An Engineering Model for Static Yawed Wind Turbines Based on Actuator Line Simulations and Symbolic Regression

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.

We evaluate the accuracy of the actuator line model (ALM) approach by performing simulations for the NREL 5‐MW wind turbine in uniform inflow using three large eddy simulation codes. The power and thrust coefficients obtained using the three codes agree within 1 % when the grid spacing m and are cross‐validated against blade element momentum (BEM) theory. We find that the results of ALM converge towards BEM theory without the need for tip correction when the numerical resolution is increased. For m, the difference between the power and thrust coefficient obtained using ALM and BEM is 4.5 % and 2.1 % , respectively, although we note that no absolute convergence between ALM and BEM can be obtained as both models use different assumptions, such as the use of a force projection method in the ALM. The difference in the local axial and tangential forces along the blades obtained from ALM simulations using m and m can be as large as 10 % . The effect of the number of actuator points on the obtained turbine power and thrust coefficients is limited as the results converge when the spacing between the actuator points is about three times the grid spacing. This insight on the required number of blade points can be used to improve the efficiency of actuator line simulations.

Steadily increasing energy consumption, fluctuating fuel costs and concerns about global climate changes have led to the research and evaluation of alternative renewable energies. The wind turbine is among the promising alternative energy sources that have recently gained more attention. In this work, the challenging aspects involved in modelling the rotor aerodynamics and wakes behind the wind turbines are studied. This report covers the literature review of Blade Element Momentum (BEM) analysis of wind turbine, limitations of BEM method, effect of stall delay, wake aerodynamics, atmospheric boundary layer and its effects on the wake characteristics and previous different wake models of near and far wake regions. In this project, experimental data of NREL Phase VI Turbine (sequence S) were used to corroborate the results. There are two main objectives of this project. The first objective is to improve the BEM analysis to account for the three-dimensional (3D) effects due to the rotation of the turbine. The second objective is to contemplate on the effects of atmospheric boundary layers (ABL) on the wake characteristics. These two objectives act as a roadway to enhance coupled BEM-CFD analysis, which is left for the future works. In the coupled BEM-CFD analysis, the BEM method will be applied to calculate the aerodynamic forces of the aerofoil sections along the blade span. The main drawback of BEM analysis is the use of the twodimensional (2D) aerofoil characteristics (CL and CD ) which considers only the axial flow but not radial or spanwise flow along the blade span. This leads to a considerable difference in the lift coefficients between the rotating and non rotating blades, especially at inboard sections of the blade. This 3D phenomenon is called stall delay. The current study includes different proposals for the extrapolation of 2D aerofoil characteristics of the S809 aerofoil and their implementation in BEM analysis and comparison of power predicted with experimental results. Also, four existing stall delay correction models in BEM analysis are examined. In general, these models result in over-prediction of power, especially at high inflow wind speeds. An improved inverse BEM method is developed to compute 3D aerofoil characteristics at different radial locations along the blade span. In addition to five radial locations as described in the NREL/NASA Ames test analysis, 13 additional radial locations are considered for a better understanding of stall delay. A new BEM model with the local radius effect of aerofoil characteristics (other than as a function of Reynolds number and angle of attack only) is proposed. Implementation of the new model showed a good agreement with aerofoil characteristics distribution along the blade span with the 3D aerofoil characteristics computed from the CFD analyses using inverse BEM method. MATLAB code was developed for both BEM and Inverse BEM analyses. Most important in the wind farm analysis is the effect of the atmospheric boundary layer since the turbulence properties of the atmosphere affect the wake characteristics. In this work, the NREL Phase VI Turbine is virtually placed in different atmospheric boundary layers from open sea to city/forest. Simulations are performed with direct rotor modelling using sliding mesh analysis. Since the experiment results of wake characteristics of the NREL Phase VI Turbine was not available, different empirical models are used for comparison. It was evident that wake recovers at a faster rate as the roughness length of the ground increases. Also, it was noted that the turbulence intensity of the wake varies both laterally and vertically, but existing analytical wake turbulence intensity models provide only an averaged value The possible methods for indirect rotor modelling like Actuator Disk, Actuator Line and Actuator Surface methods that lead to coupled BEM-CFD analysis of wind turbine is discussed in brief. The possible ways of improving these indirect rotor models by using the aerodynamic forces computed from improved BEM analysis and wake aerodynamics are provided for the future works.

Abstract. To simulate transient wind turbine wake interaction problems using limited wind turbine data, two new variants of the actuator line technique are proposed in which the rotor blade forces are computed locally using generic load data. The proposed models, which are extensions of the actuator disk force models proposed by Navarro Diaz et al. (2019a) and Sørensen et al. (2020), only demand thrust and power coefficients and the tip speed ratio as input parameters. In the paper the analogy between the actuator disk model (ADM) and the actuator line model (ALM) is shown, and from this a simple methodology to implement local forces in the ALM without the need for knowledge of blade geometry and local airfoil data is derived. Two simplified variants of ALMs are proposed, an analytical one based on Sørensen et al. (2020) and a numerical one based on Navarro Diaz et al. (2019a). The proposed models are compared to the ADM using analogous data, as well as to the classical ALM based on blade element theory, which provides more detailed force distributions by using airfoil data. To evaluate the local force calculation, the analysis of a partial-wake interaction case between two wind turbines is carried out for a uniform laminar inflow and for a turbulent neutral atmospheric boundary layer inflow. The computations are performed using the large eddy simulation facility in Open Source Field Operation and Manipulation (OpenFOAM), including Simulator for Wind Farm Applications (SOWFA) libraries and the reference National Renewable Energy Laboratory (NREL) 5 MW wind turbine as the test case. In the single-turbine case, computed normal and tangential force distributions along the blade showed a very good agreement between the employed models. The two new ALMs exhibited the same distribution as the ALM based on geometry and airfoil data, with minor differences due to the particular tip correction needed in the ALM. For the challenging partially impacted wake case, both the analytical and the numerical approaches manage to correctly capture the force distribution at the different regions of the rotor area, with, however, a consistent overestimation of the normal force outside the wake and an underestimation inside the wake. The analytical approach shows a slightly better performance in wake impact cases compared to the numerical one. As expected, the ALMs gave a much more detailed prediction of the higher-frequency power output fluctuations than the ADM. These promising findings open the possibility to simulate commercial wind farms in transient inflows using the ALM without having to get access to actual wind turbine and airfoil data, which in most cases are restricted due to confidentiality.

In the present paper the methodology and the procedures for the implicit coupling of an Actuator Line (AL) aerodynamic code with a beam like structural code for the analysis of wind turbine rotors are detailed. Results from benchmark aeroelastic simulations of canonical inflow conditions, comparing the newly developed AL model against a standard Blade Element Momentum (BEM) model are presented in the paper. The two models provide very similar results in simple, uniform inflow, axisymmetric flow cases. The advantages of this newly developed tool emerge when more complex inflow conditions are addressed. In the present paper, besides axial flow conditions, operation under high yaw misalignment is also considered. BEM model accounts for the effect of the wake skewness through the application of an a posteriori engineering correction. Therefore, in this particular non symmetric flow case, deviations between AL and BEM are expected to be higher, especially as yaw misalignment angles increase. In the paper the above differences are assessed and interpreted.

In this paper, the accuracy of an in-house Actuator Line (AL) model is tested on aeroelastic simulations of a Wind Turbine (WT) rotor and a helicopter Main Rotor (MR) under uniform free-stream flow. For the scope of aeroelastic analyses, the AL model is coupled with an in-house multibody dynamics code in which the blades are modeled as beams. The advantage from the introduction of CFD analysis in rotorcraft aeroelasticity is related to its capability to account in detail for the interaction of the rotor wake with the boundary layer developed on the surrounding bodies. This has proven to be of great importance in order to accurately estimate the aerodynamic forces and thus the corresponding structural loads and deflections of the blades. In wind turbine applications, a good example of the above is the rotor/ground interaction. In helicopter configurations, the interaction of MR with the ground or the fuselage and the interaction of tail rotor with the duct in fenestron configurations are typical examples. Furthermore, CFD aerodynamic analysis is an obvious modeling option in which the above mentioned asset can be combined with the consideration of the mutual interaction of the rotor with the ambient turbulence. A WT rotor operating inside the atmospheric boundary layer under turbulent free-stream flow is such a case. In the paper, AL results are compared against Blade Element Momentum (BEM) and Lifting Line (LL) model results in the case of the WT, whereas LL and measured data are considered in the helicopter cases. Blade loads and deflections are mainly compared as azimuthal variations. In the helicopter MR cases, where comparison is made against experimental data, harmonic analysis of structural loads is shown as well. Overall, AL proves to be as reliable as LL in the canonical cases addressed in this paper in terms of loads and deflections predictions. Therefore, it can be trusted in more complex flow conditions where viscous effects are pronounced.

Investigation of wind turbine wakes and wake recovery in a tandem configuration using actuator line model with LES

A wind turbine wake causes a decrease in wind speed and an increase in turbulence intensity. The wind turbine wake interaction is essential for predicting the power output of a wind farm consisting of many wind turbines. This research proposes a CFD method able to reproduce wake interactions and power outputs of multiple wind turbines with high speed and accuracy. Large eddy simulations with the lattice Boltzmann method are used for fluid calculations, specifically for large-scale CFD simulations. The wind turbines are represented using an actuator line model. Optimal power generation efficiency is achieved by controlling the rotor speed and blade pitch angle. Large-scale simulations of eight aligned wind turbines are conducted using 1.75 billion grid points and 40 GPUs. We compare two cases with and without control to investigate the effect of turbine control on wake and power output. Both the instantaneous and mean streamwise velocities confirm that the turbine control reduces the wake velocity deficit of the downwind wind turbine. High-speed inflow of wind to the downstream turbines augments their power output. With implementation of turbine control, the power outputs of the downstream turbines agree well with the observation data obtained in an earlier study. The results demonstrate the importance of controlling the rotational speed and pitch angle for actuator line simulations.

This wind tunnel study was conducted to investigate the similarity laws involved in the reasonable simulation of the wake characteristics of a full-scale wind turbine. A 5 MW scaled wind turbine model was designed using an optimization method based on the blade element momentum (BEM) theory. Subsequently, wind tunnel tests were carried out on the geometrically similar model and the thrust-optimized model, with different yaw angles and under various upstream flow conditions. The results indicated that the wake development of the wind turbine model was closely related to the thrust forces of the wind turbine, and both kinematic and dynamic similarity laws should be observed to achieve wake characteristics that are reasonably similar to those of a full-scale wind turbine. This study investigated the aerodynamic similarity principles of small-scale wind turbine models to develop a more effective method for simulating full-scale turbine wake characteristics in wind tunnel tests. The outcomes of this study revealed the limitations of the anomalously low thrust coefficients in geometrically similar wind turbine models and present reasonable model design methodologies for small-scale wind turbine models in wind tunnel tests.

Large-scale wind turbine installations are sited using layouts based on site topology, real estate costs and restrictions, and turbine power output. Existing optimization programs have limited capabilities to site multiple turbines and are based on simple geometric turbine wake models, which typically overestimate individual turbine output. Alternatively, complete CFD modeling of entire wind turbine fields requires enormous computational resources, which has led to the development of blade modeling techniques which are combined with CFD field computations. The most promising method, using the actuator line model, typically uses an exponential function to spread blade forces over CFD grid points. In addition, little development work has been performed to determine the optimal grid point density and force spreading radius for these methods. In this paper, we report on our ongoing efforts to develop an advanced actuator line formulation which uses an alternate geometric method for distributing blade forces to the CFD field. Domain and blade force application parameters are currently being developed to determine optimum run time conditions for the new actuator line model. The Actuator line method is implemented using the parallel CFD program, NEK5000. NEK5000 is an advanced Navier Stokes code which uses spectral methods for the spatial discretization, and has been proven to provide high-resolution results with significantly reduced compute resources. A Large Eddy Simulation turbulence model is used. In this paper, we report on our current work using large scale supercomputer resources at the Extreme Science and Engineering Discovery Environment (XSEDE) to perform computational experiments to validate our codes, and perform parametric studies to develop optimum run time parameters. Development and verification work is centered around domain size, grid spacing and clustering, and development of steady state conditions. The parametric studies are underway and are based on investigating various selection volume and force application point settings. Continuing work will compare the new actuator line method with a traditional exponential force distribution model.

This paper challenges the standard wind turbine design numerically assessing the wake and aerodynamic performance of two- and three-bladed wind turbine models implementing downwind and upwind rotor configurations, respectively. The simulations are conducted using the actuator line model (ALM) coupled with a three-dimensional Navier Stokes solver implementing the k−ω shear stress transport turbulence model. The sensitivity of the ALM to multiple simulation parameters is analyzed in detail and numerical results are compared against experimental data. These analyses highlight the most suitable Gaussian radius at the rotor to be equal to twice the chord length at 95% of the blade for a tip-speed ratio (TSR) of ten, while the Gaussian radius at the tower and the number of actuator points have a low incidence on the flow field computations overall. The numerical axial velocity profiles show better agreement upstream than downstream the rotor, while the discrepancies are not consistent through all the assessed operating conditions, thus highlighting that the ALM parameters are also dependent on the wind turbine's operating conditions rather than being merely geometric parameters. Particularly, for the upwind three-bladed wind turbine model, the accuracy of the total thrust computations improves as the TSR increases, while the least accurate wake predictions are found for its design TSR. Finally, when comparing both turbine models, an accurate representation of the downwind configuration is observed as well as realistic power extraction estimates. Indeed, the results confirm that rotors with fewer blades are more suitable to operate at high TSRs.

Offshore wind is generally stronger and more consistent than wind on land. A large part of the offshore wind resource is however located in deep water, where floating wind turbines can harvest more energy. This paper describes a systematic experiment and a simulation analysis (FAST code) about the cyclic pitch control of blades. This work was performed to investigate performance fluctuation of a floating wind turbine utilizing cyclic pitch control. The experiment was carried out in an open wind tunnel with mainstream wind velocity of 10 m/s with the front inflow wind and the oblique inflow wind conditions. A model wind turbine is two-bladed downwind wind turbine with diameter of 1.6 m. Moment and force acts on the model wind turbine were measured by a six-component balance. Fluctuation of power coefficient and thrust coefficient was investigated in the cyclic pitch control. The model wind turbine and the experimental conditions were simulated by FAST code. The comparison of the experimental data and the simulation results of FAST code show that the power coefficient and thrust coefficient are in good agreement. Keywords: Floating Offshore Wind Turbine, Aerodynamic Forces, Cyclic Pitch Control, FAST Code, Wind Tunnel ExperimentArticle History: Received February 11st 2017; Received in revised form April 29th 2017; Accepted June 2nd 2017; Available onlineHow to Cite This Article: Sang, L.Q., Maeda, T., Kamada, Y. and Li, Q. (2017) Experiment and simulation effect of cyclic pitch control on performance of horizontal axis wind turbine to International Journal of Renewable Energy Development, 6(2), 119-125.https://doi.org/10.14710/ijred.6.2.119-125

As wind turbine technology proceeds towards the development of more advanced and complex machines, modelling tools with fidelity higher than the ubiquitous Blade Element Momentum (BEM) method are needed. Among them, the Actuator Line Method (ALM) stands out in terms of accuracy and computational cost. Moving from this background, an advanced ALM method has been developed within the commercial solver CONVERGE®. As elements of novelty, this tool features a Lagrangian method for sampling the local inflow velocity and a piece-wise smearing function for the force projection process. Various sub-models for both Horizontal Axis Wind Turbines (HAWTs) (e.g. the Shen tip loss correction) and Vertical Axis Wind Turbines (VAWTs) (e.g. the MIT dynamic stall model) has also been included. Aim of the research is to address the new challenges posed by modern machines. HAWTs are in fact getting larger and larger, shifting the research focus on the interaction of increasingly deformable blades with the atmosphere at the micro- and mesoscale level. VAWTs on the other hand, whose popularity has arisen in the last years, thanks to their advantages in non-conventional applications, e.g. floating offshore installations, are extremely complex machines to study, due to their inherently unsteady aerodynamics. The approach has been validated on selected test cases, i.e. the DTU 10MW turbine and a real 2-blade H-rotor, for which both high-fidelity CFD and experimental data are available.

The objective of this study is to develop a reduced order model (ROM) that accurately predicts the key features of the wake generated by a wind turbine, based on the results of a computational fluid dynamics (CFD) simulation with the actuator line model (ALM). The simulation of a three-bladed up-wind wind turbine was performed using Reynolds-averaged Navier-Stokes (RANS) equations and the finite volume method. The two-equation turbulence model K-ωSST was used to approximate the Reynolds stresses and the Actuator Line Method (ALM) was used to simulate the effect of the wind turbine rotor on the flow field, representing the rotor blades as a distribution of forces acting on the fluid. Data from the RANS simulation was collected to be used by the Dynamic Mode Decomposition (DMD) algorithm. Velocity field was defined as the object of study for the construction of the reduced order model (ROM). From the implementation of the DMD algorithm, the eigenvalues and energy content were obtained for the field of interest. From these results, the main modes and their spectrum were calculated. The velocity field reconstruction was performed using the DMD algorithm, and the RMSE was computed relative to the simulation and experimental data, yielding a good approximation. Due to the turbulence model used, very stable results were obtained in the reduced order model, showing great capability to predict the fields of interest in time.

This work presents a significantly improved engineering model for the prediction of the loads in yawed flow. The newly developed model focuses on the so‐called skewed wake effect. This effect leads to an azimuthal variation of the axial induction velocity which depends on the yaw angle, tip speed ratio, wind speed, and radial position. The azimuthal variation of the induced velocities leads to a variation in blade loads, which is important for the prediction of fatigue loads and determines the yawing moment which can be stabilizing or destabilizing and is among others important for passively yawed turbines. The paper puts particular emphasis on the contribution of the root vorticity to the azimuthal variation of induced velocity. Current widely used models typically only take into account the skewed wake effect without the contribution of root vorticity, i.e., leading to a significant different radial dependency of the skewed wake effects. The new model is derived from computational fluid dynamics of 3 multimegawatt‐class wind turbines, namely the NREL 5MW and two 10‐MW turbines designed in the EU projects AVATAR and INNWIND.EU. Simulations were performed by means of an actuator line model. The proposed model is validated with results from a fully resolved computational fluid dynamics model, a free vortex wake code and actuator line model simulations for different wind turbines and yaw angles. The obtained results indicate that in many cases, the new model considerably improves the prediction of the azimuthal variation of axial induction factor and the resulting variation in blade loads and consequent yawing moment.