Development of an aeroelastic code based on three‐dimensional viscous–inviscid method for wind turbine computations

Aerodynamic and structural dynamic performance analysis of modern wind turbines are routinely estimated in the wind energy field using computational tools known as aeroelastic codes. Most aeroelastic codes use the blade element momentum (BEM) technique to model the rotor aerodynamics and a modal, multi‐body or the finite‐element approach to model the turbine structural dynamics. The present work describes the development of a novel aeroelastic code that combines a three‐dimensional viscous–inviscid interactive method, method for interactive rotor aerodynamic simulations (MIRAS), with the structural dynamics model used in the aeroelastic code FLEX5. The new code, called MIRAS‐FLEX, is an improvement on standard aeroelastic codes because it uses a more advanced aerodynamic model than BEM. With the new aeroelastic code, more physical aerodynamic predictions than BEM can be obtained as BEM uses empirical relations, such as tip loss corrections, to determine the flow around a rotor. Although more costly than BEM, a small cluster is sufficient to run MIRAS‐FLEX in a fast and easy way. MIRAS‐FLEX is compared against the widely used FLEX5 and FAST, as well as the participant codes from the Offshore Code Comparison Collaboration Project. Simulation tests consist of steady wind inflow conditions with different combinations of yaw error, wind shear, tower shadow and turbine‐elastic modeling. Turbulent inflow created by using a Mann box is also considered. MIRAS‐FLEX results, such as blade tip deflections and root‐bending moments, are generally in good agreement with the other codes. Copyright © 2017 John Wiley & Sons, Ltd.     

Dynamic analysis tool development for swept wind turbine blades

Because of their aeroelastic behavior, swept wind turbine blades offer the potential to increase energy capture and lower fatigue loads. This article describes work to develop a dynamic analysis code for swept wind turbine blades. This work was an outgrowth of a U.S. Department of Energy contract on swept blades, where the authors used the Adams? dynamic software (MSC Software Corporation, Santa Ana, CA, USA). The new code is based on the National Renewable Energy Laboratory's FAST code and allows for lower cost analysis and faster computation times for swept blades. The additions to the FAST code include the geometry and mode shapes required for the bending and twisting motion of the swept blade. In addition, a finite element program to determine mode shapes for the swept blade was developed. Comparisons of results obtained with the new code and analytical solutions for a curved cantilever beam show good agreement in local torsional deflections. Comparisons with field data obtained for a 750 kW wind turbine with swept blades were complicated by uncertainties in the test wind speed and turbine controller settings.Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

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.     

Changes in design driving load cases: Operating an upwind turbine with a downwind rotor configuration

This work considers the design driving load cases from a full design load basis analysis on an upwind turbine changed into a downwind configuration. The upwind turbine is a commercial class IIIA 2.1‐MW turbine, manufactured by Suzlon. The downwind turbine shows an increase in the normalized tower clearance by 6%, compared with the upwind concept. Removing the blade prebend increases the normalized minimum tower clearance by 17% in the downwind configuration compared with the upwind configuration. The extreme loads on the longitudinal tower bottom bending moment are seen to generally increase by 17% because of the overhanging gravity moment of the rotor‐nacelle assembly. The extreme blade root bending moments are reduced by 10% flapwise, because of the coning of the rotor in downwind direction. The fatigue loads suffer from the tower shadow, leading to an overall increase of the fatigue loads in the blades with up to 5% in flapwise direction in the downwind configuration. Because of blade deflection and coning direction, the downwind configuration shows a 0.75% lower annual energy production. Removing the prebend increases the annual energy production loss to 1.66%.     

Aeroelastic analysis of a floating offshore wind turbine in platform‐induced surge motion using a fully coupled CFD‐MBD method

Modern offshore wind turbines are susceptible to blade deformation because of their increased size and the recent trend of installing these turbines on floating platforms in deep sea. In this paper, an aeroelastic analysis tool for floating offshore wind turbines is presented by coupling a high‐fidelity computational fluid dynamics (CFD) solver with a general purpose multibody dynamics code, which is capable of modelling flexible bodies based on the nonlinear beam theory. With the tool developed, we demonstrated its applications to the NREL 5 MW offshore wind turbine with aeroelastic blades. The impacts of blade flexibility and platform‐induced surge motion on wind turbine aerodynamics and structural responses are studied and illustrated by the CFD results of the flow field, force, and wake structure. Results are compared with data obtained from the engineering tool FAST v8.     

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.     

Aeroelastic analysis of a wind turbine blade using the harmonic balance method

An aeroelastic model for wind turbine blades derived from the unsteady Navier‐Stokes equations and a mode shape–based structural dynamics model are presented. For turbulent flows, the system is closed with the Spalart‐Allmaras turbulence model. The computation times for the aerodynamic solution are significantly reduced using the harmonic balance method compared to a time‐accurate solution. This model is significantly more robust than standard aeroelastic codes that rely on blade element momentum theory to determine the aerodynamic forces. Comparisons with published results for the Caradonna‐Tung rotor in hover and the classical AGARD 445.6 flutter case are provided to validate the aerodynamic model and aeroelastic model, respectively. For wind turbines, flutter of the 1.5 MW WindPACT blade is considered. The results predict that the first flapwise and edgewise modes dominate flutter at the rotor speeds considered.     

Aeroelastic validation and Bayesian updating of a downwind wind turbine

Downwind wind turbine blades are subjected to tower wake forcing at every rotation, which can lead to structural fatigue. Accurate characterisation of the unsteady aeroelastic forces in the blade design phase requires detailed representation of the aerodynamics, leading to computationally expensive simulation codes, which lead to intractable uncertainty analysis and Bayesian updating. In this paper, a framework is developed to tackle this problem. Full, detailed aeroelastic model of an experimental wind turbine system based on 3‐D Reynolds‐averaged Navier‐Stokes is developed, considering all structural components including nacelle and tower. This model is validated against experimental measurements of rotating blades, and a detailed aeroelastic characterisation is presented. Aerodynamic forces from prescribed forced‐motion simulations are used to train a time‐domain autoregressive with exogenous input (ARX) model with a localised forcing term, which provides accurate and cheap aeroelastic forces. Employing ARX, prior uncertainties in the structural and rotational parameters of the wind turbine are introduced and propagated to obtain probabilistic estimates of the aeroelastic characteristics. Finally, the experimental validation data are used in a Bayesian framework to update the structural and rotational parameters of the system and thereby reduce uncertainty in the aeroelastic characteristics.     

BeamDyn: a high‐fidelity wind turbine blade solver in the FAST modular framework

This paper presents a numerical implementation of the geometrically exact beam theory based on the Legendre‐spectral‐finite‐element (LSFE) method. The displacement‐based geometrically exact beam theory is presented, and the special treatment of three‐dimensional rotation parameters is reviewed. An LSFE is a high‐order finite element with nodes located at the Gauss–Legendre–Lobatto points. These elements can be an order of magnitude more computationally efficient than low‐order finite elements for a given accuracy level. The new module, BeamDyn, is implemented in the FAST modularization framework for dynamic simulation of highly flexible composite‐material wind turbine blades within the FAST aeroelastic engineering model. The framework allows for fully interactive simulations of turbine blades in operating conditions. Numerical examples are provided to validate BeamDyn and examine the LSFE performance as well as the coupling algorithm in the FAST modularization framework. BeamDyn can also be used as a stand‐alone high‐fidelity beam tool. Copyright © 2017 John Wiley & Sons, Ltd.     

Load analysis of hydraulic‐pneumatic flywheel configurations integrated in a wind turbine rotor

In this paper, the impact on the mechanical loads of a wind turbine due to a previously proposed hydraulic‐pneumatic flywheel system is analysed. Load simulations are performed for the National Renewable Energy Laboratory (NREL) 5‐MW wind turbine using fatigue, aerodynamics, structures, and turbulence (FAST). It is discussed why FAST is applied although it cannot simulate variable rotor inertia. Several flywheel configurations, which increase the rotor inertia of the 5‐MW wind turbine by 15%, are implemented in the 61.5‐m rotor blade. Load simulations are performed twice for each configuration: Firstly, the flywheel system is discharged, and secondly, the flywheel is charged. The change in ultimate and fatigue loads on the tower, the low speed shaft, and the rotor blades is juxtaposed for all flywheel configurations. As the blades are mainly affected by the flywheel system, the increase in ultimate and fatigue loads of the blade is evaluated. Simulation results show that the initial design of the flywheel system causes the lowest impact on the mechanical loads of the rotor blades although this configuration is the heaviest.     

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.     

Wind tunnel and numerical study of a small vertical axis wind turbine

This paper presents a combined experimental and computational study into the aerodynamics and performance of a small scale vertical axis wind turbine (VAWT). Wind tunnel tests were carried out to ascertain overall performance of the turbine and two- and three-dimensional unsteady computational fluid dynamics (CFD) models were generated to help understand the aerodynamics of this performance.Wind tunnel performance results are presented for cases of different wind velocity, tip-speed ratio and solidity as well as rotor blade surface finish. It is shown experimentally that the surface roughness on the turbine rotor blades has a significant effect on performance. Below a critical wind speed (Reynolds number of 30,000) the performance of the turbine is degraded by a smooth rotor surface finish but above it, the turbine performance is enhanced by a smooth surface finish. Both two bladed and three bladed rotors were tested and a significant increase in performance coefficient is observed for the higher solidity rotors (three bladed rotors) over most of the operating range. Dynamic stalling behaviour and the resulting large and rapid changes in force coefficients and the rotor torque are shown to be the likely cause of changes to rotor pitch angle that occurred during early testing. This small change in pitch angle caused significant decreases in performance.The performance coefficient predicted by the two dimensional computational model is significantly higher than that of the experimental and the three-dimensional CFD model. The predictions show that the presence of the over tip vortices in the 3D simulations is responsible for producing the large difference in efficiency compared to the 2D predictions. The dynamic behaviour of the over tip vortex as a rotor blade rotates through each revolution is also explored in the paper.     

Shake table testing and numerical simulation of a utility‐scale wind turbine including operational effects

Shake table tests were undertaken on an actual wind turbine (65 kW rated power, 22.6 m hub height and a 16 m rotor diameter) using the Network for Earthquake Engineering Simulation Large High Performance Outdoor Shake Table at the University of California, San Diego. Each base shaking event was imparted in two states, whereas the turbine rotor was still (parked), and while it was spinning (operational). Each state was tested in two orientations of shaking direction, one parallel (fore‐aft) and another perpendicular (side‐to‐side) to the axis of rotation of the rotor. Structural response characteristics are presented for motions imparted in both configurations and both operational states. Modal parameters (natural frequencies, damping ratios and mode shapes) were estimated throughout the testing program. It is found that shaking imparted in the fore‐aft direction while spinning is the only observed situation where operational effects appear significant, with reductions up to 33% in seismic bending moment demand near the tower base. Using modifications developed by the research team to the FAST code, experimental results are compared with corresponding simulations to show that dynamic characteristics, acceleration time histories and trends in tower bending seismic demand can be numerically approximated. This experimental evidence and associated numerical simulations suggest that modeling of combined wind and earthquake loading with existing turbine specific codes produce meaningful results. Discrepancies between experimental and numerical results support that further refinement of simulation codes can improve accuracy beyond the current state. Copyright © 2013 John Wiley & Sons, Ltd.     

Predicting wind turbine blade loads and aeroelastic response using a coupled CFD–CSD method

The aeroelastic response and the airloads of horizontal-axis wind turbine rotor blades were numerically investigated using a coupled CFD–CSD method. The blade aerodynamic loads were obtained from a Navier–Stokes CFD flow solver based on unstructured meshes. The blade elastic deformation was calculated using a FEM-based CSD solver which employs a nonlinear coupled flap-lag-torsion beam theory. The coupling of the CFD and CSD solvers was accomplished in a loosely coupled manner by exchanging the information between the two solvers at infrequent intervals. At first, the present coupled CFD–CSD method was applied to the NREL 5MW reference wind turbine rotor under steady axial flow conditions, and the mean rotor loads and the static blade deformation were compared with other predicted results. Then, the unsteady blade aerodynamic loads and the dynamic blade response due to rotor shaft tilt and tower interference were investigated, along with the influence of the gravitational force. It was found that due to the aeroelastic blade deformation, the blade aerodynamic loads are significantly reduced, and the unsteady dynamic load behaviors are also changed, particularly by the torsional deformation. From the observation of the tower interference, it was also found that the aerodynamic loads are abruptly reduced as the blades pass by the tower, resulting in oscillatory blade deformation and vibratory loads, particularly in the flapwise direction.     

Whirl flutter analysis of a horizontal-axis wind turbine with a two-bladed teetering rotor

An investigation to explore the possibility of whirl flutter and to find the effect of pitch-flap coupling (δ₃) on teetering motion of the DOE/NASA Mod-2 wind turbine is presented. The equations of motion are derived for an idealized five-degree-of-freedom mathematical model of a horizontal-axis wind turbine with a two-bladed teetering rotor. The model accounts for the out-of-plane bending motion of each blade, the teetering motion of the rotor, and both the pitching and yawing motions of the rotor support. Results show that the Mod-2 design is free from whirl flutter. Selected results are presented indicating the effect of variations in rotor support damping, rotor support stiffnes, and δ₃ on pitching, yawing, teetering, and blade bending motions.     

1.5MW风力机整机定常及非定常数值模拟

本文运用计算流体力学方法,以1.5 MW风力机为例,对风力机整机三维模型的空气动力学特性开展研究。针对三翼型风力机叶片,利用改进的Wilson方法进行气动设计,并通过寻找各截面最佳雷诺数的方法进行优化修正。建立了整机三维模型,设计流域并划分网格,定义边界及区域。最后对上述模型进行额定工况下定常与非定常数值模拟,利用模拟结果开展有关压力、失速特性等空气动力学特性的分析。结果表明：非定常模拟在风轮背面上的平均压力比定常小,使风轮前后压差变大,输出功率加大,其主要原因是叶尖出力的增加;旋转使得风力机叶片发生流体分离延迟,且产生更高的升力系数。     

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.     

Simulation of wind turbine wake interaction using the vorticity transport model

The aerodynamic interactions that can occur within a wind farm can result in the constituent turbines generating a lower power output than would be possible if each of the turbines were operated in isolation. Tightening of the constraints on the siting of wind farms is likely to increase the scale of the problem in the future. The aerodynamic performance of turbine rotors and the mechanisms that couple the fluid dynamics of multiple rotors can be most readily understood by simplifying the problem and considering the interaction between only two rotors. The aerodynamic interaction between two rotors in both co‐axial and offset configurations has been simulated using the Vorticity Transport Model. The aerodynamic interaction is a function of the tip speed ratio, and both the streamwise and crosswind separation between the rotors. The simulations show that the momentum deficit at a turbine operating within the wake developed by the rotor of a second turbine is governed by the development of instabilities within the wake of the upwind rotor, and the ensuing structure of the wake as it impinges on the downwind rotor. If the wind farm configuration or wind conditions are such that a turbine rotor is subject to partial impingement by the wake produced by an upstream turbine, then significant unsteadiness in the aerodynamic loading on the rotor blades of the downwind turbine can result, and this unsteadiness can have considerable implications for the fatigue life of the blade structure and rotor hub. Copyright © 2009 John Wiley & Sons, Ltd.     

Experimental study of the wake interaction between two vertical axis wind turbines

Wakes and wake interactions in wind turbine arrays diminish energy output and raise the risk of structural fatigue; hence, comprehending the features of rotor–wake interactions is of practical relevance. Previous studies suggest that vertical axis wind turbines (VAWTs) can facilitate a quicker wake recovery. This study experimentally investigates the rotor–wake and wake–wake interaction of VAWTs; different pitch angles of the blades of the upwind VAWT are considered to assess the interactions for different wake deflections. With stereoscopic particle image velocimetry, the wake interactions of two VAWTs are analysed in nine distinct wake deflection and rotor location configurations. The time-average velocity fields at several planes upwind and downwind from the rotors are measured. Additionally, time-average loads on the VAWTs are measured via force balances. The results validate the rapid wake recovery and the efficacy of wake deflection, which increases the available power in the second rotor.