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

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

Modern wind farms comprised of horizontal-axis wind turbines (HAWTs) require significant land resources to separate each wind turbine from the adjacent turbine wakes. This aerodynamic constraint limits the amount of power that can be extracted from a given wind farm footprint. The resulting inefficiency of HAWT farms is currently compensated by using taller wind turbines to access greater wind resources at high altitudes, but this solution comes at the expense of higher engineering costs and greater visual, acoustic, radar, and environmental impacts. We investigated the use of counter-rotating vertical-axis wind turbines (VAWTs) in order to achieve higher power output per unit land area than existing wind farms consisting of HAWTs. Full-scale field tests of 10-m tall VAWTs in various counter-rotating configurations were conducted under natural wind conditions during summer 2010. Whereas modern wind farms consisting of HAWTs produce 2–3 W of power per square meter of land area, these field tests indicate that power densities an order of magnitude greater can potentially be achieved by arranging VAWTs in layouts that enable them to extract energy from adjacent wakes and from above the wind farm. Moreover, this improved performance does not require higher individual wind turbine efficiency, only closer wind turbine spacing and a sufficient vertical flux of turbulence kinetic energy from the atmospheric surface layer. The results suggest an alternative approach to wind farming that has the potential to concurrently reduce the cost, size, and environmental impacts of wind farms.

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Potential order-of-magnitude enhancement of wind farm power density via counter-rotating vertical-axis wind turbine arrays

This work is dedicated to systematically studying and predicting the wake characteristics of a yawed wind turbine immersed in a turbulent boundary layer. To achieve this goal, wind tunnel experiments were performed to characterize the wake of a horizontal-axis wind turbine model. A high-resolution stereoscopic particle image velocimetry system was used to measure the three velocity components in the turbine wake under different yaw angles and tip-speed ratios. Moreover, power and thrust measurements were carried out to analyse the performance of the wind turbine. These detailed wind tunnel measurements were then used to perform a budget study of the continuity and Reynolds-averaged Navier–Stokes equations for the wake of a yawed turbine. This theoretical analysis revealed some notable features of the wakes of yawed turbines, such as the asymmetric distribution of the wake skew angle with respect to the wake centre. Under highly yawed conditions, the formation of a counter-rotating vortex pair in the wake cross-section as well as the vertical displacement of the wake centre were shown and analysed. Finally, this study enabled us to develop general governing equations upon which a simple and computationally inexpensive analytical model was built. The proposed model aims at predicting the wake deflection and the far-wake velocity distribution for yawed turbines. Comparisons of model predictions with the wind tunnel measurements show that this simple model can acceptably predict the velocity distribution in the far wake of a yawed turbine. Apart from the ability of the model to predict wake flows in yawed conditions, it can provide valuable physical insight on the behaviour of turbine wakes in this complex situation.

Experimental and theoretical study of wind turbine wakes in yawed conditions

As wind farms become larger, the asymptotic limit of the “fully developed”, or “infinite”, wind farm has been receiving increased interest. This limit is relevant for wind farms on flat terrain whose length exceeds the height of the atmospheric boundary layer by over an order of magnitude. Recent computational studies based on Large Eddy Simulation have identified various mean velocity equilibrium layers, and have led to parameterizations of the effective roughness height that allow predicting the wind velocity at hub-height as function of parameters such as wind turbine spacing and loading factors. In the current paper, we employ this as a tool to make predictions of optimal wind turbine spacing as function of these parameters, as well as in terms of the ratio of turbine costs to land-surface costs. For realistic cost ratios, we find that the optimal average turbine spacing may be considerably higher than conventionally used in current wind-farm implementations.

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Optimal turbine spacing in fully developed wind farm boundary layers

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

This paper presents a new method (the Unrestricted Wind Farm Layout Optimization (UWFLO)) of arranging turbines in a wind farm to achieve maximum farm efficiency. The powers generated by individual turbines in a wind farm are dependent on each other, due to velocity deficits created by the wake effect. A standard analytical wake model has been used to account for the mutual influences of the turbines in a wind farm. A variable induction factor, dependent on the approaching wind velocity, estimates the velocity deficit across each turbine. Optimization is performed using a constrained Particle Swarm Optimization (PSO) algorithm. The model is validated against experimental data from a wind tunnel experiment on a scaled down wind farm. Reasonable agreement between the model and experimental results is obtained. A preliminary wind farm cost analysis is also performed to explore the effect of using turbines with different rotor diameters on the total power generation. The use of differing rotor diameters is observed to play an important role in improving the overall efficiency of a wind farm.Copyright © 2010 by ASME

Optimizing the Unrestricted Placement of Turbines of Differing Rotor Diameters in a Wind Farm for Maximum Power Generation

The classical streamtube analysis for a wind turbine couples the Bernoulli equation with the actuator-disk model to obtain the maximum possible power extraction at the wind turbine based on the difference between inlet and outlet fluxes of kinetic energy. However, the classical analysis neglects turbulence, which can play a crucial role in the various interactions of the streamtube with the turbulent Atmospheric Boundary Layer (ABL). The present study aims at examining the fluxes of kinetic energy on a wind turbine streamtube including the effects of turbulence, based on an existing Particle Image Velocimetry (PIV) data set obtained previously in a wind tunnel study of a model wind farm. The data are used to evaluate the most relevant fluxes of kinetic energy through the various parts of the control surface bounding the stream tube. It is found that the flux due to mean axial velocity, the turbulence-induced flux across the periphery of the streamtube, and the power extracted at the wind turbine are all o...

Experimental study of the kinetic energy budget in a wind turbine streamtube

The streamwise development of turbulence statistics and mean kinetic energy in a model wind farm consisting of 3 × 5 wind turbines is studied experimentally in a wind tunnel. The analysis uses planar Particle Image Velocimetry data obtained at the centerline plane of the wind farm, covering the inflow as well as four planes in between five downstream wind turbines. The data analysis is organized by dividing these measurement planes into three regions: the above-rotor, rotor-swept, and below-rotor regions. For each field, flow development is quantified using a properly defined relative difference norm based on an integration over each of the regions. Using this norm, it is found that the mean streamwise velocity approaches a fully developed state most rapidly, whereas the flow development is more gradual for the second-order statistics. The vertical entrainment flux of the mean kinetic energy by the Reynolds shear stress, ⟨U⟩⟨u′v′⟩, is observed to develop at a rate similar to that of the Reynolds shear stress rather than the mean streamwise velocity component. Its development is slowest in the layer nearest to the ground. Analysis of various terms in the mean kinetic energy equation shows that the wind turbine boundary layer has not yet reached fully developed conditions by the fifth turbine but that it is approaching such conditions. By comparing the vertical entrainment flux with the horizontal flux due to the mean flow, it is found that the former increases, whereas the latter decreases, as function of downstream distance, but that the former is already an important contributor in the developing region.

Streamwise development of the wind turbine boundary layer over a model wind turbine array

Several effects of nearly isotropic free-stream turbulence in transitionally rough turbulent boundary layers are studied using data obtained from laser Doppler anemometry measurements. The free-stream turbulence is generated with the use of an active grid, resulting in free-stream turbulence levels of up to 6.2%. The rough surface is characterized by a roughness parameter k+ ≈ 53, and measurements are performed at Reynolds numbers of up to Reθ = 11300. It is confirmed that the free-stream turbulence significantly alters the mean velocity deficit profiles in the outer region of the boundary layer. Consequently, the previously observed ability of the Zagarola & Smits (J. Fluid Mech., vol. 373, 1998, p. 33) velocity scale U∞δ*/δ to collapse results from both smooth and rough surface boundary layers, no longer applies in this boundary layer subjected to high free-stream turbulence. In inner variables, the wake region is significantly reduced with increasing free-stream turbulence, leading to decreased mean velocity gradient and production of Reynolds stress components. The effects of free-stream turbulence are clearly identifiable and significant augmentation of the streamwise Reynolds stress profiles throughout the entire boundary layer are observed, all the way down to the inner region. In contrast, the Reynolds wall-normal and shear stress profiles increase due to free-stream turbulence only in the outer part of the boundary layer due to the blocking effect of the wall. As a consequence, there is a significant portion of the boundary layer in which the addition of nearly isotropic turbulence in the free-stream, results in significant increases in anisotropy of the turbulence. To quantify which turbulence length scales contribute to this trend, second-order structure functions are examined at various distances from the wall. Results show that the anisotropy created by adding nearly isotropic turbulence in the free-stream resides mostly in the larger scales of the flow. Furthermore, by analysing the streamwise Reynolds stress equation, it can be predicted that it is the wall-normal gradient of 〈u2v〉 term that is responsible for the increase in 〈u2〉 profiles throughout the boundary layer (i.e. an efficient turbulent transport of turbulence away from the wall). Furthermore, a noticeable difference between the triple correlations for smooth and rough surfaces exists in the inner region, but no significant differences are seen due to free-stream turbulence. In addition, the boundary layer parameters δ*/δ95, H and cf are also evaluated from the experimental data. The flow parameters δ*/δ95 and H are found to increase due to roughness, but decrease due to free-stream turbulence, which has significance for flow control, particularly in delaying separation. Increases in cf due to high free-stream turbulence are also observed, associated with increased momentum flux towards the wall.

Jose Lebron

Papers

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

Optimizing the Unrestricted Placement of Turbines of Differing Rotor Diameters in a Wind Farm for Maximum Power Generation

Experimental study of the kinetic energy budget in a wind turbine streamtube

Streamwise development of the wind turbine boundary layer over a model wind turbine array

Effects of free-stream turbulence on rough surface turbulent boundary layers