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Large-eddy simulations of the atmospheric boundary layer are often performed using pseudo-spectral methods, which adopt a fringe-region approach to introduce inflow boundary conditions. However, we notice that a standard fringe-region technique excites spurious gravity waves when stratified atmospheres are considered, therefore enhancing the amount of energy reflected from the top of the domain and perturbing the velocity and pressure fields downstream. In this work, we develop a new fringe-region method that imposes the inflow conditions while limiting spurious effects on the surrounding flow. This is achieved by locally damping the convective term in the vertical momentum equation. We first apply the standard and wave-free fringe-region techniques to two-dimensional inviscid-flow simulations subjected to 169 different atmospheric states. A similar study is performed on a three-dimensional domain using a couple of atmospheric states. In all cases, the new fringe-region technique outperforms the standard method, imposing the inflow conditions with a minimal impact on the surrounding flow. Moreover, we also investigate the performance of two already existing non-reflective upper boundary conditions, that is a Rayleigh damping layer (RDL) and a radiation condition (RC). Results highlight the importance of carefully tuning the RDL to limit the distortion of the numerical solution. Also, we find that the tuned RDL outperforms the RC in all cases. Finally, the tuned RDL together with the wave-free fringe-region method are applied to an LES of a wind farm operating in a conventionally neutral boundary layer, for which we measure a reflectivity of only 0.75%.

Vertical temperature profiles influence the wind power generation of large offshore wind farms through stability-dependent effects such as blockage and gravity waves. However, wind energy resource assessments often only consider idealized temperature profiles, which are not guaranteed to represent the atmospheric state and its variation. To assist the selection of atmospheric states, we created a temperature profile atlas and representative temperature profiles for Europe. To achieve this, we developed a new, generally applicable, analytical temperature model for the atmospheric boundary layer and lower troposphere with which the European temperature profiles over the period 2016-2020 are analyzed using a double clustering approach. This methodology results in eight representative profiles and spatial clusters with similarly behaving temperature profiles, which are quantified in cluster fingerprints. These representative profiles and cluster fingerprints can be used in the selection of background profiles for wind energy simulations such as LES models and can furthermore be used to make informed comparisons of results from different wind farm sites.

As many coastal regions experience a rapid increase in offshore wind farm installations, inter-farm distances become smaller with a tendency to install larger turbines at high capacity densities. It is however not clear how the wake losses in wind farm clusters depend on the characteristics and spacing of the individual wind farms. Here, we quantify this based on multiple COSMO-CLM simulations, each of which assumes a different, spatially invariant combination of the turbine type and capacity density in a projected, future wind farm layout in the North Sea. An evaluation of the modelled wind climate with mast and lidar data for the period 2008–2020 indicates that the frequency distributions of wind speed and wind direction at turbine hub height are skillfully modelled and the seasonal and inter-annual variations in wind speed are represented well. The wind farm simulations indicate that at a capacity density of 8.1 MW km-2 and for SW-winds, inter-farm wakes can reduce the capacity factor at the inflow edge of wind farms from 59 % to between 55 % and 40 % depending on the proximity, size and number of the upwind farms. However, the long-term impact of wake losses in and between wind farms is mitigated by adopting next-generation, 15 MW wind turbines instead of 5 MW turbines, as the annual energy generation over all wind farms in the simulation is increased by 24 % at the same capacity density. In contrast, the impact of wake losses is exacerbated with increasing capacity density, as the layout-integrated, annual capacity factor varies between 54.4 % and 44.3 % over the considered range of 3.5 to 10 MW km-2. Overall, wind farm characteristics and inter-farm distances play an essential role in cluster-scale wake losses, which should be taken into account in future wind farm planning.

Numerical simulation tools such as large eddy simulations (LESs) have been extensively used in recent years to simulate and analyze turbine–wake interactions within large wind farms. However, to ensure the reliability of the performance and accuracy of such numerical solvers, validation against field measurements is essential. To this end, a measurement campaign is carried out at the Lillgrund offshore wind farm to gather data for the validation of an in-house LES solver. Flow field data are collected from the farm using three long-range WindScanners, along with turbine performance and load measurements from individual turbines. Turbulent inflow conditions are reconstructed from an existing precursor database using a scaling-and-shifting approach in an optimization framework, proposed so that the generated inflow statistics match the measurements. Thus, five different simulation cases are setup, corresponding to five different inflow conditions at the Lillgrund wind farm. Operation of the 48 Siemens 2.3 MW turbines from the Lillgrund wind farm is parameterized in the flow domain using an aeroelastic actuator sector model (AASM). Time-series turbine performance metrics from the simulated cases are compared against field measurements to evaluate the accuracy of the optimization framework, turbine model, and flow solver. In general, results from the numerical solver exhibited a good comparison in terms of the trends in power production, turbine loading, and wake recovery. For four out of the five simulated cases, the total wind farm power error was found to be below 5 %. However, when comparing individual turbine power production, statistical significant errors were observed for 16 % to 84 % of the turbines across the simulated cases, with larger errors being associated with wind directions resulting in configurations with aligned turbines. While the compared flapwise loads in general show a reasonable agreement, errors greater than 100 % were also present in some cases. Larger errors in the wake recovery in the far wake region behind the lidar installed turbines were also observed. An analysis of the observed errors reveals the need for an improved controller implementation, improvement in representing meso-scale effects, and possibly a finer simulation grid for capturing the smaller scales of wake turbulence.

Wind farm control has been a topic of research for more than two decades. It has been identified as a core component of grand challenges in wind energy science to support accelerated wind energy deployment and to transition to a clean and sustainable energy system for the 21st century. The prospect of collective control of wind turbines in an array, to increase energy extraction, reduce structural loads, improve the balance of systems, reduce operation and maintenance costs, etc. has inspired many researchers over the years to propose innovative ideas and solutions. However, practical demonstration and commercialization of some of the more advanced concepts has been limited by a wide range of challenges, which include the complex physics of turbulent flows in wind farms and the atmosphere, uncertainties related to predicting structural load and failure statistics, and the highly multi-disciplinary nature of the overall design optimization problem, among others. In the current work, we aim at providing a comprehensive overview of the state of the art and outstanding challenges, thus identifying the key research areas that could further enable commercial uptake and success of wind farm control solutions. To this end, we have structured the discussion on challenges and opportunities into four main areas: (1) insight in control flow physics, (2) algorithms and AI, (3) validation and industry implementation, and (4) integrating control with system design (co-design).

Wind farm flow control (WFFC) is a topic of interest at several research institutes and industry and certification agencies worldwide. For reliable performance assessment of the technology, the efficiency and the capability of the models applied to WFFC should be carefully evaluated. To address that, the FarmConners consortium has launched a common benchmark for code comparison under controlled operation to demonstrate its potential benefits, such as increased power production. The benchmark builds on available data sets from previous field campaigns, wind tunnel experiments, and high-fidelity simulations. Within that database, four blind tests are defined and 13 participants in total have submitted results for the analysis of single and multiple wakes under WFFC. Here, we present Part I of the FarmConners benchmark results, focusing on the blind tests with large-scale rotors. The observations and/or the model outcomes are evaluated via direct power comparisons at the upstream and downstream turbine(s), as well as the power gain at the wind farm level under wake steering control strategy. Additionally, wake loss reduction is also analysed to support the power performance comparison, where relevant. The majority of the participating models show good agreement with the observations or the reference high-fidelity simulations, especially for lower degrees of upstream misalignment and narrow wake sector. However, the benchmark clearly highlights the importance of the calibration procedure for control-oriented models. The potential effects of limited controlled operation data in calibration are particularly visible via frequent model mismatch for highly deflected wakes, as well as the power loss at the controlled turbine(s). In addition to the flow modelling, the sensitivity of the predicted WFFC benefits to the turbine representation and the implementation of the controller is also underlined. The FarmConners benchmark is the first of its kind to bring a wide variety of data sets, control settings, and model complexities for the (initial) assessment of farm flow control benefits. It forms an important basis for more detailed benchmarks in the future with extended control objectives to assess the true value of WFFC.

Wind energy is anticipated to play a central role in enabling a rapid transition from fossil fuels to a system based largely on renewable power. For wind power to fulfill its expected role as the backbone—providing nearly half of the electrical energy—of a renewable-based, carbon-neutral energy system, critical challenges around design, development, and deployment of land and offshore technologies must be addressed. During the past three years, the wind research community has invested significant effort toward understanding the nature and implications of these challenges and identifying associated gaps. The outcomes of these efforts are summarized in a series of ten articles, some under review by Wind Energy Science (WES) and others planned for submission during the coming months. This letter explains the genesis, significance, and impacts of these efforts.

Recent research suggests that atmospheric gravity waves can affect offshore wind-farm performance. A fast wind-farm boundary layer model has been proposed to simulate the effects of these gravity waves on wind-farm operation by Allaerts and Meyers (2019). The current work extends the applicability of that model to free atmospheres in which wind and stability vary with altitude. We validate the model using reference cases from literature on mountain waves. Analysis of a reference flow shows that internal gravity-wave resonance caused by the atmospheric non-uniformity can prohibit perturbations in the atmospheric boundary layer (ABL) at the wavelengths where it occurs. To determine the overall impact of the vertical variations in the atmospheric conditions on wind-farm operation, we consider 1 year of operation of the Belgian–Dutch wind-farm cluster with the extended model. We find that this impact on individual flow cases is often of the same order of magnitude as the total flow perturbation. In 16.6 % of the analyzed flows, the relative difference in upstream velocity reduction between uniform and non-uniform free atmospheres is more than 30 %. However, this impact is small when averaged over all cases. This suggests that variations in the atmospheric conditions should be taken into account when simulating wind-farm operation in specific atmospheric conditions.

The rapid growth of the offshore wind energy sector emphasizes the need for realistic projections of the lifetime energy yield of existing and planned offshore windfarms. Analyses of CMIP5 data show that, even though near-future wind speed changes over Europe and the North Sea are uncertain across models, these changes should be taken into account by wind industries due to the potentially large impact on the energy. Thanks to advances in model design and the increase in computing resources over the past decades, regional climate models (RCMs) can be used for multi-decadal simulations and that at a spatial resolution of a couple of kilometers or less. These high-resolution simulations not only allow for an improved representation of weather systems, but also allow to represent the interactions between windfarms and the atmosphere through a wind farm parametrization. In this way, RCMs can be employed for a detailed wind resource assessment for the coming decades that takes into account the wakes and energy losses induced by upwind arrays and clusters.In our wind resource assessment, we use the regional climate model COSMO-CLM, extended with the Fitch wind farm parametrization. An evaluation of a 10-year, ERA5-driven simulation at 2.8km resolution against in-situ anemometers, lidar measurements and satellite-borne ASCAT measurements that has been performed for the North Sea will be discussed. For the year 2019, the spatially-variable bias in the mean wind speed was found to be generally within +- 0.4 m/s and the overlap in the wind speed distributions generally larger than 92%. Next, array- and cluster-scale wakes, modelled at horizontal resolutions of 2.8km and 1km were analysed and compared for a present and near-future windfarm layout over the southern North Sea, providing valuable information on how regional changes to the wind farm layout will impact the farm-specific energy yields due to additional upwind wake generation under different atmospheric conditions. This research frames within the FREEWIND project of KU Leuven (freewind-project.eu), which aims to contribute to the scientific research of offshore wind energy and plans to provide wind farm planning and forecasting tools on multiple time scales over the coming years.

Before an off-shore wind farm is built a thorough resource assessment of all available locations for the farm needs to be performed. Since the power extraction of a wind farm depends on the cube of the wind speed even the mesoscale variability in the wind speed plays an important role in the resource assessment of a wind farm. In order to study mesoscale systems that occur in the vicinity of off-shore wind farms we've set up a convection permitting simulation in COSMO-CLM for the Kattegat sea strait. The Kattegat is particularly interesting since it is an area which features a very irregularly shaped coastline and pronounced coastal effects. Centrally located in the Kattegat lays the 400 MW Anholt wind farm. Operational data of the Anholt wind farm and scatterometer data of the Kattegat are used to validate our simulation. A relatively good agreement between observations and the model output has been found. A variety of mesoscale systems has been identified, both in unstable (e.g. a downburst) as in stable (e.g. gravity waves) conditions. The wind speed variability on temporal scales and on spatial scales over the Kattegat has been investigated. The interactions of the Anholt wind farm with these systems have been investigated using the COSMO-CLM model which incorporates the Fitch wind farm parametrisation. This research is part of a larger project aiming at developing a fast and accurate resource planning and forecasting platform for off-shore wind farms. More information about this project can be found on freewind-project.eu.

Recent research suggests that atmospheric gravity waves can affect off-shore wind farm performance. A fast wind-farm boundary-layer model has been proposed to simulate the effects of these gravity waves on wind-farm operation by Allaerts and Meyers (2019). The current work extends the applicability of that model to free atmospheres in which wind and stability vary with altitude. We validate the model using reference cases from literature on mountain waves. Analysis of two reference flows shows that internal gravity wave resonance caused by the atmospheric non-uniformity can prohibit perturbations in the ABL at the wavelengths where it occurs. To determine the overall impact of the vertical variations in the atmospheric conditions on wind farm operation, we consider one year of operation of the Belgian–Dutch wind-farm cluster with the extended model. We find that this impact on individual flow cases is often of the same order of magnitude as the total flow perturbation. In 16.5 % of the analysed flows, the relative difference in upstream velocity reduction between uniform and non-uniform free atmospheres is more than 30 %. However, this impact is small when averaged over all cases. This suggests that variations in the atmospheric conditions should be taken into account when simulating wind-farm operation in specific atmospheric conditions.

Wind farm flow control (WFFC) is a topic of interest at several research institutes, industry and certification agencies world-wide. For reliable performance assessment of the technology, the efficiency and the capability of the models applied to WFFC should be carefully evaluated. To address that, FarmConners consortium has launched a common benchmark for code comparison under controlled operation to demonstrate its potential benefits such as increased power production. The benchmark builds on available data sets from previous field campaigns, wind tunnel experiments and high-fidelity simulations. Within that database, 4 blind tests are defined and 13 participants in total have submitted results for the analysis of single and multiple wake under WFFC. Some participants took part in several blind tests and some participants have implemented several models. The observations and/or the model outcomes are evaluated via direct power comparisons at the upstream and downstream turbine(s), as well as the power gain at the wind farm level under wake steering control strategy. Additionally, wake loss reduction is also analysed to support the power performance comparison, where relevant. Majority of the participating models show good agreement with the observations or the reference high-fidelity simulations, especially for lower degrees of upstream misalignment and narrow wake sector. However, the benchmark clearly highlights the importance of the calibration procedure for control-oriented models. The potential effects of limited controlled operation data in calibration is particularly visible via frequent model mismatch for highly deflected wakes, as well as the power loss at the controlled turbine(s). In addition to the flow modelling, sensitivity of the predicted WFFC benefits to the turbine representation and the implementation of the controller is also underlined. FarmConners benchmark is the first of its kind to bring a wide variety of data sets, control settings and model complexities for the (initial) assessment of farm flow control benefits. It forms an important basis for more detailed benchmarks in the future with extended control objectives to assess the true value of WFFC.

Recent studies have demonstrated that large secondary motions are excited by surface roughness with dominant spanwise length scales of the order of the flow's outer length scale. Inspired by this, we explore the effect of spanwise heterogeneous surface temperature in weakly to strongly stratified closed channel flow (at$Ri_\tau =120$, 960;$Re_\tau = 180$, 550) with direct numerical simulations. The configuration consists of equally sized strips of high and low temperature at the lower and upper boundaries, while an overall stable stratification is induced by imposing an average temperature difference between the top and bottom. We consider the influence of the width of the strips (${\rm \pi} /8 \leq \lambda /h \leq 4{\rm \pi} $), Reynolds number, stability and upper boundary condition on the mean flow structure, skin friction and heat transfer. Results indicate that secondary flows are excited, with alternating high- and low-momentum pathways and vortices, similar to the patterns induced by spanwise heterogeneous surface roughness. We find that the impact of the surface heterogeneity on the outer layer depends strongly on the spanwise heterogeneity length scale of the surface temperature. Comparison to stable channel flow with uniform temperature reveals that the heterogeneous surface temperature increases the global friction coefficient and reduces the global Nusselt number in most cases. However, for the high-Reynolds cases with$\lambda /h \geq {\rm \pi} /2$, we find a reduction of the friction coefficient. At stronger stability, the vertical extent of the vortices is reduced and the impact of the heterogeneous temperature on momentum and heat transfer is smaller.

In this work, we develop a model tuning framework to calibrate analytical wind farm models by using virtual measurements from Large Eddy Simulations (LES). A Gaussian wake deficit model coupled with a recursive wake merging methodology is utilized to simulate different inflow conditions through a virtual wind farm, which has been previously used in a suite of LES to providing a reference wind farm database. Using velocity and power measurements from the reference database, a ridge regression based calibration is conducted for the wake model parameters. Without calibration, large errors up to 20% initially persisted between the analytical model and LES for the same inflow conditions, which were subsequently observed to reduce below 6% after model tuning. The tuned models were then used to analyze farm performance for cases with optimal wake steering set points, and it was observed that the predicted gains were in better accordance with LES results. ispartof: Journal of Physics : Conference Series vol:2265 ispartof: TORQUE location:Delft, Netherlands date:1 Nov - 3 Nov 2022 status: Published online

The future utility-scale deployment of airborne wind energy technologies requires the development of large-scale multi-megawatt systems. This study aims at quantifying the interaction between the atmospheric boundary layer (ABL) and large-scale airborne wind energy systems operating in a farm. To that end, we present a virtual flight simulator combining large-eddy simulations to simulate turbulent flow conditions and optimal control techniques for flight path generation and tracking. The two-way coupling between flow and system dynamics is achieved by implementing an actuator sector method that we pair to a model predictive controller. In this study, we consider ground-based power generation pumping-mode AWE systems (lift-mode AWES) and on-board power generation AWE systems (drag-mode AWES). The aircraft have wingspans of approximately 60 m and fly large loops of approximately 200 m diameter centred at 200 m altitude. For the lift-mode AWES, we additionally investigate different reel-out strategies to reduce the interaction between the tethered wing and its own wake. Further, we investigate AWE parks consisting of 25 systems organised in five rows of five systems. For both lift- and drag-mode archetypes, we consider a moderate park layout with a power density of 10 MW km−2 achieved at a rated wind speed of 12 m s−1. For the drag-mode AWES, an additional park with denser layout and power density of 28 MW km−2 is also considered. The model predictive controller achieves very satisfactory flight path tracking despite the AWE systems operating in fully waked, turbulent flow conditions. Furthermore, we observe significant wake effects for the utility-scale AWE systems considered in the study. Wake-induced performance losses increase gradually through the downstream rows of systems and reach up to 17 % in the last row of the lift-mode AWE park and up to 25 % and 45 % in the last rows of the moderate and dense-drag-mode AWE parks respectively. For an operation period of 60 min at a below-rated reference wind speed of 10 m s−1, the lift-mode AWE park generates about 84.4 MW of power, corresponding to 82.5 % of the power yield expected when AWE systems operate ideally and interaction with the ABL is negligible. For the drag-mode AWE parks, the moderate and dense layouts generate about 86.0 and 72.9 MW of power respectively corresponding to 89.2 % and 75.6 % of the ideal power yield.

© 2019 Elsevier Inc. The sensitivity of long-time averages of a hyperbolic chaotic system to parameter perturbations can be determined using the shadowing direction, the uniformly-bounded-in-time solution of the sensitivity equations. Although its existence is formally guaranteed for certain systems, methods to determine it are hardly available. One practical approach is the Least-Squares Shadowing (LSS) algorithm (Wang (2014) [18]), whereby the shadowing direction is approximated by the solution of the sensitivity equations with the least square average norm. Here, we present an alternative, potentially simpler shadowing-based algorithm, termed periodic shadowing. The key idea is to obtain a bounded solution of the sensitivity equations by complementing it with periodic boundary conditions in time. We show that this is not only justifiable when the reference trajectory is itself periodic, but also possible and effective for chaotic trajectories. Our error analysis shows that periodic shadowing has the same convergence rates as LSS when the time span T is increased: the sensitivity error first decays as 1/T and then, asymptotically as 1/T. We demonstrate the approach on the Lorenz equations, and also show that, as T tends to infinity, periodic shadowing sensitivities converge to the same value obtained from long unstable periodic orbits (Lasagna (2018) [14]) for which there is no shadowing error. Finally, finite-difference approximations of the sensitivity are also examined, and we show that subtle non-hyperbolicity features of the Lorenz system introduce a small, yet systematic, bias. ispartof: JOURNAL OF COMPUTATIONAL PHYSICS vol:391 pages:119-141 status: published

Flow blockage by large wind farms leads to an upward displacement of the boundary layer, which may excite atmospheric gravity waves in the free atmosphere and on the interface between the boundary layer and the free atmosphere. In the current study, we assess the sensitivity of wind-farm gravity-wave excitation to important dimensionless groups and investigate the feedback of gravity-wave-induced pressure fields to wind-farm energy extraction. The sensitivity analysis is performed using a fast boundary-layer model that is developed to this end. It is based on a three-layer representation of the atmosphere in an idealised barotropic environment, and is coupled with an analytical wake model to account for turbine wake interactions. We first validate the model in two-dimensional mode with data from previous large-eddy simulations of ‘infinitely’ wide wind farms, and then use the model to investigate the sensitivity of wind-farm-induced gravity waves to atmospheric state and wind-farm configuration. We find that the inversion layer induces flow physics similar to shallow-water flow and that the corresponding Froude number plays a crucial role. Gravity-wave excitation is maximal at a critical Froude number equal to one, but the feedback on energy extraction is highest when the Froude number is slightly below one due to a trade-off between amplitude and upstream impact of gravity waves. The effect of surface friction and internal gravity waves is to reduce the flow perturbation and the related power loss by dissipating or dispersing perturbation energy. With respect to the wind-farm configuration, we find that gravity-wave-induced power loss increases with wind-farm size and turbine height. Moreover, we find that gravity-wave effects are small for very wide or very long wind farms and attain a maximum at a width-to-depth ratio of approximately $3/2$.

In this experimental study, multiscale rough surfaces with regular (cuboid) elements are used to examine the effects of roughness-scale hierarchy on turbulent boundary layers. Three iterations have been used with a first iteration of large-scale cuboids onto which subsequent smaller cuboids are uniformly added, with their size decreasing with a power-law as the number increases. The drag is directly measured through a floating-element drag balance, while particle image velocimetry allowed the assessment of the flow field. The drag measurements revealed the smallest roughness iteration can contribute to nearly 7 of the overall drag of a full surface, while the intermediate iterations are responsible for over (at the highest Reynolds number tested). It is shown that the aerodynamic roughness length scale between subsequent iterations varies linearly, and can be described with a geometrical parameter proportional to the frontal solidity. Mean and turbulent statistics are evaluated using the drag information, and highlighted substantial changes within the canopy region as well as in the outer flow, with modifications to the inertial sublayer (ISL) and the wake region. These changes are shown to be caused by the presence of large-scale secondary motions in the cross-plane, which itself is believed to be a consequence of the largest multiscale roughness phase (spacing between largest cuboids), shown to be of the same order of magnitude as the boundary-layer thickness. Implications on the classical similarity laws are additionally discussed.

Recently, it has been shown that flow blockage in large wind farms may lift up the top of the boundary layer, thereby triggering atmospheric gravity waves in the inversion layer and in the free atmosphere. These waves impose significant pressure gradients in the boundary layer, causing detrimental consequences in terms of a farm's efficiency. In the current study, we investigate the idea of controlling the wind farm in order to mitigate the efficiency drop due to wind-farm-induced gravity waves and blockage. The analysis is performed using a fast boundary layer model which divides the vertical structure of the atmosphere into three layers. The wind-farm drag force is applied over the whole wind-farm area in the lowest layer and is directly proportional to the wind-farm thrust set-point distribution. We implement an optimization model in order to derive the thrust-coefficient distribution, which maximizes the wind-farm energy extraction. We use a continuous adjoint method to efficiently compute gradients for the optimization algorithm, which is based on a quasi-Newton method. Power gains are evaluated with respect to a reference thrust-coefficient distribution based on the Betz–Joukowsky set point. We consider thrust coefficients that can change in space, as well as in time, i.e. considering time-periodic signals. However, in all our optimization results, we find that optimal thrust-coefficient distributions are steady; any time-periodic distribution is less optimal. The (steady) optimal thrust-coefficient distribution is inversely related to the vertical displacement of the boundary layer. Hence, it assumes a sinusoidal behaviour in the streamwise direction in subcritical flow conditions, whereas it becomes a U-shaped curve when the flow is supercritical. The sensitivity of the power gain to the atmospheric state is studied using the developed optimization tool for almost 2000 different atmospheric states. Overall, power gains above 4 % were observed for 77 % of the cases with peaks up to 14 % for weakly stratified atmospheres in critical flow regimes.

The difference in surface roughness between land and sea, and the terrain complexities, lead to spatially heterogeneous atmospheric conditions, and therefore affect the propagation and dynamics of wind‐turbine and wind‐farm wakes. Currently, these flow heterogeneities and their effects on plant aerodynamics are not modeled in the majority of engineering wake models. In this study, we address this issue by developing a new wake‐merging method capable of superimposing the waked flow on a heterogeneous background velocity field. We couple the proposed wake‐merging method with four different wake models, i.e. the Gaussian, super‐Gaussian, double‐Gaussian and Ishihara model, and we test its performance against LES results, dual‐Doppler radar measurements and SCADA data from the Horns Rev, London Array, and Westermost Rough farms. The standard Jensen model with quadratic superposition is also included. In homogeneous conditions, the new method predicts slightly higher velocity deficits than the linear superposition method. Overall, the distributions of the difference in power ratio between the two wake‐merging methods predictions and observations show a similar mean absolute error (MAE) and interquartile range (IQR) in such conditions. On the other hand, the new wake‐merging method predictions display a lower MAE with a similar IQR in case of a spatially varying background velocity, being overall more accurate than the ones obtained with linear superposition. The most accurate estimates are obtained when the wake‐merging methods are coupled with the double‐Gaussian and Gaussian single‐wake models. In contrast, the Jensen and super‐Gaussian wake models overestimate the velocity deficits for the majority of cases analyzed.

One of the major uncertainties in dispersion-based simulations at the local scale is the representation of terrain effects. The aim of the current study is to quantify this type of uncertainty for dose-rate predictions over a homogeneous forest cover. At the Belgian reactor BR1, situated in a forested environment, ambient gamma-dose-rate data from routine Ar-41 releases are available in the first 300 m from the release point. We develop a forest parameterization that meets the site-specific needs, and integrate it in different dispersion models. Using different terrain-roughness parameterizations, we compare three types of models: a dispersion model driven by a Langevin equation, an advection-diffusion model, and a Gaussian plume model as a special case of the latter one. We find that all models are biased up to a factor of four, partly due to an uncertain source strength. The dose-rate uncertainty due to the model choice is a factor of 2.2 for a stack release and a factor of 14 for a ground release.

Recently, it has been shown that flow blockage in large wind farms may lift up the top of the boundary layer, thereby triggering atmospheric gravity waves in the inversion layer and in the free atmosphere. These waves impose significant pressure gradients in the boundary layer causing detrimental consequences in terms of farm's efficiency. In the current study, we investigate the idea of controlling the wind farm in order to mitigate the efficiency drop due to wind-farm induced gravity waves and blockage. The analysis is performed using a fast boundary layer model which divides the vertical structure of the atmosphere into three layers. The wind-farm drag force is applied over the whole wind-farm area in the lowest layer and is directly proportional to the wind-farm thrust set-point distribution. We implement an optimization model in order to derive the thrust-coefficient distribution which maximizes the wind-farm energy extraction. We use a continuous adjoint method to efficiently compute gradients for the optimization algorithm, which is based on a quasi-Newton method. Energy gains are evaluated with respect to a reference thrust-coefficient distribution based on the Betz–Joukowsky set point. We consider thrust coefficients that can change in space, as well as in time, i.e. considering time-periodic signals. However, in all our optimization results, we find that optimal thrust-coefficient distributions are steady; any time-periodic distribution is less optimal. The (steady) optimal thrust-coefficient distribution is inversely related to the vertical displacement of the boundary layer. Hence, it assumes a sinusoidal behaviour in the streamwise direction in subcritical flow conditions, whereas it becomes a U-shaped curve when the flow is supercritical. The sensitivity of the energy gain to the atmospheric state is studied using the developed optimization tool for almost two thousand different atmospheric states. Energy gains of up to 14 % are found for weakly stratified atmospheres in critical flow regimes.

We study the energy convergence of the Karhunen-Lo\`eve decomposition of the turbulent velocity field in a high-Reynolds-number pressure-driven boundary layer as a function of the number of modes. An energy-optimal Karhunen-Lo\`eve (KL) decomposition is obtained from wall-modeled large-eddy simulations at "infinite" Reynolds number. By explicitly using Fourier modes for the horizontal homogeneous directions, we are able to construct a basis of full rank, and we demonstrate that our results have reached statistical convergence. The KL dimension, corresponding to the number of modes per unit volume required to capture 90% of the total turbulent kinetic energy, is found to be $2.4 \times 10^5 |\Omega|/H^3$ (with $|\Omega|$ the domain volume and $H$ the boundary layer height). This is significantly higher than current estimates, which are mostly based on the method of snapshots. In our analysis, we carefully correct for the effect of subgrid scales on these estimates.

We investigate the reconstruction of a turbulent flow field in the atmospheric boundary layer from a time series of lidar measurements, using Large-Eddy Simulations (LES) and a 4D-Var data assimilation algorithm. This leads to an optimisation problem in which the error between measurements and simulations is minimised over an observation time horizon. To exploit the spatial coherence of the turbulence, we use a quadratic regularisation in the objective function, that is based on the two-point covariance matrix. Moreover, to improve conditioning, and remove continuity constraints, the problem is transformed into a Karhunen-Lo\`eve basis. For the optimisation, we use a quasi-Newton limited-memory BFGS algorithm combined with an adjoint approach for the gradient. We also consider reconstruction based on a Taylor's frozen turbulence (TFT) model as point of comparison. To evaluate the approach, we construct a series of virtual lidar measurements from a fine-grid LES of a pressure-driven boundary-layer. The reconstruction uses LES on a coarser mesh and smaller domain, and results are compared to the fine-grid reference. Two lidar scanning modes are considered: a classical plan-position-indicator mode, which swipes the lidar beam in a horizontal plane, and a 3D pattern that is based on a Lissajous curve. We find that normalised errors lie between 15% and 25% (error variance normalised by background variance) in the scanning region, and increase to $100\%$ over a distance that is comparable to the correlation length scale outside this scanning region. Moreover, LES outperforms TFT by 30% to 70% depending on scanning mode and location.

Careful validation of the modelling and control actions is of vital importance to build confidence in the value of coordinated wind farm control (WFC). The efficiency of flow models applied to WFC should be evaluated to provide reliable assessment of the performance of WFC. In order to achieve that, FarmConners launches a common benchmark for code comparison to demonstrate the potential benefits of WFC, such as increased power production and mitigation of loads. The benchmark builds on available data sets from previous and ongoing campaigns: synthetic data from high-fidelity simulations, measurements from wind tunnel experiments, and field data from a real wind farm. The participating WFC models are first to be calibrated or trained using normal operation periods. For the blind test, both the axial induction and wake steering control approaches are included in the dataset and to be evaluated through the designed test cases. Three main test cases are specified, addressing the impact of WFC on single full wake, single partial wake, and multiple wake. The WFC model outcomes will be compared during the blind test phase, through power gain and wake loss reduction as well as alleviation of wake-added turbulence intensity and structural loads. The probabilistic validation will be based on the median and quartiles of the observations and WFC model predictions. Every benchmark participant will be involved in the final publication, where the comparison of different tools will be performed using the defined test cases. Instructions on how to participate are also provided on farmconners.readthedocs.io.

Wake interactions between wind turbines in wind farms lead to reduced energy extraction in downstream rows. In recent work, optimization and large-eddy simulation were combined with the optimal dynamic induction control of wind farms to study the mitigation of these effects, showing potential power gains of up to 20 % (Munters and Meyers, 2017, Phil. Trans. R. Soc. A, 375, 20160100, https://doi.org/10.1098/rsta.2016.010). However, the computational cost associated with these optimal control simulations impedes the practical implementation of this approach. Furthermore, the resulting control signals optimally react to the specific instantaneous turbulent flow realizations in the simulations so that they cannot be simply used in general. The current work focuses on the detailed analysis of the optimization results of Munters and Meyers, with the aim to identify simplified control strategies that mimic the optimal control results and can be used in practice. The analysis shows that wind-farm controls are optimized in a parabolic manner with little upstream propagation of information. Moreover, turbines can be classified into first-row, intermediate-row, and last-row turbines based on their optimal control dynamics. At the moment, the control mechanisms for intermediate-row turbines remain unclear, but for first-row turbines we find that the optimal controls increase wake mixing through the periodic shedding of vortex rings. This behavior can be mimicked with a simple sinusoidal thrust control strategy for first-row turbines, resulting in robust power gains for turbines in the entrance region of the farm.

Recent experiments have revealed the existence of very long streamwise features, denoted as very-large-scale motions (VLSMs), in the thermally neutral atmospheric boundary layer (ABL) (Hutchins et al., Boundary-Layer Meteorol., vol. 145(2), 2012, pp. 273–306). The aim of our study is to elaborate the role of these large-scale anisotropic patterns in wind-energy harvesting with special emphasis on the organization of turbulent fields around wind turbines. To this end, we perform large-eddy simulation (LES) of a turbine row operating under neutral conditions. The ABL data are produced separately in a very long domain of $240\unicode[STIX]{x1D6FF}$, where $\unicode[STIX]{x1D6FF}$ is the ABL thickness, to ensure a realistic representation for very large scales of $O(10\unicode[STIX]{x1D6FF})$. VLSMs are extracted from the LES database using a cutoff at streamwise wavelength $\unicode[STIX]{x1D706}_{x}=5\unicode[STIX]{x1D6FF}$, or $\unicode[STIX]{x1D706}_{x}=50D$ in terms of turbine diameter. Reynolds averaging of low-pass filtered fields shows that the interaction of VLSMs and turbines produce very-long-wavelength motions in the wake region, which contain approximately $20\,\%$ of the resolved Reynolds shear stress, and $30\,\%$ of the resolved streamwise kinetic energy in the shear layers. To further elucidate these statistics, we conduct a geometrical analysis using conditional averaging based on large-scale low- and high-velocity events. The conditional eddies provide evidence for very long (${\sim}10\unicode[STIX]{x1D6FF}$) and wide (${\sim}\unicode[STIX]{x1D6FF}$) streak–roller structures around the turbine row. Although all of these eddies share the same streak–roller topology, there are remarkable modifications in the morphology of the conditional eddies whose cores are located sideways to the turbines. In these cases, the turbine row pushes the whole low- or high-momentum streak aside, and prevails as a sharp boundary to the low–high-momentum streak pair. In this process, accompanying rollers remain relatively unaffected. This creates a two-way flux towards the turbine row. These observations provide some insights about the high lateral spreading observed in the large-scale Reynolds stress fields.

This paper is an extended version of our paper presented at the 2016 TORQUE conference (Shapiro et al., 2016). We investigate the use of wind farms to provide secondary frequency regulation for a power grid using a model-based receding horizon control framework. In order to enable real-time implementation, the control actions are computed based on a time-varying one-dimensional wake model. This model describes wake advection and wake interactions, both of which play an important role in wind farm power production. In order to test the control strategy, it is implemented in a large-eddy simulation (LES) model of an 84-turbine wind farm using the actuator disk turbine representation. Rotor-averaged velocity measurements at each turbine are used to provide feedback for error correction. The importance of including the dynamics of wake advection in the underlying wake model is tested by comparing the performance of this dynamic-model control approach to a comparable static-model control approach that relies on a modified Jensen model. We compare the performance of both control approaches using two types of regulation signals, “RegA” and “RegD”, which are used by PJM, an independent system operator in the eastern United States. The poor performance of the static-model control relative to the dynamic-model control demonstrates that modeling the dynamics of wake advection is key to providing the proposed type of model-based coordinated control of large wind farms. We further explore the performance of the dynamic-model control via composite performance scores used by PJM to qualify plants for regulation services or markets. Our results demonstrate that the dynamic-model-controlled wind farm consistently performs well, passing the qualification threshold for all fast-acting RegD signals. For the RegA signal, which changes over slower timescales, the dynamic-model control leads to average performance that surpasses the qualification threshold, but further work is needed to enable this controlled wind farm to achieve qualifying performance for all regulation signals.

We use large-eddy simulations (LES) to investigate the impact of stable stratification on gravity-wave excitation and energy extraction in a large wind farm. To this end, the development of an equilibrium conventionally neutral boundary layer into a stable boundary layer over a period of 8 h is considered, using two different cooling rates. We find that turbulence decay has considerable influence on the energy extraction at the beginning of the boundary-layer transition, but afterwards, energy extraction is dominated by geometrical and jet effects induced by an inertial oscillation. It is further shown that the inertial oscillation enhances gravity-wave excitation. By comparing LES results with a simple one-dimensional model, we show that this is related to an interplay between wind-farm drag, variations in the Froude number and the dispersive effects of vertically-propagating gravity waves. We further find that the pressure gradients induced by gravity waves lead to significant upstream flow deceleration, reducing the average turbine output compared to a turbine in isolated operation. This leads us to the definition of a non-local wind-farm efficiency, next to a more standard wind-farm wake efficiency, and we show that both can be of the same order of magnitude. Finally, an energy flux analysis is performed to further elucidate the effect of gravity waves on the flow in the wind farm. ispartof: Boundary-Layer Meteorology vol:166 issue:2 pages:269-299 ispartof: location:Netherlands status: published

©2017 Cambridge University Press. While neutral atmospheric boundary layers are rare over land, they occur frequently over sea. In these cases they are almost always of the conventionally neutral type, in which the neutral boundary layer is capped by a strong inversion layer and a stably stratified atmosphere aloft. In the current study, we use large-eddy simulations (LES) to investigate the interaction between a large wind farm that has a fetch of 15 km and a conventionally neutral boundary layer (CNBL) in typical offshore conditions. At the domain inlet, we consider three different equilibrium CNBLs with heights of approximately 300m, 500m and 1000m that are generated in a separate precursor LES. We find that the height of the inflow boundary layer has a significant impact on the wind farm flow development. First of all, above the farm, an internal boundary layer develops that interacts downwind with the capping inversion for the two lowest CNBL cases. Secondly, the upward displacement of the boundary layer by flow deceleration in the wind farm excites gravity waves in the inversion layer and the free atmosphere above. For the lower CNBL cases, these waves induce significant pressure gradients in the farm (both favourable and unfavourable depending on location and case). A detailed energy budget analysis in the turbine region shows that energy extracted by the wind turbines comes both from flow deceleration and from vertical turbulent entrainment. Though turbulent transport dominates near the end of the farm, flow deceleration remains significant, i.e. up to 35 % of the turbulent flux for the lowest CNBL case. In fact, while the turbulent fluxes are fully developed after eight turbine rows, the mean flow does not reach a stationary regime. A further energy budget analysis over the rest of the CNBL reveals that all energy available at turbine level comes from upwind kinetic energy in the boundary layer. In the lower CNBL cases, the pressure field induced by gravity waves plays an important role in redistributing this energy throughout the farm. Overall, in all cases entrainment at the capping inversion is negligible, and also the work done by the mean background pressure gradient, arising from the geostrophic balance in the free atmosphere, is small. license: © 2017 Cambridge University Press This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited. ispartof: Journal of Fluid Mechanics vol:814 pages:95-130 status: published

Given a wind farm with known dimensions and number of wind turbines, we try to find the optimum positioning of wind turbines that maximises wind-farm energy production. In practice, given that optimisation has to be performed for many wind directions, and taking into account the yearly wind distribution, such an optimisation is computationally only feasible using fast engineering wake models such as the Jensen model. These models are known to have accuracy issues, in particular since their representation of wake interaction is very simple. In the present work, we propose an optimisation approach that is based on a hybrid combination of large-eddy simulation (LES) and the Jensen model; in this approach, optimisation is mainly performed using the Jensen model, and LES is used at a few points only during optimisation for online tuning of the wake-expansion coefficient in the Jensen model, as well as for validation of the results. An optimisation case study is considered, in which the placement of 30 turbines in a 4 km by 3 km rectangular domain is optimised in a neutral atmospheric boundary layer. Optimisation for both a single wind direction and multiple wind directions is discussed.

Wind farm control is an active and growing field of research in which the control actions of individual turbines in a farm are coordinated, accounting for inter-turbine aerodynamic interaction, to improve the overall performance of the wind farm and to reduce costs. The primary objectives of wind farm control include increasing power production, reducing turbine loads, and providing electricity grid support services. Additional objectives include improving reliability or reducing external impacts to the environment and communities. In 2019, a European research project (FarmConners) was started with the main goal of providing an overview of the state-of-the-art in wind farm control, identifying consensus of research findings, data sets, and best practices, providing a summary of the main research challenges, and establishing a roadmap on how to address these challenges. Complementary to the FarmConners project, an IEA Wind Topical Expert Meeting (TEM) and two rounds of surveys among experts were performed. From these events we can clearly identify an interest in more public validation campaigns. Additionally, a deeper understanding of the mechanical loads and the uncertainties concerning the effectiveness of wind farm control are considered two major research gaps.

Airborne wind energy is an emerging technology that uses tethered unmanned aerial vehicles for harvesting wind energy at altitudes higher than conventional towered wind turbines. To make the technology competitive to other renewable energy technologies an automatic control system is required that allows autonomously operating the system throughout all phases of flight. In this study a modular control system is presented, adapting the underlying kinematic and dynamic framework from conventional aerospace terminology and applying this to tethered crosswind flight with varying tether length. The high level control strategy in form of a state machine as well as the cascaded flight control structure consisting of path-following guidance and control, attitude and rate loop is presented along with the winch controller. The present work is a first step towards a methodology for the systematic development of reliable and high-performance control solutions for airborne wind energy systems. Models for the airborne system, ground station, as well as the tether connecting the ground system with the airframe will be presented. Results from a simulation study in a realistic wind field will be used to demonstrate the feasibility of the proposed concept and to identify particularly challenging situations in the operational envelope. ispartof: Aiaa Journal ispartof: AIAA Scitech 2019 Forum location:San Diego, California date:7 Jan - 11 Jan 2019 status: published

The power output of wind farms depends strongly on spatial turbine arrangement, and the resulting turbulent interactions with the atmospheric boundary layer. The main goal of this work is to study the effect of turbine layout on the power output for large wind farms approaching a fully-developed regime. For this purpose we employ an experimental setup of a scaled wind farm with one-hundred porous disk models, of which sixty are instrumented with strain gages. Our experiments cover a parametric space of fifty-six different layouts for which the turbine-area-density is constant, focusing on different turbine arrangements including non-uniform spacings. The strain-gage measurements are used to deduce surrogate power and unsteady loading on turbines for each layout. Our results indicate that the power asymptote at the end of the wind farm depends on the layout in different ways. Firstly, for layouts with a relatively uniform spacing we find that the power asymptote in the fully developed regime reaches approximately the same value, similarly to the prediction of available analytical models. Secondly, we show that the power asymptote in the fully-developed regime can be lowered by inefficient turbine placement, for instance when a large number of the turbines are located in the near wake of upstream turbines. Thirdly, our experiments indicate that an uneven spacing between turbines can improve the overall power output for both the developing and fully-developed part of large wind farms. Specifically, we find a higher power asymptote for a turbine layout with a significant streamwise uneven spacing (i.e. a large streamwise spacing between pairs of closely spaced rows that are slightly staggered). Our results thereby indicate that such a layout may promote beneficial flow interactions in the fully-developed regime for conditions with a strongly prevailing wind direction., Submitted to Physical Review Fluids

In this paper we report the results of a workshop organised by the Delft University of Technology in 2014, aiming at the comparison between different state-of-the-art numerical models for the simulation of wind turbine wakes. The chosen benchmark case is a wind tunnel measurement, where stereoscopic Particle Image Velocimetry was employed to obtain the velocity field and turbulence statistics in the near wake of a two-bladed wind turbine model and of a porous disc, which mimics the numerical actuator used in the simulations. Researchers have been invited to simulate the experimental case based on the disc drag coefficient and the inflow characteristics. Four large eddy simulation (LES) codes from different institutions and a vortex model are part of the comparison. The purpose of this benchmark is to validate the numerical predictions of the flow field statistics in the near wake of an actuator disc, a case that is highly relevant for full wind farm applications. The comparison has shown that, despite its extreme simplicity, the vortex model is capable of reproducing the wake expansion and the centreline velocity with very high accuracy. Also all tested LES models are able to predict the velocity deficit in the very near wake well, contrary to what was expected from previous literature. However, the resolved velocity fluctuations in the LES are below the experimentally measured values.