In recent years, wake steering has been established as a promising method to increase the energy yield of a wind farm. Current practice in estimating the benefit of wake steering on the annual energy production (AEP) consists of evaluating the wind farm with simplified surrogate models, casting a large uncertainty on the estimated benefit. This paper presents a framework for determining the benefit of wake steering on the AEP, incorporating simulation results from a surrogate model and large eddy simulations in order to reduce the uncertainty. Furthermore, a time-varying wind direction is considered for a better representation of the ambient conditions at the real wind farm site. Gaussian process regression is used to combine the two data sets into a single improved model of the energy gain. This model estimates a 0.60% gain in AEP for the considered wind farm, which is a 76% increase compared to the estimate of the surrogate model.
In large eddy simulation of atmospheric boundary layer flows over wind farms, wall-layer models are generally imposed for the surface fluxes without considering the spatial variability of the surface roughness. In this study, we consider the near-surface model in conjunction with square of the velocity gradient tensor to model the adaptive dissipation of turbulence production. The surface roughness is incorporated through Monin-Obhukhov similarity theory for the computational cells immediately adjacent to the Earth's surface. The underlying proposed near-surface model captures the significant …
Large eddy simulations of wind farms are performed to study the effects of wind turbine row alignment with respect to the incoming flow direction. Various wind farms with fixed stream-wise spacing (7.85 rotor diameters) and varying lateral displacements and span-wise turbine spacings are considered, for a fixed inflow direction. Simulations show that, contrary to common belief, a perfectly staggered (checker-board) configuration does not necessarily give the highest average power output. Instead, the highest mean wind farm power output is found to depend on several factors, the most important …
Numerous studies have shown that wind turbine wakes within a large wind farm bring about changes to both the dynamics and thermodynamics of the atmospheric boundary layers (ABL). Previously, we investigated the relative humidity budget within a wind farm via field measurements in the near-wake region and large eddy simulations (LES). The effect of the compounding wakes within a large wind farm on the relative humidity was also investigated by LES. In this study, we investigate how the areas of relative humidity variation, that was observed in the near-wake, develop downstream in the shadow reg…
In large wind farms, wake distribution behind a wind turbine causes a considerable reduction of wind velocity for downstream wind turbines, resulting in a significant amount of power loss. Therefore, it is very crucial to predict wind turbine wakes efficiently. Thus, we propose a large-eddy simulation (LES) methodology, which takes the vorticity stretching to model transients in wind turbine wakes. In addition, we present an improved actuator disk model, which accounts for two-way feedback between the atmosphere and the wakes. First, we show that the vertical profile of the mean wind predicted…
Fluctuations represent a major challenge for the incorporation of electric power from large wind-farms into power grids. Wind farm power output fluctuates strongly in time, over various time scales. Understanding these fluctuations, especially their spatio-temporal characteristics, is particularly important for the design of backup power systems that must be readily available in conjunction with wind-farms. In this work we analyze the power fluctuations associated with the wind-input variability at scales between minutes to several hours, using large eddy simulations (LES) of extended wind-par…
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 corre…
We present here a computational fluid dynamics (CFD) simulation of Lillgrund offshore wind farm, which is located in the Oresund Strait between Sweden and Denmark. The simulation combines a dynamic representation of wind turbines embedded within a Large-Eddy Simulation CFD solver, and uses hr-adaptive meshing to increase or decrease mesh resolution where required. This allows the resolution of both large scale flow structures around the wind farm, and local flow conditions at individual turbines; consequently, the response of each turbine to local conditions can be modelled, as well as the res…
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…
High-fidelity large-eddy simulations are suitable to obtain insight into the complex flow dynamics in extended wind farms. In order to better understand these flow dynamics, we use dynamic mode decomposition (DMD) to analyze and reconstruct the flow field in large-scale numerically simulated wind farms by large-eddy simulations (LES). Different wind farm layouts are considered, and we find that a combination of horizontal and vertical staggering leads to improved wind farm performance compared to traditional horizontal staggering. We analyze the wind farm flows using the amplitude selection (A…
The flow speed-up generated by windbreaks can be used to increase the power production of wind turbines. However, due to the increased drag imposed by the windbreaks, their use in large wind turbine arrays has been questioned. We use large eddy simulations to show that windbreaks can increase the power production of large wind farms. A crucial finding is that windbreaks in a wind farm should be much lower than for a single turbine case. In fact, the optimal windbreak for an isolated turbine can reduce wind farm performance. The optimal windbreak height in a wind farm namely depends on the righ…
We introduce a gradient-free data-driven framework for optimizing the power output of a wind farm based on a Bayesian approach and large-eddy simulations. In contrast with conventional wind farm layout optimization strategies, which make use of simple wake models, the proposed framework accounts for complex flow phenomena such as wake meandering, local speed-ups and the interaction of the wind turbines with the atmospheric flow. The capabilities of the framework are demonstrated for the case of a small wind farm consisting of five wind turbines. It is shown that it can find optimal designs wit…
Recent large eddy simulations have led to improved parameterizations of the effective roughness height of wind farms. This effective roughness height can be used to predict the wind velocity at hub-height as function of the geometric mean of the spanwise and streamwise turbine spacings and the turbine loading factors. Meyers and Meneveau (Wind Energy 15, 305-317 (2012)) used these parameterizations to make predictions for the optimal wind turbine spacing in infinitely large wind farms. They found that for a realistic cost ratio between the turbines and the used land surface the optimal turbine…
The multi-rotor (MR) wind turbine concept can be used to upscale wind turbines without increasing the rotor diameter, which can be beneficial for transport, manufacture and design of wind turbines blades. The rotor interaction of a MR wind turbine leads to a faster wake recovery compared to an equivalent single-rotor (SR) wind turbine wake. In this article, the benefit of the faster wake recovery of MR wind turbines is quantified using Reynolds-averaged Navier-Stokes simulations of a 4x4 rectangular MR wind farm, for three different inter wind turbine spacings. The simulations predict an incre…
As a generalization of the mass-flux based classical stream-tube, the concept of momentum and energy transport tubes is discussed as a flow visualization tool. These transport tubes have the property, respectively, that no fluxes of momentum or energy exist over their respective tube mantles. As an example application using data from large-eddy simulation, such tubes are visualized for the mean-flow structure of turbulent flow in large wind farms, in fully developed wind-turbine-array boundary layers. The three-dimensional organization of energy transport tubes changes considerably when turbin…
Turbine wake and farm blockage effects may significantly impact the power produced by large wind farms. In this study, we perform Large-Eddy Simulations (LES) of 50 infinitely large offshore wind farms with different turbine layouts and wind directions. The LES results are combined with the two-scale momentum theory (Nishino & Dunstan 2020, J. Fluid Mech. 894, A2) to investigate the aerodynamic performance of large but finite-sized farms as well. The power of infinitely large farms is found to be a strong function of the array density, whereas the power of large finite-sized farms depends on b…
Reynolds-averaged Navier-Stokes (RANS) is one of the most cost-efficient approaches to simulate wind-farm-atmosphere interactions. However, the applicability of RANS-based methods is always limited by the accuracy of turbulence closure models, which introduce various uncertainties into the models. In this study, we estimate model-form uncertainties in RANS simulations of wind farms. For this purpose, we compare different RANS models to a large-eddy simulation (LES). We find that the realizable k-epsilon model is a representative RANS model for predicting the mean velocity, the turbulence inten…
We present results from large eddy simulations (LES) of extended wind-farms for several turbine configurations with a range of different spanwise and streamwise spacing combinations. The results show that for wind-farms arranged in a staggered configuration with spanwise spacings in the range $\approx[3.5,8]$D, where $D$ is the turbine diameter, the power output in the fully developed regime depends primarily on the geometric mean of the spanwise and streamwise turbine spacings. In contrast, for the aligned configuration the power output in the fully developed regime strongly depends on the st…
The actuator disk model (ADM) continues to be a popular wind turbine representation in large eddy simulations (LES) of large wind farms. Computational restrictions typically limit the number of grid points across the rotor of each actuator disk and require spatial filtering to smoothly distribute the applied force distribution on discrete grid points. At typical grid resolutions, simulations cannot capture all of the vorticity shed behind the disk and subsequently over-predict power by upwards of 10%. To correct these modeling errors, we propose a vortex cylinder model to quantify the shed vor…
This paper solves an approximate form of conservation of mass and momentum for a turbine in a wind farm array. The solution is a fairly simple explicit relationship that predicts the streamwise velocity distribution within a wind farm with an arbitrary layout. As this model is obtained by solving flow governing equations directly for a turbine that is subject to upwind turbine wakes, no ad hoc superposition technique is needed to predict wind farm flows. A suite of large-eddy simulations (LES) of wind farm arrays is used to examine self-similarity as well as validity of the so-called conservat…
A two-scale modelling approach is discussed to predict the performance and energetics of a large number (more than a few hundred) of marine turbines installed as a power farm in a general coastal environment. The kernel of this approach is that the outer, or coastal-scale, model/simulation is to assess the reduction of flow passing through a given farm area as a function of the increase of head loss across the farm, whereas the inner, or device-scale, model/simulation employs this function to account for the (otherwise unknown) effect of coastal dynamics for that farm site, i.e. diminution of …
Turbine wake and local blockage effects are known to alter wind farm power production in two different ways: (1) by changing the wind speed locally in front of each turbine; and (2) by changing the overall flow resistance in the farm and thus the so-called farm blockage effect. To better predict these effects with low computational costs, we develop data-driven emulators of the `local' or `internal' turbine thrust coefficient $C_T^*$ as a function of turbine layout. We train the model using a multi-fidelity Gaussian Process (GP) regression with a combination of low (engineering wake model) and…
Computational fluid dynamics using the Reynolds-averaged Navier-Stokes (RANS) remains the most cost-effective approach to study wake flows and power losses in wind farms. The underlying assumptions associated with turbulence closures are one of the biggest sources of errors and uncertainties in the model predictions. This work aims to quantify model-form uncertainties in RANS simulations of wind farms at high Reynolds numbers under neutrally stratified conditions by perturbing the Reynolds stress tensor through a data-driven machine-learning technique. To this end, a two-step feature-selection…
While a theoretical limit has long been established for the performance of a single turbine, no corresponding upper bound exists for the power output from a large wind farm, making it difficult to evaluate the available potential for further performance gains. Here we build a model describing the essential features of a large array of turbines with arbitrary design and layout, by considering a fully-developed wind farm whose upper edge is bounded by a self-similar boundary layer. The exchanges between the wind farm, the overlaying boundary layer, and the outer flow are parameterized by means o…
The expected growth in wind energy capacity requires efficient and accurate models for wind farm layout optimization, control, and annual energy predictions. Although analytical wake models are widely used for these applications, several model components must be better understood to improve their accuracy. To this end, we propose a Bayesian uncertainty quantification framework for physics-guided data-driven model enhancement. The framework incorporates turbulence-related aleatoric uncertainty in historical wind farm data, epistemic uncertainty in the empirical parameters, and systematic uncert…
Low-level jets (LLJs) are the wind maxima in the lowest 50 to 1000 m of atmospheric boundary layers. Due to their significant influence on the power production of wind farms it is crucial to understand the interaction between LLJs and wind farms. In the presence of an LLJ, there are positive and negative shear regions in the velocity profile. The positive shear regions of LLJs are continuously turbulent, while the negative shear regions have limited turbulence. We present large-eddy simulations of wind farms in which the LLJ is above, below, or in the middle of the turbine rotor swept area. We…
In this study, we focus on Langmuir turbulence in the deep ocean with the presence of a large macroalgal farm using a Large Eddy Simulation method. The wave-current interactions are modelled by solving the wave-averaged equations. The hydrodynamic process over the farm is found to drive a persistent flow pattern similar to Langmuir circulations but is locked in space across the farm. These secondary circulations are generated because the cross-stream shear produced by the rows of canopy elements leads to a steady vertical vorticity field, which is then rotated to the downstream direction under…
Under the term global blockage, the cumulative induction of wind turbines in a wind farm has been recently suspected to be responsible for observed overestimations of the energy yield in large-size wind farms. In this paper, the practice of modeling this effect after linear superposition of single turbine inductions, calculated with three of the most recent analytic models, is compared to Large-Eddy-Simulations of wind farms. We compare the models across two different farms, composed of 9 and 49 turbines, with two different heights of the atmospheric boundary layer, 300 and 500 m. The results …
We present and test the coupled wake boundary layer (CWBL) model that describes the distribution of the power output in a wind-farm. The model couples the traditional, industry-standard wake model approach with a "top-down" model for the overall wind-farm boundary layer structure. This wake model captures the effect of turbine positioning, while the "top-down" portion of the model adds the interactions between the wind-turbine wakes and the atmospheric boundary layer. Each portion of the model requires specification of a parameter that is not known a-priori. For the wake model, the wake expans…
Low-level jets (LLJs) are the wind maxima in the lower regions of the atmosphere with a high wind energy potential. Here we use large-eddy simulations to study the effect of LLJ height on the flow dynamics in a wind farm with $10\times4$ turbines. We change the LLJ height and atmospheric thermal stratification by varying the surface cooling rate. We find that the first row power production is higher in the presence of a LLJ compared to a neutral reference case without LLJ. Besides, we show that the first row power production increases with decreasing LLJ height. Due to the higher turbulence in…
Co-locating horizontal- and vertical-axis wind turbines has been recently proposed as a possible approach to enhance the land-area power density of wind farms. In this work, we aim to study the benefits associated with such a co-location using large-eddy simulation (LES) and analytical wake models. In this regard, small-scale vertical-axis wind turbines (VAWTs) in triangular clusters are deployed within a finite-size wind farm consisting of horizontal-axis wind turbines (HAWTs). Wake flow within the wind farm and the effect of VAWTs on the overall wind-farm efficiency are investigated and quan…
A quantitative understanding of the dominant mechanisms that govern the generation and decay of the counter-rotating vortex pair (CVP) produced by yawed wind turbines is needed to fully realize the potential of yawing for wind farm power maximization and regulation. Observations from large eddy simulations (LES) of yawed wind turbines in the turbulent atmospheric boundary layer and concepts from the airplane trailing vortex literature inform a model for the shed vorticity and circulation. The model is formed through analytical integration of simplified forms of the vorticity transport equation…
Low-fidelity analytical models of turbine wakes have traditionally been used for wind farm planning, performance evaluation, and demonstrating the utility of advanced control algorithms in increasing the annual energy production. In practice, however, it remains challenging to correctly estimate the flow and achieve significant performance gains using conventional low-fidelity models. This is due to the over-simplified static nature of wake predictions from models that are agnostic to the effects of atmospheric boundary layer turbulence and the complex aerodynamic interactions among wind turbi…
Marine hydrokinetic (MHK) power generation systems enable harvesting energy from waterways without the need for water impoundment. A major research challenge for numerical simulations of field-scale MHK farms stems from the large disparity in scales between the size of waterway and the energy harvesting device. We propose a large-eddy simulation (LES) framework to perform high-fidelity, multi-resolution simulations of MHK arrays in a real-life marine environment using a novel unstructured Cartesian flow solver coupled with a sharp-interface immersed boundary method. The potential of the method…
