The k‐ε‐fP model applied to double wind turbine wakes using different actuator disk force methods

The newly developed k‐ε‐f_P eddy viscosity model is applied to double wind turbine wake configurations in a neutral atmospheric boundary layer, using a Reynolds‐Averaged Navier–Stokes solver. The wind turbines are represented by actuator disks. A proposed variable actuator disk force method is employed to estimate the power production of the interacting wind turbines, and the results are compared with two existing methods: a method based on tabulated airfoil data and a method based on the axial induction from 1D momentum theory. The proposed method calculates the correct power, while the other two methods overpredict it. The results of the k‐ε‐f_P eddy viscosity model are also compared with the original k‐ε eddy viscosity model and large‐eddy simulations. Compared to the large‐eddy simulations‐predicted velocity and power deficits, the k‐ε‐f_P is superior to the original k‐ε model. Copyright © 2014 John Wiley & Sons, Ltd.     

An improved k‐ ϵ model applied to a wind turbine wake in atmospheric turbulence

An improved k‐ ? turbulence model is developed and applied to a single wind turbine wake in a neutral atmospheric boundary layer using a Reynolds averaged Navier–Stokes solver. The proposed model includes a flow‐dependent C_μ that is sensitive to high velocity gradients, e.g., at the edge of a wind turbine wake. The modified k‐ ? model is compared with the original k‐ ? eddy viscosity model, Large‐Eddy Simulations and field measurements using eight test cases. The comparison shows that the velocity wake deficits, predicted by the proposed model are much closer to the ones calculated by the Large‐Eddy Simulation and those observed in the measurements, than predicted by the original k‐ ? model. Copyright © 2014 John Wiley & Sons, Ltd.     

A new k‐epsilon model consistent with Monin–Obukhov similarity theory

A new k‐? model is introduced that is consistent with Monin–Obukhov similarity theory (MOST). The proposed k‐? model is compared with another k‐? model that was developed in an attempt to maintain inlet profiles compatible with MOST. It is shown that the previous k‐? model is not consistent with MOST for unstable conditions, while the proposed k‐? model can maintain MOST inlet profiles over distances of 50km. Copyright © 2016 John Wiley & Sons, Ltd.     

Comparison of the near‐wake between actuator‐line simulations and a simplified vortex model of a horizontal‐axis wind turbine

The flow around an isolated horizontal‐axis wind turbine is estimated by means of a new vortex code based on the Biot–Savart law with constant circulation along the blades. The results have been compared with numerical simulations where the wind turbine blades are replaced with actuator lines. Two different wind turbines have been simulated: one with constant circulation along the blades, to replicate the vortex method approximations, and the other with a realistic circulation distribution, to compare the outcomes of the vortex model with real operative wind‐turbine conditions (Tjæreborg wind turbine). The vortex model matched the numerical simulation of the turbine with constant blade circulation in terms of the near‐wake structure and local forces along the blade. The results from the Tjæreborg turbine case showed some discrepancies between the two approaches, but overall, the agreement is qualitatively good, validating the analytical method for more general conditions. The present results show that a simple vortex code is able to provide an estimation of the flow around the wind turbine similar to the actuator‐line approach but with a negligible computational effort. Copyright © 2015 John Wiley & Sons, Ltd.     

Thermal transport phenomena of turbulent jet diffusion flames by means of anisotropic k–ϵ–t2–ϵt model

A numerical study is performed on transport phenomena in a turbulent jet diffusion flame of hydrogen from a vertical circular nozzle. An anisotropic k–ϵ–t² –ϵ_t model and the eddy‐dissipation model are employed to simulate thermal fluid flow and combustion phenomena, respectively. The governing boundary‐layer equations are discretized by means of a control volume finite‐difference technique and are numerically solved. The model predicts the experimental data in the existing literature. It is found from the study that (i) the model employed here can be applied to combustion phenomenon, and (ii) the presence of flame enhances the anisotropy of turbulence and causes a substantial attenuation in the turbulent kinetic energy, that is, most turbulent kinetic energy in the flame in the downstream part is laden exclusively in the streamwise fluctuation. Copyright © 1999 John Wiley & Sons, Ltd.     

Parabolic RANS solver for low‐computational‐cost simulations of wind turbine wakes

A numerical framework for simulations of wake interactions associated with a wind turbine column is presented. A Reynolds‐averaged Navier‐Stokes (RANS) solver is developed for axisymmetric wake flows using parabolic and boundary‐layer approximations to reduce computational cost while capturing the essential wake physics. Turbulence effects on downstream evolution of the time‐averaged wake velocity field are taken into account through Boussinesq hypothesis and a mixing length model, which is only a function of the streamwise location. The calibration of the turbulence closure model is performed through wake turbulence statistics obtained from large‐eddy simulations of wind turbine wakes. This strategy ensures capturing the proper wake mixing level for a given incoming turbulence and turbine operating condition and, thus, accurately estimating the wake velocity field. The power capture from turbines is mimicked as a forcing in the RANS equations through the actuator disk model with rotation. The RANS simulations of the wake velocity field associated with an isolated 5‐MW NREL wind turbine operating with different tip speed ratios and turbulence intensity of the incoming wind agree well with the analogous velocity data obtained through high‐fidelity large‐eddy simulations. Furthermore, different cases of columns of wind turbines operating with different tip speed ratios and downstream spacing are also simulated with great accuracy. Therefore, the proposed RANS solver is a powerful tool for simulations of wind turbine wakes tailored for optimization problems, where a good trade‐off between accuracy and low‐computational cost is desirable.     

Laminar‐turbulent flow simulation for wind turbine profiles using the γ– transition model

The accurate prediction of the laminar‐turbulence transition process is fundamental in predicting the aerodynamic performance of wind turbine profiles. Fully turbulent flow simulations have been shown to over‐predict the aerodynamic performance and thereby negatively impacting the design of airfoils in flow regimes where the possible presence of laminar flow could be exploited to improve the performance of wind turbine rotors. Correlation‐based transition modelling offers a fully computational fluid dynamics compatible approach, where the model integrates completely with the existing turbulence model, allows for the prediction of various transition mechanisms, is applicable to three‐dimensional flows and compatible to adjoint‐based design optimization frameworks. The present paper addresses several modifications necessary for a robust transition model and investigates the accuracy of the model for a wide range of angles of attack and Reynolds numbers, which are necessary for a thorough validation of the correlation‐based transition model for wind turbine profiles. The transition model was employed to predict the transition locations; and an assessment of the various transition mechanisms, Reynolds number effects, sectional characteristics and aerodynamic performance for the NLF(1)‐0416 and S809 airfoils is presented with comparisons to experimental data and numerical solutions. Copyright © 2013 John Wiley & Sons, Ltd.     

Tip‐vortex breakdown of wind turbines subject to shear

Sheared velocity profiles pervade all wind‐turbine applications, thus making it important to understand their effect on the wake. In this study, a single wind turbine is modeled using the actuator‐line method in the incompressible Navier–Stokes equations. The tip vortices are perturbed harmonically, and the growth rate of the response is evaluated under uniform inflow and a linear velocity profile. Whereas previous investigations of this kind were conducted in the rotating frame of reference, this study evaluates the excitation response in the fixed frame of reference, thus necessitating a frequency transformation. It is shown that increasing the shear decreases the spatial growth rate in the upper half of the wake while increasing it in the lower half. When scaled with the local tip vortex parameters, the growth rate along the entire azimuth collapses to a single value for the investigated wavenumbers. We conclude that even though the tip‐vortex breakdown is asymmetric in sheared flow, the scaled growth rates follow the behavior of axisymmetric helical vortices. An excitation amplitude reduction by an order of magnitude extends the linear growth region of the wake by one radius for uniform inflow. In the sheared setup, the linear growth region is extended further in the top half than in the bottom half because of the progressive distortion of the helical tip vortices. An existing model to determine the stable wake length was shown to be in close agreement with the observed numerical results when adjusted for shear.     

Self‐similarity and turbulence characteristics of wind turbine wakes via large‐eddy simulation

Mean and turbulent properties of the wake generated by a single wind turbine are studied in this paper with a new large eddy simulation (LES) code, the wind turbine and turbulence simulator (WiTTS hereafter). WiTTS uses a scale‐dependent Lagrangian dynamical model of the sub‐grid shear stress and actuator lines to simulate the effects of the rotating blades. WiTTS is first tested by simulating neutral boundary layers without and with a wind turbine and then used to study the common assumptions of self‐similarity and axisymmetry of the wake under neutral conditions for a variety of wind speeds and turbine properties. We find that the wind velocity deficit generally remains self similarity to a Gaussian distribution in the horizontal. In the vertical, the Gaussian self‐similarity is still valid in the upper part of the wake, but it breaks down in the region of the wake close to the ground. The horizontal expansion of the wake is always faster and greater than the vertical expansion under neutral stability due to wind shear and impact with the ground. Two modifications to existing equations for the mean velocity deficit and the maximum added turbulence intensity are proposed and successfully tested. The anisotropic wake expansion is taken into account in the modified model of the mean velocity deficit. Turbulent kinetic energy (TKE) budgets show that production and advection exceed dissipation and turbulent transport. The nacelle causes significant increase of every term in the TKE budget in the near wake. In conclusion, WiTTS performs satisfactorily in the rotor region of wind turbine wakes under neutral stability. Copyright © 2014 John Wiley & Sons, Ltd.     

Computational Fluid Dynamics model of stratified atmospheric boundary‐layer flow

For wind resource assessment, the wind industry is increasingly relying on computational fluid dynamics models of the neutrally stratified surface‐layer. So far, physical processes that are important to the whole atmospheric boundary‐layer, such as the Coriolis effect, buoyancy forces and heat transport, are mostly ignored. In order to decrease the uncertainty of wind resource assessment, the present work focuses on atmospheric flows that include stability and Coriolis effects. The influence of these effects on the whole atmospheric boundary‐layer are examined using a Reynolds‐averaged Navier–Stokes k‐ ε model. To validate the model implementations, results are compared against measurements from several large‐scale field campaigns, wind tunnel experiments, and previous simulations and are shown to significantly improve the predictions. Copyright © 2013 John Wiley & Sons, Ltd.     

The effective velocity model: An improved approach to velocity sampling in actuator line models

Actuator line modeling of wind turbines requires the definition of a free-stream velocity in a computational mesh and a regularization kernel to project the computed body forces onto the domain. Both choices strongly influence the results. In this work, a novel velocity sampling method—the so-called effective velocity model (EVM)—is implemented in the CFD software SOWFA, validated, and compared to pre-existing approaches. Results show superior method robustness with respect to the regularization kernel width ( $ϵ$) choice while preserving acceptable accuracy. In particular, the power predicted by the EVM is nearly independent of the $ϵ$ value.     

Dynamic stall analysis using harmonic balance and correlation‐based γ– transition models for wind turbine applications

In this paper, we use the harmonic balance method to study an oscillating S809 airfoil in dynamic stall. The periodic behavior of this problem makes it well suited for the harmonic balance method, which is able to model unsteady aerodynamics at greatly reduced computational costs when compared with time‐accurate unsteady‐flow solvers. A finite‐volume technique based on the lower–upper symmetric Gauss–Seidel scheme with Roe fluxes is used to solve the Reynolds‐averaged Navier–Stokes equations. The turbulent viscosity is computed with the one‐equation Spalart–Allmaras turbulence model. In addition, the laminar–turbulent transition is modeled using a correlation‐based approach originally developed by Langtry and Menter. Comparisons with experimental data for steady flows with the S809 airfoil highlight the necessity of the transition model to accurately predict the onset of static stall. For unsteady cases, the transition model provides improved agreement with experimental data, predicting dynamic stall when the fully turbulent model cannot. Copyright © 2014 John Wiley & Sons, Ltd.     

Large‐eddy simulation of turbulent flow past wind turbines/farms: the Virtual Wind Simulator (VWiS)

A large‐eddy simulation framework, dubbed as the Virtual Wind Simulator (VWiS), for simulating turbulent flow over wind turbines and wind farms in complex terrain is developed and validated. The wind turbines are parameterized using the actuator line model. The complex terrain is represented by the curvilinear immersed boundary method. The predictive capability of the present method is evaluated by simulating two available wind tunnel experimental cases: the flow over a stand‐alone turbine and an aligned wind turbine array. Systematic grid refinement studies are carried out, for both single turbine and multi‐turbine array cases, and the accuracy of the computed results is assessed through detailed comparisons with wind tunnel experiments. The model is further applied to simulate the flow over an operational utility‐scale wind farm. The inflow velocities for this case are interpolated from a mesoscale simulation using a Weather Research and Forecasting (WRF) model with and without adding synthetic turbulence to the WRF‐computed velocity fields. Improvements on power predictions are obtained when synthetic turbulence is added at the inlet. Finally the VWiS is applied to simulate a yet undeveloped wind farm at a complex terrain site where wind resource measurements have already been obtained. Good agreement with field measurements is obtained in terms of the time‐averaged streamwise velocity profiles. To demonstrate the ability of the model to simulate the interactions of terrain‐induced turbulence with wind turbines, eight hypothetical turbines are placed in this area. The computed extracted power underscores the significant effect of site‐specific topography on turbine performance. Copyright © 2014 John Wiley & Sons, Ltd.     

Simulating the aerodynamic performance and wake dynamics of a vertical‐axis wind turbine

The accurate prediction of the aerodynamics and performance of vertical‐axis wind turbines is essential if their design is to be improved but poses a significant challenge to numerical simulation tools. The cyclic motion of the blades induces large variations in the angle of attack of the blades that can manifest as dynamic stall. In addition, predicting the interaction between the blades and the wake developed by the rotor requires a high‐fidelity representation of the vortical structures within the flow field in which the turbine operates. The aerodynamic performance and wake dynamics of a Darrieus‐type vertical‐axis wind turbine consisting of two straight blades is simulated using Brown's Vorticity Transport Model. The predicted variation with azimuth of the normal and tangential force on the turbine blades compares well with experimental measurements. The interaction between the blades and the vortices that are shed and trailed in previous revolutions of the turbine is shown to have a significant effect on the distribution of aerodynamic loading on the blades. Furthermore, it is suggested that the disagreement between experimental and numerical data that has been presented in previous studies arises because the blade–vortex interactions on the rotor were not modelled with sufficient fidelity. Copyright © 2010 John Wiley & Sons, Ltd.     

Generalized coupled wake boundary layer model: applications and comparisons with field and LES data for two wind farms

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 obtained using both models converges in the ‘deep‐array’ portion (fully developed region) of the wind farm. The approach accounts for the effect of the wind direction by enforcing the coupling for each wind direction. Here, we present detailed comparisons of model predictions with large eddy simulation results and field measurements for the Horns Rev and Nysted wind farms operating over a wide range of wind inflow directions. Our results demonstrate that two‐way coupling between the Jensen wake model, and a ‘top‐down’ model enables the generalized CWBL model to predict the ‘deep‐array’ performance of a wind farm better than the Jensen wake model alone. The results also show that the new generalization allows us to study a much larger class of wind farms than the original CWBL model, which increases the utility of the approach for wind farm designers. Copyright © 2016 John Wiley & Sons, Ltd.     

Influence of model parameters on the design of large diameter monopiles for multi‐megawatt offshore wind turbines at 50‐m water depths

Relevant modelling approaches towards the design of a large diameter monopile for 10 MW offshore wind turbines at 50‐m water depths are considered to evaluate their respective impacts on the structural integrity. The analysed models or model parameters include soil‐structure interaction, construction errors, and damping. The study is conducted on a reference structure verified with respect to fatigue, ultimate (strength, stability, and soil capacity), and serviceability limit states after fully coupled load simulations. Models and their parameters are carefully obtained in line with the case in hand. Perturbation analysis is used to assess the impact of the soil model, the geometric imperfections, and the damping on the structure safety and robustness. Results show that all of them significantly influence the fatigue lifetime, the geometric imperfections and the soil model impact the ultimate stresses, and the soil model affects the deformations of the final design, from which guidance on the optimal selection of these parameters leading to material savings is made.     

Two improvements to the dynamic wake meandering model: including the effects of atmospheric shear on wake turbulence and incorporating turbulence build‐up in a row of wind turbines

The dynamic wake meandering (DWM) model is an engineering wake model designed to physically model the wake deficit evolution and the unsteady meandering that occurs in wind turbine wakes. The present study aims at improving two features of the model:

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New M5P model tree‐based control for doubly fed induction generator in wind energy conversion system

This paper presents a new algorithm based on the combination of fuzzy logic control with M5 decision tree algorithm for doubly fed induction generator active and reactive power control. The M5 model tree is a machine learning algorithm that uses the extracted dataset from fuzzy logic for the aim of control performance enhancement. Because the fuzzy logic provides high design and implementation complexity, the new control approach is proposed to reduce its complexity and to achieve fast dynamic control by translating the fuzzy logic algorithm into simple if‐then instructions using M5 model tree. The obtained model shows good agreement with fuzzy logic in rotor side control. The effectiveness of the proposed control approach is investigated through Matlab/Simulink software. Furthermore, a cosimulated through processor in the loop testing is performed as an experimental verification using a low‐cost STM32F407 discovery board.     

RANS simulations of neutral atmospheric boundary layer flow over complex terrain with comparisons to field measurements

Micro‐scale Reynolds‐averaged Navier‐Stokes (RANS) simulations of the neutral atmospheric boundary layer (ABL) over complex terrain and a comparison of the results with conditionally averaged met‐tower data are presented. A robust conditional sampling procedure for the meteorological tower (met‐tower) data to identify near‐neutral conditions based on a criterion for the turbulence intensity is developed. The conditionally averaged wind data on 14 met‐towers are used for the model validation. The ABL flow simulations are conducted over complex terrain which includes a prominent hill using the OpenFOAM‐based simulator for on/offshore wind farm applications (SOWFA) with the k?? and the SST k?ω turbulence models. The discretization of the production term in the transport equation for the turbulent kinetic energy (TKE) is modified to greatly reduce the commonly observed nonphysical near surface TKE peak. The driving inflow is generated through an iterative approach using a precursor method to reproduce the measured wind statistics at the reference tower. Both of the RANS models are able to capture the flow behavior windward of the hill. The SST k?ω model predicts more intense flow separation than the k?? model downstream of the steepest sections of the hill. The wind statistics predicted at the location of the met‐towers by both of the RANS models are fairly consistent. Overall, the comparisons of the direction, mean, and standard deviation of the wind between the simulations and the tower data show reasonable agreement except for the differences of the mean wind speeds at four met‐towers located closer to the main ridge of the hill in a region of strong terrain variations.