Extracting lift and drag polars from blade‐resolved computational fluid dynamics for use in actuator line modelling of horizontal axis turbines

Low order rotor models such as the actuator line method are desirable as an efficient method of computing the large range of operating and environmental conditions, required to design wind and tidal rotors and arrays. However, the integrated thrust and torque predictions for each rotor are dominated by the blade loading on the outboard sections, where three‐dimensional (3D) effects become increasingly significant, and the accuracy of the reduced order methods remains uncertain. To investigate the accuracy of the spanwise blade loading on an individual rotor, actuator line and blade boundary layer resolved computations of the Model Rotor Experiments in Controlled Conditions (MEXICO) rotor are presented. The high fidelity blade‐resolved simulations give good agreement with measured pressure coefficient and particle image velocimetry data. Alternative lift and drag polars are extracted from the 3D simulated flow fields as a function of radial position. These are then used as replacement inputs for the actuator line method. Significant improvement in the accuracy of the actuator line predictions is found when using these 3D extracted polars, compared with using simulated two‐dimensional lift and drag polars with empirical correction applied to the spanwise loading distribution. Additionally, the 3D flow field data is used to derive different axial and tangential spanwise loading corrections for use with the two‐dimensional blade polars. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

New dynamic‐inflow engineering models based on linear and nonlinear actuator disc vortex models

Two new engineering models are presented for the aerodynamic induction of a wind turbine under dynamic thrust. The models are developed using the differential form of Duhamel integrals of indicial responses of actuator disc type vortex models. The time constants of the indicial functions are obtained by the indicial responses of a linear and a nonlinear actuator disc model. The new dynamic‐inflow engineering models are verified against the results of a Computational Fluid Dynamics (CFD) model and compared against the dynamic‐inflow engineering models of Pitt‐Peters, Øye, and Energy Research Center of the Netherlands (ECN), for several load cases. Comparisons of all models show that two time constants are necessary to predict the dynamic induction. The amplitude and phase delay of the velocity distribution shows a strong radial dependency. Verifying the models against results from the CFD model shows that the model based on the linear actuator disc vortex model predicts a similar performance as the Øye model. The model based on the nonlinear actuator disc vortex model predicts the dynamic induction better than the other models concerning both phase delay and amplitude, especially at high load.     

A new dynamic inflow model for vertical‐axis wind turbines

This paper presents a new dynamic inflow model for vertical‐axis wind turbines (VAWTs). The model uses the principle of Duhamel's integral. The indicial function of the inflow‐ and crossflow‐induction required to apply Duhamel's integral is represented by an exponential function depending on the thrust coefficient and the azimuthal position. The parameters of this approximation are calibrated using a free wake vortex model. The model is compared with the results of a vortex model and higher fidelity computational fluid dynamic (CFD) simulations for the response of an actuator cylinder to a step input of the thrust and to a cyclic thrust. It is found that the discrepancies of the dynamic inflow model increase with increasing reduced frequency and baseline thrust. However, the deviations remain small. Analysing the application of a finite‐bladed floating VAWT with non‐uniform loading and validating it against actuator line CFD results that intrinsically include dynamic inflow shows that the new dynamic inflow model significantly outperforms the Larsen and Madsen model (which is the current standard in fully coupled VAWT models) and enhances the modelling of VAWTs.     

Application of the actuator surface concept to wind turbine rotor aerodynamics

The structure of blade tip vortices is recognized as a key issue in wind turbine aerodynamic modelling by many researchers in the field. In the search for an intermediate model between full Navier–Stokes and blade‐element momentum simulations, this article presents a method using rotating actuator surfaces to model wind turbine aerodynamics. An actuator surface is a simple planar surface, porous to the flow, which is characterized by velocity and pressure discontinuities, whose action on the flow is achieved through an attached system of forces. These discontinuities and forces are determined from blade‐element analysis and the Kutta–Joukowski relation. After implementing this concept in a three‐dimensional CFD (Computational Fluid Dynamics) method, results are produced for the experimental rotors of NREL and TUDelft. The method is validated against both experimental measurements and the predictions of three other numerical models for wind turbine aerodynamic analysis. Qualitative and quantitative comparisons show that the actuator surface concept agrees well with the other numerical models. In addition to rotor aerodynamic analysis, the actuator surface concept can be used in the study of wake aerodynamics, or as the Eulerian flow solver in hybrid methods. Copyright © 2009 John Wiley & Sons, Ltd.     

An actuator sector method for efficient transient wind turbine simulation

This paper investigates a new method for transient simulation of flow through a wind turbine using an actuator technique. The aim, in the context of wind turbine wake simulation, is to develop an alternative to the widely used actuator disc model with an increased resolution and range of applications, for the same or less computational expense. In this new model, the actuator sector method, forces applied to the fluid are distributed azimuthally to maintain a continuous flow solution for increased time‐step intervals compared with the actuator line method. Actuator sector results are presented in comparison with actuator disc and actuator line models initially for a non‐dimensionalized turbine in laminar onset flow. Subsequent results are presented for a turbine operating in a turbulent atmospheric boundary layer. Results show significant increases in flow fidelity compared with actuator disc model results; this includes the resolution of diametric variation in rotor loading caused by horizontal or vertical wind shear and the helical vortex system shed from the turbine blade tips. Significant reductions in computational processing time were achieved with wake velocities and turbulence statistics comparable with actuator line model results. The actuator sector method offers an improved alternative to applications employing conventional actuator disc models, with little or no additional computational cost. This technique in conjunction with a Cartesian mesh‐based parallel flow solver leads to efficient simulation of turbines in atmospheric boundary layer flows. Copyright © 2014 John Wiley & Sons, Ltd.     

Numerical modeling of the hydraulic blade pitch actuator in a spar‐type floating wind turbine considering fault conditions and their effects on global dynamic responses

This paper deals with numerical modeling of the hydraulic blade pitch actuator and its effect on the dynamic responses of a floating spar‐type wind turbine under valve fault conditions. A spar‐type floating wind turbine concept is modeled and simulated using an aero‐hydro‐servo‐elastic simulation tool (Simo‐Riflex [SR]). Because the blade pitch system has the highest failure rate, a numerical model of the hydraulic blade pitch actuator with/without valve faults is developed and linked to SR to study the effects of faults on global responses of the spar‐type floating wind turbine for different faults, fault magnitudes, and environmental conditions. The consequence of valve faults in the pitch actuator is that the blade cannot be pitched to the desired angle, so there may be a delay in the response due to excessive friction and the wrong voltage, or slit lock may cause runaway blade pitch. A short circuit may cause the blade to get stuck at a particular pitch angle. These faults contribute to rotor imbalance, which result in different effects on the turbine structure and the platform motions. The proposed method for combining global and hydraulic actuator models is demonstrated in case studies with stochastic wind and wave conditions and different types of valve faults.     

Near‐wake flow simulation of a vertical axis turbine using an actuator line model

In the present work, the near‐wake generated for a vertical axis wind turbine (VAWT) was simulated using an actuator line model (ALM) in order to validate and evaluate its accuracy. The sensitivity of the model to the variation of the spatial and temporal discretization was studied and showed a bigger response to the variation in the mesh size as compared with the temporal discretization. The large eddy simulation (LES) approach was used to predict the turbulence effects. The performance of Smagorinsky, dynamic k‐equation, and dynamic Lagrangian turbulence models was tested, showing very little relevant differences between them. Generally, predicted results agree well with experimental data for velocity and vorticity fields in representative sections. The presented ALM was able to characterize the main phenomena involved in the flow pattern using a relatively low computational cost without stability concerns, identified the general wake structure (qualitatively and quantitatively), and the contribution from the blade tips and motion on it. Additionally, the effects of the tower and struts were investigated with respect to the overall structure of the wake, showing no significant modification. Similarities and discrepancies between numerical and experimental results are discussed. The obtained results from the various simulations carried out here can be used as a practical reference guideline for choosing parameters in VAWTs simulations using the ALM.     

Large eddy simulations of the flow past wind turbines: actuator line and disk modeling

Large eddy simulations of the flow through wind turbines have been carried out using actuator disk and actuator line models for the turbine rotor aerodynamics. In this study, we compare the performance of these two models in producing wind turbine wakes. We also examine parameters that strongly affect the performance of these models, namely, grid resolution and the way in which the actuator force is projected onto the flow field. The proper choice of these two parameters has not been adequately addressed in previous works. We see that as the grid is coarsened, the predicted power decreases. As the width of the body force projection function is increased, the predicted power increases. The actuator disk and actuator line models produce similar wake profiles and predict power within 1% of one another when subject to the same uniform inflow. The actuator line model is able to generate flow structures near the blades such as root and tip vortices which the actuator disk model does not, but in the far wake, the predicted mean wakes are very similar. In order to perform validation against experimental data, the actuator line model output was compared with data from the wind tunnel experiment conducted at the Norwegian University of Science and Technology, Trondheim. Agreement between measured and predicted power, wake profiles, and turbulent kinetic energy has been observed for most tip speed ratios; larger discrepancies in power and thrust coefficient, though, have been found for tip speed ratios of 9 and 12. Copyright © 2014 John Wiley & Sons, Ltd.     

Cylindrical vortex wake model: right cylinder

The vortex system consisting of a bound vortex disk, a root vortex and a vortex cylinder as introduced by Joukowski in 1912 is further studied in this paper. This system can be used for simple modeling of rotors (e.g. wind turbines) with infinite number of blades and finite tip‐speed ratios. For each vortex element, the velocity components in all directions and in the entire domain are computed analytically in a novel approach. In particular, the velocity field from the vortex actuator disk is derived for the first time. The induction from the entire vortex system is studied and is seen to recall results from 1D momentum theory. It is shown that a superposition of concentric cylindrical systems predicts the independence of annuli, which is assumed in blade element theory and stream‐tube analyses. A simple example of application for the estimation of the velocity deficit upstream of a wind turbine is provided. Copyright © 2014 John Wiley & Sons, Ltd.     

Filtered actuator disks: Theory and application to wind turbine models in large eddy simulation

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 overpredict power by upwards of 10%. To correct these modeling errors, we propose a vortex cylinder model to quantify the shed vorticity when a filtered force distribution is applied at the actuator disk. This model is then used to derive a correction factor for numerical simulations that collapses the power curve for simulations at various filter widths and grid resolutions onto the curve obtained using axial momentum theory. The proposed correction, which is analytically derived from first principles, facilitates accurate power measurements in LES without resorting to highly refined numerical grids or empirical correction factors.     

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.     

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.     

An actuator line method with novel blade flow field coupling based on potential flow equivalence

A Reynolds‐averaged Navier–Stokes‐embedded actuator line model for wind and tidal turbine simulation has been implemented and validated using the National Renewable Energy Laboratory Phase VI wind tunnel experimental results. Actuator line models, first introduced by Sørensen and Shen, represent the blades virtually, enabling time‐resolved rotor simulations without requiring blade boundary layer discretization. This results in a lower computational cost than blade‐resolved simulations while preserving the predominant features of the rotor flow. The present method introduces a novel technique, based on potential flow equivalence, to determine the local flow velocity at the blade, and a method of projecting the resulting momentum sources to the flow field. These methods circumvent the requirement for smearing techniques used in other actuator line models. In addition, the model is adapted for use with an unstructured mesh, thereby enabling turbine components such as the tower and nacelle to be explicitly included in the domain. The model is validated through comparison of computed integrated loads and local force coefficients with the National Renewable Energy Laboratory Phase VI experimental results. Results for local force coefficients indicate general agreement with experiment, although discrepancies associated with three‐dimensional flow effects are observed at the tips. Copyright © 2014 John Wiley & Sons, Ltd.     

Verification and validation of an actuator disc model

Wind turbine wake can be studied in computational fluid dynamics with the use of permeable body forces (e.g. actuator disc, line and surface). This paper presents a general flexible method to redistribute wind turbine blade forces as permeable body forces in a computational domain. The method can take any kind of shape discretization, determine the intersectional elements with the computational grid and use the size of these elements to redistribute proportionally the forces. This method can potentially reduce the need for mesh refinement in the region surrounding the rotor and, therefore, also reduce the computational cost of large wind farm wake simulations. The special case of the actuator disc is successfully validated with an analytical solution for heavily loaded turbines and with a full‐rotor computation in computational fluid dynamics. Copyright © 2013 John Wiley & Sons, Ltd.     

Mesh and load distribution requirements for actuator line CFD simulations

Fundamental numerical testing has been carried out to determine mesh density and force distribution guidelines for an actuator line‐based computational fluid dynamics method for simulating kinetic turbines. The method computes forces from lifting surfaces (i.e. wings or blades) by using the evolving flowfield and tabulated airfoil data. The forces are applied to the flow as momentum source terms distributed with a Gaussian smoothing function about the physical locations of the blade/wing quarter‐chord line. The chosen length scale of the Gaussian distribution affects the magnitude and distribution of the resulting induction and necessitates a minimum grid resolution for accurate results. Tests have been conducted to determine appropriate distribution length scales and mesh spacing by using an infinite span wing and finite span wings with constant and elliptical spanwise circulation distributions. These test cases were chosen because they have simple analytical solutions derived from lifting line theory. The eventual goal is to simulate turbine rotors; however, these fundamental test cases provide a means to evaluate the required mesh spacing and the appropriate distribution length scale without the complexity of modeling a turbine rotor wake. It was found that the source distribution length scale ? should be proportional to the local airfoil chord length c with a ratio ? / c of approximately 1/4 and that the mesh spacing at the actuator line should satisfy ? / Δ_grid ≥ 4. This limit is likely somewhat code specific and should be evaluated for all solvers used for actuator line simulations. Copyright © 2012 John Wiley & Sons, Ltd.     

Optimal smoothing length scale for actuator line models of wind turbine blades based on Gaussian body force distribution

The actuator line model (ALM) is a commonly used method to represent lifting surfaces such as wind turbine blades within large‐eddy simulations (LES). In the ALM, the lift and drag forces are replaced by an imposed body force that is typically smoothed over several grid points using a Gaussian kernel with some prescribed smoothing width ε. To date, the choice of ε has most often been based on numerical considerations related to the grid spacing used in LES. However, especially for finely resolved LES with grid spacings on the order of or smaller than the chord length of the blade, the best choice of ε is not known. In this work, a theoretical approach is followed to determine the most suitable value of ε, based on an analytical solution to the linearized inviscid flow response to a Gaussian force. We find that the optimal smoothing width ε^opt is on the order of 14%‐25% of the chord length of the blade, and the center of force is located at about 13%‐26% downstream of the leading edge of the blade for the cases considered. These optimal values do not depend on angle of attack and depend only weakly on the type of lifting surface. It is then shown that an even more realistic velocity field can be induced by a 2‐D elliptical Gaussian lift‐force kernel. Some results are also provided regarding drag force representation. Copyright © 2017 John Wiley & Sons, Ltd.     

Marangoni convective nanofluid flow over an electromagnetic actuator in the presence of first‐order chemical reaction

The present study aims to investigate Marangoni‐forced convective nanofluid flow over an electromagnetic actuator (Riga plate). A first‐order homogeneous chemical reaction is considered. The thermocapillary and solutocapillary Marangoni effect developed by the surface tension is considered as a driving force for the nanofluid. In addition, Grinberg‐term is accounted to involve the impact of Lorentz force impinged by the actuator in the model. A set of nonlinear ordinary differential equations is obtained via suitable transformations for a nonsimilar analysis. Series solutions are achieved through homotopy to discuss the behavior of the velocity field, thermal distribution, and concentration of the nanoparticles graphically. The variation in Nusselt and Sherwood numbers is discussed. The outcomes declared that the flow parallel to the surface of the plate is assisted by the Lorentz forces generated by electromagnetic bars of the actuator resulting in an enhancement in the fluid motion. Furthermore, the stronger Marangoni effect resulted in the declining trend of the temperature profile. The concentration of nanoparticles near the surface reduced intensive chemical reaction inside the nanofluid.     

Investigation of wake interaction using full‐scale lidar measurements and large eddy simulation

In this paper, wake interaction resulting from two stall regulated turbines aligned with the incoming wind is studied experimentally and numerically. The experimental work is based on a full‐scale remote sensing campaign involving three nacelle mounted scanning lidars. A thorough analysis and interpretation of the measurements is performed to overcome either the lack of or the poor calibration of relevant turbine operational sensors, as well as other uncertainties inherent in resolving wakes from full‐scale experiments. The numerical work is based on the in‐house EllipSys3D computational fluid dynamics flow solver, using large eddy simulation and fully turbulent inflow. The rotors are modelled using the actuator disc technique. A mutual validation of the computational fluid dynamics model with the measurements is conducted for a selected dataset, where wake interaction occurs. This validation is based on a comparison between wake deficit, wake generated turbulence, turbine power production and thrust force. An excellent agreement between measurement and simulation is seen in both the fixed and the meandering frame of reference. Copyright © 2015 John Wiley & Sons, Ltd.     

Superposition of vortex cylinders for steady and unsteady simulation of rotors of finite tip‐speed ratio

Joukowski introduced in 1912 a helical vortex model to represent the vorticity of a rotor and its wake. For an infinite number of blades but finite tip‐speed ratio, the model consists of a vortex cylinder of longitudinal and tangential vorticity, a root vortex and a bound vortex disk. A superposition of cylinders is used in this paper to model rotors of radially varying circulation. The relations required to form a consistent system of cylinders are derived. The model contains a term which is not accounted for in the standard blade element momentum (BEM) algorithm. This term is identified as the contribution from the pressure drop due to the wake rotation. The BEM algorithm can be corrected to account for this effect. Unlike previous work on the topic, the contribution is derived for a radially varying circulation. A high‐thrust correction is also presented to extend the model. The optimal power coefficient obtained with this model for the constant circulation rotor is assessed and compared with that of existing solutions. Results from prescribed thrust distributions are compared with that of actuator disk simulations. Steady simulations are performed to compare with the BEM algorithm. The model is also applied to compute the velocity field in the entire domain and perform unsteady simulations. Results for an unsteady simulation corresponding to a pitch change of the rotor is used to compare the model with measurements and a BEM code with a dynamic inflow model. Copyright © 2015 John Wiley & Sons, Ltd.