A finite element method for the solution of two-dimensional transonic flows in cascades

Steady two-dimensional transonic flow is calculated in cascades of compressor and turbine blades using a mesh of triangular finite elements. A velocity potential is used, the equations being solved by the Newton-Raphson technique. The resulting computer program is fast, and is shown to give good accuracy. Shock waves are well represented, provided they are not too strong.     

透平机械叶尖间隙流场研究的进展

叶尖间隙流动对透平机械性能有很大影响。长期以来,叶尖间隙流动机理一直是透平机械领域研究的一个热点,同时也是一个尚未认识清楚的难点。把叶尖间隙内流动的研究进展分成两个部分:一部分是透平叶栅和透平转子内部叶尖间隙流场的研究进展,另一部分是压气机叶栅和压气机转子内部叶尖间隙流场的研究进展。对目前叶尖间隙研究集中的问题,如泄漏涡系结构,泄漏流动模型,泄漏涡旋涡强度的变化,泄漏涡和激波的相互作用等进行了简要的总结。文中还对透平机械叶尖间隙泄漏流动常用的数值计算方法进行了总结。认为今后应进一步对以下问题进行研究,其中包括研究高速透平机械叶尖泄漏涡旋涡强度变化问题,径流式叶轮机械叶尖间隙泄漏流动过程及泄漏涡发生发展规律问题,泄漏涡与激波相互作用产生阻塞区域的大小问题。      

Problems of incompressible flow past thin blades and correction of their shape

Solutions to the problem of the flow of an ideal fluid past a blade or cascade of blades with low blocking factor are found in the framework of the first approximation of the theory of perturbations of the flow past infinitely thin arcs. Problems of correction of the shape of the blades are also considered. Problems associated with the application of perturbation theory in problems of flow past bodies are discussed in Van Dyke's monograph [1]. The present paper includes an example of realization of this theory for the thin curved blades that are widely used in compressor construction. Searches for effective methods for calculating the shape of blades to ensure necessary gas-dynamic properties, for example, a given distribution on the blades of the velocity of separationless flow, led to the appearance of algorithms based on the theory of small perturbations for a thin wing of finite span [2] and a single airfoil in a gas flow [3]. In such an approach, the problem of constructing the required profile can be formulated as a sequence of corrections of the boundary of the flow region with respect to small variations of the boundary values of the flow velocity. The paper contains a general formulation of the linear problem of the correction of the flow boundary, an algorithm for its solution in the case of thin blades in an incompressible flow, and analysis of the obtained solutions. Examples of calculations are presented.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 130–137, January–February, 1992.We thank S.A. Smirnov for assistance in the calculations.     

A design method for turbomachinery blading in three-dimensional flow

A mixed spectral finite element scheme for the implementation of a design method for turbomachinery blading in three-dimensional subcritical compressible flow is presented. The method gives the detailed blade shape that would produce a prescribed tangential mean swirl schedule, given the hub and shroud profiles, the number of blades and their stacking position. After a presentation of the mathematical formulation of the design theory, the current numerical approach is described. It is then applied to the design of blading for radial inflow turbine impellers in three-dimensional flow.     

涡轮冷却叶片气动与传热设计优化

提出了航空发动机涡轮冷却叶片叶栅气动与传热自动优化方法,利用函数解析成型方法实现了冷却叶片几何模型的参数化与自动生成,可以建立任意冷却内腔数量的叶片模型;基于N-S方程实现叶片流体域与固体域的流-热耦合分析;采用KS函数方法将多目标优化问题转化为单目标函数进行优化,以总压损失、叶片最高温度和平均温度最小为优化目标进行了自动优化,改善了叶片性能。     

汽轮机动叶片的可靠性设计方法

提出了汽轮机叶片可靠性设计方法,介绍了叶片可靠性的含义和计算方法。该方法以概率论和统计学为基础,把汽轮机叶片的静应力、动应力、叶片疲劳强度、叶片安全倍率、叶片振动频率和激振力频率处理为随机变量,通过试验数据的统计分析和计算,确定有关随机变量的分布参数。使用概率设计法、应力与强度干涉模型确定汽轮机叶片疲劳强度和振动设计的可靠度。文中给出了叶片疲劳强度的动应力设计法和安全倍率设计法以及第一种调频叶片、第二种调频叶片和整圈连接叶片组的振动可靠性设计的计算公式和一些应用实例。使用这些方法,可以在设计阶段确定汽轮机叶片设计的可靠度,为汽轮机叶片的可靠性设计提供了科学的依据。     

A study of thermal nonequilibrium effects in low-pressure wet-steam turbines using a blade-to-blade time-marching technique

A theoretical analysis of the wet-steam flow in the low pressure cylinder of a 500 MW steam turbine using a blade-to-blade time-marching computer program is described. The calculating method can compute most types of wet-steam flow found in LP turbines, including those involving both primary and secondary nucleations in transonic and supersonic blading with shock waves. In particular, condensing flows in highly staggered rotor tip sections can be computed without difficulty. Extensive results are presented showing the effect of departures from thermal equilibrium on the blade surface pressure and velocity distributions, the blade outlet relative flow angle, the mass flow coefficient and the thermodynamic loss coefficient. On the basis of the analysis, recommendations are made concerning the application of nonequilibrium wet-steam theory to steam turbine design.     

Analogy between a flapping wing and a wind turbine with a vertical axis of revolution

Based on an analysis of available experimental data, the hypothesis about an analogy between a flapping wing and a wind turbine of the Darrieus rotor type is justified. It is demonstrated that the torque on the shaft of the Darrieus rotor is generated by thrust forces acting on the blades in a pulsed flow. A conclusion is drawn that it is necessary to perform aerodynamic calculations of blades on the basis of the nonlinear theory of the wing in an unsteady flow with allowance for the airfoil thickness. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 2, pp. 152–155, March–April, 2009.     

A Vibration Estimation Method for Wind Turbine Blades

This paper reports the development of a vibration monitoring system for wind turbine blades. This system is used to estimate the deflection at the tip blade on a wind turbine tower. Technical accidents of wind turbine blades have become increasingly common. Thus, regular monitoring of the blades is very important to prevent breakdowns, especially in cases when the blades begin to vibrate excessively. The monitoring system developed in this study satisfies two main objectives for practicality. First, our system is easy to install on existing wind turbines. Second, blade deflection is measured in real time. Our system can be operated using a few strain gages attached at the blade root, and the deflection is calculated based on the monitored stress. Thus, direct measurement of deflection at the blade tip is unnecessary. An estimation algorithm for this purpose is adopted based on the experimental modal analysis. This paper focuses on the evaluation of the estimation algorithm to investigate the feasibility of our system. Basic experiments were conducted using a simple blade model of a 300 W scaled wind turbine under rotation. Signals from the strain gages were acquired by a sensor network and sent to a computer through a wireless connection. The results show that the estimation accuracy is acceptably high. Therefore, we conclude that our proposed system is practical.     

Simulation of impact between rigid elements

The objective of this paper is to apply the concepts and theories of global impact based on a modern formulation in which the impact is considered with sliding, adherence or transition between sliding and adherence. The energy dissipated in the contact may be quantified by different definitions of the coefficient of restitution in Newton’s law and Poisson’s law. The method is applied to the impact between the damper (parabolic elements) and the platform of the blades in an airborne gas turbine. A numerical solution is calculated using a computer program constructed on the Matlab Platform.     

基于CFD技术的垂直轴风力机动态尾流特性研究

利用CFD软件对麦克马斯特大学垂直轴风力机进行不同叶尖速比下的数值模拟,计算结果与风洞试验数据吻合良好。近场尾流中,与单叶片的风力机模拟结果比较,上游叶片产生并向下游延伸的旋涡影响下游运行轨道上叶片的升阻力特性,不仅使叶片扭矩输出峰值降低,而且峰值产生的时间延迟。对垂直轴风力机叶片叶梢进行修改,模拟结果显示,叶片扭矩输出峰值不变,但是谷值有所降低,修改后风力机沿风向推力幅值降低明显;远场尾流中,采用风速轮廓线原理,以瑞典的法尔肯贝里市200kW垂直轴风力机为原型,按照真实的空间排布进行数值模拟。模拟结果显示,上游风力机上下两端处产生较为集中的远场尾流,影响下游风力机叶片下半段的气动性能,下游风力机功率输出降低明显。     

基于Schmitz理论的风叶气动设计研究

应用Schmitz理论进行叶片气动设计,考虑了风力机叶片的气动损失,用Schmitz理论推导出风力机叶片的基本设计参数的计算公式,并考虑了风力机在启动和空载时风力机的实际工作点偏离了设计点,对叶片的气动性能参数进行了修正。通过对200kW风力机的算例表明:随着叶片半径的增大,入流角逐渐减小;叶片弦长先增大后减小,修正后得到的风力机在非设计点处的推力、驱动力矩、功率与实际风力机的特性规律相符。     

Progresses in application of computational fluid dynamic methods to large scale wind turbine aerodynamics

The computational fluid dynamics (CFD) methods are applied to aerodynamic problems for large scale wind turbines. The progresses including the aerodynamic analyses of wind turbine profiles, numerical flow simulation of wind turbine blades, evaluation of aerodynamic performance, and multi-objective blade optimization are discussed. Based on the CFD methods, significant improvements are obtained to predict two/three dimensional aerodynamic characteristics of wind turbine airfoils and blades, and the vortical structure in their wake flows is accurately captured. Combining with a multi-objective genetic algorithm, a 1.5 MW NH-1500 optimized blade is designed with high efficiency in wind energy conversion.     

Supercritical and subcritical dynamic flow-induced instabilities of a small-scale wind turbine blade placed in uniform flow

There is a growing interest in extracting more power per turbine by increasing the rotor size in offshore wind turbines. As a result, the turbine blades will become longer and therefore more flexible, and a flexible blade is susceptible to flow-induced instabilities. In order to design and build stable large wind turbine blades, the onset of possible flow-induced instabilities should be considered in the design process. Currently, there is a lack of experimental work on flow-induced instabilities of wind turbine blades. In the present study, a series of experiments were conducted and flow-induced instabilities were observed in wind turbine blades. A small-scale flexible blade based on the NREL 5 MW reference wind turbine blade was built using three-dimensional printing technique. The blade was placed in the test section of a wind tunnel and was subjected to uniform oncoming flow, representing the case of a parked wind turbine blade. The blade׳s tip displacement was measured using a non-contacting displacement measurement device as the oncoming wind speed was increased. At a critical wind speed, the blade became unstable and experienced limit cycle oscillations. The amplitude of these oscillations increased with increasing wind speed. Both supercritical and subcritical dynamic instabilities were observed. The instabilities were observed at different angles of attack and for blades both with and without a geometric twist. It was found that the blade twist had a significant influence on the observed instability: a blade without a twist experienced a strong subcritical instability.     

Large chord turbine cascade testing at engine Mach and Reynolds numbers

A technique is presented for producing a flow through a linear cascade of turbine blades of large chord which gives the pressure distribution around a blade the same as that obtained in an infinite cascade for Mach and Reynolds numbers typical of gas turbine operating conditions. Results of experiments with a cascade of three blades of large chord are compared with results from a cascade of nine blades of smaller chord to confirm the validity of the technique. Experiments are performed on the large-chord cascade to examine surface phenomena with high spatial resolution. Boundary layer scales are also increased and profiles on both suction and pressure surfaces of the blade are obtained.     

Experimental scanning for simplifying the model of a stirred-tank flow

 Velocity measurements by two-component laser Doppler velocimetry (LDV) and laser sheet visualizations were used to analyze the 3D turbulent flow field in a stirred tank, for the purpose of reducing the intricacy of the hydrodynamics to more simple models. We first deal with the mean flow field measured, and the instantaneous visualized patterns, to appreciate the deviation from steadiness and predict the dispersion of particles from the mean motion alone. The study then focuses on the discharge flow from the agitator (Rushton turbine). The jet at the exit from the turbine is modeled in mean values. The flow instability as shown experimentally indicates that the Reynolds number plays no part in this phenomenon. A study based on dynamical system theory, considering a frequency modulation of the flow, shows the possibility of describing rather simply the deterministic component in the velocity fluctuation due to the blades. Received: 29 July 1997/Accepted: 11 November 1997     

近海风机叶片模态局部化产生机理及定量分析研究

在摄动理论的基础上,结合失谐度、模态密集度以及模态置信准则对模态局部化的产生机理做了定量描述,并用26自由度弹簧质点结构验证了其可行性。其次,用ANSYS建立了风机叶片模型,并通过改变材料的密度和弹性模量模拟了四种失谐情况,发现风机叶片刚度和质量的小量失谐也会对其模态振型产生显著的影响,同时通过定义新的模态局部因子来定量描述风机叶片结构的模态局部化程度。最后,对风机叶片失谐振型中谐调振型的成分进行了分析,研究表明,其成分越复杂,模态局部化程度也越强。     

二维扩压叶栅非定常分离流控制途径探索

二维扩压叶栅非定常黏性数值模拟结果表明,在一定攻角范围内,叶片前缘点附近的周期性吹吸气激励能有效控制混乱的非定常分离流．详细研究了非定常激励频率、幅值、位置对流场的影响．满足一定条件的非定常激励能够使流动由无序变为有序,时均气动性能提高。     

A three-dimensional blockage theory for the stability of an axial compressor row

The concept of ‘blockage’ between the blades of an axial compressor row as a theoretical device to replace loss was used by Stenning and Kriebel (1) to derive their well-known stability criterion for the stability of two-dimensional cascades. In their work they ignored the influence of that blockage upon the term describing the inertia of the fluid between the blades. The first part of the present work includes this influence and a modified stability criterion is derived that links the stability parameter with ‘stall cell’ speed and number. In the second part the blockage principle is extended to the problem of an isolated rotor row of arbitrary hub/tip ratio, treated as a ‘semi-actuator disc’, and perturbation of the upstream potential arising from changes of blockage are studied. The method proceeds by analysing the response of the flow to an imposed pressure discontinuity within the blade row. Rotating stall modes as such are not predicted but the theory demonstrates regions of the span which are undamped and on this basis a comparison can be made with two-dimensional ‘strip’ theory and it is shown that blades of low aspect ratio have broader undamped regions when zero damping is first encountered.     

叶片转动对涡轮间隙内部流动影响的数值研究

机匣与叶片的相对转动是影响涡轮叶顶间隙流动的重要冈素之一.对LISA 1.5级轴流涡轮间隙内部流动的数值计算结果表明:叶片转动对涡轮间隙流动有阻塞作用.叶片静止时,由于阻塞作用消失,导致间隙入口速度增大,间隙流鼍增加,并且通过间隙的流体全部卷起形成间隙涡.同时在叶片顶部吸力面侧前缘、中部各形成一个间隙涡,使得间隙流动损失增加.而且转速下降会加剧动叶出口截面气流过偏/偏转不足现象.同时叶片静止时,间隙前部各个弦长截面内静压自间隙入口开始一直呈增加趋势,直到叶片尾缘附近截面,间隙截面内静压才逐渐稳定.