Wind Turbines: Unsteady Aerodynamics And Inflow Noise
Downloaded from orbit.dtu.dk on: Mar 23, 2021Wind Turbines: Unsteady Aerodynamics and Inflow NoiseBroe, Brian RigetPublication date:2009Document VersionPublisher's PDF, also known as Version of recordLink back to DTU OrbitCitation (APA):Broe, B. R. (2009). Wind Turbines: Unsteady Aerodynamics and Inflow Noise. Risø National Laboratory forSustainable Energy. Risø-PhD No. 47(EN)General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyrightowners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. Users may download and print one copy of any publication from the public portal for the purpose of private study or research. You may not further distribute the material or use it for any profit-making activity or commercial gain You may freely distribute the URL identifying the publication in the public portalIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.
Risø-PhD-ReportWind Turbines: Unsteady Aerodynamics andInflow NoiseIm L 2ΠBrian Riget BroeRisø-PhD-47(EN)December 20090.20.1Re L 2Π 0.20.2 0.10.40.60.81
Figure on front page:Plot of the lift response of a sinusoidal gust as function of reduced wave number. The black line isthe 1-D sinusoidal gust on a flat aerofoil (Section 2.1.2). The absolute value of the lift response L isthe distance from the origin of the plot to a point on, say, the black line. The argument of L is thecorresponding phase of the lift relative to the phase of the gust at the midpoint of the aerofoil to thegust. The green and red lines show a 2-D sinusoidal gust on a 2-D flat aerofoil (Section 2.1.4). Thered lines are functions of the chordwise wave number for different values of fixed spanwise wavenumber. The green lines are functions of the spanwise wave number when the chord wise wavenumber is fixed.
Author: Brian Riget BroeTitle: Wind Turbines: UnsteadyDivision: Wind Energy DivisionAerodynamics and Inflow NoiseAbstract (max. 2000 char.):Aerodynamical noise from wind turbines due to atmospheric turbulence hasthe highest emphasis in semi-empirical models. However it is an openquestion whether inflow noise has a high emphasis. This illustrates the needto investigate and improve the semi-empirical model for noise due toatmospheric turbulence. Three different aerodynamical models areinvestigated in order to estimate the lift fluctuations due to unsteadyaerodynamics (Sears, W. R.: 1941, Some aspects of non-stationary airfoiltheory and its practical application; Goldstein, M. E. and Atassi, H. M.:1976, A complete second-order theory for the unsteady flow about anairfoil due to a periodic gust; and Graham, J. M. R.: 1970, Lifting surfacetheory for the problem of an arbitrarily yawed sinusoidal gust incident on athin aerofoil in incompressible flow). Two of these models are investigatedto find the unsteady lift distribution or pressure difference as function ofchordwise position on the aerofoil (Sears, W. R.: 1941; and Graham, J. M.R.: 1970). An acoustic model is investigated using a model for the liftdistribution as input (Amiet, R. K.: 1975, Acoustic radiation from an airfoilin a turbulent stream). The two models for lift distribution are used in theacoustic model. One of the models for lift distribution is for completelyanisotropic turbulence and the other for perfectly isotropic turbulence, andso is also the corresponding models for the lift fluctuations derived fromthe models for lift distribution. The models for lift distribution and lift arecompared with pressure data which are obtained by microphones placedflush with the surface of an aerofoil. The pressure data are from twoexperiments in a wind tunnel, one experiment with a NACA0015 profileand a second with a NACA63415 profile. The turbulence is measured by atriple wired hotwire instrument in the experiment with a NACA0015profile. Comparison of the aerodynamical models with data shows that themodels capture the general characteristics of the measurements, but the dataare hampered by background noise from the fan propellers in the windtunnel. The measurements are in between the completely anisotropicturbulent model and the perfectly isotropic turbulent model. This indicatesthat the models capture the aerodynamics well. Thus the measurementssuggest that the noise due to atmospheric turbulence can be described andmodeled by the two models for lift distribution. It was not possible to testthe acoustical model by the measurements presented in this work.Risø-PhD-47(EN)December 2009ISSN 0106-2840ISBN 978-87-550-3727-4Contract no.:Group's own reg. no.:PSP: 1191014-01Sponsorship:Cover :Plot of the lift response of asinusoidal gust as function ofreduced wave number. The blackline is the 1-D sinusoidal gust on aflat aerofoil (Section 2.1.2). Theabsolute value of the lift response L is the distance from the origin of theplot to a point on, say, the black line.The argument of L is thecorresponding phase of the liftrelative to the phase of the gust atthe midpoint of the aerofoil to thegust. The green and red lines show a2-D sinusoidal gust on a 2-D flataerofoil (Section 2.1.4). The redlines are functions of the chordwisewave number for different values offixed spanwise wave number. Thegreen lines are functions of thespanwise wave number when thechord wise wave number is fixed.Pages: 124Tables: 11References: 35Information Service DepartmentRisø National Laboratory forSustainable EnergyTechnical University of DenmarkP.O.Box 49DK-4000 RoskildeDenmarkTelephone 45 46774005bibl@risoe.dtu.dkFax 45 46774013www.risoe.dtu.dk
www.risoe.dtu.dk
1AcknowledgementsI thank my supervisors, Jakob Mann at Risø DTU, and Jens NørkærSørensen, for the valuable discussions in the course of this work.This work was never done without the moral support and fruitful discussions with Sven-Erik Gryning. Further Lise Lotte Sørensen has contributedwith moral support, which has been highly appreciated.I also use the opportunity to express my gratitude to my colleagues inthe Wind Energy Department at Risø DTU for their support in the courseof the Ph.D. study.
ContentsNomenclature41 Introduction92 Theory and Models2.1 Aerodynamics . . . . . . . . . . . . . . . . . . . . . .2.1.1 Steady Flow . . . . . . . . . . . . . . . . . . .2.1.2 1-D Unsteady Aerodynamics . . . . . . . . . .2.1.3 2-D Unsteady Aerodynamics . . . . . . . . . .2.1.4 3-D Unsteady Aerodynamics . . . . . . . . . .2.2 Statistical Measures and their Properties . . . . . . .2.3 Turbulence . . . . . . . . . . . . . . . . . . . . . . . .2.4 Inflow Noise Model . . . . . . . . . . . . . . . . . . .2.4.1 Derivation of Acoustical Pressure Spectrum .2.4.2 Estimation of one third octave Sound Pressure2.5 Other Aeroacoustic Sources . . . . . . . . . . . . . .2.6 Conclusions Regarding Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Level. . . . . . .131415192731384143434951523 Experiments3.1 Setup of Experiments in Velux Wind Tunnel3.1.1 Setup of Experiment 1: NACA0015 .3.1.2 Setup of Experiment 2: NACA634153.2 Results . . . . . . . . . . . . . . . . . . . . .3.2.1 Experiment 1: NACA0015 . . . . . .3.2.2 Experiment 2: NACA63415 . . . . .3.3 Data from Bridge Deck Simulation . . . . .3.4 Conclusions Regarding Experiments . . . . .545457646868788283.4 Comparison of Models and Experiments854.1 Numerical Treatments . . . . . . . . . . . . . . . . . . . . . . 854.1.1 Numerical Treatment of Models . . . . . . . . . . . . . 86
CONTENTS4.24.34.44.54.634.1.2 Model Parameters from Data . . . . . . . .Pressure . . . . . . . . . . . . . . . . . . . . . . . .4.2.1 Estimation of Pressure Spectra from Models4.2.2 Comparison of Models and Data . . . . . . .Fluctuating Lift . . . . . . . . . . . . . . . . . . . .4.3.1 Estimation of Lift Spectra from Models . . .4.3.2 Estimation of Lift Spectra from Data . . . .4.3.3 Comparison of Models and Data . . . . . . .Sound Pressure Level . . . . . . . . . . . . . . . . .Bridge Deck Simulation . . . . . . . . . . . . . . . .Conclusions Regarding Analysis . . . . . . . . . . .5 ConclusionA Bessel FunctionsA.1 Bessel Functions of First Kind . . . . . . . .A.2 Bessel Functions of Second and Third Kind .A.3 Modified Bessel Functions of First Kind . . .A.4 Modified Bessel Functions of Second Kind .A.5 Generating Function for Bessel Functions . .B Auxiliary 3116.118. 118. 120. 121. 123. 126128130
NomenclatureaaiayanA(ρ, c, U)AdAijAmbBBijcc0ch (z)cohww1/2cohww1/2cohLLC(κ)dd1d2E(k)EA (κ)Ev [ ]ff (D, d)fcfhflfHf0w (x)Dimensionless constant in Section 2.4.Acceleration in Section 2.2.Vertical acceleration in aerofoil plane.Normal acceleration in cylinder plane.Amplification factor. A(ρ, c, U) 21 ρcUAdmittance.Coefficients defined in Section 2.1.4.Coefficient for the complex acceleration potential, m 0.Half chord, b 2c .Length of bridge section.Coefficients defined in Section 2.1.4.Chord length.Speed of sound in air, c0 340m/s.Coefficient, ch (z) sin(h arccos(z)), h 1, c0 (z) π2 arcsin(z).hCoherence of vertical turbulence.Co-coherence of vertical turbulence.Co-coherence of lift.K1 (ıκ)Theodorsen function, C(κ) K0 (ıκ) K.1 (ıκ)Half span.Diameter of hole flush with surface of aerofoil.Diameter of microphone membrane.Total turbulent kinetic energy.Function defined in Section 2.1.3.Expected value.Cyclic frequency.Function defined in Section 2.4.Center frequency in the one third octave band.Upper frequency in the one third octave band.Lower frequency in the one third octave band.Eigenfrequency of a Helmholtz resonator.Functions defined in Section 2.1.4, w {1, 2, 3}.
CONTENTSfw (z)FF (z)F (z)ggzgG(ω̂)GA (z)h1h2h3(1)Hn (z)H (z)ıIIwtjJnJ (z)kckkkekxk̂xkyk̂yk1k2k3KnKxK̂xK1′ (z)lLLLTL′5fw (z) f0w (x).Acoustic force.Function defined in Section 2.1.4.Function defined in Section 2.1.3.Acceleration due to gravity in Section 2.1.1.Vertical acceleration due to gravity in Section 2.1.1.Transfer function for either lift distribution or lift.Transfer function for lift distribution.Function defined in Section 2.1.3.Length of tube.Height to estimate V in Eqn. (3.2).Height to estimate V in Eqn. (3.2).Bessel functions of third kind (Hankel functions) of order n.(1)(1)H0 (z) ıH1 (z).Imaginary unit in the complex time domain.σ2Turbulence intensity, I U U .Turbulence intensity at tip speed of wind turbine.Imaginary unit in the spatial complex plane.Bessel function of first kind of order n.J0 (z) ıJ1 (z).κ ıµ in Section 2.1.4.Wave number vector.Wavenumber vector. π Γ(5/6).L Γ(1/3)Chordwise wave number, Uω .kx /ke .Spanwise wave number.ky /ke .Chordwise wave number.Spanwise wave number.Vertical wave number.Modified Bessel function of second kind of order n. Uω .Kx /ke .K1 (z), z 0, K1 ( z), z 0, , z 0.Lift distribution, p(x), on aerofoil.Lift force vector.Absolute value of lift in Section 2.1.1.Length scale of turbulence.lift fluctuation.
�)SScavSi(x)SpSLSP PSQQSUSVSVSWSvartTFTTi (z)uuu u2UUwtEffective length of a flanged tube, L′ h1 1.7d1 /2, in Section 3.1.Response (transfer) function of lift due to AOA.Response (transfer) function of lift due to camber.Acoustic lift.Second order fit coefficient to camber line.Mach number, cU0 .Vector of unit length.Normal force.Complex acceleration potential, o(z) φ(z) jψ(z).Complex velocity potential.Pressure.Coefficient, Pm ( ı)m Jm (κ).Acoustic pressure at receiver position in Section 2.4.Radius of cylinder.2 cos θ1 .Distance of integration.Cross correlation of pressure.Total response (transfer) function of lift in 2-D modelDistance along surface of aerofoil from leading edge.Sears function, S(κ) 2π[{J0 (κ) ıJ1 (κ)}C(κ) ıJ1 (κ)].Integration domain of aerofoil surface in Section 2.1.4.Area, Scav π(d1 /2)2 , Rin Section 3.1.xSine integral. Si(x) 0 sint t dt.Pressure spectrum.Lift spectrum.Cross spectrum of acoustic pressure.Cross spectrum of pressure difference.Spectrum of turbulent velocity in direction of mean flow.Spectrum of Volt signal in Chapter 3.1.Spectrum of turbulent horizontal velocity perpendicular to mean flow.Spectrum of turbulent vertical velocity.Spectrum of variable var.Time.Tangential force in Section 2.1.1.Limit of time integration in Section 2.4.Chebychev polynomial of ith order, Ti (z) cos(i arccos(z)).Velocity vector.Amplitude of chordwise gust in Section 2.1.3.Friction velocity.Variance of velocity in direction of mean flow.Velocity in direction of mean flow.Tip speed of wind turbine.
CONTENTSU(z)U �AOAααcorβtββAγγ1γ2Γδ()δij f p P PTǫζ7Logarithmic wind profile.Mean velocity in direction of mean flow.1-D gust in Section 2.1.2.vertical gust in Section 2.1.4.Volume between tube and microphone membrane in Section 3.1.Horizontal velocity perpendicular to mean flow.vertical gustFourier amplitude of vertical velocity.Fourier amplitude of vertical velocity at a given mode in Section 2.4.Upwash at aerofoil.Upwash in wake.Integration domain over the wake in Section 2.1.4.Vertical velocity (z-direction).Chordwise coordinate.Chordwise coordinate restricted to the aerofoil in Section 2.1.4.kyCoordinate transformation, yt 1 k, in Section 4.1.1.ySpanwise coordinate.Spanwise coordinate restricted to the aerofoil in Section 2.1.4.Complex coordinate, zc x jz in Section 2.1.1 and Section 2.1.2.Normalized chordwise coordinate, zn 2x 1 in Section 2.1.4.cVariable, which can be both complex and real.Vertical coordinate.Normalized chordwise coordinate, zn,0 2xc 0 1 in Section 2.1.4.Rougness length in Section 4.4.Angle of attack (AOA) in Section 2.1.1.Spectral Kolmogorov constant set to 1.7.Free stream corrected AOA.Angleto the horizontal of the trailing edge in the aerofoil plane in Section 2.1.1. 1 M 2 in Section 2.4.AOA in radians, β AOAπ.180 Constant.Chordwise vorticity.Spanwise vorticity.Gamma function.Dirac Delta function.Kroenecker delta, δij 0, i 6 j, δij 1, i j,.The width of a frequency band in the one third octave band.Pressure difference of pressure fluctuations.Pressure difference.Pressure difference in Fourier space (frequency domain).Energy dissipation rate.Complex coordinate in the aerofoil plane.
8ηθθ1Θ κcκKκλΛ Lψωωω̂()hiCONTENTSSeparation distance, η y2 y1 .Complex argument, ejθ , in the cylinder plane.θ.2Function defined in Section 2.1.3.Circulation in Section 2.1.1.von Kármán constant set to 0.4 in Section 4.4.Reduced chordwise wavenumber, κ k2x c .Joukowski parameter in Section 2.1.1.Function defined in Section 2.1.3.Vertical reduced wave number, µ k2z c , in Section 2.1.3.Reduced spanwise wave number, ν k2y c µc.2Kinematic viscosity 1.6 · 10 5m2 /s.Air density.Mean air density.pAuxiliary distance parameter, σ x2 β 2 (y 2 z 2 ).Chebychev coefficient.Standard deviation of variable var.Variance of variable var.Time.Velocity potential in Section 2.1.1.Acceleration potential.Energy spectrum of turbulence by von Kármán in velocity components ij.Energy spectrum of turbulence by von Kármán of vertical velocities.Cross spectrum of vertical turbulence.Cross spectrum of lift.Streamlines of acceleration.Vorticity in Section 2.1.1.Angular frequency.Reduced angular frequency, ω̂ ωb.UComplex conjugate.Mean of quantity in h i.
Chapter 1IntroductionNoise from wind turbines is a subject which has a considerable publicinterest in Denmark. It is a subject of much debate before establishing windturbines at any site. Therefore it is important to gain knowledge of noisefrom wind turbines.The noise from wind turbines can be split up into two major sources, amechanical source and an aero acoustic source (Wagner, Bareiß and Guidati1996). The mechanical source of noise can be avoided or minimized by engineering means (Henderson 2005). The aero acoustic part can not be avoidedbut the design of the aerofoil has an important role of how much noise isproduced by aero acoustical means.The aero acoustic source is due to turbulence in the flow around the windturbine blades. The turbulence is generated by different mechanisms suchas atmospheric turbulence and separation and thus the aero acoustic sourcecan be split up into several components (Wagner et al. 1996).The aero acoustic noise due to atmospheric turbulence is the subject ofthis thesis. It is also called inflow noise. The atmospheric flow is not steadybut contains eddies, turbulence (Panofsky and Dutton 1984). The pressureat any point is constant in time when the flow is steady, incompressible,and inviscid. The turbulence create pressure fluctuations. Some part ofthe pressure fluctuations caused by the turbulence will be emitted as sound(Amiet 1975). The nature of turbulence causes the noise to be emitted ina continuum of frequencies and the inflow noise is of broadband character(Wagner et al. 1996).The aeroacoustic noise can be treated by computational fluid dynamics(Zhu 2007) which is time consuming and demands powerful computer resources, or it can be treated in a semi-empirical approach which simplifiesthe physics (Amiet 1975).The inflow noise has been treated in a semi-empirical approach (Amiet
10Figure 1.1: Plot of the SPL1/3 at the one third octave frequencies for aeroacoustic sources described in Moriarty and Migliore (2003). This figure isidentical to Figure 9 in Moriarty and Migliore (2003).1975). The semi-empirical approach has the advantage that it is less demanding on computer resources as compared to approaches based on computational fluid dynamics. The semi-empirical approach is suitable for guidelines for design purposes because an answer is quickly obtained when designparameters are changed.The semi-empirical inflow model, which is widely used, accounts for themajor part of the total aero acoustical noise, Moriarty and Migliore (2003),as seen in Figure 1.1. According to this model inflow noise is seen to be dominating. Some experimental evidence indicates, however, that inflow noise isnot the most significant aero acoustic component (Personal communication,P. Moriarty). Trailing edge noise is argued to be responsible for major part ofthe noise emitted aero acoustically (Moriarty and Migliore 2003, Oerlemans,Sijtsmaa and López 2007).It follows from the discussion above that the semi-empirical model of noisedue to atmospheric turbulence must be revised because it has too much emphasis of the total aero acoustical noise compared to trailing edge noise.Other approaches to improve the semi-empirical noise model due to atmo-
11spheric turbulence have been carried out by Guidati (2004) and by Moriarty,Guidati and Migliore (2005). The input models by Sears (1941), Goldsteinand Atassi (1976), and Graham (1970) in the acoustical model by Amiet(1975) are investigated in this thesis.The model of inflow noise shown in Figure 1.1 is based on the model byAmiet (1975). This model assumes that the noise due to atmospheric turbulence is emitted like a dipole. It is based on isotropic turbulence as describedby von Kármán (1948), and the lift distribution (pressure difference) due toturbulence along the chord of the aerofoil described by Adamczyk (1974).The lift distribution due to turbulence is also described by Sears (1941)and Graham (1970). The models by Adamczyk (1974), Sears (1941), andGraham (1970) are all based on a flat plate. Further a model for the fluctuating lift due to turbulence is described, where the aerofoil is a bend flatplate at an angle of attack (Goldstein and Atassi 1
Title: Wind Turbines: Unsteady Aerodynamics and Inflow Noise Division: Wind Energy Division Risø-PhD-47(EN) December 2009 Abstract (max. 2000 char.): Aerodynamical noise from wind turbines due to atmospheric turbulence has the highest emphasis in semi-empirical models. However it is an open question whether inflow noise has a high emphasis.
Chapter 13: Aerodynamics of Wind Turbines. Chapter 13: Aerodynamics of Wind Turbines. Chapter 13: Aerodynamics of Wind Turbines. Time accurate predictions for a 2-bladed HAWT are shown in the next figure (13.22) At high tip speed ratio (low wind speeds) vortex ring state (part a)
boat wind turbines and make them facing the wind [3]. The number of blades of boat wind turbines is often 3. Three-bladed boat wind turbines can produce power at low wind speed and can be self-started by the wind. This paper is focused on three-bladed boat wind turbines with passive yaw motion.
WIND TURBINES Wind Turbines AP-Power-Wind Turbines-13a Wind power is popular. The market for wind turbines is expanding rapidly and with it is an increasing demand for turbines to be i
Common concerns about wind power, June 2017 1 Contents Introduction page 2 1 Wind turbines and energy payback times page 5 2 Materials consumption and life cycle impacts of wind power page 11 3 Wind power costs and subsidies page 19 4 Efficiency and capacity factors of wind turbines page 27 5 Intermittency of wind turbines page 33 6 Offshore wind turbines page 41
aerodynamics performance will in turn affect the structure safety and instability. Besides, due to operating in complex wind with varying di-rections and magnitudes for horizontal axial wind turbines (HAWTs), or operating on the plunging platform for floating offshore wind turbines (FOWTs), it often happens that wind turbines works under yaw .
and optimization of wind turbines. Aerodynamic modeling also concerns the design of specific parts of wind turbines, such as rotor-blade geometry, and the performance predictions of wind farms. The aerodynamics of wind turbines is in many ways different from the aerodynamics of fixed-wing aircraft or helicopters, for example.
Human chain at Tinos harbor as a form of protest against the wind turbines. [5] Peaceful protest on the mountain that the new wind turbines are planned to be installed. [5] Protest in Athens city center against the wind turbines. [5] Citizens of Tinos blocking the coming of the materials needed for the installation of the new wind turbines. [5] 8
2 For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM Standards volume information, refer to the standard’s Document Summary page on the ASTM website. 3 National Fenestration Rating Council, 84884 Georgia Ave., Suite 320, Silver Spring, MD 20910. 1
