Wind turbine blade vibration at standstill conditions—the effect of imposing lag on the aerodynamic response of an elastically mounted airfoil

The present study investigated physical phenomena related to stall‐induced vibrations potentially existing on wind turbine blades at standstill conditions. The study considered two‐dimensional airfoil sections while it omitted three‐dimensional effects. In the study, a new engineering‐type computational model for the aeroelastic response of an elastically mounted airfoil was used to investigate the influence of temporal lag in the aerodynamic response on the aeroelastic stability in deep stall. The study indicated that even a relatively low lag significantly increases the damping of the model. A comparison between the results from a model with lag imposed on all force components with the results from a model with lag imposed exclusively on the lift showed only marginal difference between the damping in the two cases. A parameter study involving positions of the elastic hinge point and the center of gravity indicated that the stability is relatively independent of these parameters. Another parameter study involving spring constants showed that the stability of each mode is dependent only on the spring constant acting in the direction of the leading motion of the mode. An investigation of the influence of the added mass terms showed that only the pitch‐rate and flapwise‐acceleration terms have any influence on the stability. An investigation of three different profiles showed that the stability is heavily dependent on the aerodynamic characteristics of the profiles—mainly on the lift. It was also shown that only the edgewise mode is unstable in deep stall. Moreover, independent of the amount of temporal lag in the aerodynamic response of the model, the inflow‐angle region in the vicinity of 180° remains unstable in the edgewise mode. Therefore, this inflow‐angle region may create stability problems in real life. The other type of vibrations potentially present at standstill conditions is vortex‐induced, being outside the scope of the present study. Copyright © 2014 John Wiley & Sons, Ltd.     

Self‐induced vibrations of a DU96‐W‐180 airfoil in stall

This work presents an analysis of two‐dimensional (2D) and three‐dimensional (3D) non‐moving, prescribed motion and elastically mounted airfoil computational fluid dynamics (CFD) computations. The elastically mounted airfoil computations were performed by means of a 2D structural model with two degrees of freedom. The computations aimed at investigating the mechanisms of both vortex‐induced and stall‐induced vibrations related to a wind turbine blade at standstill conditions. In this work, a DU96‐W‐180 airfoil was used in the angle‐of‐attack region potentially corresponding to stall‐induced vibrations. The analysis showed significant differences between the aerodynamic stability limits predicted by 2D and 3D CFD computations. A general agreement was reached between the prescribed motion and elastically mounted airfoil computations. 3D computations indicated that vortex‐induced vibrations are likely to occur at modern wind turbine blades at standstill. In contrast, the predicted cut‐in wind speed necessary for the onset of stall‐induced vibrations appeared high enough for such vibrations to be unlikely. Copyright © 2013 John Wiley & Sons, Ltd.     

Vortex‐induced vibrations on a modern wind turbine blade

This article investigates the aero‐elastic response of the DTU 10‐MW RWT blade in deep stall conditions with angles of attack in the vicinity of 90 degrees. The simulations were conducted with the high‐fidelity fluid–structure interaction simulation tool HAWC2CFD employing the multi‐body‐based structural model of HAWC2 and the incompressible computational fluid dynamics solver EllipSys3D. The study utilizes detached eddy simulation computations and considers the three‐dimensional blade geometry including blade twist and taper. A preliminary frequency analysis of the load variations on a stiff blade showed that an inclined inflow with a velocity component along the blade axis can trigger a spanwise correlated vortex shedding over large parts of the blade. Moderate wind speeds were sufficient to generate vortex shedding with frequencies close to the first edgewise eigenfrequency of the blade. Aero‐elastic computations of the elastic blade confirmed the findings of the frequency analysis. Inflow conditions with inclination angles between Ψ = 20° and Ψ = 55° and relatively low to moderate wind speeds between V = 16 and V = 26ms^?1 were sufficient to trigger severe edgewise blade vibrations with blade tip amplitudes of several metres. The investigated inflow conditions are considered realistic and might occur when the wind turbine is idling or standing still and the yaw system is unable to align the wind turbine with the incoming wind. Copyright © 2016 John Wiley & Sons, Ltd.     

Parabolic RANS solver for low‐computational‐cost simulations of wind turbine wakes

A numerical framework for simulations of wake interactions associated with a wind turbine column is presented. A Reynolds‐averaged Navier‐Stokes (RANS) solver is developed for axisymmetric wake flows using parabolic and boundary‐layer approximations to reduce computational cost while capturing the essential wake physics. Turbulence effects on downstream evolution of the time‐averaged wake velocity field are taken into account through Boussinesq hypothesis and a mixing length model, which is only a function of the streamwise location. The calibration of the turbulence closure model is performed through wake turbulence statistics obtained from large‐eddy simulations of wind turbine wakes. This strategy ensures capturing the proper wake mixing level for a given incoming turbulence and turbine operating condition and, thus, accurately estimating the wake velocity field. The power capture from turbines is mimicked as a forcing in the RANS equations through the actuator disk model with rotation. The RANS simulations of the wake velocity field associated with an isolated 5‐MW NREL wind turbine operating with different tip speed ratios and turbulence intensity of the incoming wind agree well with the analogous velocity data obtained through high‐fidelity large‐eddy simulations. Furthermore, different cases of columns of wind turbines operating with different tip speed ratios and downstream spacing are also simulated with great accuracy. Therefore, the proposed RANS solver is a powerful tool for simulations of wind turbine wakes tailored for optimization problems, where a good trade‐off between accuracy and low‐computational cost is desirable.     

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.     

Wake modelling of a VAWT in dynamic stall: impact on the prediction of flow and induction fields

Dynamic stall is a relevant phenomenon in the design and operation of a vertical axis wind turbine (VAWT) as it impacts loading, control and wake dynamics. Although streamtube models and single‐wake vortex models are commonly used for VAWT simulation, they either do not explicitly simulate the distribution of vorticity in the wake (streamtube models) or simplify it into a single‐wake release point (single‐wake vortex models). This can lead to inaccurate predictions of the vorticity distribution and wake dynamics, and therefore of the induction field, rotor loading and wake development, including wake mixing and re‐energizing. In this work, we use a double‐wake panel model developed for the simulation of dynamic stall in a VAWT to analyse (i) what is the flow field in dynamic stall, including the induction field, (ii) what is the error due to assuming a simplified wake, in both vorticity distribution and induction and (iii) how an incorrect simulation of the vorticity distribution can affect the prediction of the dynamics of the near and far wake. The results demonstrate that for mild separation (tip speed ratio λ≥3), single‐wake models can produce acceptable results. However, for lower tip speed ratios (λ < 3), the inaccuracy in the prediction of loads, induction field and vorticity distribution becomes significant because of an inadequate representation of the wake dynamics. These results imply that using lower order models can lead to inaccurate estimations of loads, performance and power control requirements at low tip speed ratios. Copyright © 2014 John Wiley & Sons, Ltd.     

水平轴风力机翼型大攻角分离流动的数值模拟

翼型的失速特性是失调速节型水风力机的气动性能分析和颤振分析的基础，许多涉及这类问题的研究大多只给出了翼型刚开始失速时的计算结果，然而在正常运行工况下叶片端部翼型的深失速特性是风力机的最关键的一类问题，通过求解二维非常，可压的Ｎ－Ｓ方程计算了风力机常用翼型ＮＡＣＡ４４１８的绕流特性，Ｎ－Ｓ方程在贴体坐标系中给出用Ｐｏｉｓｓｏｎ方程法生成了Ｃ型网格，数值计算了采用了一种改进的ＬＵ－ＳＧＳ格式。将翼型的     

Fluid–structure interaction computations for geometrically resolved rotor simulations using CFD

This paper presents a newly developed high‐fidelity fluid–structure interaction simulation tool for geometrically resolved rotor simulations of wind turbines. The tool consists of a partitioned coupling between the structural part of the aero‐elastic solver HAWC2 and the finite volume computational fluid dynamics (CFD) solver EllipSys3D. The paper shows that the implemented loose coupling scheme, despite a non‐conservative force transfer, maintains a sufficient numerical stability and a second‐order time accuracy. The use of a strong coupling is found to be redundant. In a first test case, the newly developed coupling between HAWC2 and EllipSys3D (HAWC2CFD) is utilized to compute the aero‐elastic response of the NREL 5‐MW reference wind turbine (RWT) under normal operational conditions. A comparison with the low‐fidelity but state‐of‐the‐art aero‐elastic solver HAWC2 reveals a very good agreement between the two approaches. In a second test case, the response of the NREL 5‐MW RWT is computed during a yawed and thus asymmetric inflow. The continuous good agreement confirms the qualities of HAWC2CFD but also illustrates the strengths of a computationally cheaper blade element momentum theory (BEM) based solver, as long as the solver is applied within the boundaries of the employed engineering models. Two further test cases encompass flow situations, which are expected to exceed the limits of the BEM model. However, the simulation of the NREL 5‐MW RWT during an emergency shut down situation still shows good agreements in the predicted structural responses of HAWC2 and HAWC2CFD since the differences in the computed force signals only persist for an insignificantly short time span. The considerable new capabilities of HAWC2CFD are finally demonstrated by simulating vortex‐induced vibrations on the DTU 10‐MW wind turbine blade in standstill. Copyright © 2016 John Wiley & Sons, Ltd.     

Optimized linearization of chord and twist angle profiles for fixed-pitch fixed-speed wind turbine blades

The chord and twist angle radial profiles of a fixed-pitch fixed-speed (FPFS) horizontal-axis wind turbine blade are based on a particular design wind speed and design tip speed ratio. Because the tip speed ratio varies with wind speed, the originally optimized chord and twist angle radial profiles for a preliminary blade design through optimum rotor theory do not necessarily provide the highest annual energy production (AEP) for the wind turbine on a specific site with known wind resources. This paper aims to demonstrate a novel optimal blade design method for an FPFS wind turbine through adopting linear radial profiles of the blade chord and twist angle and optimizing the slope of these two lines. The radial profiles of the blade chord and twist angle are linearized on a heuristic basis with fixed values at the blade tip and floating values at the blade root based on the preliminary blade design, and the best solution is determined using the highest AEP for a particular wind speed Weibull distribution as the optimization criteria with constraints of the top limit power output of the wind turbine. The outcomes demonstrate clearly that the proposed blade design optimization method offers a good opportunity for FPFS wind turbine blade design to achieve a better power performance and low manufacturing cost. This approach can be used for any practice of FPFS wind turbine blade design and refurbishment.     

Analysis of throw distances of detached objects from horizontal‐axis wind turbines

This paper aims at predicting trajectories of the detached fragments from wind turbines, in order to better quantify consequences of wind turbine failures. The trajectories of thrown objects are attained using the solution to equations of motion and rotation, with the external loads and moments obtained using blade element approach. We have extended an earlier work by taking into account dynamic stall and wind variations due to shear, and investigated different scenarios of throw including throw of the entire or a part of blade, as well as throw of accumulated ice on the blade. Trajectories are simulated for modern wind turbines ranging in size from 2 to 20 MW using upscaling laws. Extensive parametric analyses are performed against initial release angle, tip speed ratio, detachment geometry, and blade pitch setting. It is found that, while at tip speeds of about 70 m/s (normal operating conditions), pieces of blade (with weights in the range of approximately 7‐16 ton) would be thrown out less than 700 m for the entire range of wind turbines, and turbines operating at the extreme tip speed of 150 m/s may be subject to blade throw of up to 2 km from the turbine. For the ice throw cases, maximum distances of approximately 100 and 600 m are obtained for standstill and normal operating conditions of the wind turbine, respectively, with the ice pieces weighting from 0.4 to 6.5 kg. The simulations can be useful for revision of wind turbine setback standards, especially when combined with risk assessment studies. Copyright © 2015 John Wiley & Sons, Ltd.     

An insight into the separate flow and stall delay for HAWT

The flow characteristics and the stall delay phenomenon of wind turbine rotor due to blade rotation in the steady state non-yawed conditions are investigated. An incompressible Reynolds-averaged Navier–Stokes solver is applied to carry out all the cases at different wind speeds from 5 m/s to 10 m/s with an interval of 1 m/s. CFD results turn out to agree well with experimental ones at incoming wind speeds below 10 m/s, though at 10 m/s some deviations exist due to the relative large flow separation and 3D spanwise flow over the suction surface of the blade. In the meanwhile, a lifting surface code with and without Du–Selig stall delay model is used to predict the power. A MATLAB code is developed to extract aerodynamic force coefficients from 3D CFD computations which are compared with the 2D airfoil wind tunnel experiment to demonstrate the stall delay and augmented lift phenomenon particularly at inboard span locations of the blade. The computational results are compared with the corrected value by the Du–Selig model and a lifting surface method derived data based on the measurements of the Unsteady Aerodynamic Experiment at the NASA Ames wind tunnel.     

Simulating dynamic stall in a two‐dimensional vertical‐axis wind turbine: verification and validation with particle image velocimetry data

The implementation of wind energy conversion systems in the built environment has renewed the interest and the research on Vertical Axis Wind Turbines (VAWTs). The VAWT has an inherent unsteady aerodynamic behavior due to the variation of angle of attack and perceived velocity with azimuth angle. The phenomenon of dynamic stall is then an intrinsic effect of the operation at low tip speed ratios, impacting both loads and power. The complexity of the problem and the need for new design approaches for VAWTs for the built environment have driven the authors to focus this research on the CFD modeling of VAWTs on:

• Comparing the results between commonly used turbulence models: Unsteady Reynolds Averaged Navier‐Stokes – URANS (Spalart‐Allmaras and k‐?) and large eddy models (Large Eddy Simulation and Detached Eddy Simulation).
• Verifying the sensitivity of the model to its grid refinement (space and time).
• Evaluating the suitability of using Particle Image Velocimetry (PIV) experimental data for model validation.

The current work investigates the impact of accurately modeling the separated shed wake resulting from dynamic stall, and the importance of validation of the flow field rather than validation with only load data. The structure and magnitude of the wake are validated with PIV results, and it demonstrated that the accuracy of the different models in simulating a correct wake structure has a large impact in loads.     

垂直轴风力机变桨控制策略及气动性能影响研究

以H型Darrieus垂直轴风力机为研究对象,基于不同尖速比下攻角随相位角变化规律,提出一种俯仰角控制策略,即攻角较大时俯仰变化幅值较大,而攻角较小时幅值较小。通过数值计算了解此控制方式对气动性能的影响规律,分析变桨后不同旋转角度下风力机涡量场的变化,并讨论气动载荷变化的原因。结果表明：所提俯仰角控制策略可显著增强风力机功率系数,且尖速比较低时提升效果越显著,在TSR为1.25时功率系数提升高达146%。     

Spectral analysis of New MEXICO standstill measurements to investigate vortex shedding in deep stall

Spectral analysis was performed on the time series data computed from pressure measurements on the New MEXICO (Model Rotor Experiments under Controlled Conditions) rotor in standstill conditions. As a priori, 3D airfoil polars were recreated from standstill measurements and compared against 2D airfoil polars and flat plate theory results to verify the measurements. The spectral analysis revealed the presence of dominant shedding frequencies for certain ranges of the geometric angle of attack. Two dominant shedding modes were identified: One was associated with bluff body vortex shedding, and the other was associated with low Strouhal number shedding. No dominant shedding frequencies were observed for angles of attack beyond 50°. The research improves on our current understanding of the unsteady nature of the stall regime, along with providing insight into the existence of vortex‐induced vibrations on a wind turbine in standstill conditions.     

A deep learning framework for hydrogen-fueled turbulent combustion simulation

The high cost of high-resolution computational fluid/flame dynamics (CFD) has hindered its application in combustion related design, research and optimization. In this study, we propose a new framework for turbulent combustion simulation based on the deep learning approach. An optimized deep convolutional neural network (CNN) inspired by a U-Net architecture and inception module is designed for constructing the framework of the deep learning solver, named CFDNN. CFDNN is then trained on the simulation results of hydrogen combustion in a cavity with different inlet velocities. After training, CFDNN can not only accurately predict the flow and combustion fields within the range of the training set, but also shows an extrapolation ability for prediction outside the training set. The results from the CFDNN solver show excellent consistency with conventional CFD results in terms of both predicted spatial distributions and temporal dynamics. Meanwhile, two orders of magnitude of acceleration is achieved by using the CFDNN solver compared to a conventional CFD solver. The successful development of such a deep learning-based solver opens up new possibilities of low-cost, high-accuracy simulations, fast prototyping, design optimization and real-time control of combustion systems such as gas turbines and scramjets.     

Structural design of spars for 100-m biplane wind turbine blades

Large wind turbine blades are being developed at lengths of 75–100 m, in order to improve energy capture and reduce the cost of wind energy. Bending loads in the inboard region of the blade make large blade development challenging. The “biplane blade” design was proposed to use a biplane inboard region to improve the design of the inboard region and improve overall performance of large blades. This paper focuses on the design of the internal “biplane spar” structure for 100-m biplane blades. Several spars were designed to approximate the Sandia SNL100-00 blade (“monoplane spar”) and the biplane blade (“biplane spar”). Analytical and computational models are developed to analyze these spars. The analytical model used the method of minimum total potential energy; the computational model used beam finite elements with cross-sectional analysis. Simple load cases were applied to each spar and their deflections, bending moments, axial forces, and stresses were compared. Similar performance trends are identified with both the analytical and computational models. An approximate buckling analysis shows that compressive loads in the inboard biplane region do not exceed buckling loads. A parametric analysis shows biplane spar configurations have 25–35% smaller tip deflections and 75% smaller maximum root bending moments than monoplane spars of the same length and mass per unit span. Root bending moments in the biplane spar are largely relieved by axial forces in the biplane region, which are not significant in the monoplane spar. The benefits for the inboard region could lead to weight reductions in wind turbine blades. Innovations that create lighter blades can make large blades a reality, suggesting that the biplane blade may be an attractive design for large (100-m) blades.     

Stall characteristics and tip clearance effects in forward swept axial compressor rotors

Tilting the blade sections to the flow direction (blade sweep) would increase the operating range of an axial compressor due to modifications in the pressure and velocity fields on the suction surface. On the other hand, blade tip gap, though finite, has great influence on the performance of a turbomachine. The present paper investigates the combined effect of these two factors on various flow characteristics in a low speed axial flow compressor. For this present study, nine computational domains were modeled; three rotor sweep configurations (0°, 20° and 30°) and for three different clearance levels for each rotor. Commercial CFD solver ANSYS CFX 11.0 is used for the simulations. Results indicated that tip chordline sweep is found to improve the stall margin of the compressor by modifying the suction surface boundary layer migration phenomenon. Diffusion Factor (DF) contours showed the severity of stalling with unswept rotor. For the swept rotors, the zones of high probable stall are less severe and they become less in size with increasing sweep. Increment in the tip gap is found to gradually affect the performance of unswept rotor, while the effect is very high for the two swept rotors for the earlier increments. As a minimum clearance is unavoidable, swept rotors suffer relatively higher deviation from the idealistic behavior than the unswept rotor due to tip clearance.     

A new stall delay algorithm for predicting the aerodynamics loads on wind turbine blades for axial and yawed conditions

Stall delay is a complicated phenomenon that has gained for many years the attention of industry and academics in the fields of helicopter and wind turbine aerodynamics. Since most of the potential flow theories still rely on the use of 2D aerofoil data for simulating loads on a rotating blade, less degree of accuracy is expected because of 3D rotational effects. In this work, a new model for correcting the 2D steady aerodynamic data for 3D effects is presented. The model can reduce the uncertainty in the blade design process and, subsequently, make wind turbines more cost‐effective. This model combines the stall delay model of Corrigan and Schillings, a modified version of an inviscid stall delay model, a new modification factor to account for the effect of the angle of attack changes and a new tip loss factor. Furthermore, the model applies the use of the separation factor of Du and Selig to evaluate the area on the rotor disc where stall delay is most prominent. The new stall delay model was embedded in a free‐wake vortex model to estimate the aerodynamic loads on the National Renewable Energy Laboratory Phase VI rotor blades consisting of the S809 aerofoil sections. The results in this study confirm the validity of the 3D corrections by the proposed new model under both axial and yawed flow conditions. Copyright © 2017 John Wiley & Sons, Ltd.     

New vortex‐lift and tangential‐force models for HAWT aerodynamic load prediction

Horizontal axis wind turbines (HAWTs) experience three‐dimensional rotational and unsteady aerodynamic phenomena at the rotor blades sections. These highly unsteady three‐dimensional effects have a dramatic impact on the aerodynamic load distributions on the blades, in particular, when they occur at high angles of attack due to stall delay and dynamic stall. Unfortunately, there is no complete understanding of the flow physics yet at these unsteady 3D flow conditions, and hence, the existing published theoretical models are often incapable of modelling the impact on the turbine response realistically. The purpose of this paper is to provide an insight on the combined influence of the stall delay and dynamic stall on the blade load history of wind turbines in controlled and uncontrolled conditions. New dynamic stall vortex and nonlinear tangential force coefficient modules, which integrally take into account the three dimensional rotational effect, are also proposed in this paper. This module along with the unsteady influence of turbulent wind speed and tower shadow is implemented in a blade element momentum (BEM) model to estimate the aerodynamic loads on a rotating blade more accurately. This work presents an important step to help modelling the combined influence of the stall delay and dynamic stall on the load history of the rotating wind turbine blades which is vital to have lighter turbine blades and improved wind turbine design systems.     

Assessment of a comprehensive aeroelastic tool for horizontal‐axis wind turbine rotor analysis

This paper presents the development of a computational aeroelastic tool for the analysis of performance, response and stability of horizontal‐axis wind turbines. A nonlinear beam model for blades structural dynamics is coupled with a state‐space model for unsteady sectional aerodynamic loads, including dynamic stall effects. Several computational fluid dynamics structural dynamics coupling approaches are investigated to take into account rotor wake inflow influence on downwash, all based on a Boundary Element Method for the solution of incompressible, potential, attached flows. Sectional steady aerodynamic coefficients are extended to high angles of attack in order to characterize wind turbine operations in deep stall regimes. The Galerkin method is applied to the resulting aeroelastic differential system. In this context, a novel approach for the spatial integration of additional aerodynamic states, related to wake vorticity and dynamic stall, is introduced and assessed. Steady‐periodic blade responses are evaluated by a harmonic balance approach, whilst a standard eigenproblem is solved for aeroelastic stability analyses. Drawbacks and potentialities of the proposed model are investigated through numerical and experimental comparisons, with particular attention to rotor blades unsteady aerodynamic modelling issues. Copyright © 2016 John Wiley & Sons, Ltd.