New dynamic‐inflow engineering models based on linear and nonlinear actuator disc vortex models

Two new engineering models are presented for the aerodynamic induction of a wind turbine under dynamic thrust. The models are developed using the differential form of Duhamel integrals of indicial responses of actuator disc type vortex models. The time constants of the indicial functions are obtained by the indicial responses of a linear and a nonlinear actuator disc model. The new dynamic‐inflow engineering models are verified against the results of a Computational Fluid Dynamics (CFD) model and compared against the dynamic‐inflow engineering models of Pitt‐Peters, Øye, and Energy Research Center of the Netherlands (ECN), for several load cases. Comparisons of all models show that two time constants are necessary to predict the dynamic induction. The amplitude and phase delay of the velocity distribution shows a strong radial dependency. Verifying the models against results from the CFD model shows that the model based on the linear actuator disc vortex model predicts a similar performance as the Øye model. The model based on the nonlinear actuator disc vortex model predicts the dynamic induction better than the other models concerning both phase delay and amplitude, especially at high load.     

雾霾之后的反思

新年过后的第二个周末,浓重的雾霾已在全国多个城市肆虐,这让人们的心情变得糟糕。数据显示,截至1月13日零时,全国有33个城市的部分监测点PM2.5浓度超过300微克/立方米,个别城市出现PM2.5"爆表",比如北京的PM2.5浓度最高达到950微克/立方米。环保专家称,如此严重的空气质量污染,可以说已近人类所能承受的极限。于是,人们看到了政府有关方面发布的紧急预案,比如通知市民减少户外活动,要求学校停止户外体育锻炼,这体现了政府的责任意识。但我们是满足于制定完美的灾情应对预案,还是谋求从根本上消除灾难?     

Cylindrical vortex wake model: skewed cylinder,application to yawed or tilted rotors

A vortex system consisting of a bound vortex disk, a root vortex and a vortex cylinder is presented and applied for skewed wake situations. Both the longitudinal and tangential components of vorticity of the cylinder are considered. A subset of this system leads to a model, which is commonly used in Blade Element Momentum method codes for yawed conditions. Here, all the components of the full vortex system are analyzed in view of extending Blade Element Momentum models. The main assumptions of the current study are a constant uniform circulation, an infinite number of blades, an un‐expanding wake shape and a finite tip‐speed ratio. The investigation remains within the context of inviscid potential flow theory. The model is derived for horizontal‐axis rotors in general, but results are presented for wind‐turbine applications. For each vortex element, the velocity components in all directions are computed analytically or semi‐analytically for the entire domain. Simplified engineering models are provided to ease the evaluation of velocities in the rotor plane. The predominant velocity components are assessed. Copyright © 2015 John Wiley & Sons, Ltd.     

Influence of wake dynamics on the performance and aeroelasticity of wind turbines

Wind turbines are currently a rapidly expanding form of renewable energy. However, there are numerous technological challenges that must be overcome before wind energy provides a significant amount of power in the United States. One of the primary challenges in wind turbine design and analysis is accurately accounting for the aerodynamic environment. This study is focused on a comprehensive verification and validation of the NREL FAST code, which is enhanced to include a free vortex wake model. The verification and validation is carried out through a comparison of blade lift distribution, wind turbine power and force and moment coefficients using a combination of CFD and experimental data. The results are also compared against Blade Element Momentum theory, and results from a 2001 double-blind NREL study on the prediction capabilities of wind turbine modeling tools. Results indicate that the enhanced aeroelastic code generally provides improved predictions. However, in several notable cases the predictions are only marginally improved, or even worse, than those generated using Blade Element Momentum theory aerodynamics. It is concluded that modeling of the aerodynamic environment remains incomplete, even after inclusion of wake effects. One important aspect identified is modeling of the unsteady aerodynamic lift characteristics of the rotor. Finally, the aeroelastic response in the combined presence of wake effects and inflow turbulence is examined. Significant differences are observed in loads, power, and structural response between results computed using the free wake model or simpler models, such as Blade Element Momentum theory.     

A new dynamic inflow model for vertical‐axis wind turbines

This paper presents a new dynamic inflow model for vertical‐axis wind turbines (VAWTs). The model uses the principle of Duhamel's integral. The indicial function of the inflow‐ and crossflow‐induction required to apply Duhamel's integral is represented by an exponential function depending on the thrust coefficient and the azimuthal position. The parameters of this approximation are calibrated using a free wake vortex model. The model is compared with the results of a vortex model and higher fidelity computational fluid dynamic (CFD) simulations for the response of an actuator cylinder to a step input of the thrust and to a cyclic thrust. It is found that the discrepancies of the dynamic inflow model increase with increasing reduced frequency and baseline thrust. However, the deviations remain small. Analysing the application of a finite‐bladed floating VAWT with non‐uniform loading and validating it against actuator line CFD results that intrinsically include dynamic inflow shows that the new dynamic inflow model significantly outperforms the Larsen and Madsen model (which is the current standard in fully coupled VAWT models) and enhances the modelling of VAWTs.     

Superposition of vortex cylinders for steady and unsteady simulation of rotors of finite tip‐speed ratio

Joukowski introduced in 1912 a helical vortex model to represent the vorticity of a rotor and its wake. For an infinite number of blades but finite tip‐speed ratio, the model consists of a vortex cylinder of longitudinal and tangential vorticity, a root vortex and a bound vortex disk. A superposition of cylinders is used in this paper to model rotors of radially varying circulation. The relations required to form a consistent system of cylinders are derived. The model contains a term which is not accounted for in the standard blade element momentum (BEM) algorithm. This term is identified as the contribution from the pressure drop due to the wake rotation. The BEM algorithm can be corrected to account for this effect. Unlike previous work on the topic, the contribution is derived for a radially varying circulation. A high‐thrust correction is also presented to extend the model. The optimal power coefficient obtained with this model for the constant circulation rotor is assessed and compared with that of existing solutions. Results from prescribed thrust distributions are compared with that of actuator disk simulations. Steady simulations are performed to compare with the BEM algorithm. The model is also applied to compute the velocity field in the entire domain and perform unsteady simulations. Results for an unsteady simulation corresponding to a pitch change of the rotor is used to compare the model with measurements and a BEM code with a dynamic inflow model. Copyright © 2015 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.     

Validation and modification of the Blade Element Momentum theory based on comparisons with actuator disc simulations

A comprehensive investigation of the Blade Element Momentum (BEM) model using detailed numerical simulations with an axis symmetric actuator disc (AD) model has been carried out. The present implementation of the BEM model is in a version where exactly the same input in the form of non‐dimensional axial and tangential load coefficients can be used for the BEM model as for the numerical AD model. At a rotor disc loading corresponding to maximum power coefficient, we found close correlation between the AD and BEM model as concerns the integral value of the power coefficient. However, locally along the blade radius, we found considerable deviations with the general tendency, that the BEM model underestimates the power coefficient on the inboard part of the rotor and overestimates the coefficient on the outboard part. A closer investigation of the deviations showed that underestimation of the power coefficient on the inboard part could be ascribed to the pressure variation in the rotating wake not taken into account in the BEM model. We further found that the overestimation of the power coefficient on the outboard part of the rotor is due to the expansion of the flow causing a non‐uniform induction although the loading is uniform. Based on the findings we derived two small engineering sub‐models to be included in the BEM model to account for the physical mechanisms causing the deviations. Finally, the influence of using the corrected BEM model, BEM_cor on two rotor designs is presented. Copyright © 2009 John Wiley & Sons, Ltd.     

基于致动线模型的风力机尾流场数值研究

针对致动盘模型存在的不足,使用非定常计算,提出了致动线方法,在致动盘模型的基础上改进了体积力的分布方式,利用体积力代替风力机叶片,结合不可压缩N-S方程,采用均匀分布和高斯分布两种不同体积分布方式,在FLUENT中对Nibe A型风机尾流进行模拟计算,研究了尾流区域的速度变化与湍流强度等,并将计算结果与试验数据进行比较。结果表明,体积力的分布方式对致动线方法的计算结果有一定影响,尤其是远尾流区域差异明显,高斯分布下的模拟结果更加接近试验数据,优于均匀分布;致动线方法用于风力机尾流场的计算基本能满足工程需要,但在远尾流场的模拟计算上精度还不够,需结合实际对模型作进一步改进。     

Impact of aerodynamic modelling on seakeeping performance of a floating vertical axis wind turbine

This study focuses on the impact of the aerodynamic model on the dynamic response of a floating vertical axis wind turbine (VAWT). It compares a state‐of‐the‐art quasi‐steady double multiple streamtube (DMS) solver, a prescribed vortex wake (PVW), and a free vortex wake (FVW) solver. The aerodynamic loads acting on a bottom‐fixed VAWT and computed with the three aerodynamic solvers are compared, then the dynamic responses of the floating turbine in irregular waves and turbulent wind with the different aerodynamic solvers are compared. Differences are observed, particularly in the mean motions of the platform. Eventually, the aerodynamic damping computed by the solvers are estimated with aerodynamic simulations on the turbine with imposed surge and pitch motions. The estimated damping can then be correlated with the dynamic response amplitude of the VAWT. Substantial discrepancies are observed between the three solvers at high tip speed ratio, when the rotor is highly loaded. It is shown that the quasi‐steady DMS solver seems to give greater amplitude of motions for the floating VAWT because of strong rotor/wake interaction that are not correctly accounted for.     

Comparison of wind turbine wake properties in non‐sheared inflow predicted by different computational fluid dynamics rotor models

The wake of the 5MW reference wind turbine designed by the National Renewable Energy Laboratory (NREL) is simulated using computational fluid dynamics with a fully resolved rotor geometry, an actuator line method and an actuator disc method, respectively. Simulations are carried out prescribing both uniform and turbulent inflows, and the wake properties predicted by the three models are compared. In uniform inflow, the wake properties predicted by the actuator disc and line methods are found to be in very close agreement but differ significantly from the wake of the fully resolved rotor, which is characterized by much higher turbulence levels. In the simulations with turbulent inflow, the wake characteristics predicted by the three methods are in close agreement, indicating that the differences observed in uniform inflow do not play an important role if the inflow is turbulent. Copyright © 2014 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.     

Loading effects on floating offshore horizontal axis wind turbines in surge motion

Previous experimental work under controlled conditions on a small scale floating offshore horizontal axis wind turbine has shown an increasing amplitude of the cyclic thrust and power generation against tip speed ratio under the influence of surge motion. A numerical study is performed using an actuator disc Navier Stokes model, a Blade Element Momentum model and a Generalized Dynamic Wake model on the NREL 5 MW reference rotor in order to confirm or reject these observations on a full-scale surging rotor. The hypothesis was confirmed and the underlying reasons for the observed behaviour were studied on the basis of the near wake physics. It was found that the analysis of transient effects such as fatigue cannot be performed without an adequate aerodynamic model of the wake. Characterization of quasi-steady and unsteady regimes may be useful to establish when detailed aerodynamic wake models are necessary.     

HAWT dynamic stall response asymmetries under yawed flow conditions

Horizontal axis wind turbines can experience significant time‐varying aerodynamic loads, potentially causing adverse effects on structures, mechanical components and power production. As designers attempt lighter and more flexible wind energy machines, greater accuracy and robustness will become even more critical in future aerodynamics models. Aerodynamics modelling advances, in turn, will rely on more thorough comprehension of the three‐dimensional, unsteady, vortical flows that dominate wind turbine blade aerodynamics under high‐load conditions. To experimentally characterize these flows, turbine blade surface pressures were acquired at multiple span locations via the NREL Phase IV Unsteady Aerodynamics Experiment. Surface pressures and associated normal force histories were used to characterize dynamic stall vortex kinematics and normal force amplification. Dynamic stall vortices and normal force amplification were confirmed to occur in response to angle‐of‐attack excursions above the static stall threshold. Stall vortices occupied approximately one‐half of the blade span and persisted for nearly one‐fourth of the blade rotation cycle. Stall vortex convection varied along the blade, resulting in dramatic deformation of the vortex. Presence and deformation of the dynamic stall vortex produced corresponding amplification of normal forces. Analyses revealed consistent alterations to vortex kinematics in response to changes in reduced frequency, span location and yaw error. Finally, vortex structures and kinematics not previously documented for wind turbine blades were isolated. Published in 2000 by John Wiley & Sons, Ltd.     

Experimental and numerical investigation of tip vortex generation and evolution on horizontal axis wind turbines

The tip vortex of a wind turbine rotor blade is the result of a distribution of aerodynamic loads and circulation over the blade tip. The current knowledge on the generation of the tip vorticity in a 3D rotating environment still lacks detailed experimental evidence, particularly for yawed flow. The aim of this paper is to investigate how circulation at the blade tip behaves and how vorticity is eventually released in the wake, for both axial and 30° yawed flow conditions through the combination of experimental and numerical simulations. Stereo particle image velocimetry is used to measure the flow field at the tip of a 2m diameter, two‐bladed rotor at the TU Delft Open Jet Facility, for both axial and yawed flow; numerical simulations of the experiments are performed using a 3D, unsteady potential flow free‐wake vortex model. The generation mechanisms of the tip vorticity are established. The spanwise circulation along the blade exhibits a similar variation in both axial and yaw cases. A comparison of the chordwise directed circulation variation along the chord between axial and yawed flow is also presented and shown to be different. The analysis is based on contour integration of the velocity field. The tip vortex trajectory for axial flow confirms previous observations on the MEXICO rotor. The experimental results for yawed conditions have clearly shown how vorticity is swept radially away from the blade under the influence of the in‐plane radial component of flow. Such phenomena were only partially captured by the numerical model. The results of this work have important implications on the modelling of blade tip corrections. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

Wind turbine performance in shear flow and in the wake of another turbine through high fidelity numerical simulations with moving mesh technique

We present numerical simulations of two horizontal axis wind turbines, one operating under the wake of the other, under an incoming sheared velocity profile. We use a moving mesh technique to represent the rotation of the turbine blades and solve the unsteady Reynolds averaged Navier–Stokes equations with a shear stress transport k ? ω turbulence model. Temporal evolution of the lift and drag coefficients of the front turbine show a phase shift in the periodic cycle due to the non‐uniform incoming free stream velocity. Comparisons of the lift and drag coefficients for the back turbine with the unperturbed behaviour of the front demonstrate the complex non‐linear interactions of the blades with the wake, with a significant decrease in overall performance and two peaks at specific points in the cycle associated with local angle of attack modification in the wake. The vorticity field in the near wake shows tilting of the vortex lines in the wake due to the shear and a faster diffusion of the tip vortical signature compared with the uniform free stream velocity case. Observations of the wake–wake interaction show good agreement with recent studies that use different methodologies. Copyright © 2012 John Wiley & Sons, Ltd.     

Validation of four LES and a vortex model against stereo-PIV measurements in the near wake of an actuator disc and a wind turbine

In this paper we report the results of a workshop organised by the Delft University of Technology in 2014, aiming at the comparison between different state-of-the-art numerical models for the simulation of wind turbine wakes. The chosen benchmark case is a wind tunnel measurement, where stereoscopic Particle Image Velocimetry was employed to obtain the velocity field and turbulence statistics in the near wake of a two-bladed wind turbine model and of a porous disc, which mimics the numerical actuator used in the simulations. Researchers have been invited to simulate the experimental case based on the disc drag coefficient and the inflow characteristics. Four large eddy simulation (LES) codes from different institutions and a vortex model are part of the comparison. The purpose of this benchmark is to validate the numerical predictions of the flow field statistics in the near wake of an actuator disc, a case that is highly relevant for full wind farm applications. The comparison has shown that, despite its extreme simplicity, the vortex model is capable of reproducing the wake expansion and the centreline velocity with very high accuracy. Also all tested LES models are able to predict the velocity deficit in the very near wake well, contrary to what was expected from previous literature. However, the resolved velocity fluctuations in the LES are below the experimentally measured values.     

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.