Shape optimization of wind turbine blades

This paper presents a design tool for optimizing wind turbine blades. The design model is based on an aerodynamic/aero‐elastic code that includes the structural dynamics of the blades and the Blade Element Momentum (BEM) theory. To model the main aero‐elastic behaviour of a real wind turbine, the code employs 11 basic degrees of freedom corresponding to 11 elastic structural equations. In the BEM theory, a refined tip loss correction model is used. The objective of the optimization model is to minimize the cost of energy which is calculated from the annual energy production and the cost of the rotor. The design variables used in the current study are the blade shape parameters, including chord, twist and relative thickness. To validate the implementation of the aerodynamic/aero‐elastic model, the computed aerodynamic results are compared to experimental data for the experimental rotor used in the European Commision‐sponsored project Model Experiments in Controlled Conditions, (MEXICO) and the computed aero‐elastic results are examined against the FLEX code for flow past the Tjæreborg 2 MW rotor. To illustrate the optimization technique, three wind turbine rotors of different sizes (the MEXICO 25 kW experimental rotor, the Tjæreborg 2 MW rotor and the NREL 5 MW virtual rotor) are applied. The results show that the optimization model can reduce the cost of energy of the original rotors, especially for the investigated 2 MW and 5 MW rotors. Copyright © 2009 John Wiley & Sons, Ltd.     

Isogeometric based framework for aeroelastic wind turbine blade analysis

A framework based on isogeometric analysis is presented for parametrizing a wind turbine rotor blade and evaluating its response. The framework consists of a multi‐fidelity approach for wind turbine rotor analysis. The aeroelastic loads are determined using a low‐fidelity model. The model is based on isogeometric approach to model both the structural and aerodynamic properties. The structural deformations are solved using an isogeometric formulation of geometrically exact 3D beam theory. The aerodynamic loads are calculated using a standard Blade Element Momentum(BEM) theory. Moreover, the aerodynamic loads calculated using BEM theory are modified to account for the change in the blade shape due to blade deformation. The aeroelastic loads are applied in finite element solver Nastran, and both the stress response and buckling response are extracted. Furthermore, the capabilities of Nastran are extended such that design dependent loads can be applied, resulting in correct aeroelastic sensitivities of Nastran responses, making this framework suitable for optimization. The framework is verified against results from the commercial codes FAST and GH Bladed, using the NREL 61.5m rotor blade as a baseline for comparison, showing good agreement. Copyright © 2016 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.     

Aerodynamic wind-turbine rotor design using surrogate modeling and three-dimensional viscous–inviscid interaction technique

In this paper a surrogate optimization methodology using a three-dimensional viscous-inviscid interaction code for the aerodynamic design of wind-turbine rotors is presented. The framework presents a unique approach because it does not require the commonly-used blade element momentum (BEM) method. The three-dimensional viscous-inviscid interaction code used here is the accurate and fast MIRAS code developed at the Technical University of Denmark. In comparison with BEM, MIRAS is a higher-fidelity aerodynamic tool and thus more computationally expensive as well. Designing a rotor using MIRAS instead of an inexpensive BEM code represents a challenge, which is resolved by using the proposed surrogate-based approach. As a verification case, the methodology is applied to design a model wind-turbine rotor and is compared in detail with the one designed with BEM. Results demonstrate that nearly identical aerodynamic performance can be achieved using the new design method and that the methodology is effective for the aerodynamic design of wind-turbine rotors.     

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.     

Effect of rotor–tower interaction,tilt angle,and yaw misalignment on the aeroelasticity of a large horizontal axis wind turbine with composite blades

This paper presents a detailed analysis of the rotor–tower interaction and the effects of the rotor's tilt angle and yaw misalignment on a large horizontal axis wind turbine. A high‐fidelity aeroelastic model is employed, coupling computational fluid dynamics (CFD) and structural mechanics (CSM). The wind velocity stratification induced by the atmospheric boundary layer (ABL) is modeled. On the CSM side, the complex composite structure of each blade is accurately modeled using shell elements. The rotor–tower interaction is analyzed by comparing results of a rotor‐only simulation and a full‐machine simulation, observing a sudden drop in loads, deformations, and power production of each blade, when passing in front of the tower. Subsequently, a tilt angle is introduced on the rotor, and its effect on blade displacements, loads, and performance is studied, representing a novelty with respect to the available literature. The tilt angle leads to a different contribution of gravity to the blade deformations, sensibly affecting the stresses in the composite material. Lastly, a yaw misalignment is introduced with respect to the incoming wind, and the resulting changes in the blade solicitations are analyzed. In particular, a reduction of the blade axial displacement amplitude during each revolution is observed.     

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.     

Prediction of the wind turbine performance by using BEM with airfoil data extracted from CFD

Blade element momentum (BEM) theory with airfoil data is a widely used technique for prediction of wind turbine aerodynamic performance, but the reliability of the airfoil data is an important factor for the prediction accuracy of aerodynamic loads and power. The airfoil characteristics used in BEM codes are mostly based on 2D wind tunnel measurements of airfoils with constant span. Due to 3D effects, a BEM code using airfoil data obtained directly from 2D wind tunnel measurements will not yield the correct loading and power. As a consequence, 2D airfoil characteristics have to be corrected before they can be used in a BEM code. In this article, we consider the MEXICO (Model EXperiments In Controlled cOnditions) rotor where airfoil data are extracted from CFD (Computational Fluid Dynamics) results. The azimuthally averaged velocity is used as the sectional velocity to define the angle of attack and the coefficient of lift and drag is determined by the forces on the blade. The extracted airfoil data are put into a BEM code without further corrections, and the calculated axial and tangential forces are compared to both computations using BEM with Shen's tip loss correction model and experimental data. The comparisons show that the recalculated forces by using airfoil data extracted from CFD have good agreements with the experiment.     

基于升力线理论的大型风力机气弹响应研究

针对风力机不断向大型化发展的趋势,导致结构柔度增加,气弹耦合特性和振动增强,研究了大型风力机高效精确的气弹响应分析方法。为了更准确模拟大型风力机气流沿叶片展向的三维流动现象,采用螺旋尾涡升力线模型代替传统叶素动量理论,建立了叶片气动载荷分析模型,进而结合风力机多体系统动力学模型,构建了机组的气弹耦合动力学方程和数值求解方法。以某10 MW风力机叶片为例,研究了稳态风况下不同风速的叶片气动性能,以及有效攻角、切向力等沿叶展方向的分布特点,并与采用修正叶素动量理论的气弹分析程序（HAWC）对比,结果表明,升力线理论无需引入经验修正模型即能获得叶素动量理论经修正后的分析精度。最后,通过非稳态风况下风力机的气弹响应分析,证明本文方法对大型风力机气弹耦合分析的有效性和准确性。     

Open‐loop frequency response analysis of a wind turbine using a high‐order linear aeroelastic model

Wind turbine controllers are commonly designed on the basis of low‐order linear models to capture the aeroelastic wind turbine response due to control actions and disturbances. This paper characterizes the aeroelastic wind turbine dynamics that influence the open‐loop frequency response from generator torque and collective pitch control actions of a modern non‐floating wind turbine based on a high‐order linear model. The model is a linearization of a geometrically non‐linear finite beam element model coupled with an unsteady blade element momentum model of aerodynamic forces including effects of shed vorticity and dynamic stall. The main findings are that the lowest collective flap modes have limited influence on the response from generator torque to generator speed, due to large aerodynamic damping. The transfer function from collective pitch to generator speed is affected by two non‐minimum phase zeros below the frequency of the first drivetrain mode. To correctly predict the non‐minimum phase zeros, it is essential to include lateral tower and blade flap degrees of freedom. Copyright © 2013 John Wiley & Sons, Ltd.     

Wind turbine aerodynamic response under atmospheric icing conditions

This article deals with the atmospheric ice accumulation on wind turbine blades and its effect on the aerodynamic performance and structural response. The role of eight atmospheric and system parameters on the ice accretion profiles was estimated using the 2D ice accumulation software lewice Twenty‐four hours of icing, with time varying wind speed and atmospheric icing conditions, was simulated on a rotor. Computational fluid dynamics code, FLUENT, was used to estimate the aerodynamic coefficients of the blade after icing. The results were also validated against wind tunnel measurements performed at LM Wind Power using a NACA64618 airfoil. The effects of changes in geometry and surface roughness are considered in the simulation. A blade element momentum code WT‐Perf is then used to quantify the degradation in performance curves. The dynamic responses of the wind turbine under normal and iced conditions were simulated with the wind turbine aeroelastic code HAWC2. The results show different behaviors below and above rated wind speeds. In below rated wind speed, for a 5 MW virtual NREL wind turbine, power loss up to 35% is observed, and the rated power is shifted from wind speed of 11 to 19 m s^?1. However, the thrust of the iced rotor in below rated wind speed is smaller than the clean rotor up to 14%, but after rated wind speed, it is up to 40% bigger than the clean rotor. Finally, it is briefly indicated how the results of this paper can be used for condition monitoring and ice detection. Copyright © 2012 John Wiley & Sons, Ltd.     

Impact of aerodynamic modeling on seakeeping performance of a floating horizontal axis wind turbine

Over the last decade, several coupled simulation tools have been developed in order to design and optimize floating wind turbines (FWTs). In most of these tools, the aerodynamic modeling is based on quasi‐steady aerodynamic models such as the blade element momentum (BEM). It may not be accurate enough for FWTs as the motion of the platform induces highly unsteady phenomena around the rotor. To address this issue, a new design tool has been developed coupling a seakeeping solver with an unsteady aerodynamic solver based on the free vortex wake (FVW) theory. This tool is here compared with the reference code FAST, which is based on the BEM theory in order to characterize the impact of the aerodynamic model on the seakeeping of a floating horizontal axis wind turbine (HAWT). Aerodynamic solvers are compared for the case of the free floating NREL 5MW HAWT supported by the OC3Hywind SPAR. Differences obtained between the models have been analyzed through a study of the aerodynamic loads acting on the same turbine in imposed harmonic surge and pitch motions. This provides a better understanding of the intrinsic differences between the quasi‐steady and unsteady aerodynamic solvers. The study shows that differences can be observed between the three aerodynamic solvers, especially at high tip speed ratio (TSR) for which unsteady aerodynamic phenomena and complex wake dynamics occur. Observed discrepancies in the predictions of the FWT dynamic response can raise issues when designing such a system with a state‐of‐the‐art design tool.     

A coupled near and far wake model for wind turbine aerodynamics

In this paper, an aerodynamic model consisting of a lifting line‐based trailed vorticity model and a blade element momentum (BEM) model is described. The focus is on the trailed vorticity model, which is based on the near wake model (NWM) by Beddoes and has been extended to include the effects of downwind convection and to enable a faster and more accurate computation of the induction, especially close to the blade root and tip. The NWM is introduced to model the detailed steady and unsteady induction from the first part of the trailed vorticity behind the individual rotor blades. The model adds a radial coupling between the blade sections and provides a computation of tip loss effects that depends on the actual blade geometry and the respective operating point. Moreover, the coupling of the NWM with a BEM theory‐based far wake model is presented. To avoid accounting for the near wake induction twice, the induction from the BEM model is reduced by a coupling factor, which is continuously updated during the computation to ensure a good behavior of the model in varying operating conditions. The coupled near and far wake model is compared with a simple prescribed wake lifting line model, a BEM model and full rotor computational fluid dynamics (CFD) to evaluate the steady‐state results in different cases. The model is shown to deliver good results across the whole operation range of the NREL 5‐MW reference wind turbine. Copyright © 2016 John Wiley & Sons, Ltd.     

Implicit Floquet analysis of wind turbines using tangent matrices of a non‐linear aeroelastic code

The aeroelastic code BHawC for calculation of the dynamic response of a wind turbine uses a non‐linear finite element formulation. Most wind turbine stability tools for calculation of the aeroelastic modes are, however, based on separate linearized models. This paper presents an approach to modal analysis where the linear structural model is extracted directly from BHawC using the tangent system matrices when the turbine is in a steady state. A purely structural modal analysis of the periodic system for an isotropic rotor operating at a stationary steady state was performed by eigenvalue analysis after describing the rotor degrees of freedom in the inertial frame with the Coleman transformation. For general anisotropic systems, implicit Floquet analysis, which is less computationally intensive than classical Floquet analysis, was used to extract the least damped modes. Both methods were applied to a model of a three‐bladed 2.3 MW Siemens wind turbine model. Frequencies matched individually and with a modal identification on time simulations with the non‐linear model. The implicit Floquet analysis performed for an anisotropic system in a periodic steady state showed that the response of a single mode contains multiple harmonic components differing in frequency by the rotor speed. Copyright © 2011 John Wiley & Sons, Ltd.     

Evaluation of a wind speed estimator for effective hub‐height and shear components

Estimates of the effective wind speed disturbances acting on a wind turbine are useful in a variety of control applications. With some simplifications, it is shown that for zero yaw error, any wind field interacting with a turbine can be equivalently described using a hub‐height (uniform) component as well as linear horizontal and vertical shear components. A Kalman filter‐based wind speed estimator is presented for estimation of these effective hub‐height and shear components. The wind speed estimator is evaluated in the frequency domain using the FAST aeroelastic simulator with the National Renewable Energy Laboratory's 5 MW reference wind turbine model and realistic hub‐height and shear disturbances. In addition, the impact of the inflow model, used to simulate the rotor aerodynamics, on the Kalman filter performance is investigated. It is found that the estimator accuracy strongly depends on the inflow model used. In general, the estimator performs well up to a bandwidth of 1 Hz when the inflow model used for simulation matches the model used to create the linear Kalman filter model and blade pitch angle remains close to the linearization operating point. However, inaccuracies in the linear model of the turbine when dynamic inflow is used for simulation as well as nonlinearities in the turbine dynamics due to blade pitch actuation cause performance to degrade. Finally, the improvement gained by employing a non‐causal wind speed estimator is assessed, showing a minor increase in performance. Copyright © 2014 John Wiley & Sons, Ltd.     

Parked aeroelastic field rotor response for a 20% scaled demonstrator of a 13-MW downwind turbine

Aeroelastic parked testing of a unique downwind two-bladed subscale rotor was completed to characterize the response of an extreme-scale 13-MW turbine in high-wind parked conditions. A 20% geometric scaling was used resulting in scaled 20-m-long blades, whose structural and stiffness properties were designed using aeroelastic scaling to replicate the nondimensional structural aeroelastic deflections and dynamics that would occur for a lightweight, downwind 13-MW rotor. The subscale rotor was mounted and field tested on the two-bladed Controls Advanced Research Turbine (CART2) at the National Renewable Energy Laboratory's Flatiron Campus (NREL FC). The parked testing of these highly flexible blades included both pitch-to-run and pitch-to-feather configurations with the blades in the horizontal braked orientation. The collected experimental data includes the unsteady flapwise root bending moments and tip deflections as a function of inflow wind conditions. The bending moments are based on strain gauges located in the root section, whereas the tip deflections are captured by a video camera on the hub of the turbine pointed toward the tip of the blade. The experimental results are compared against computational predictions generated by FAST, a wind turbine simulation software, for the subscale and full-scale models with consistent unsteady wind fields. FAST reasonably predicted the bending moments and deflections of the experimental data in terms of both the mean and standard deviations. These results demonstrate the efficacy of the first such aeroelastically scaled turbine test and demonstrate that a highly flexible lightweight downwind coned rotor can be designed to withstand extreme loads in parked conditions.     

Estimating the angle of attack from blade pressure measurements on the National Renewable Energy Laboratory phase VI rotor using a free wake vortex model: yawed conditions

Wind turbine design codes for calculating blade loads are usually based on a blade element momentum (BEM) approach. Since wind turbine rotors often operate in off‐design conditions, such as yawed flow, several engineering methods have been developed to take into account such conditions. An essential feature of a BEM code is the coupling of local blade element loads with an external (induced) velocity field determined with momentum theory through the angle of attack. Local blade loads follow directly from blade pressure measurements as performed in the National Renewable Energy Laboratory (NREL) phase IV campaign, but corresponding angles of attack cannot (on principle) be measured. By developing a free wake vortex method using measured local blade loads, time‐dependent angle of attack and induced velocity distributions are reconstructed. In a previous paper, a method was described for deriving such distributions in conjunction with blade pressure measurements for the NREL phase VI wind turbine in axial (non‐yawed) conditions. In this paper, the same method is applied to investigate yawed conditions on the same turbine. The study considered different operating conditions in yaw in both attached and separated flows over the blades. The derived free wake geometry solutions are used to determine induced velocity distributions at the rotor blade. These are then used to determine the local (azimuth time dependent) angle of attack, as well as the corresponding lift and drag for each blade section. The derived results are helpful to develop better engineering models for wind turbine design codes. Copyright © 2008 John Wiley & Sons, Ltd.     

Effect of wind turbine surge motion on rotor thrust and induced velocity

Offshore wind turbines on floating platforms will experience larger motions than comparable bottom fixed wind turbines—for which the majority of industry standard design codes have been developed and validated. In this paper, the effect of a periodic surge motion on the integrated loads and induced velocity on a wind turbine rotor is investigated. Specifically, the performance of blade element momentum theory with a quasisteady wake as well as two widely used engineering dynamic inflow models is evaluated. A moving actuator disc model is used as reference, since the dynamics associated with the wake will be inherently included in the solution of the associated fluid dynamic problem. Through analysis of integrated rotor loads, induced velocities and aerodynamic damping, it is concluded that typical surge motions are sufficiently slow to not affect the wake dynamics predicted by engineering models significantly. Copyright © 2012 John Wiley & Sons, Ltd.