Here, a thermally stratified wind turbine array boundary layer is studied in detail using a combination of Lumley and barycentric maps together with the recently introduced spheroid and color maps. The atmospheric flow is modelled using a large eddy simulation driven by a constant geostrophic wind and a time-varying ground surface temperature, obtained from a selected period of the Cooperative Atmosphere-Surface Exchange Study-99 field experiment. The wind farm is modelled using the traditional actuator-disk with rotation and yaw-alignment. The results show that turbulence under unstable stratification tends to be more isotropic than that under neutral and stable stratification. The turbulent mixing attributed to positive buoyancy in unstable regimes determines the energy distribution between flow layers, directly affecting the vertical distribution of anisotropy. Contrarily, in the stably stratified flow, negative buoyancy damps the turbulent fluctuations, hence affecting the evolution of the Reynolds stress, leading to an increase of flow anisotropy. In both thermal stratification regimes, wind turbines alter the structure of the turbulence within the atmospheric boundary layer by creating regions of greater anisotropy and expanding the boundary layer vertically. For the modeling community, it is important to note that the wind turbine wakes display a larger degree of anisotropy that is related well to the production of turbulent kinetic energy and mean kinetic energy entrainment, and hence, it is important to model correctly for accurate power forecasting. Leveraging the new insights into wind turbine/atmospheric boundary layer interaction found here will benefit the formulation of a new generation of efficient low order models for commercial application.

Turbulence characteristics of a thermally stratified wind turbine array boundary layer via proper orthogonal decomposition

A large eddy simulation framework is used to explore the structure of the turbulent flow in a thermally stratified wind turbine array boundary layer. The flow field is driven by a constant geostrophic wind with time-varying surface boundary conditions obtained from a selected period of the CASES-99 field experiment. Proper orthogonal decomposition is used to extract coherent structures of the turbulent flow under the considered thermal stratification regimes. The flow structure is discussed in the context of three-dimensional representations of key modes, which demonstrate features ranging in size from the wind turbine wakes to the atmospheric boundary layer. Results demonstrate that structures related to the atmospheric boundary layer flow dominate over those introduced by the wind farm for the unstable and neutrally stratified regimes; large structures in atmospheric turbulence are beneficial for the wake recovery, and consequently the presence of the turbulent wind turbine wakes is diminished. Contrarily, the flow in the stably stratified case is fully dominated by the presence of the turbines and highly influenced by the Coriolis force. A comparative analysis of the test cases indicates that during the stable regime, higher-order modes contribute less to the overall character of the flow. Under neutral and unstable stratification, important turbulence dynamics are distributed over a larger range of basis functions. The influence of the wind turbines on the structure of the atmospheric boundary layer is mainly quantified via the turbulence kinetic energy of the first ten modes. Linking the new insights into structure of the wind turbine/atmospheric boundary layer and their interaction addressed here will benefit the formulation of new simplified models for commercial application.

Inverse structure functions in the canonical wind turbine array boundary layer

Wind tunnel measurements for a 3 × 3 canonical wind turbine array boundary layer are obtained using hot-wire anemometer velocity signals. Two downstream locations are considered, referring to the near- and far-wake, and 21 vertical points are acquired per profile. Velocity increments and exit distances are used to quantify inverse structure functions at both downstream locations. Inverse structure functions in the near-wake show a similar profile for the main vertical locations, but diverge as the moment is increased. In the far-wake, inverse structure functions converge toward a single function for all vertical location and moments. The scaling exponents for inverse structure functions are calculated directly and relatively, using extended self similarity. Scaling exponents show strong dependence on vertical position along the wind turbine profile in the near-wake and remain relatively constant in the far-wake. Intermittency in the near-wake is indicated by the nonlinear behavior of the direct and relative scaling exponents when plotted against their respective moments.

Structure functions, scaling exponents and intermittency in the wake of a wind turbine array

Hot-wire measurements obtained in a 3 × 3 wind turbine array boundary layer are utilized to analyze high order structure functions, intermittency effects as well as the probability density functions of velocity increments at different scales within the energy cascade. The intermittency exponent is found to be greater in the far-wake region in comparison with the near-wake. At hub height, the intermittency exponent is found to be null. Extended self-similarity scaling exponents of the second, fourth, and fifth order structure functions remain relatively constant as a function of height in the far-wake; whereas in the near-wake, these are highly affected by the passage of the rotor where tip vortices reside, thus showing a dependence on physical location. When comparing with proposed models, these generally overpredict the structure functions in the far-wake region. The probability density function distributions in the far-wake region display wider tails compared to the near-wake region, and the constant skewness hypothesis based on the local isotropy is disrupted in the wake.

Effect of downwind swells on offshore wind energy harvesting – A large-eddy simulation study

The effect of ocean downwind swells on the harvesting of offshore wind energy is studied using large-eddy simulation of fully developed wind turbine array boundary layers, which is dynamically coupled with high-order spectral simulation of sea-surface wave field with and without the presence of a downwind swell. For the two moderate wind speeds of 7 m/s and 10 m/s considered in this study, the swell is found to induce a temporal oscillation in the extracted wind power at the swell frequency, with a magnitude of 6.7% and 4.0% of the mean wind power output, respectively. Furthermore, the averaged wind power extraction is found to be increased by as much as 18.8% and 13.6%, respectively. Statistical analysis of the wind field indicates that the wind speed in the lower portion of the boundary layer oscillates periodically with fast wind above the swell trough and slow wind above the swell crest, resulting in the observed wind power oscillation. The wind above the swell accelerates due to the strong wave forcing, causes a net upward flux of kinetic energy into the wind turbine layer, and thus acts to increase the extracted wind power of the turbines. For a high wind speed of 17 m/s, the wave-induced motion becomes relatively weak and the swell effect on the wind turbine performance diminishes.

Solution of the Fokker–Planck equation in a wind turbine array boundary layer

Hot-wire velocity signals from a model wind turbine array boundary layer flow wind tunnel experiment are analyzed. In confirming Markovian properties, a description of the evolution of the probability density function of velocity increments via the Fokker–Planck equation is attained. Solution of the Fokker–Planck equation is possible due to the direct computation of the drift and diffusion coefficients from the experimental measurement data which were acquired within the turbine canopy. A good agreement is observed in the probability density functions between the experimental data and numerical solutions resulting from the Fokker–Planck equation, especially in the far-wake region. The results serve as a tool for improved estimation of wind velocity within the array and provide evidence that the evolution of such a complex and turbulent flow is also governed by a Fokker–Planck equation at certain scales.

Identification of Markov process within a wind turbine array boundary layer

The Markovian properties within a wind turbine array boundary layer are explored for data taken in a wind tunnel containing a model wind turbine array. A stochastic analysis of the data is carried out using the mathematics of Markov processes. The data were obtained using hot-wire anemometry thus providing point velocity statistics. The theory of Markov process is applied to obtain a statistical description of longitudinal velocity increments inside the turbine wake. Comparison of two- and three-scale conditional probability density functions indicates the existence of Markovian properties in longitudinal velocity increments for scale differences larger than the Taylor microscale. This result is quantified by use of the Wilcoxon rank-sum test which verifies that this relationship holds independent of initial scale selection outside of the near-wake region behind a wind turbine. Furthermore, at the locations which demonstrate Markovian properties, there appears to be a well defined inertial subrange which follows Kolmogorov's −5/3 scaling behavior. The results show that directly behind the tips of the rotor and the hub, the complex turbulent interactions and large scale structures of the near-wake affect the Markovian nature of the field. The presence of a Markov process in the remaining locations leads to characterization of the development multiscale statistics of the wind turbine wakes using the most recent states of the flow.

A concurrent precursor inflow method for Large Eddy Simulations and applications to finite length wind farms

In order to enable simulations of developing wind turbine array boundary layers with highly realistic inflow conditions a concurrent precursor method for Large Eddy Simulations is proposed. In this method we consider two domains simultaneously, i.e. in one domain a turbulent Atmospheric Boundary Layer (ABL) without wind turbines is simulated in order to generate the turbulent inflow conditions for a second domain in which the wind turbines are placed. The benefit of this approach is that a) it avoids the need for large databases in which the turbulent inflow conditions are stored and the correspondingly slow I/O operations and b) we are sure that the simulations are not negatively affected by statically swept fixed inflow fields or synthetic fields lacking the proper ABL coherent structures. Sample applications are presented, in which, in agreement with field data a strong decrease of the power output of downstream wind-turbines with respect to the first row of wind-turbines is observed for perfectly aligned inflow.

Large eddy simulation study of scalar transport in fully developed wind-turbine array boundary layers

Wind harvesting is fast becoming an important alternative source of energy. As wind farms become larger, they begin to attain scales at which two-way interactions with the atmospheric boundary layer (ABL) must be taken into account. Several studies have shown that there is a quantifiable effect of wind farms on the local meteorology, mainly through changes in the land-atmosphere fluxes of heat and moisture. In particular, the observed trends suggest that wind farms increase fluxes at the surface and this could be due to increased turbulence in the wakes. Conversely, simulations and laboratory experiments show that underneath wind farms, the friction velocity is decreased due to extraction of momentum by the wind turbines, a factor that could decrease scalar fluxes at the surface. In order to study this issue in more detail, a suite of large eddy simulations of an infinite (fully developed) wind turbine array boundary layer, including scalar transport from the ground surface without stratification, is performed. Results show an overall increase in the scalar fluxes of about 10%–15% when wind turbines are present in the ABL, and that the increase does not strongly depend upon wind farm loading as described by the turbines’ thrust coefficient and the wind turbines spacings. A single-column analysis including scalar transport shows that the presence of wind farms can be expected to increase slightly the scalar transport from the bottom surface and that this slight increase is due to a delicate balance between two strong opposing trends.

Large eddy simulation study of fully developed wind-turbine array boundary layers

It is well known that when wind turbines are deployed in large arrays, their efficiency decreases due to complex interactions among themselves and with the atmospheric boundary layer (ABL). For wind farms whose length exceeds the height of the ABL by over an order of magnitude, a “fully developed” flow regime can be established. In this asymptotic regime, changes in the streamwise direction can be neglected and the relevant exchanges occur in the vertical direction. Such a fully developed wind-turbine array boundary layer (WTABL) has not been studied systematically before. A suite of large eddy simulations (LES), in which wind turbines are modeled using the classical “drag disk” concept, is performed for various wind-turbine arrangements, turbine loading factors, and surface roughness values. The results are used to quantify the vertical transport of momentum and kinetic energy across the boundary layer. It is shown that the vertical fluxes of kinetic energy are of the same order of magnitude as the power extracted by the forces modeling the wind turbines. In the fully developed WTABL, the kinetic energy extracted by the wind turbines is transported into the wind-turbine region by vertical fluxes associated with turbulence. The results are also used to develop improved models for effective roughness length scales experienced by the ABL. The effective roughness scale is often used to model wind-turbine arrays in simulations of atmospheric dynamics at larger (regional and global) scales. The results from the LES are compared to several existing models for effective roughness lengths. Based on the observed trends, a modified model is proposed, showing improvement in the predicted effective roughness length.

Experimental study of the horizontally averaged flow structure in a model wind-turbine array boundary layer

When wind turbines are deployed in large arrays, their ability to extract kinetic energy from the flow decreases due to complex interactions among them, the terrain topography and the atmospheric boundary layer. In order to improve the understanding of the vertical transport of momentum and kinetic energy across a boundary layer flow with wind turbines, a wind-tunnel experiment is performed. The boundary layer flow includes a 3×3 array of model wind turbines. Particle-image-velocity measurements in a volume surrounding a target wind turbine are used to compute mean velocity and turbulence properties averaged on horizontal planes. Results are compared with simple momentum theory and with expressions for effective roughness length scales used to parametrize wind-turbine arrays in large-scale computer models. The impact of vertical transport of kinetic energy due to turbulence and mean flow correlations is quantified. It is found that the fluxes of kinetic energy associated with the Reynolds shear stresses are of the same order of magnitude as the power extracted by the wind turbines, highlighting the importance of vertical transport in the boundary layer.