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.     

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 simple improvement of a tip loss model for actuator disc simulations

The loading of a wind turbine decreases towards the blade tip because of the velocities induced by the tip vortex. This tip loss effect has to be taken into account when performing actuator disc simulations, where the single blades of the turbine are not modeled. A widely used method applies a factor on the axial and tangential loading of the turbine. This factor decreases when approaching the blade tip. It has been shown that the factor should be different for the axial and tangential loading of the turbine to model the rotation of the resulting force vector at the airfoil sections caused by the induced velocity. The present article contains the derivation of a simple correction for the tangential load factor that takes this rotation into account. The correction does not need any additional curve fitting but just depends on the local airfoil characteristics and angle of attack. Actuator disc computations with the modified tip loss correction show improved agreement with results from actuator line, free wake lifting line, and blade element momentum simulations.     

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.     

水平轴潮流涡轮池壁效应修正方法分析

通过数值仿真与模型试验的方式分析池壁效应对水平轴潮流涡轮水动力性能的影响。通过总结公开发表文献中池壁效应修正方法,获取不同流域以及来流流速下5种池壁效应的修正结果,并与无限流域下水平轴潮流涡轮的能量转换效率以及阻力系数进行对比,进而获得可准确预估无限流域下水平轴潮流涡轮水动力性能的池壁效应修正方法。结果表明：池壁效应会对潮流涡轮的水动力性能产生较为明显的影响,受限流域下潮流涡轮能量转换效率以及阻力系数高于无限流域下的结果,且池壁效应对潮流涡轮的能量转换效率的影响伴随尖速比的增加呈逐渐增大的趋势。受阻塞因子与尖速比的影响,不同池壁效应修正方法的预估精度不同;其中,Pope-Harper以及Bahaj这2种池壁效应修正结果在不同来流流速、阻塞因子以及尖速比下与无限流域下潮流涡轮的水动力性能吻合良好。     

叶顶开槽——小翼结构对提升轴流风机性能影响的数值研究

为了有效抑制叶顶泄漏流的发展,降低叶顶泄漏损失,针对两级动叶可调轴流风机提出在吸力面构造叶顶小翼并开设斜槽的新型叶顶改型方案。采用Fluent数值模拟了5种叶顶改型方案对风机性能和流场特征的影响,分析了不同方案下流场、叶顶静压、叶顶泄漏量和动叶区做功能力的变化。结果表明：吸力面小翼可有效降低叶顶损失,小翼上开设顺流向斜槽可进一步提高风机性能,逆流向斜槽会使性能略有降低;顺流向单斜槽为最佳改型方案,在设计流量下全压和效率分别提升166 Pa和0.942%;叶顶间隙处产生额外的涡流,叶顶泄漏流得到抑制,动叶区做功能力得以提升。     

Heat transfer performance of wet porous solar collectors under periodic conditions

Fourier's law was often used to study the heat transfer of collector plates. However, some scholars have found that under time-varying periodic boundary conditions, using Fourier's law for research will produce certain deviations. In the current work, periodic boundary conditions are used, so the effect of non-Fourier efficiency on the heat transfer of the collector plate needs to be considered. Based on the Cattaneo–Vernotte equation, a heat transfer model of the solar collector plate with a limited heat transfer rate is constructed, and the problem is solved by the lattice Boltzmann method. On this basis, the influence of radiation, porous media, humidity, and relaxation time on solar collectors is considered. And the average efficiency, tip temperature, and exergy loss of the collectors are quantitatively analyzed. The results show that when the non-Fourier effect is considered, the tip temperature of the collector plate decreases, the average efficiency and the exergy loss increase. Moreover, with the increase of relaxation time, the tip temperature is lower, the efficiency and the exergy loss are greater. As the humidity and radiation increase, the tip temperature decreases, and the exergy loss and average efficiency increase. When other factors remain unchanged, the average efficiency, tip temperature, and exergy loss increased with an increase in porosity.     

Shape optimization of wind turbine blades

This paper presents a design tool for optimizing wind turbine blades. The design model is based on an aerodynamic/aero‐elastic code that includes the structural dynamics of the blades and the Blade Element Momentum (BEM) theory. To model the main aero‐elastic behaviour of a real wind turbine, the code employs 11 basic degrees of freedom corresponding to 11 elastic structural equations. In the BEM theory, a refined tip loss correction model is used. The objective of the optimization model is to minimize the cost of energy which is calculated from the annual energy production and the cost of the rotor. The design variables used in the current study are the blade shape parameters, including chord, twist and relative thickness. To validate the implementation of the aerodynamic/aero‐elastic model, the computed aerodynamic results are compared to experimental data for the experimental rotor used in the European Commision‐sponsored project Model Experiments in Controlled Conditions, (MEXICO) and the computed aero‐elastic results are examined against the FLEX code for flow past the Tjæreborg 2 MW rotor. To illustrate the optimization technique, three wind turbine rotors of different sizes (the MEXICO 25 kW experimental rotor, the Tjæreborg 2 MW rotor and the NREL 5 MW virtual rotor) are applied. The results show that the optimization model can reduce the cost of energy of the original rotors, especially for the investigated 2 MW and 5 MW rotors. Copyright © 2009 John Wiley & Sons, Ltd.     

相同叶尖速比不同转速的垂直轴风力机气动性能分析

在不考虑连杆、转轴及叶尖损失的简化模型基础上,利用Fluent软件采用雷诺平均Navier-Stokes方程与k-ωSST湍流模型对直叶片垂直轴风力机进行了数值模拟.对比了相同叶尖速比λ=4,叶轮半径r分别为1 m和2 m的垂直轴风力机的气动性能.结果表明,在来流风速V∞和叶尖速比λ相同的情况下,不同半径的垂直轴风力机具有十分相似的翼型表面压力分布,对应位置处的升、阻力系数相差不大.     

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。     

Optimization of a Trapezoidal Profile Annular Fin

The article presented here is an analysis that leads to the optimization for a design of an annular trapezoidal fin using a new approach to a two-dimensional analytical method. A comparison between the new analytical approach and the generally used method for a rectangular annular fin is made to show the exactness of the new method of approach. For an annular trapezoidal fin, the heat loss, fin tip radius, and fin base height are optimized as a function of the ratio of convection characteristic numbers, fin shape factor, dimensionless fin volume, dimensionless fin base radius, and convection characteristic number.     

Helical vortex theory and blade element analysis of multi-bladed windmills

Multi-bladed windmills usually pump water for agriculture and domestic consumption, often in remote locations. Although they have been around for over 150 years, their aerodynamic performance is still poorly understood. This paper describes the use of helical vortex theory (HVT) and blade element momentum (BEM) analysis to predict windmill thrust, torque, and extracted power. We emphasize the unusual features of windmills: low Reynolds numbers and tip speed ratios and high solidity, all related to the generation of high torque at low wind speeds. Wind tunnel tests on a model rotor with 3, 6, 12, and 24 circular-arc, constant-chord blades determined the thrust, torque, and extracted power over a range of tip speed ratio that extended to runaway. For comparison, BEM was implemented with a correction for finite blade number derived from HVT, as well as the classical Prandtl tip loss factor. The HVT correction predicted the rotor power coefficient to within 3% of the test data on the average. At low tip speed ratios and smaller blade numbers, HVT was consistently more accurate than the Prandtl factor. At all blade numbers, the measured rotor torque exceeded the BEM predictions at the lowest tip speed ratios indicating stall delay which became more important (and more beneficial for windmill performance) as the blade number increased. The Prandtl formulation predicted the thrust to within a mean accuracy of 13% and was more accurate than the HVT method.     

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 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.     

Flowfield and heat transfer past an unshrouded gas turbine blade tip with different shapes

This paper describes the numerical investigations of flow and heat transfer in an unshrouded turbine rotor blade of a heavy duty gas turbine with four tip configurations. By comparing the calculated contours of heat transfer coefficients on the flat tip of the HP turbine rotor blade in the GE-E³ aircraft engine with the corresponding experimental data, the κ-ω turbulence model was chosen for the present numerical simulations. The inlet and outlet boundary conditions for the turbine rotor blade are specified as the real gas turbine, which were obtained from the 3D full stage simulations. The rotor blade and the hub endwall are rotary and the casing is stationary. The influences of tip configurations on the tip leakage flow and blade tip heat transfer were discussed. It’s showed that the different tip configurations changed the leakage flow patterns and the pressure distributions on the suction surface near the blade tip. Compared with the flat tip, the total pressure loss caused by the leakage flow was decreased for the full squealer tip and pressure side squealer tip, while increased for the suction side squealer tip. The suction side squealer tip results in the lowest averaged heat transfer coefficient on the blade tip compared to the other tip configurations.     

Removal of the influence of stress triaxiality on crack tip opening displacement fracture toughness by continuum damage mechanics approach

Experimental data for AS 1405-180, AS 1204-350, HY 80 and C-Mn steels shows that the crack tip opening displacement (CTOD) elastic-plastic fracture toughness at initiation δ_c decreases with increasing crack tip stress trifaxiality. This trend is confirmed by the continuum damage analysis in this paper. The dependence of the CTOD parameter at initiation on the local constraint, i.e. the stress triaxiality, provides the motivation to seek parameters that could rank the toughness of steels. Since the local effective plastic strain can be related to the CTOD, a relationship is described between the initiation CTOD toughness and the crack tip constraint, i.e. the stress triaxiality, on the basis of a new local damage theory for ductile fracture. Furthermore, a new constraint corrected toughness parameter δ_dc (and corresponding criterion) for ductile fracture is proposed, in which both crack tip deformation and crack tip constraint intensity are taken into account. Several series of experimental data have shown that the parameter δ_dc is nearly a constant or independent of the local constraint. It is found that the toughness variation with constraint changes can effectively be removed by use of the constraint correction procedure proposed in this paper.     

基于弯曲叶片的氦气轴流压气机优化设计

针对高负荷氦气压气机中角区分离、叶顶泄漏严重带来的效率损失问题,以单级氦气压缩机为研究对象,利用CFD方法,分析了不同弯曲角度下氦气压气机内部的角区损失和叶顶泄漏损失,并优化了现有五级轴流氦气压气机。结果表明：叶片正弯会增加端区处的静压,减少角区分离,进而降低角区损失;对动叶而言,在设计攻角下正弯也会增加前缘损失;动叶叶顶反弯使泄漏流远离下一个叶片的压力面,而合适的反弯角度可以降低叶顶泄漏量;选取合适的弯曲角度使五级轴流压气机设计点效率提高1.85%。     

Soot temperature measurements and implications for time-resolved laser-induced incandescence (TIRE-LII)

Emission spectroscopy has been used to determine soot particle temperatures in an ethene diffusion flame both under normal combustion conditions and also after irradiation with an intense laser pulse. On the basis of these measurements, a check on the models and an improvement of parameters underlying time-resolved laser-induced incandescence (TIRE-LII) was performed. With this technique a two-dimensionally resolved measurement of soot primary particle sizes is feasible in a combustion process from the ratio of emission signals obtained at two delay times after a laser pulse, as the cooling behavior is characteristic of particle size. For accurate measurements, local gas temperatures must be known, which can be derived from the temperatures of the soot particles themselves. These have been measured by fitting full Planck curves to line-of-sight emission spectra after an inversion algorithm. The temperature and heat of vaporization of soot, which govern the energy and mass loss at high temperatures, were obtained by measurements of maximum particle temperature for various laser irradiances and a fit procedure to the theoretical dependence. Finally, the temperature decay of laser-heated soot was measured with high temporal resolution. Comparisons with model predictions show that soot temperatures are roughly 300 K higher than expected after the onset of vaporization, which indicates deficiencies in the present models of vaporization. It is demonstrated that the TIRE-LII performance is essentially unaffected by these shortcomings if LII signals are detected in a period where conductive heat transfer dominates and an appropriate correction is performed.     

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.     

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.