In this study, we present an improved formulation for the wake-added turbulence to enhance the accuracy of intra-farm and farm-to-farm wake modeling through analytical frameworks. Our goal is to address the tendency of a commonly used formulation to overestimate turbulence intensity within wind farms and to overcome its limitations in predicting the streamwise evolution of turbulence intensity beyond them. To this end, we utilize high-fidelity data and adopt an optimization technique to derive an optimized functional form of the wake-added turbulence. We then integrate the achieved formulation with a widely used Gaussian wake model to study various intra-farm and farm-to-farm scenarios. The outcomes reveal that the new methodology effectively addresses the overestimation of power in both standalone wind farms and those impacted by upstream counterparts. Our new approach meets the need for accurate and lightweight models, ensuring the effective coexistence of wind farms within clusters as the wind-energy capacity rapidly expands.
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…
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…
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…
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…
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…
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…
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…
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…
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…
This paper introduces a dynamic parametric wind farm model that is capable of simulating floating wind turbine platform motion coupled with wake transport under time-varying wind conditions. The simulator is named FOWFSim-Dyn as it is a dynamic extension of the previously developed steady-state Floating Offshore Wind Farm Simulator (FOWFSim). One-dimensional momentum conservation is used to model dynamic propagation of wake centerline locations and average velocities, while momentum recovery is approximated with the assumption of a constant temporal wake expansion rate. Platform dynamics are c…
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…
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…
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 cons…
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 …
Wind farm global blockage as an adverse pressure gradient problem: turbulence amplification and spectral modification in the induction region of a model wind farm
Wind farm flow control aims to improve wind turbine performance by reducing aerodynamic wake interaction between turbines. Dynamic, physics-based models of wind farm flows have been essential for exploring control strategies such as wake redirection and dynamic induction control. Free vortex methods can provide a computationally efficient way to model wind turbine wake dynamics for control optimisation. We present a control-oriented free-vortex wake model of a 2D and 3D actuator disc to represent wind turbine wakes. The novel derivation of the discrete adjoint equations allows efficient gradie…
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…
The effect of freestream turbulence on the spreading of the near wake of a circular cylinder is investigated through particle image velocimetry (PIV) data. Different ``flavours'' of freestream turbulence, in which the turbulence intensity and integral length scale are independently varied, are subjected to the cylinder. The time-averaged spreading of the near wake is decoupled into the growth through entrainment and the envelope of the spatial extent of the instantaneous wake due to wake ``meandering'', induced by the presence of large-scale coherent structures, i.e. the von Karman vortex stre…
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…
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 …
Several novel wind energy systems produce wakes with annular cross-sections, which are qualitatively different from the wakes with circular cross-sections commonly generated by conventional horizontal-axis wind turbines and by compact obstacles. Since wind farms use arrays of hundreds of turbines, good analytical wake models are essential for efficient wind farm planning. Several models already exist for circular wakes; however, none have yet been proposed for annular wakes, making it impossible to estimate their array performance. We use the entrainment hypothesis to develop a reduced-order m…
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…
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…
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…
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…
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…
Collective wind farm flow control, where wind turbines are operated in an individually suboptimal strategy to benefit the aggregate farm, has demonstrated potential to reduce wake interactions and increase farm energy production. However, existing wake models used for flow control often estimate the thrust and power of yaw misaligned turbines using simplified empirical expressions which require expensive calibration data and do not accurately extrapolate between turbine models. The thrust, wake velocity deficit, wake deflection, and power of a yawed wind turbine depend on its induced velocity.…
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 …
Recent analytical models concerning the limiting efficiency of marine hydrokinetic (MHK) turbines are reviewed with an emphasis on the significance of blockages (of local as well as global flow passages) and wake mixing. Also discussed is the efficiency of power generation from fully developed turbulent open channel flows. These issues are primarily concerned with the design/optimization of tidal turbine arrays; however, some of them are relevant to wind turbines as well.
Particles suspended in turbulent flows are affected by the turbulence and at the same time act back on the flow. The resulting coupling can give rise to rich variability in their dynamics. Here we report experimental results from an investigation of finite-sized buoyant spheres in turbulence. We find that even a marginal reduction in the particle's density from that of the fluid can result in strong modification of its dynamics. In contrast to classical spatial filtering arguments and predictions of particle models, we find that the particle acceleration variance increases with size. We trace …
As wind energy continues to expand, increased interaction between wind farms and their surroundings can be expected. Using natural snowfall to visualize the air flow in the wake of a utility-scale wind turbine at unprecedented spatio-temporal resolution, we observe intermittent periods of strong interaction between the wake and the ground surface and quantify the momentum flux during these periods. Significantly, we identify two turbine operational-dependent pathways that lead to these periods of increased wake-ground interaction. Data from a nearby meteorological tower provides further insigh…
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 ~ …
