A numerical study of tilt‐based wake steering using a hybrid free‐wake method

This study investigates the potential of using tilt‐based wake steering to alleviate wake shielding problems experienced by downwind turbines. Numerical simulations of turbine wakes have been conducted using a hybrid free‐wake analysis combining vortex lattice method (VLM) and an innovative free‐wake model called constant circulation contour method (CCCM). Simulation results indicate tilting a horizontal axis wind turbine's shaft upward causes its wake to ascend, carrying energy‐depleted air upward and pumping more energetic replacement air into downstream turbines, thereby having the potential to recover downstream turbine power generation. Wake cross section vorticity and velocity distributions reveal that the wake upward transport is caused by the formation of near‐wake streamwise vorticity components, and furthermore, the wake velocity deficit is weakened because of the skewed wake structure. Beyond the single turbine wake simulation, an inline two‐turbine case is performed as an assessment of the wake steering influence on the two‐turbine system and as an exploratory work of simulating turbine‐wake interactions using the hybrid free‐wake model. Individual and total turbine powers are calculated. A comparison between different tilting angles suggests turbine power enhancement may be achieved by tilting the upstream turbine and steering its wakes away from the downstream turbine.     

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.     

A new stall delay algorithm for predicting the aerodynamics loads on wind turbine blades for axial and yawed conditions

Stall delay is a complicated phenomenon that has gained for many years the attention of industry and academics in the fields of helicopter and wind turbine aerodynamics. Since most of the potential flow theories still rely on the use of 2D aerofoil data for simulating loads on a rotating blade, less degree of accuracy is expected because of 3D rotational effects. In this work, a new model for correcting the 2D steady aerodynamic data for 3D effects is presented. The model can reduce the uncertainty in the blade design process and, subsequently, make wind turbines more cost‐effective. This model combines the stall delay model of Corrigan and Schillings, a modified version of an inviscid stall delay model, a new modification factor to account for the effect of the angle of attack changes and a new tip loss factor. Furthermore, the model applies the use of the separation factor of Du and Selig to evaluate the area on the rotor disc where stall delay is most prominent. The new stall delay model was embedded in a free‐wake vortex model to estimate the aerodynamic loads on the National Renewable Energy Laboratory Phase VI rotor blades consisting of the S809 aerofoil sections. The results in this study confirm the validity of the 3D corrections by the proposed new model under both axial and yawed flow conditions. Copyright © 2017 John Wiley & Sons, Ltd.     

Estimating the angle of attack from blade pressure measurements on the National Renewable Energy Laboratory phase VI rotor using a free wake vortex model: yawed conditions

Wind turbine design codes for calculating blade loads are usually based on a blade element momentum (BEM) approach. Since wind turbine rotors often operate in off‐design conditions, such as yawed flow, several engineering methods have been developed to take into account such conditions. An essential feature of a BEM code is the coupling of local blade element loads with an external (induced) velocity field determined with momentum theory through the angle of attack. Local blade loads follow directly from blade pressure measurements as performed in the National Renewable Energy Laboratory (NREL) phase IV campaign, but corresponding angles of attack cannot (on principle) be measured. By developing a free wake vortex method using measured local blade loads, time‐dependent angle of attack and induced velocity distributions are reconstructed. In a previous paper, a method was described for deriving such distributions in conjunction with blade pressure measurements for the NREL phase VI wind turbine in axial (non‐yawed) conditions. In this paper, the same method is applied to investigate yawed conditions on the same turbine. The study considered different operating conditions in yaw in both attached and separated flows over the blades. The derived free wake geometry solutions are used to determine induced velocity distributions at the rotor blade. These are then used to determine the local (azimuth time dependent) angle of attack, as well as the corresponding lift and drag for each blade section. The derived results are helpful to develop better engineering models for wind turbine design codes. Copyright © 2008 John Wiley & Sons, Ltd.     

A new class of actuator surface models for wind turbines

Actuator line model has been widely used in wind turbine simulations. However, the standard actuator line model does not include a model for the turbine nacelle which can significantly impact turbine wake characteristics. Another disadvantage of the standard actuator line model is that more geometrical features of turbine blades cannot be resolved on a finer mesh. To alleviate these disadvantages of the standard model, we develop a new class of actuator surface models for turbine blades and nacelle to take into account more geometrical details of turbine blades and include the effect of turbine nacelle. The actuator surface model for nacelle is evaluated by simulating the flow over periodically placed nacelles. Both the actuator surface simulation and the wall‐resolved large‐eddy simulation are conducted. The comparison shows that the actuator surface model is able to give acceptable results especially at far wake locations on a very coarse mesh. It is noted that although this model is used for the turbine nacelle in this work, it is also applicable to other bluff bodies. The capability of the actuator surface model in predicting turbine wakes is assessed by simulating the flow over the MEXICO (Model experiments in Controlled Conditions) turbine and the hydrokinetic turbine of Kang, Yang, and Sotiropoulos (Journal of Fluid Mechanics 744 (2014): 376‐403). Comparisons of the computed results with measurements show that the proposed actuator surface model is able to predict the tip vortices, turbulence statistics, and meandering of turbine wake with good accuracy.     

Wind turbine performance in shear flow and in the wake of another turbine through high fidelity numerical simulations with moving mesh technique

We present numerical simulations of two horizontal axis wind turbines, one operating under the wake of the other, under an incoming sheared velocity profile. We use a moving mesh technique to represent the rotation of the turbine blades and solve the unsteady Reynolds averaged Navier–Stokes equations with a shear stress transport k ? ω turbulence model. Temporal evolution of the lift and drag coefficients of the front turbine show a phase shift in the periodic cycle due to the non‐uniform incoming free stream velocity. Comparisons of the lift and drag coefficients for the back turbine with the unperturbed behaviour of the front demonstrate the complex non‐linear interactions of the blades with the wake, with a significant decrease in overall performance and two peaks at specific points in the cycle associated with local angle of attack modification in the wake. The vorticity field in the near wake shows tilting of the vortex lines in the wake due to the shear and a faster diffusion of the tip vortical signature compared with the uniform free stream velocity case. Observations of the wake–wake interaction show good agreement with recent studies that use different methodologies. Copyright © 2012 John Wiley & Sons, Ltd.     

A vortex panel model for the simulation of the wake flow past a vertical axis wind turbine in dynamic stall

A 2D vortex panel model with a viscous boundary layer formulation has been developed for the numerical simulation of a vertical axis wind turbine (VAWT), including the operation in dynamic stall. The model uses the ‘double wake’ concept to reproduce the main features of the unsteady separated flow, including the formation and shedding of strong vortical structures and the wake–blade interaction. The potential flow equations are solved together with the integral boundary layer equations by using a semi‐inverse iterative algorithm. A new criterion for the reattachment of the boundary layer during the downstroke of a dynamically stalled aerofoil is implemented. The model has been validated against experimental data of steady aerofoils and pitching aerofoils in dynamic stall at high and low Reynolds numbers (Re = 1.5 × 10⁶ and Re = 5 × 10⁴). For the low Reynolds number case, time‐resolved 2D particle image velocimetry (PIV) measurements have been performed on a pitching NACA 0012 aerofoil in dynamic stall. The PIV vorticity fields past the oscillating aerofoil are used to test the model capability of capturing the formation, growth and release of the strong leading edge vortex that characterizes the dynamic stall. Furthermore, the forces extracted from the PIV velocity fields are compared with the predicted ones for a quantitative validation of the model. Finally, the model is applied to the computation of the wake flow past a VAWT in dynamic stall; the predicted vorticity fields and forces are in good agreement with phase‐locked PIV data and CFD‐DES available in the literature. Copyright © 2012 John Wiley & Sons, Ltd.     

Application and validation of incrementally complex models for wind turbine aerodynamics,isolated wind turbine in uniform inflow conditions

A comparison of several incrementally complex methods for predicting wind turbine performance, aeroelastic behavior, and wakes is provided. Depending on a wind farm's design, wake interference can cause large power losses and increased turbulence levels within the farm. The goal is to employ modeling methods to reach an improved understanding of wake effects and to use this information to better optimize the layout of new wind farms. A critical decision faced by modelers is the fidelity of the model that is selected to perform simulations. The choice of model fidelity can affect the accuracy, but will also greatly impact the computational time and resource requirements for simulations. To help address this critical question, three modeling methods of varying fidelity have been developed side by side and are compared in this article. The models from low to high complexity are as follows: a blade element‐based method with a free‐vortex wake, an actuator disc‐based method, and a full rotor‐based method. Fluid/structure interfaces are developed for the aerodynamic modeling approaches that allow modeling of discrete blades and are then coupled with a multibody structural dynamics solver in order to perform an aeroelastic analysis. Similar methods have individually been tested by researchers, but we suggest that by developing a suite of models, they can be cross‐compared to grasp the subtleties of each method. The modeling methods are applied to the National Renewable Energy Laboratory Phase VI rotor to predict the turbine aerodynamic and structural loads and then also the wind velocities in the wake. The full rotor method provides the most accurate predictions at the turbine and the use of adaptive mesh refinement to capture the wake to 20 radii downstream is proven particularly successful. Though the full rotor method is unmatched by the lower fidelity methods in stalled conditions and detailed prediction of the downstream wake, there are other less complex conditions where these methods perform as accurately as the full rotor method. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

6种风力机叶片翼型的气动性能数值模拟研究

选取NACA4412,NACA4418,FFA-W3-211,FFA-W3-360,FX60-126和NREL-S809等6种常用风力机叶片翼型,进行二维几何建模和计算域网格划分,运用FLUENT软件对风力机叶片翼型的空气动力性能进行数值模拟和仿真分析;并与实验数据进行参照、对比和分析,验证数值模拟的可靠性.对风力机叶片常用翼型进行气动数值模拟计算和分析,可深化了解风力机翼型的气动性能,为风力机叶片翼型选型和叶片翼型改型设计和研发工作提供技术参数和指导意见.     

水平轴风力机尾迹三维流场的热线测量

利用单斜丝热线旋转进行水平轴风力机模型的尾迹流场测量。热线测量过程中采用了周期性采样和锁相平均技术,获得了风轮下游尾迹三维流场的定量信息,并利用自行编制的MATLAB程序求出尾迹流场的三维平均速度。试验结果表明：采用旋转单斜丝热线结合周期性多点采样技术构成的热线测量系统,能够获得风轮流场速度分布等准确的定量信息,是一种比较有效的风力机三维流场动态测试方法。风轮下游的尾迹区内存在速度亏损,速度亏损随着风轮下游轴向位置的增加而减弱。风轮下游4倍弦长外,尾迹区的速度就已经基本恢复到主流速度。在气流向下游流动的过程中尾迹的轴向速度亏损形成的波谷曲线渐趋平缓,尾迹区的宽度不断扩大,2倍弦长以后尾迹宽度基本不再扩大,并逐渐与主流掺混融合。     

The near wake of a model horizontal-axis wind turbine—I. Experimental arrangements and initial results

This paper is the first of a series describing measurements in the near wake of a small horizontal-axis wind turbine over a range of tip speed ratios. The primary aim was to document the formation and development of the three-dimensional near-wake; this was done at six axial locations within two chord lengths of the blades. This paper describes the experimental arrangements, the measurement techniques based on hot-wire anemometry, and the results which relate directly to the simple wake models that lead, for instance, to the Betz limit and are used in traditional blade element theory. Later papers will describe the complex, three-dimensional flow field, the properties of the tip vortices, and the process by which the hub “vortices” may diffuse to form a cylindrical vortex sheet. For the conditions giving the largest power coefficient, the bound circulation of the blade is approximately constant with radius and the velocity distribution immediately behind a blade is similar to that behind an aerofoil with the same circulation. This good agreement with aerofoil behaviour extends to the highest tip speed ratio measured. At the lowest tip speed ratio, the turbulence level in the wake is very high, suggesting separation from the blades which are operating at high angles of attack. It is also shown that the three-dimensionality does not contribute significantly to the balance of angular momentum in the wake. There is evidence that increasing amounts of angular momentum reside in the tip vortices as the tip speed ratio increases.     

Predictions of unsteady HAWT aerodynamics in yawing and pitching using the free vortex method

To predict the unsteady aerodynamic loads of horizontal-axis wind turbines (HAWTs) during operations under yawing and pitching conditions, an unsteady numerical simulation method is proposed. This method includes a nonlinear lifting line method to compute the aerodynamic loads on the blades and a time-accurate free-vortex method to simulate the wake. To improve the convergence property in the nonlinear lifting line method, an iterative algorithm based on the Newton–Raphson method is developed. To increase the computational efficiency and the accuracy of the calculation, a new wake vortex model consisting of the vortex core model, the vortex sheet model and the tip vortex model is used. Wind turbines with different diameters, such as NREL Phase VI, the TU Delft model turbine and the Tjæreborg wind turbine, are used to validate the method for rotors operating at given yaw and/or pitch angles and during yawing and/or pitching processes at different wind speeds. The results, including the blade loads, the rotor torque and the locations of the tip vortex cores in the wake, agree well with the measured data and the computed data. It is shown that the proposed method can be used for predictions of unsteady aerodynamic loads and rotor wakes in the operational processes of blade pitching and/or rotor yawing.     

Validation of the dynamic wake meander model for loads and power production in the Egmond aan Zee wind farm

This paper investigates wake effects on load and power production by using the dynamic wake meander (DWM) model implemented in the aeroelastic code HAWC2. The instationary wind farm flow characteristics are modeled by treating the wind turbine wakes as passive tracers transported downstream using a meandering process driven by the low frequent cross‐wind turbulence components. The model complex is validated by comparing simulated and measured loads for the Dutch Egmond aan Zee wind farm consisting of 36 Vestas V90 turbine located outside the coast of the Netherlands. Loads and production are compared for two distinct wind directions—a free wind situation from the dominating southwest and a full wake situation from northwest, where the observed turbine is operating in wake from five turbines in a row with 7D spacing. The measurements have a very high quality, allowing for detailed comparison of both fatigue and min–mean–max loads for blade root flap, tower yaw and tower bottom bending moments, respectively. Since the observed turbine is located deep inside a row of turbines, a new method on how to handle multiple wakes interaction is proposed. The agreement between measurements and simulations is excellent regarding power production in both free and wake sector, and a very good agreement is seen for the load comparisons too. This enables the conclusion that wake meandering, caused by large scale ambient turbulence, is indeed an important contribution to wake loading in wind farms. Copyright © 2012 John Wiley & Sons, Ltd.     

Wake impacts on downstream wind turbine performance and yaw alignment

Aerodynamic wake interaction between commercial scale wind turbines can be a significant source of power losses and increased fatigue loads across a wind farm. Significant research has been dedicated to the study of wind turbine wakes and wake model development. This paper profiles influential wake regions for an onshore wind farm using 6 months of recorded SCADA (supervisory control and data acquisition) data. An average wind velocity deficit of over 30% was observed corresponding to power coefficient losses of 0.2 in the wake region. Wind speed fluctuations are also quantified for an array of turbines, inferring an increase in turbulence within the wake region. A study of yaw data within the array showed turbine nacelle misalignment under a range of downstream wake angles, indicating a characteristic of wind turbine behaviour not generally considered in wake studies. The turbines yaw independently in order to capture the increased wind speeds present due to the lateral influx of turbulent wind, contrary to many experimental and simulation methods found in the literature. Improvements are suggested for wind farm control strategies that may improve farm‐wide power output. Additionally, possible causes for wind farm wake model overestimation of wake losses are proposed.Copyright © 2012 John Wiley & Sons, Ltd.     

Three‐dimensional viscous‐inviscid coupling method for wind turbine computations

In this paper, a computational model for predicting the aerodynamic behavior of wind turbine wakes and blades subjected to unsteady motions and viscous effects is presented. The model is based on a three‐dimensional panel method using a surface distribution of quadrilateral sources and doublets, which is coupled to a viscous boundary layer solver. Unlike Navier‐Stokes codes that need to solve the entire flow domain, the panel method solves the flow around a complex geometry by distributing singularity elements on the body surface, obtaining a faster solution and making this type of codes suitable for the design of wind turbines. A free‐wake model has been employed to simulate the wake behind a wind turbine by using vortex filaments that carry the vorticity shed by the trailing edge of the blades. Viscous and rotational effects inside the boundary layer are taken into account via the transpiration velocity concept, applied using strip theory with the cross sectional angle of attack as coupling parameter. The transpiration velocity is obtained from the solution of the integral boundary layer equations with extension for rotational effects. It is found that viscosity plays a very important role in the predictions of blade aerodynamics and wake dynamics, especially at high angles of attack just before and after boundary layer separation takes place. The present code is validated in detail against the well‐known MEXICO experiment and a set of non‐rotating cases. Copyright © 2014 John Wiley & Sons, Ltd.     

A general momentum theory applied to an energy‐extracting actuator disc

A general momentum theory for an energy‐extracting actuator disc modelling a rotor with a multiplicity of blades having radially uniform circulation is presented that includes the effects of wake rotation and expansion. A parallel theory directed at the propeller has been published elsewhere, but not one intended for the wind turbine. The rotation of the wake is shown to be accompanied by a fall in static pressure that is additional to that which occurs across the actuator disc and accounts for the energy extraction from the wind. Energy extraction is recognized in the fully developed wake by the flow regaining the static pressure of the undisturbed wind at the expense of the kinetic energy in the wake. Because the wake is still rotating in the fully developed wake, the additional fall in static pressure appears there also and so does not augment the energy extraction. However, the additional fall in pressure would cause a discontinuity in pressure across the fully developed wake but is prevented by a further slowing down of the wake. The additional slowing down extracts a little more energy from the flow than that predicted by the simple momentum theory, which does not include wake rotation. The overall effect of wake rotation on energy extraction is very small for wind turbines operating at high tip speed ratios but can significantly increase the predicted power output for turbines operating at low tip speed ratios. Copyright © 2004 John Wiley & Sons, Ltd.     

分形尾缘叶片气动性能及流场数值模拟

针对风力机存在尾流效应问题,通过在垂直轴风力机叶片尾缘布置分形孔的方法,建立分形叶片三维实体造型,进行了分形叶片和原始叶片三维非定常不可压流动的分析,得出叶片绕流流场数值模拟结果,重点研究具有分形特征的尾缘对叶片尾流流场及叶片气动特性的影响。结果表明:分形叶片对改善叶片尾流流场有较显著作用。在8°~18°攻角范围内,分形叶片升、阻力系数随攻角变化波动性小于原始叶片;当攻角大于原始叶片失速攻角时,这种波动性差距更大。分形孔的存在使叶片周围流场结构及气动参数对攻角变化敏感性降低:在攻角大于原始叶片失速攻角时,分形叶片阻力系数随攻角变化标准差仅为原始叶片的0.6倍,升力系数标准差仅为原始叶片0.4倍。研究结果将改善垂直轴风力机叶片尾流互相干扰及水平轴风力机叶尖脱落涡情况。     

Atmospheric stability‐dependent infinite wind‐farm models and the wake‐decay coefficient

We extend the infinite wind‐farm boundary‐layer (IWFBL) model of Frandsen to take into account atmospheric static stability effects. This extended model is compared with the IWFBL model of Emeis and to the Park wake model used in Wind Atlas Analysis and Application Program (WAsP), which is computed for an infinite wind farm. The models show similar behavior for the wind‐speed reduction when accounting for a number of surface roughness lengths, turbine to turbine separations and wind speeds under neutral conditions. For a wide range of atmospheric stability and surface roughness length values, the extended IWFBL model of Frandsen shows a much higher wind‐speed reduction dependency on atmospheric stability than on roughness length (roughness has been generally thought to have a major effect on the wind‐speed reduction). We further adjust the wake‐decay coefficient of the Park wake model for an infinite wind farm to match the wind‐speed reduction estimated by the extended IWFBL model of Frandsen for different roughness lengths, turbine to turbine separations and atmospheric stability conditions. It is found that the WAsP‐recommended values for the wake‐decay coefficient of the Park wake model are (i) larger than the adjusted values for a wide range of neutral to stable atmospheric stability conditions, a number of roughness lengths and turbine separations lower than ～ 10 rotor diameters and (ii) too large compared with those obtained by a semiempirical formulation (relating the ratio of the friction to the hub‐height free velocity) for all types of roughness and atmospheric stability conditions. © 2013 The Authors. Wind Energy published by John Wiley & Sons, Ltd.