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 conservation of momentum deficit for turbine wakes in wind farms. The simulations are performed with and without the presence of some specific turbines in the wind farm. This allows us to systematically study some of the assumptions made to develop the analytical model. A modified version of the conservation of momentum deficit is also proposed to provide slightly better results at short downwind distances, as well as in the far wake of turbines deep inside a wind farm. Model predictions are validated against the LES data for turbines in both full-wake and partial-wake conditions. While our results highlight the limitation in capturing the flow speed-up between adjacent turbine columns, the model is overall able to acceptably predict flow distributions for a moderately sized wind farm. Finally, the paper employs the new model to provide insights on the accuracy of common wake superposition methods.
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…
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…
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 …
Understanding wind turbine wake mixing and recovery is critical for improving the power generation and structural stability of downwind turbines in a wind farm. In the field, where incoming flow and turbine operation are constantly changing, wake recovery can be significantly influenced by dynamic wake modulation, which has not yet been explored. Here we present the first investigation of dynamic wake modulation in the near wake of a utility-scale turbine and quantify its relationship with changing conditions. This investigation is enabled using novel super-large-scale flow visualization with …
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…
Reducing wake losses in wind farms by deflecting the wakes through turbine yawing has been shown to be a feasible wind farm controls approach. Nonetheless, the effectiveness of yawing depends not only on the degree of wake deflection but also on the resulting shape of the wake. In this work, the deflection and morphology of wakes behind a wind turbine operating in yawed conditions are studied using wind tunnel experiments of a wind turbine modeled as a porous disk in a uniform inflow. First, by measuring velocity distributions at various downstream positions and comparing with prior studies, w…
An extended theoretical approach is proposed to predict the average power of wind turbines in a large finite-size wind farm. The approach is based on the two-scale momentum theory proposed recently for the modelling of ideal very large wind farms, but the theory is now generalised by introducing the effect of additional pressure difference induced by the farm between the upstream and downstream sides of the farm, making the approach applicable to real wind farms that are large but not as large as the size of the relevant atmospheric system driving the flow over the farm. To validate the genera…
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…
As wind energy expands worldwide, the demand of reliable, fast, cost-efficient wind turbine wake models is growing. This is a significant challenge as wind turbines face various inflow conditions, that include turbulence, inhomogeneities/instationarities and upstream wakes. In consequence, an enormous number of engineering models, each one based on different physical concepts, has been proposed. The majority focuses on the far wake where the mean velocity recovers and turbulence decays after it built up. We argue that the most important, or the leading, parameter for wake modeling is the lengt…
Wind turbine wakes negatively impact downwind turbines in wind farms reducing their global efficiency. The reduction of wake-turbine interactions by actuating control on yaw angles and induction factors is an active area of research. In this study, the capability of spanwise-periodic wind turbine arrays with tilted rotors to reduce negative turbine-wakes interaction is investigated by means of large-eddy simulations. It is shown that by means of rotor tilt it is possible to replace turbine far wakes with high-speed streaks where the streamwise velocity exceeds the freestream velocity at hub he…
A new theoretical method is presented for future multi-scale aerodynamic optimisation of very large wind farms. The new method combines a recent two-scale coupled momentum analysis of ideal wind turbine arrays with the classical blade-element-momentum (BEM) theory for turbine rotor design, making it possible to explore some potentially important relationships between the design of rotors and their performance in a very large wind farm. The details of the original two-scale momentum model are described first, followed by the new coupling procedure with the classical BEM theory and some example …
This work is dedicated to studying the influence of yaw angle on the wake characteristics of a 2.5 MW utility-scale wind turbine using large-eddy simulations with the turbine's blades and nacelle parameterized as actuator surfaces. Four different yaw angles are simulated, i.e., $γ=0^{\circ},10^{\circ},20^{\circ},30^{\circ}$ for three different tip-speed ratios $λ= 7,8,9$. Similarities are observed for both time-averaged velocity fields and the turbulence statistics of turbine wakes. Specifically, it is found that the temporal average of the wake deflection, the velocity deficit and the transve…
The flows behind a model wind turbine under two turbine operating regimes are investigated using wind tunnel experiments and large-eddy simulations. Measurements from the model wind turbine experiment reveal that the power coefficient and turbine wake are affected by the operating regime. Simulations employing a new class of actuator surface methods which parameterize both the turbine blades and nacelle with and without a nacelle model are carried out for each operating condition to study the influence of the operating regime and nacelle. For simulations with a nacelle model, the mean flow fie…
In this paper, wake steering is applied to multirotor turbines to determine whether it has the potential to reduce wind plant wake losses. Through application of rotor yaw to multirotor turbines, a new degree of freedom is introduced to wind farm control such that wakes can be expanded, channelled, or redirected to improve inflow conditions for downstream turbines. Five different yaw configurations are investigated (including a baseline case) by employing large-eddy simulations (LES) to generate a detailed representation of the velocity field downwind of a multirotor wind turbine. Two lower-fi…
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…
Super-large-scale particle image velocimetry and flow visualization with natural snowfall is used to collect and analyze multiple datasets in the near wake of a 2.5 MW wind turbine. Each dataset captures the full vertical span of the wake from a different perspective. Together, these datasets compose a three-dimensional picture of the near-wake flow, including the effect of the tower and hub and the variation of instantaneous wake expansion in response to changes in turbine operation. A region of high-speed flow is observed directly behind the hub, and a region of low-speed flow appears behind…
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 diff…
The near wake of a small-scale wind turbine is investigated using Particle Image Velocimetry (PIV) experiments at different tip speed ratios ($λ$). The wind turbine model had a nacelle and a tower mimicking real scale wind turbines. The near wake is found to be dominated by multiple coherent structures including the tip vortices, distinct vortex sheddings from the nacelle and tower, and wake meandering. The merging of the tip vortices is found to be strongly dependent on $λ$. A convective length scale ($L_c$) related to the pitch of the helical vortices is defined which is shown to be a better…
To design and optimize arrays of vertical-axis wind turbines (VAWTs) for maximal power density and minimal wake losses, a careful consideration of the inherently three-dimensional structure of the wakes of these turbines in real operating conditions is needed. Accordingly, a new volumetric particle-tracking velocimetry method was developed to measure three-dimensional flow fields around full-scale VAWTs in field conditions. Experiments were conducted at the Field Laboratory for Optimized Wind Energy (FLOWE) in Lancaster, CA, using six cameras and artificial snow as tracer particles. Velocity a…
Wind turbine's wake, being convectively unstable, may behave as an amplifier of upstream perturbations and make the downstream turbine experience strong inflow fluctuations. In this work, we investigate the effects of the side-to-side motion of a floating offshore wind turbine (FOWT) on wake dynamics using large-eddy simulation and linear stability analysis (LSA) on the NREL 5MW baseline offshore wind turbine. Simulation results reveal that the turbine motion can lead to wake meandering for motion frequencies with the Strouhal number $St = fD/U_\infty \in (0.2,0.6)$ (where $f$ is the motion fr…
The efficiency of tidal-stream turbines in a large array depends on the balance between negative effects of turbine-wake interactions and positive effects of bypass-flow acceleration due to local blockage, both of which are functions of the layout of turbines. Here we investigate the hydrodynamics of turbines in an infinitely large array with aligned or staggered layouts for a range of streamwise and lateral turbine spacing. First, we present a theoretical analysis based on an extension of the Linear Momentum Actuator Disc Theory (LMADT) for perfectly aligned and staggered layouts, employing a…
Motivated by the need for compact descriptions of the evolution of non-classical wakes behind yawed wind turbines, we develop an analytical model to predict the shape of curled wakes. Interest in such modelling arises due to the potential of wake steering as a strategy for mitigating power reduction and unsteady loading of downstream turbines in wind farms. We first estimate the distribution of the shed vorticity at the wake edge due to both yaw offset and rotating blades. By considering the wake edge as an ideally thin vortex sheet, we describe its evolution in time moving with the flow. Vort…
Arrays of Vertical Axis Wind Turbines (VAWTs) can achieve larger power generation per land area than horizontal axis turbines farms, due to the positive synergy between VATs in close proximity. Theoretical wake models enable the reliable design of the array layout that maximises the energy output, which need to depict the driving wake dynamics. VAWTs generate a highly complex wake that evolves according to two governing length-scales, namely the turbine rotor's diameter and height which define a rectangular shape of the wake cross-section, and feature distinct wake expansion rates. This paper …
The current study uses large eddy simulations to investigate the transient response of a utility-scale wind turbine wake to dynamic changes in atmospheric and operational conditions, as observed in previous field-scale measurements. Most wind turbine wake investigations assume quasi-steady conditions, but real wind turbines operate in a highly stochastic atmosphere, and their operation (e.g., blade pitch, yaw angle) changes constantly in response. Furthermore, dynamic control strategies have been recently proposed to optimize wind farm power generation and longevity. Therefore, improved unders…
The near-wake of a vertical-axis cross-flow turbine (CFT) was modeled numerically via blade-resolved $k$-$ω$ SST and Spalart-Allmaras RANS models in two and three dimensions. Results for each case are compared with experimental measurements of the turbine shaft power, overall drag, mean velocity, turbulence kinetic energy, and momentum transport terms in the near-wake at one diameter downstream. It was shown that 2-D simulations overpredict turbine loading and do not resolve mean vertical momentum transport, which plays an important role in the near-wake's momentum balance. The 3-D simulations…
An extended analytical wake model and applications to yawed wind turbines in atmospheric boundary layers with different levels of stratification and veer
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…
The fluid dynamics video considers an array of two NREL 5-MW turbines separated by seven rotor diameters in a neutral atmospheric boundary layer (ABL). The neutral atmospheric boundary-layer flow data were obtained from a precursor ABL simulation using a Large-Eddy Simulation (LES) framework within OpenFOAM. The mean wind speed at hub height is 8m/s, and the surface roughness is 0.2m. The actuator line method (ALM) is used to model the wind turbine blades by means of body forces added to the momentum equation. The fluid dynamics video shows the root and tip vortices emanating from the blades f…
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…
Many wind farms are placed near coastal regions or in proximity of orographic obstacles. The meso-scale gradients that develop in these zones make wind farms operating in velocity fields that are rarely uniform. However, all existing wake-merging methods in engineering wind-farm wake models assume a homogeneous background velocity field in and around the farm, relying on a single wind-speed value usually measured several hundreds of meters upstream of the first row of turbines. In this study, we derive a new momentum-conserving wake-merging method capable of superimposing the waked flow on a h…
Super-large-scale particle image velocimetry (SLPIV) using natural snowfall is used to investigate the influence of nacelle and tower generated flow structures on the near-wake of a 2.5 MW wind turbine at the EOLOS field station. The analysis is based on the data collected in a field campaign on March 12th, 2017, with a sample area of 125 m (vertical) x 70 m (streamwise) centred on the plane behind the turbine support tower. The SLPIV measurement provides the velocity field over the entire rotor span, revealing a region of accelerated flow around the hub caused by the reduction in axial induct…
Tidal turbines are deployed in sites which have elevated levels of free stream turbulence (FST). Accounting for elevated FST on their operation become vital from a design standpoint. Detailed experimental measurements of the dynamic near-wake of a tidal turbine model in elevated FST environments is presented; an active grid turbulence generator developed by our group was used to seed in the elevated FST and evaluate the influence of turbulence intensity (Ti) and inflow integral length scale (L) on the near-wake of the turbine. Three inflow conditions are tested: a quasi-laminar flow with Ti ~ …
We describe a generalization of the Coupled Wake Boundary Layer (CWBL) model for wind-farms that can be used to evaluate the performance of wind-farms under arbitrary wind inflow directions whereas the original CWBL model (Stevens et al., J. Renewable and Sustainable Energy 7, 023115 (2015)) focused on aligned or staggered wind-farms. The generalized CWBL approach combines an analytical Jensen wake model with a "top-down" boundary layer model coupled through an iterative determination of the wake expansion coefficient and an effective wake coverage area for which the velocity at hub-height obt…
Turbulence-resolving simulations of wind turbine wakes are presented using a high--order flow solver combined with both a standard and a novel dynamic implicit spectral vanishing viscosity (iSVV and dynamic iSVV) model to account for subgrid-scale (SGS) stresses. The numerical solutions are compared against wind tunnel measurements, which include mean velocity and turbulent intensity profiles, as well as integral rotor quantities such as power and thrust coefficients. For the standard (also termed static) case the magnitude of the spectral vanishing viscosity is selected via a heuristic analys…
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…
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…
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…
