Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

The Structure of Turbulent Shear Flow By Dr. A. A. Townsend. Pp. xii + 315. 8¾ in. × 5½ in. (Cambridge: At the University Press.) 40s.

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The Structure of Turbulent Shear Flow

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...

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

Turbulence, Coherent Structures, Dynamical Systems and SymmetryP. Holmes, J. L. Lumley, G. Berkooz, and C. W. Rowley, 2nd ed., Cambridge University Press, Cambridge, England, U.K., 2012, 386 pp., $90

Wind energy, together with other renewable energy sources, are expected to grow substantially in the coming decades and play a key role in mitigating climate change and achieving energy sustainability. One of the main challenges in optimizing the design, operation, control, and grid integration of wind farms is the prediction of their performance, owing to the complex multiscale two-way interactions between wind farms and the turbulent atmospheric boundary layer (ABL). From a fluid mechanical perspective, these interactions are complicated by the high Reynolds number of the ABL flow, its inherent unsteadiness due to the diurnal cycle and synoptic-forcing variability, the ubiquitous nature of thermal effects, and the heterogeneity of the terrain. Particularly important is the effect of ABL turbulence on wind-turbine wake flows and their superposition, as they are responsible for considerable turbine power losses and fatigue loads in wind farms. These flow interactions affect, in turn, the structure of the ABL and the turbulent fluxes of momentum and scalars. This review summarizes recent experimental, computational, and theoretical research efforts that have contributed to improving our understanding and ability to predict the interactions of ABL flow with wind turbines and wind farms.

https://link.springer.com/content/pdf/10.1007/s10546-019-00473-0.pdf

Wind-Turbine and Wind-Farm Flows: A Review

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 a...

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

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For large wind farms, kinetic energy must be entrained from the flow above the wind turbines to replenish wakes and enable power extraction in the array. Various statistical features of turbulence causing vertical entrainment of mean-flow kinetic energy are studied using hot-wire velocimetry data taken in a model wind farm in a scaled wind tunnel experiment. Conditional statistics and spectral decompositions are employed to characterize the most relevant turbulent flow structures and determine their length-scales. Sweep and ejection events are shown to be the largest contributors to the vertical kinetic energy flux, although their relative contribution depends upon the location in the wake. Sweeps are shown to be dominant in the region above the wind turbine array. A spectral analysis of the data shows that large scales of the flow, about the size of the rotor diameter in length or larger, dominate the vertical entrainment. The flow is less incoherent below the array, causing decreased vertical fluxes there. The results show that improving the rate of vertical kinetic energy entrainment into wind turbine arrays is a standing challenge and would require modifying the large-scale structures of the flow. Such an optimization would in the future aid recovery of the wind turbine wake towards conditions corresponding to the undisturbed atmospheric boundary layer.

Statistical analysis of kinetic energy entrainment in a model wind turbine array boundary layer

Laser Doppler anemometry measurements are carried out in order to investigate the influences of the external conditions on a transitionally rough favorable pressure gradient turbulent boundary layer. The acquired data is normalized using the scalings obtained by the means of equilibrium similarity of the outer flow. The point at hand is to not only understand the interaction between the rough surface and the outer flow but also to include the external pressure gradient as the flow evolves in the streamwise direction. It is found that the velocity profiles show the effects of the upstream conditions imposed on the flow when normalized with the free-stream velocity. However, the profiles do collapse when normalized with U ∞ δ*/δ, demonstrating that this scaling absorbs the roughness effects and upstream conditions. An augmentation in the Reynolds stresses occurs with an increase in the roughness parameter and a decrease due to the external favorable pressure gradient. However, close to the wall, there is an...

Influence of the external conditions on transitionally rough favorable pressure gradient turbulent boundary layers

Wind tunnel experiments were performed, where the development of the wake of a model wind turbine was measured using stereo Particle Image Velocimetry to observe the influence of platform pitch motion. The wakes of a classical bottom fixed turbine and a streamwise oscillating turbine are compared. Results indicate that platform pitch creates an upward shift in all components of the flow and their fluctuations. The vertical flow created by the pitch motion as well as the reduced entrainment of kinetic energy from undisturbed flows above the turbine result in potentially higher loads and less available kinetic energy for a downwind turbine. Experimental results are compared with four wake models. The wake models employed are consistent with experimental results in describing the shapes and magnitudes of the streamwise velocity component of the wake for a fixed turbine. Inconsistencies between the model predictions and experimental results arise in the floating case particularly regarding the vertical displacement of the velocity components of the flow. Furthermore, it is found that the additional degrees of freedom of a floating wind turbine add to the complexity of the wake aerodynamics and improved wake models are needed, considering vertical flows and displacements due to pitch motion.

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Raúl Bayoán Cal

Papers

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

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

Statistical analysis of kinetic energy entrainment in a model wind turbine array boundary layer

Influence of the external conditions on transitionally rough favorable pressure gradient turbulent boundary layers

Experimental Study on Influence of Pitch Motion on the Wake of a Floating Wind Turbine Model