Analysis of a tip correction factor for horizontal axis turbines

It is imperative to include three‐dimensional tip flow corrections when using low‐order rotor models that rely on the flow independence principle to compute the blade forces. These corrections aim to account for the effect of pressure equalization at the tips and the accompanying spanwise pressure gradients on the outboard sections, by reducing the computed axial and tangential forces as the blade tips are approached. While Glauert‐type corrections are conventionally employed for actuator disc‐type computations, alternative corrections are required for actuator line computations as they use a finite blade representation. We present actuator line computations of the Model Rotor Experiments in Controlled Conditions (MEXICO) rotor to investigate tip corrections. Using the tip correction factor proposed by Shen et al. (Wind Energy 2005; 8:457–475), the actuator line computations show an improvement in accuracy over similar computations undertaken without a tip correction factor included. Further improvement to the blade loading is achieved by recalibrating the tip correction factor using data extracted from blade resolved computations of the model rotor experiments in controlled conditions rotor. From the rotor resolved computations, the tip loss (reduction in the blade loading on the outboard sections) is found to be more aggressive in the tangential direction than the axial direction. To account for this, we recalibrate the tip correction factor separately in the axial and tangential directions to develop new directionally dependent tip corrections. The resulting actuator line computations show a further improvement in accuracy of the tangential blade loading, resulting in better prediction of the rotor power. Copyright © 2017 John Wiley & Sons, Ltd.     

Prediction of the wind turbine performance by using BEM with airfoil data extracted from CFD

Blade element momentum (BEM) theory with airfoil data is a widely used technique for prediction of wind turbine aerodynamic performance, but the reliability of the airfoil data is an important factor for the prediction accuracy of aerodynamic loads and power. The airfoil characteristics used in BEM codes are mostly based on 2D wind tunnel measurements of airfoils with constant span. Due to 3D effects, a BEM code using airfoil data obtained directly from 2D wind tunnel measurements will not yield the correct loading and power. As a consequence, 2D airfoil characteristics have to be corrected before they can be used in a BEM code. In this article, we consider the MEXICO (Model EXperiments In Controlled cOnditions) rotor where airfoil data are extracted from CFD (Computational Fluid Dynamics) results. The azimuthally averaged velocity is used as the sectional velocity to define the angle of attack and the coefficient of lift and drag is determined by the forces on the blade. The extracted airfoil data are put into a BEM code without further corrections, and the calculated axial and tangential forces are compared to both computations using BEM with Shen's tip loss correction model and experimental data. The comparisons show that the recalculated forces by using airfoil data extracted from CFD have good agreements with the experiment.     

A refined tip correction based on decambering

A new tip correction for use in performance codes based on the blade element momentum (BEM) or the lifting‐line technique is presented. The correction modifies the circulation by taking into account the additional influence of the induction of the vortices in the wake, using the so‐called decambering effect and thin‐airfoil theory. A limitation of the standard Prandtl tip correction is that it represents the surface loading by a line distribution that does not take into account the actual shape of the rotor blade. Thus, the chord distribution does not appear as a parameter in the model, and the loading in the proximity of the tip is generally found to be overestimated. The new tip correction is implemented as an additional correction in order to represent the surface loading by a line distribution. Comparing computations using the new model with standard BEM results and computations using a 3D panel code show that the inclusion of the correction greatly improves the results. The new model also explains some of the discrepancies that earlier on have been observed when using a BEM technique based alone upon standard tip corrections. Copyright © 2015 John Wiley & Sons, Ltd.     

A new tip correction for actuator line computations

The actuator line method (ALM) is today widely used to represent wind turbine loadings in computational fluid dynamics (CFD). As opposed to resolving the whole blade geometry, the methodology does not require geometry‐fitted meshes, which makes it fast to apply. In ALM, tabulated airfoil data are used to determine the local blade loadings, which subsequently are projected to the CFD grid using a Gaussian smearing function. To achieve accurate blade loadings at the tip regions of the blades, the width of the projection function needs to be narrower than the local chord lengths, requiring CFD grids that are much finer than what is actually needed in order to resolve the energy containing turbulent structures of the atmospheric boundary layer (ABL). On the other hand, employing large widths of the projection function may result in too large tip loadings. Therefore, the number of grid points required to resolve the blade and the width of the projection function have to be restricted to certain minimum values if unphysical corrections are to be avoided. In this paper, we investigate the cause of the overestimated tip loadings when using coarse CFD grids and, based on this, introduce a simple and physical consistent correction technique to rectify the problem. To validate the new correction, it is first applied on a planar wing where results are compared with the lifting‐line technique. Next, the NREL 5‐MW and Phase VI turbines are employed to test the correction on rotors. Here, the resulting blade loadings are compared with results from the blade‐element momentum (BEM) method. In both cases, it is found that the new correction greatly improves the results for both normal and tangential loads and that it is possible to obtain accurate results even when using a very coarse blade resolution.     

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.     

垂直轴风力机两种翼型气动性能比较研究

叶片是风力机最重要的组成部分,在不同的风能资源情况下,翼型的选择对垂直轴风力机气动特性有着重要的影响。文章分别以NACA0018翼型(对称翼型)和NACA4418翼型(非对称翼型)建立3叶片H型垂直轴风力机二维仿真模型。应用数值模拟的研究方法,从功率系数、单个叶片切向力系数等方面比较两种风力机模型在不同叶尖速比下的气动特性,并采用风洞实验数据验证了流场计算的准确性。CFD计算结果表明:在低叶尖速比下,NACA4418翼型风力机气动特性优于NACA0018翼型风力机,适用于低风速区域;在高叶尖速比下,NACA0018翼型风力机气动特性较好,适用于高风速地区。而且在高叶尖速比时,NACA0018翼型在上风区时,切向力系数平均值要高于NACA4418翼型,在下风区时,NACA418翼型切向力系数平均值高。该研究可为小型垂直轴风力机翼型的选择提供参考。     

An actuator disk method with tip‐loss correction based on local effective upstream velocities

This work aims at assessing the performance of a tip‐loss correction for advanced actuator disk (AD) methods coupled to large eddy simulation and making this correction possible in a wind farm configuration. The classical Glauert tip‐loss factor, commonly used in the blade element momentum method, is added here to correct the tip and the root induced velocities at the rotor. However, it requires a reference upstream velocity, which is problematic to define in complex flows, such as in wind farms. A methodology is proposed here to infer an effective upstream velocity local to each disk element, based on the one‐dimensional momentum theory and using only the local data at the rotor. This estimation is verified through a set of simulations, leading to good results in spite of the crude assumptions of the one‐dimensional momentum theory. This AD supplemented with the tip‐loss correction is compared with a high fidelity vortex particle‐mesh method, through the simulations in uniform wind of a constant circulation wind turbine and of a more realistic machine, the NREL‐5MW rotor. The results show that the AD behavior is clearly improved by the addition of a tip‐loss factor and the potential errors on the effective upstream velocity estimation have a moderate impact on the tip‐loss correction.     

风力机叶片三维效应翼型气动参数修正研究

以NREL Phase VI风力机为研究对象,对低雷诺数下叶片三维效应翼型气动参数修正进行研究。通过三维CFD数值模拟与二维翼型风洞实验,比较和检验现有的Snel、Lindenburg、Du&Selig、Chaviaropoulos&Hansen这4种修正公式。结果显示修正效果明显不同,以Du&Selig修正公式效果最佳,但它在叶尖和叶根部位的修正误差较大,而且随着尖速比的减小,叶片上的修正值与三维CFD结果吻合的区域减小,尤其不适合负攻角流动的修正。     

Analysis of aerodynamic load on straight-bladed vertical axis wind turbine

This paper presents a wind tunnel experiment for the evaluation of energy performance and aerodynamic forces acting on a small straight-bladed vertical axis wind turbine (VAWT) depending on several values of tip speed ratio. In the present study, the wind turbine is a four-bladed VAWT. The test airfoil of blade is symmetry airfoil (NACA0021) with 32 pressure ports used for the pressure measurements on blade surface. Based on the pressure distributions which are acted on the surface of rotor blade measured during rotation by multiport pressure-scanner mounted on a hub, the power, tangential force, lift and drag coefficients which are obtained by pressure distribution are discussed as a function of azimuthally position. And then, the loads which are applied to the entire wind turbine are compared with the experiment data of pressure distribution. As a result, it is clarified that aerodynamic forces take maximum value when the blade is moving to upstream side, and become small and smooth at downstream side. The power and torque coefficients which are based on the pressure distribution are larger than that by torque meter.     

Lift correction model for local shear flow effect on wind turbine airfoils

Wind turbines operate under various wind conditions in which turbulence virtually always exists. Therefore, unsteady wind turbine simulation methods to estimate wind loading in turbulent inflow conditions are very important for developing optimally designed wind turbines. Several methods have been developed for this purpose and are usually based on the blade element momentum theory (BEMT), which is used for calculation of the wind loading on turbine blades. The local shear flow effect induced by turbulence, however, is not explicitly considered in the popular BEMT-based simulations. Extreme situations can occur in a large-scale wind farm where the inflow field of a wind turbine may contain strong tip vortices generated from upstream turbines. In this study, the effects of idealized local shear flows around a two-dimensional airfoil, S809, on its aerodynamic characteristics were analyzed by CFD simulations. Various parameters including reference inflow velocity, shear rate, angle of attack, and cord length of the airfoil were examined. From the simulation results, several important characteristics were found. The shear rate in a flow causes some changes in the lift coefficient depending on its sign and magnitude, while the angle of attack does not have a distinguishable influence. The chord length and reference inflow also cause proportional and inversely proportional changes in the lift coefficient, respectively. Based on these observations, we adopted an analytic expression for the lift coefficient from the thin airfoil theory and proposed a lift correction model, which is easily applicable to the traditional load analysis procedure based on the BEMT.     

Numerical optimization of axial turbine with self‐pitch‐controlled blades used for wave energy conversion

Wells turbines are among the most practical wave energy converters despite their low aerodynamic efficiency and power produced. It is proposed to improve the performance of Wells turbines by optimizing the blade pitch angle. Optimization is implemented using a fully automated optimization algorithm. Two different airfoil geometries are numerically investigated: the standard NACA 0021 and an airfoil with an optimized profile. Numerical results show that each airfoil has its own optimum blade pitch angle. The present computational fluid dynamics optimization results show that the optimum blade pitch angle for NACA 0021 is +0.3° while that of the airfoil with an optimized profile equals +0.6°.The performance of the investigated airfoils is substantially improved by setting the blades at the optimum blade pitch angle. Both the turbine efficiency and tangential force coefficient are improved, especially at low flow rate and during turbine startup. Up to 4.3% average increase in turbine efficiency is achieved by optimizing the blade pitch angle. A slight improvement of the tangential force coefficient and decrease of the axial force coefficient are also obtained. A tangible increase of the stall‐free operating range is also achieved by optimizing the blade pitch angle. Copyright © 2013 John Wiley & Sons, Ltd.     

Parametric dependencies of the yawed wind‐turbine wake development

Yaw misalignment is currently being treated as one of the most promising methods for optimizing the power of wind farms. Therefore, detailed knowledge of the impact of yaw on the wake development is necessary for a range of operating conditions. This study numerically investigates the wake development behind a single yawed wind turbine operating at different tip‐speed ratios and yaw angles using the actuator‐line method in the spectral‐element code Nek5000. It is shown that depending on the tip‐speed ratio, the blade loading varies along the azimuth, resulting in a wake that is asymmetric in both the horizontal and vertical directions. Large tip‐speed ratios as well as large yaw angles are shown to decrease the vertical asymmetry of the yaw‐induced counter‐rotating vortex pair. Both parameters have the effect that they increase the spanwise force induced by yaw relative to the wake rotation. However, while the strength of the counter‐rotating vortex pair in the far wake increases with yaw angle, it is shown to decrease with the tip‐speed ratio. The vertical shift in the wake center is found to be highly dependent on the yaw angle and the tip‐speed ratio. These detailed insights into the yawed wake are important when optimizing potential downstream turbines.     

有弯度翼型垂直轴风力机的数值模拟研究

应用计算流体动力学有限体积法SIMPLE算法,配合SST k-ω湍流模型和滑动网格技术模拟分析了有弯度翼型4叶片垂直轴风力机的气动特性,以其作为有弯度翼型垂直轴风力机设计的参考依据。研究结果发现,在入口流速为10 m/s,尖速比为1.6时,该种风力机单个叶片的瞬时力矩系数为-0.03～0.18,并且在一个转动周期内正的瞬时力矩系数历时较长;整个风轮的的力矩系数在尖速比为1.6左右时达到最大值,功率系数在尖速比为1.7左右时达到最大值。     

Direct calculation of wind turbine tip loss

The usual method to account for a finite number of blades in blade element calculations of wind turbine performance is through a tip loss factor. Most analyses use the tip loss approximation due to Prandtl which is easily and cheaply calculated but is known to be inaccurate at low tip speed ratio. We develop three methods for the direct calculation of the tip loss. The first is the computationally expensive calculation of the velocities induced by the helicoidal wake which requires the evaluation of infinite sums of products of Bessel functions. The second uses the asymptotic evaluation of those sums by Kawada. The third uses the approximation due to Okulov which avoids the sums altogether. These methods are compared to the tip loss determined independently and exactly for an ideal three-bladed rotor at tip speed ratios between zero and 15. Kawada's asymptotic approximation and Okulov's equations are preferable to the Prandtl factor at all tip speed ratios, with the Okulov equations being generally more accurate. In particular the tip loss factor exceeds unity near the axis of rotation by a large amount at all tip speed ratios, which Prandtl's factor cannot reproduce. Neither the Kawada nor the Okulov equations impose a large computational burden on a blade element program.     

An engineering model for wind turbines under yawed conditions derived from high fidelity models

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.     

气冷涡轮转子变叶尖间距性能试验及数值研究

为量化评估工程应用的气冷低压涡轮带冠转子叶片的叶尖间距大小对涡轮气动性能的影响,综合现有涡轮部件试验能力,以单级轴流低压涡轮性能试验件为基础,通过控制圆度的机加方式磨削转子外环内壁以实现叶尖间距的变化,采用控制冷气流量比的方法,开展5次不同叶尖间距大小的涡轮级性能试验,得到多工况下涡轮效率、换算流量和换算功率等特性参数。采用加载冷气及考虑转子叶冠结构的数值模型进行三维仿真计算,并与试验结果对比分析。研究表明：叶尖间距由0.6 mm增加至3.2 mm,低压涡轮流通能力增大1%,叶冠泄漏量增多3.4%,但做功能力下降2.3%。涡轮效率变化与叶尖间距大小近似呈线性关系,叶尖间距每增加1 mm,效率约降低0.7%,同时,叶尖间距的增加导致了叶冠腔的旋涡结构、气流掺混及主流入侵强度逐渐增大,引起动叶总压损失的增大,叶尖间距增加至3.2 mm导致叶间位置总压损失由0.88增至2.3。     

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.     

Multi-objective optimization of the airfoil shape of Wells turbine used for wave energy conversion

Wells turbine is one of the technical systems allowing an efficient use of the power contained in oceans’ and seas’ waves with a relatively low investment level. It converts the pneumatic power of the air stream induced by an Oscillating Water Column into mechanical energy. The standard Wells turbines show several well-known disadvantages: low tangential force, leading to low power output from the turbine; high undesired axial force; usually a low aerodynamic efficiency and a limited range of operation due to stall. In the present work an optimization process is employed in order to increase the tangential force induced by a monoplane Wells turbine using symmetric airfoil blades. The automatic optimization procedure is carried out by coupling an in-house optimization library (OPAL (OPtimization ALgorithms)) with an industrial CFD (Computational Fluid Dynamics) code (ANSYS-Fluent). This multi-objective optimization relying on Evolutionary Algorithms takes into account both tangential force coefficient and turbine efficiency. Detailed comparisons are finally presented between the optimal design and the classical Wells turbine using symmetric airfoils, demonstrating the superiority of the proposed solution. The optimization of the airfoil shape leads to a considerably increased power output (average relative gain of +11.3%) and simultaneously to an increase of efficiency (+1%) throughout the full operating range.     

Analysis of numerically generated wake structures

Direct numerical simulations of the Navier–Stokes equations are performed to achieve a better understanding of the behaviour of wakes generated by wind turbines. The simulations are performed by combining the in‐house developed computer code EllipSys3D with the actuator‐line methodology. In the actuator‐line method, the blades are represented by lines along which body forces representing the loading are introduced. The body forces are determined by computing local angles of attack and using tabulated aerofoil coefficients. The advantage of using the actuator‐line technique is that it is not needed to resolve blade boundary layers and instead the computational resources are devoted to simulating the dynamics of the flow structures. In the present study, approximately 5 million mesh points are used to resolve the wake structure in a 120‐degree domain behind the turbine. The results from the computational fluid dynamics (CFD) simulations are evaluated and the downstream evolution of the velocity field is depicted. Special interest is given to the structure and position of the tip vortices. Further, the circulation from the wake flow field is computed and compared to the distribution of circulation on the blades. Copyright © 2008 John Wiley & Sons, Ltd.     

超低水头轴流式水轮机CFD优化及流动特性研究

结合某水电站改造要求,研发了一种设计水头为2.75 m的超低水头轴流式水轮机并对其性能进行优化,以达到有效利用低水头水力资源的目的。基于不可压缩连续方程及雷诺时均Navier-Stokes方程,采用Spalart-Allmaras湍流模型和SIMPLEC算法对轴流式水轮机进行三维全流场数值模拟,分别分析了轴流式转轮叶片翼型、轮毂比、导叶开度及安放角对水轮机性能的影响,并对最优模型进行实测验证。结果表明,在满足设计水头为2.75 m的情况下,选用配置叶片B、轮毂比为0.30、叶片相对安放角为-2°的水轮机,当导叶相对开度为0°时,装置水力损失最小,最高效率达83.7%,且数值模拟计算所得出力与实测结果误差小于099%,表明基于CFD的数值模拟对超低水头轴流式水轮机的性能预测精度较高。