Optimization‐based study of bend–twist coupled rotor blades for passive and integrated passive/active load alleviation

This work is concerned with the design of wind turbine blades with bend‐twist‐to‐feather coupling that self‐react to wind fluctuations by reducing the angle of attack, thereby inducing a load mitigation effect. This behavior is obtained here by exploiting the orthotropic properties of composite materials by rotating the fibers away from the pitch axis. The first part of this study investigates the possible configurations for achieving bend‐twist coupling. At first, fully coupled blades are designed by rotating the fibers for the whole blade span, and a best compromise solution is found to limit weight increase by rotations both in the spar caps and in the skin. Next, partially coupled blades are designed where fibers are rotated only on the outboard part of the blade, this way achieving good load mitigation capabilities together with weight savings. All blades are designed with a multilevel constrained optimization procedure, on the basis of combined cross‐sectional, multibody aero‐servo‐elastic and three‐dimensional finite element models. Finally, the best configuration of the passive coupled blade is combined with an active individual pitch controller. The synergistic use of passive and active load mitigation technologies is shown to allow for significant load reductions while limiting the increase in actuator duty cycle, thanks to the opposite effects on this performance metric of the passive and active control solutions. Copyright © 2012 John Wiley & Sons, Ltd.     

Load Mitigation with Bending/Twist‐coupled Blades on Rotors using Modern Control Strategies

The prospect of installing blades that twist as they bend and/or extend on horizontal axis wind turbines provides opportunities for enhanced energy capture and/or load mitigation. Although this coupling could be achieved in either an active or a passive manner, the passive approach is much more attractive owing to its simplicity and economy. As an example, a blade design might employ coupling between bending and twisting, so that as the blade bends owing to the action of the aerodynamic loads, it also twists, modifying the aerodynamic performance in some way. For reducing loads the blades are designed to twist towards feather as they bend. For variable‐speed pitch‐controlled rotors, dynamic computer simulations with turbulent inflow show that twist coupling substantially decreases fatigue damage over all wind speeds, without reducing average power. Maximum loads also decrease modestly. For constant‐speed stall‐controlled and variable‐speed stall‐controlled rotors, significant decreases in fatigue damage are observed at the lower wind speeds and smaller decreases at the higher wind speeds. Maximum loads also decrease slightly. As a general observation, whenever a rotor is operating in the linear aerodynamic range (lower wind speeds for stall control and all wind speeds for pitch control), substantial reductions in fatigue damage are realized. Copyright © 2002 John Wiley & Sons, Ltd.     

Integration of multiple passive load mitigation technologies by automated design optimization—The case study of a medium‐size onshore wind turbine

The present work considers the application to a medium‐size onshore wind turbine of passive load mitigation technologies, first individually and then integrated together. The study is conducted with the help of a comprehensive automated design optimization procedure, which eases the generation and comparison of consistent solutions, each satisfying the same overall requirements. Passive load mitigation is here obtained by inducing bend‐twist coupling to the blades. The coupling is generated by rotating the fibers of anisotropic laminates, by the aerodynamic sweeping of the blade and by offsetting the spar caps in opposite directions on the pressure and suction sides. The first two solutions yield significant benefits, while the third, for this particular wind turbine, is ineffective. In addition, the typical power losses associated with bend‐twist coupled blades are reduced by a novel regulation strategy that varies the fine pitch setting in the partial load region. After having considered each load mitigation technology by itself, fiber rotation and sweeping are combined together and used to design a rotor with a larger swept area. The final design generates cost of energy savings thanks to a large‐diameter, highly coned, soft‐in‐bending rotor that results in lower turbine costs and a higher energy capture compared with the baseline design.     

A parametric study of coupled‐mode flutter for MW‐size wind turbine blades

With the increasing size of offshore wind turbine rotors, the design criteria used for the blades may also evolve. Current offshore technology utilizes three relatively stiff blades in an upwind configuration. With the goal of minimizing the mass, there is an interest in the lightweight rotors that instead utilize two flexible blades oriented downwind. These longer blades are more flexible and thus susceptible to experience flow‐induced instability. Coupled‐mode flutter is one of the destructive aeroelastic instabilities that can occur in flexible structures subjected to aerodynamic loading. Because of variation in one of the system parameters, e.g., flow velocity, structural modes coalesce at a critical flow velocity, and coupled‐flutter occurs. In the present work, a parametric study is conducted in order to study the influence of the natural frequencies in the torsional and flapwise directions on the critical flutter speed for wind turbine blades. Three MW‐size wind turbine blades are studied using a three‐dimensional blade model, which includes coupled flapwise and torsional displacements. The results show that the three blades have very similar behavior as the system parameters vary. It is shown that the first torsional natural frequency and the ratio of the first torsional natural frequency to the first flapwise natural frequency are the most critical parameters affecting the onset of instability. Critical flutter speeds even lower than the blade rated speed can be observed for blades with low torsional natural frequencies. Copyright © 2015 John Wiley & Sons, Ltd.     

A morphing downwind‐aligned rotor concept based on a 13‐MW wind turbine

To alleviate the mass‐scaling issues associated with conventional upwind rotors of extreme‐scale wind turbines (≥10 MW), a morphing downwind‐aligned rotor (MoDaR) concept is proposed herein. The concept employs a downwind rotor with blades whose elements are stiff (no intentional flexibility) but with hub‐joints that can be unlocked to allow for moment‐free downwind alignment. Aligning the combination of gravitational, centrifugal and thrust forces along the blade path reduces downwind cantilever loads, resulting in primarily tensile loading. For control simplicity, the blade curvature can be fixed with a single morphing degree of freedom using a near‐hub joint for coning angle: 22° at rated conditions. The conventional baseline was set as the 13.2‐MW Sandia 100‐m all glass blade in a three‐bladed upwind configuration. To quantify potential mass savings, a downwind load‐aligning, two‐bladed rotor was designed. Because of the reduced number of blades, the MoDaR concept had a favorable 33% mass reduction. The blade reduction and coning led to a reduction in rated power, but morphing increased energy capture at lower speeds such that both the MoDaR and conventional rotors have the same average power: 5.4 MW. A finite element analysis showed that quasi‐steady structural stresses could be reduced, over a range of operating wind speeds and azimuthal angles, despite the increases in loading per blade. However, the concept feasibility requires additional investigation of the mass, cost and complexity of the morphing hinge, the impact of unsteady aeroelastic influence because of turbulence and off‐design conditions, along with system‐level Levelized Cost of Energy analysis. Copyright © 2015 John Wiley & Sons, Ltd.     

Improved Modal Dynamics of Wind Turbines to Avoid Stall‐induced Vibrations

Stall‐induced edgewise blade vibrations have occasionally been observed on three‐bladed wind turbines over the last decade. Experiments and numerical simulations have shown that these blade vibrations are related to certain vibration modes of the turbines. A recent experiment with a 600 kW turbine has shown that a backward whirling mode associated with edgewise blade vibrations is less aerodynamically damped than the corresponding forward whirling mode. In this article the mode shapes of the particular turbine are analysed, based on a simplified turbine model described in a multi‐blade formulation. It is shown that the vibrations of the blades for the backward and forward edgewise whirling modes are different, which can explain the measured difference in aerodynamic damping. The modal dynamics of the entire turbine is important for stability assessments; blade‐only analysis can be misleading. In some cases the modal dynamics may even be improved to avoid stall‐induced vibrations. Copyright © 2003 John Wiley & Sons, Ltd.     

Modal re‐analysis of rotary wind turbine blades in refinement design

A modal re‐analysis approach is proposed for refinement designs of rotary wind turbine blades on the basis of matrix perturbation methods. The approach entails effects of stress stiffening, spin softening, uncertainty of material properties and structural modifications of blades. Three perturbation methods are used to conduct the re‐analysis approach, including the standard perturbation method and two improvements proposed by H. C. Hu and S. H. Chen, respectively. Numerical results of a typical wind turbine blade indicate that the two improved methods deliver better accuracy than the standard perturbation method in terms of eigenpairs. In application to blade designs, Chen's method is suitable for a multi‐step modal re‐analysis with explicit small parameters and cultivates the first‐order and second‐order perturbations of eigenpairs as well. In contrast, Hu's method is a better choice for a single‐step modal re‐analysis without determining any small parameter explicitly and directly offers approximate eigenpairs instead of somehow tedious perturbation processes. Copyright © 2012 John Wiley & Sons, Ltd.     

新型阻尼结构叶片振动特性试验研究

干摩擦阻尼结构被广泛应用于透平叶片中来降低其振动应力。文章设计并搭建了干摩擦阻尼块结构叶片振动特性测试试验台,通过测量一新型阻尼结构叶片的振动响应值,获得了不同激振力及模拟离心力转速下叶片频率响应曲线及模态阻尼比。试验结果表明：当激振力较小时（4N、5N和6N）,叶片的共振频率随模拟离心力转速的上升而不断增加,而模态阻尼比则先增加再减小,在40％模拟离心力转速工况下模态阻尼比最大,叶片减振效果最好;当激振力较大时（12N、18N和24N）,叶片振动更加剧烈,使得阻尼块接触刚度降低,叶片的共振频率接近自由叶片固有频率,而模态阻尼比随着模拟离心力转速的上升不断降低。     

Analytic analysis of load alignment for coning extreme‐scale rotors

Extreme‐scale wind turbines (rated powers greater than 10 MW) with large rotor diameters and conventional upwind designs must resist extreme downwind and gravity loads. This can lead to significant structural design challenges and high blade masses that can impede the reduction of levelized cost of wind energy. Herein, the theoretical basis for downwind load alignment is developed. This alignment can be addressed with active downwind coning to reduce/eliminate flapwise bending loads by balancing the transverse components of thrust, centrifugal, and gravitational force. Equations are developed herein that estimates the optimal coning angle that reduces flapwise loads by a specified amount. This analysis is then applied to a 13.2‐MW scale with 100‐m‐level wind turbine blades, where it is found that a load alignment coning schedule can substantially reduce the root flapwise bending moments. This moment reduction in this example can allow the rotor mass to be decreased significantly when compared with a conventional upwind three‐bladed rotor while maintaining structural performance and annual energy output.     

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.     

Coupled aeroelastic oscillations of a turbine blade row in 3D transonic flow

heodctionThe trend of imPrved gas ndine engine designwith higher Hntalc blade loadin and sInallerPhysical size attraCtS much Mon to the aeroelasticbehayour of blades not Ouly in comPI'essors, bu also intuIbines. Flow-induced triine and comPressor bladesoscillations can lead to fatigUe failures of a constrUctionand so rePrsent imPorIant Problems of reliability, safety,and operatin cost.The hahonal aPProach in flutter calculations ofblW disks is based on twency doInain analysis"ro,in whi…     

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.     

Representation of wind turbine blade responses in power production load cases by linear mode shapes

The wind turbine industry is designing large MW size turbines with very long blades, which exhibit large deflections during their operational life. These large deflections decrease the accuracy of linear models such as linear finite element and modal‐based models, in which the structure is represented by linear mode shapes. The aim of this study is to investigate the competence of the mode shapes to represent the large blade responses in normal operation load cases. For this purpose, blade deflections are projected onto the linear modal space, swept by mode shape vectors. The projection shows the contribution of each mode and the projection error. The blade deflections are calculated by a nonlinear aero‐servo‐elastic solver for power production fatigue load cases with normal turbulence. The mode shapes are calculated at the steady‐state deflected blade position computed at different wind speeds. Three reference turbine blades are used in the study to evaluate the effects of various blade design parameters such as length, stiffness, mass, and prebend. The results show that although the linear mode shapes can represent the flapwise and edgewise deflections accurately, axial and torsional deflections cannot be captured with good accuracy. The geometric nonlinear effects are more apparent in the latter directions. The results indicate that the blade deflections occur beyond the linear assumptions.     

增压器涡轮叶片模态特性研究

基于有限元法，对增压器涡轮吉进行模态特性研究，从理论上探讨了材料参数，离心惯性及工作温度对涡轮叶片模态特性的影响。根据Ｈａｍｉｌｔｏｎ原理，推导了考虑离心惯性力影响的涡轮叶片振动方程。给出了材料参数，工作温度对涡轮叶片模态特性影响的解析式。在涡轮转速不十分高时，引入等效弹性模量的概念，得出涡轮转速对叶片模态特性影响的近似公式。     

Aero‐structural investigation of biplane wind turbine blades

As wind turbines grow larger, loads increase dramatically, particularly in the inboard region of the blade. A key problem is to design a strong inboard region that supports these loads without sacrificing too much aerodynamic performance. A new design is proposed: a biplane inboard region that transitions into a joint, which connects to a monoplane outboard region. The objective is to develop biplane inboard configurations that improve the aero‐structural performance of blades. To approximately compare a conventional inboard region with a biplane inboard region, cross‐sectional properties of a thick monoplane and a biplane were measured. Numerical simulations were used to explicitly compare the aerodynamic performance of a thick monoplane with a biplane. Then, several model beams were designed to be simple approximations of a conventional blade (‘monoplane beam’) and the biplane blade (‘biplane beam’). Canonical bending loads were applied to each model beam, and their deflections were compared. Numerical simulations show that the lift‐to‐drag ratio is significantly greater for the biplane than the thick monoplane for 0° < α < 15.5°. A parametric analysis of biplane beam configurations shows that their tip deflections are smaller than monoplane beams of the same length. These benefits for the inboard region of (i) improved aerodynamics and (ii) improved strength could lead to weight reductions in wind turbine blades. Innovations that create lighter blades can make large blades a reality. These results suggest that the biplane blade is an attractive design for large blades. Copyright © 2012 John Wiley & Sons, Ltd.     

Passive control of wind turbine vibrations including blade/tower interaction and rotationally sampled turbulence

This paper investigates the use of a passive control device, namely, a tuned mass damper (TMD), for the mitigation of vibrations due to the along‐wind forced vibration response of a simplified wind turbine. The wind turbine assembly consists of three rotating uniform rotor blades connected to the top of a flexible uniform annular tower, constituting a multi‐body dynamic system. First, the free vibration properties of the tower and rotating blades are each obtained separately using a discrete parameter approach, with those of the tower including the presence of a rigid mass at the top, representing the nacelle, and those of the blade including the effects of centrifugal stiffening due to blade rotation and self‐weight. Drag‐based loading is assumed to act on the rotating blades, in which the phenomenon of rotationally sampled wind turbulence is included. Blade response time histories are obtained using the mode acceleration method, allowing base shear forces due to flapping motion for the three blades to be calculated. The resultant base shear is imparted into the top of the tower. Wind drag loading on the tower is also considered, and includes Davenport‐type spatial coherence information. The tower/nacelle is then coupled with the rotating blades by combining their equations of motion. A TMD is placed at the top of the tower, and when added to the formulation, a Fourier transform approach allows for the solution of the displacement at the top of the tower under compatibility of response conditions. An inverse Fourier transform of this frequency domain response yields the response time history of the coupled blades/tower/damper system. A numerical example is included to qualitatively investigate the influence of the damper. Copyright © 2007 John Wiley & Sons, Ltd.     

Combined analytical/FEA-based coupled aero structure simulation of a wind turbine with bend–twist adaptive blades

The simulation of wind turbines with bend–twist adaptive blades is a coupled aero-structure (CAS) procedure. The blade twist due to elastic coupling is a required parameter for wind turbine performance evaluation and can be predicted through a finite element (FE) structural analyser. FEA-based codes are far too slow to be useful in the aerodynamic design/optimisation of a blade. This paper presents a combined analytical/FEA-based method for CAS simulation of wind turbines utilising bend–twist adaptive blades. This method of simulation employs the induced twist distribution and the flap bending at the hub of the blade predicted through a FEA-based CAS simulation at a reference wind turbine run condition to determine the wind turbine performance at other wind turbine run conditions. This reduces the computational time significantly and makes the aerodynamic design/optimisation of bend–twist adaptive blades practical. Comparison of the results of a case study which applies both combined analytical/FEA-based and FEA-based CAS simulation shows that when using the combined method the required computational time for generating a power curve reduces to less than 5%, while the relative difference between the predicted powers by two methods is only about 1%.     

Aero‐structural dynamics of a flexible hub connection for load reduction on two‐bladed wind turbines

In this study, an innovative concept for load reduction on the two‐bladed Skywind 3.4 MW prototype is presented. The load reduction system consists of a flexible coupling between the hub mount, carrying the drive train components including the hub assembly, and a nacelle carrier supported by the yaw bearing. This paper intends to assess the impact of introducing a flexible hub connection on the system dynamics and the aero‐elastic response to aerodynamic load imbalances. In order to limit the rotational joint motion, a cardanic spring‐damper element is introduced between the hub mount and the nacelle carrier flange, which affects the system response and the loads. A parameter variation of the stiffness and damping of the connecting spring‐damper element has been performed in the multi‐body simulation solver Simpack. A deterministic, vertically sheared wind field is applied to induce a periodic aerodynamic imbalance on the rotor. The aero‐structural load reduction mechanisms of the coupled system are thereby identified. It is shown that the fatigue loads on the blades and the turbine support structure are reduced significantly. For a very low structural coupling, however, the corresponding rotational deflections of the hub mount exceed the design limit of operation. The analysis of the interaction between the hub mount motion and the blade aerodynamics in a transient inflow environment indicates a reduction of the angle of attack amplitudes and the corresponding fluctuations of the blade loading. Hence, it can be concluded that load reduction is achieved by a combination of reduced structural coupling and a mitigation of aerodynamic load imbalances. Copyright © 2016 John Wiley & Sons, Ltd.     

5 MW风力机叶片模态特性分析

为了研究叶片铺层和主梁形式对大型自适应叶片动态特性的影响,利用Ansys软件建立了5 MW风力机叶片的有限元模型.对不同梁帽铺层角度和主梁形式的叶片进行了模态分析,给出了各模型的前十阶固有频率和振型,分析了叶片梁帽铺层角度、主梁形式和转速对风力机叶片固有频率的影响.结果表明：叶片梁帽铺层角度和叶片主梁形式对固有频率具有重要影响;在叶片的弯扭耦合设计过程中,要考虑设计参数对叶片模态特性的影响,以避免叶片发生振动性能失效.     

Optimum aerodynamic design for wind turbine blade with a Rankine vortex wake

This paper presents a model to optimize the distribution of chord and twist angle of horizontal axis wind turbine blades, taking into account the influence of the wake, by using a Rankine vortex. This model is applied to both large and small wind turbines, aiming to improve the aerodynamics of the wind rotor, and particularly useful for the case of wind turbines operating at low tip-speed ratios. The proposed optimization is based on maximizing the power coefficient, coupled with the general relationship between the axial induction factor in the rotor plane and in the wake. The results show an increase in the chord and a slightly decrease in the twist angle distributions as compared to other classical optimization methods, resulting in an improved aerodynamic shape of the blade. An evaluation of the efficiency of wind rotors designed with the proposed model is developed and compared other optimization models in the literature, showing an improvement in the power coefficient of the wind turbine.