Dynamic study of a wind turbine blade with horizontal axis

The study of the dynamic behavior of a wind turbine with horizontal axis can be undertaken by various methods of analysis. The effects of the change of the aerodynamic flow (in the steady and unsteady cases), the variation of parameters of the cinematic movement (angle of attack, pitch angle and yaw angle) and the definition of subsystems characteristics that makes the wind turbine (blade, nacelle and pylon) allow one to characterize the structural dynamic behavior of the wind turbine. It is therefore necessary to develop these items. Once this is done, the structural dynamic behavior of the system can be improved. The term `improve' means the increase of the life duration by mastering the fatigue effects and the reduction of cost without sacrificing the aerodynamic output. The present study aims to examine the behavior of the blade, which is the main part of the wind turbine in that it that transmits forces to all other parts of the structure. The model is based on the theory of three-dimensional beams, under the assumption of variable sections of the type NACA 4415 airfoil, and takes into account membrane, transversal shear, flexion and free torsion effects. With regards to the aerodynamic loads (the lift, the drag and the pitching moment), a validation has been undertaken by considering experimental data and numerical results obtained by a CFD code (Fluent). The forces are obtained by means of a parametric CAD method interpolation of the aerodynamic poles by Bézier patch under geometrical constraints solved by a Simplex type algorithm. The emphasis is put on dynamic aspects by a complete processing of the dynamic equilibrium equation, applied to the wind turbine blade with horizontal axis.     

Computational analysis of vertical axis wind turbine arrays

Canonical problems involving single, pairs, and arrays of vertical axis wind turbines (VAWTs) are investigated numerically with the objective of understanding the underlying flow structures and their implications on energy production. Experimental studies by Dabiri (J Renew Sustain Energy 3, 2011) suggest that VAWTs demand less stringent spacing requirements than their horizontal axis counterparts and additional benefits may be obtained by optimizing the placement and rotational direction of VAWTs. The flowfield of pairs of co-/counter-rotating VAWTs shows some similarities with pairs of cylinders in terms of wake structure and vortex shedding. When multiple VAWTs are placed in a column, the extent of the wake is seen to spread further downstream, irrespective of the direction of rotation of individual turbines. However, the aerodynamic interference between turbines gives rise to regions of excess momentum between the turbines which lead to significant power augmentations. Studies of VAWTs arranged in multiple columns show that the downstream columns can actually be more efficient than the leading column, a proposition that could lead to radical improvements in wind farm productivity.     

垂直轴自由变偏角水轮机的多体耦合数值求解方法

基于达朗伯原理建立了自由变偏角水轮机结构动力学模型,并结合粘性CFD方法,形成了一种用于分析自由变偏角潮流能水轮机水动力特性的多体耦合数值计算方法.将该方法与试验及非耦合算法进行了对比分析,并研究了自启动、流速变化和负载变化对水轮机性能的影响规律.研究表明:本文建立的数值计算方法能够有效模拟自由变偏角水轮机在各种非定常过程中的运动特性和动力特性.     

Rotational modes of motion for an aerodynamic pendulum with a vertical rotation axis

An aerodynamic pendulum placed in a steady horizontal air flow is studied in connection with modeling a wind-receiving element of a vertical-axis wind turbine (VAWT). When modeling the medium effects on the pendulum, the following two approaches are combined: the quasi-static one based on stationary wind tunnel experiments and the unsteady one based on the added mass effects. The existence of stable and unstable rotational modes is analyzed analytically (via the Poincaré-Pontryagin method) and numerically. The dependence on the parameters responsible for the viscous friction at the rotation axis and for the added mass effects is taken into account.     

Visualization by PIV of dynamic stall on a vertical axis wind turbine

The aerodynamic behavior of a vertical axis wind turbine (VAWT) is analyzed by means of 2D particle image velocimetry (PIV), focusing on the development of dynamic stall at different tip speed ratios. The VAWT has an unsteady aerodynamic behavior due to the variation with the azimuth angle θ of the blade’s sections’ angle of attack, perceived velocity and Reynolds number. The phenomenon of dynamic stall is then an inherent effect of the operation of a VAWT at low tip speed ratios, impacting both loads and power. The present work is driven by the need to understand this phenomenon, by visualizing and quantifying it, and to create a database for model validation. The experimental method uses PIV to visualize the development of the flow over the suction side of the airfoil for two different reference Reynolds numbers and three tip speed ratios in the operational regime of a small urban wind turbine. The field-of-view of the experiment covers the entire rotation of the blade and almost the entire rotor area. The analysis describes the evolution of the flow around the airfoil and in the rotor area, with special focus on the leading edge separation vortex and trailing edge shed vorticity development. The method also allows the quantification of the flow, both the velocity field and the vorticity/circulation (only the results of the vorticity/circulation distribution are presented), in terms of the phase locked average and the random component.     

新型升阻混合型垂直轴风力机气动特性研究

考虑S型与H型垂直轴风力机的特点,设计了一种新型升阻混合型垂直轴风力机,采用CFD法计算其启动与气动性能。结果表明,原始H型垂直轴风力机数值结果与试验值在各工况下吻合良好;新型升阻混合型垂直轴风力机不同方位角下的启动力矩均大于原始H型风力机,最小及最大值分别提升232%和83.3%;S型风轮输出功率随叶片重叠比增加而减小,完全重叠时输出功率基本为0;新型升阻混合型垂直轴风力机最大风能利用率为0.298,具有更复杂的流场特性。     

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.     

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。     

Wake impacts on aerodynamic and aeroelastic behaviors of a horizontal axis wind turbine blade for sheared and turbulent flow conditions

The magnitude and temporal variations of wind speed considerably influence aerodynamic and structural responses of MW-sized horizontal axis wind turbines. Thus, this paper investigates the variations in airloads and blade behavior of a wind turbine blade resulting from operations in sheared and turbulent flow conditions. First, in order to validate the present methods, comparisons of aerodynamic results were made among the blade element momentum method, free-wake method, and numerical results from the previous studies. Then, the validated methods were applied to a national renewable energy laboratory 5 MW reference wind turbine model for fluid–structure interaction analyses. From the numerical simulations, it can be clearly seen that unfavorable airloads and blade deformations occur due to the sheared and turbulent flow conditions. In addition, it is clear that wake impacts are not as substantial at those of high wind speeds; however, the effects obviously affect the aerodynamic and structural behaviors of the blade at lower wind speeds. Therefore, it is concluded that the numerical results markedly indicate the demand for accurate assessment of wake dynamics for accurate estimations of the aerodynamic and structural responses for sheared and turbulent flow environments.     

涡轮叶片的持久寿命预测模型

镍基高温合金用于制造发动机的高压涡轮叶片.为了提高涡轮叶片持久寿命设计参数选取和设计方法的可靠性,从涡轮叶片代表性部位取材并设计、加工试验试件,进行持久寿命试验.试验过程中记录试件的变形量,进而推算出其蟠变应变,然后利用修正θ-Project Concept法来建立其持久寿命预测方程,并对其进行验证.     

Two-dimensional integral equation for a thin wind turbine blade rotating in the round tunnel

The paper presents a mathematical treatment of the aerodynamic problem about a thin wind turbine blade rotating in the round tunnel. The radius of the blade is almost the radius of the tunnel. This permits formulation of the boundary condition on the tip vortex line to the simple slip condition over the surface of the tunnel. By applying a standard technique from potential theory, the problem is reduced to a two-dimensional integral equation whose kernel is connected with a special Green's function satisfying the homogeneous Neumann boundary condition on the tunnel surface. This Green's function is constructed in an explicit analytical form.     

Two-equation turbulence models for prediction of heat transfer on a transonic turbine blade

Two versions of the two-equation k–ω model and a shear stress transport (SST) model are used in a three-dimensional, multi-block, Navier–Stokes code to compare the detailed heat transfer measurements on a transonic turbine blade. It is found that the SST model resolves the passage vortex better on the suction side of the blade, thus yielding a better comparison with the experimental data than either of the k–ω models. However, the comparison is still deficient on the suction side of the blade. Use of the SST model does require the computation of distance from a wall, which for a multi-block grid, such as in the present case, can be complicated. However, a relatively easy fix for this problem was devised. Also addressed are issues such as (1) computation of the production term in the turbulence equations for aerodynamic applications, and (2) the relation between the computational and experimental values for the turbulence length scale, and its influence on the passage vortex on the suction side of the turbine blade.     

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。     

Analytical formulation of the Jacobian matrix for non-linear calculation of the forced response of turbine blade assemblies with wedge friction dampers

A fundamental issue in turbomachinery design is the dynamical stress assessment of turbine blades. In order to reduce stress peaks in the turbine blades at engine orders corresponding to blade natural frequencies, friction dampers are employed. Blade response calculation requires the solution of a set of non-linear equations originated by the introduction of friction damping.

Such a set of non-linear equations is solved using the iterative numerical Newton–Raphson method. However, calculation of the Jacobian matrix of the system using classical numerical finite difference schemes makes frequency domain solver prohibitively expensive for structures with many contact points. Large computation time results from the evaluation of partial derivatives of the non-linear equations with respect to the displacements.

In this work a methodology to compute efficiently the Jacobian matrix of a dynamic system having wedge dampers is presented. It is exact and completely analytical.

The proposed methods have been successfully applied to a real intermediate pressure turbine (IPT) blade under cyclic symmetry boundary conditions with underplatform wedge dampers. Its implementation showed to be very effective, and allowed to achieve relevant time savings without loss of precision.     

Turbulent kinetic energy balance measurements in the wake of a low-pressure turbine blade

The turbulent kinetic energy budget in the wake generated by a high lift, low-pressure two-dimensional blade cascade of the T106 profile was investigated experimentally using hot-wire anemometry. The purpose of this study is to examine the transport mechanism of the turbulent kinetic energy and provide validation data for turbulence modeling. Point measurements were conducted on a high spatial resolution, two-dimensional grid that allowed precise derivative calculations. Positioning of the probe was achieved using a high accuracy traversing mechanism. The turbulent kinetic energy (TKE) convection, production, viscous diffusion and turbulent diffusion were all obtained directly from experimental measurements. Dissipation and pressure diffusion were calculated indirectly using techniques presented and validated by previous investigators. Results for all terms of the turbulent kinetic energy budget are presented and discussed in detail in the present work.