prediction and analysis of infra and low frequency noise of upwind horizontal axis wind turbine using statistical wind speed model

Prediction and analysis of infra and low-frequency noiseof upwind horizontal axis wind turbine using statistical wind speed model Gwang-Se Lee and Cheolung Cheonga School of Mechanical E

wind turbine using statistical wind speed model

Gwang-Se Lee and Cheolung Cheong

Citation: AIP Advances 4, 127117 (2014); doi: 10.1063/1.4904028

View online: http://dx.doi.org/10.1063/1.4904028

View Table of Contents: http://aip.scitation.org/toc/adv/4/12

Published by the American Institute of Physics

Prediction and analysis of infra and low-frequency noise

of upwind horizontal axis wind turbine using statistical wind speed model

Gwang-Se Lee and Cheolung Cheonga

School of Mechanical Engineering, Pusan National University,

Busan, 609-745, Rep of Korea

(Received 4 August 2014; accepted 26 November 2014; published online 9 December 2014)

Despite increasing concern about low-frequency noise of modern large horizontal-axis wind turbines (HAWTs), few studies have focused on its origin or its prediction methods In this paper, infra- and low-frequency (the ILF) wind turbine noise are closely examined and an efficient method is developed for its prediction Although most previous studies have assumed that the ILF noise consists primarily of blade passing frequency (BPF) noise components, these tonal noise components are seldom identified in the measured noise spectrum, except for the case of downwind wind turbines In reality, since modern HAWTs are very large, during rotation, a single blade of the turbine experiences inflow with variation in wind speed in time as well as

in space, breaking periodic perturbations of the BPF Consequently, this transforms acoustic contributions at the BPF harmonics into broadband noise components In this study, the ILF noise of wind turbines is predicted by combining Lowson’s acoustic analogy with the stochastic wind model, which is employed to reproduce realistic wind speed conditions In order to predict the effects of these wind conditions

on pressure variation on the blade surface, unsteadiness in the incident wind speed is incorporated into the XFOIL code by varying incident flow velocities on each blade section, which depend on the azimuthal locations of the rotating blade The calculated surface pressure distribution is subsequently used to predict acoustic pressure at an observing location by using Lowson’s analogy These predictions are compared with measured data, which ensures that the present method can reproduce the broadband characteristics of the measured low-frequency noise spectrum Further investigations are carried out to characterize the IFL noise in terms of pressure loading on blade surface, narrow-band noise spectrum and noise maps around the turbine C 2014 Au-thor(s) All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License.[http://dx.doi.org/10.1063/1.4904028]

I INTRODUCTION

With decreasing mechanical noise in wind turbines (WTs), aerodynamic noise is the main hindrance to its widespread dissemination.1 3 Sources of aerodynamic noise in modern upwind horizontal-axis wind turbines (HAWTs) are categorized into low-frequency noise, inflow-turbulence noise, and airfoil self-noise.4 , 5The blade passing frequency (BPF) noise of a modern large HAWT generally belongs to the infra-sound frequency range up to about 10 Hz because of the very low rotational speed of the turbine In contrast, inflow- and self-noise are considered to contribute mainly as audible noise components

As a purpose for identification of main noise source within audible frequency range, acoustic visualization techniques were performed, previously.5It was found that the trailing edge noise is dominant in the frequency range 500 Hz to 3000 Hz of the spectrum of acoustic waves radiating

a Electronic mail: ccheong@pusan.ac.kr

from the pitch-controlled upwind-type wind turbine Numerous studies also reported that trailing edge noise of wind turbines predicted using semi-empirical models showed good agreements with measurements.69This semi-empirical model was developed by using scaling law of trailing edge noise and huge measurements for various flow conditions including attack of angle, flow speed, and geometric size of NACA0012 airfoil.10 For applying the semi-empirical model, the averaged flow field information was obtained from computational fluid dynamics techniques It is seen from these results that the trailing-edge noise is dominant in the middle frequency range of noise spectrum from the large upwind-type horizontal axis wind turbine

As described in the IEC 61400-11 which is the international code for the measurement and assessment of acoustic power of wind turbines, infrasound, low-frequency noise, and low-frequency modulation of broadband or tonal noise are important factors to characterize wind turbine noise.11 Although there is needs about research to characterize infra- and low-frequency (ILF) noise from modern HAWTs, few studies have been performed to understand its origin Most previous studies have assumed that the ILF noise consists primarily of BPF noise components Jung et al.12and Lee

et al.13have reported the ILF noise results from unidentified noise source components that evidently have a broad spectral distribution rather than tonal In reality, the long trajectory of a single blade in

a broad range of altitude levels during its slow rotation inevitably subjects the blade to incident wind with speeds varying in time as well as in space, which perturb the blade randomly As a result, acoustic contributions at the BPF harmonics are transformed into broadband noise components, as observed in the radiated noise Since the length scale of turbulent boundary layer (TBL) thickness on the turbine blade is too short to be responsible for low-frequency noise, it is understood that contribution of trail-ing edge noise to low frequency components is marginal Correspondtrail-ingly, inflow broadband noise can be considered to be main source of wind turbine noise in low frequency range, and its dominant source is mainly due to atmospheric turbulence in wind of length scale large enough to cause the infrasonic and low frequency noise

Several experimental studies reported difficulties in measuring the low-frequency wind turbine noise due to the masking effect of background noise Bray and James14analyzed the masking effects

on the measurement Leventhall15 reported the case where high background noise contaminates the measurement under 40 Hz Fégeant16reported more serious influences of background noise at higher wind speeds

Most previous studies to predict wind turbine noise using hybrid CAA methods were based on the averaged wind speed profile, which is simply computed from empirical formulae in the form

of power or logarithmic functions with a parameter describing ground roughness approximately.6 9 Therefore, these methods are not capable of considering time- and space- variations in the lift and drag of the rotating blade sections due to randomly fluctuating incident wind speeds

To investigate effects of power fluctuation induced by unsteadiness of incident wind on the control strategy, stochastic wind models at a given altitude have been developed.17 In this study, these stochastic wind models are employed to reproduce more realistic wind profiles varying in space and time, which are considered to cause the broadband components in the ILF noise of WTs

By incorporating the hybrid CAA method with the stochastic model for the incident wind speeds, the ILF noise of WTs is predicted in present paper For the hybrid CAA model, the XFOIL code18 and Lowson’s acoustic analogy19are used The former is used to predict the aerodynamic response

of the turbine blade sections, and the latter is used to predict the acoustic wave propagation from the rotating sources to the fixed receiver

In SectionII, the statistical wind speed model employed in this paper is described In Section

III, Lowson’s acoustic analogy is briefly introduced and the acoustic code based on Lowson’s for-mula is validated by comparing its prediction with that using the Ffowcs-Williams and Hawkings (FW-H) formula20in the commercial code In SectionIV, the measured data for the IFL noise of the target WT is described In SectionsV, the results obtained using the present prediction methods are compared with the measurements Finally, in SectionVI, the detailed analysis on the IFL noise of the WT is carried out by investigating pressure loading on the turbine blade, narrow-band acoustic pressure spectrum, and noise maps around the turbine

II STATISTICAL WIND SPEED MODEL

In order to predict the performance of WTs, a real-time wind speed model has been used.17 The real-time wind model is made up of two components: a quasi-steady term obtained from Van der Hoven’s model and an unsteady term computed by a stochastic model Van der Hoven’s wind model is associated with time scales on the order of hours and days, which constitutes a steady model in terms of the acoustic whose time scale is on the order of seconds The stochastic model represents wind speed in time intervals on the order of seconds Both wind speed models contain the same parameters which can be determined from the environmental conditions at the site of the wind turbines Therefore, real-time wind speed, v, including the quasi-steady and the unsteady terms can

be expressed in the form:

v(t, z) = Vz(z) + σv(z)vt(t, z), (1) where Vzdenotes the steady component, vt represents the unsteady component, and σvis the esti-mated standard deviation First, the steady wind speed Vzalong altitudes z can be computed using a power or logarithmic model The logarithmic wind speed model is written in the form:

Vs= Vz(z)









ln

zref

z0ref



lnHz

0



ln

 H

z0ref



lnzz

0











where zref is the reference height, 10 m; z is the height of the anemometer; H is the rotor center height; z0is ground roughness length, which is 0.05 m in the present study; z0ref is the reference roughness of 0.05 m; and Vsis the standardized wind speed.11 Using Eq (2) with Vz at a given height, the averaged wind speeds along heights of z are computed Next, the unsteady wind speed components are determined based on the procedure by Nichita et al.17In their study, the unsteady components had been defined by colored noise as

vt(t, z) =

 t 0

where h(τ, z) is the impulse response of filters, which is used to describe statistical characteristics of atmospheric inflow, and w(t) is white noise The impulse response may be written as

h(t, z) = 2π

 ∞ 0

where

P(ω, z) = Re



Kt(z) (1 + jωTf(z))5/6



Kt(z) ≈



B 1

2,1 3



Tf(z)

Tf = TL(z)

The low pass filter, P(ω, z), to compute the impulse response, is a function of: the gain, Kt; the sampling period, Ts; and a characteristic time scale, Tf, which is related to the atmospheric turbulent length scale along the heights, TL In this paper, TLis computed from an empirical formula depending on ground roughness conditions.6Finally, the stochastic wind speed is computed from the product of the unsteady component vt and the estimated standard deviation σv The standard deviation may be experimentally determined from regression analysis of the wind speeds measured

at a given site

The above-described procedure for computation of the fluctuating wind speed is roughly based

on the approach of Nichita et al However, numerical quadrature integration is applied to compute

FIG 1 Time histories of wind speeds computed by using statistical model of Eq ( 1 ) in a height range of 0 to 150 m, for an averaged wind speed of 6 m /s at a height of 10 m and with a ground roughness of 0.05m.

the impulse in this study, whereas Nichita et al used the discrete impulse hi(t) The accuracy of the discrete impulse function depends on spectral bandwidth ∆ω, which has to be small for reliable prediction If the spectral bandwidth is given, the procedure to compute the discrete impulse function

is faster than numerical quadrature integration However, an additional step of estimating the spectral bandwidth is required to optimize the spectral band in this prediction, unless the band is known By applying numerical integration, the optimization procedure can be simplified during the computation

of the fluctuating components, and the accuracy of the impulse function is acceptable for large ranges

of wind speeds along altitudes without an additional step to estimate the bandwidth

Illustrative computation for reproducing real wind conditions is carried out using the steady wind profile along the height in Eq (2) and the turbulent length scale computed from the empirical formula in the form:6

TL(z) = 25z0.35z0−0.063, (8) The resultant temporal and spatial wind fluctuations are shown in Fig.1, from which the fluctuations

of wind speed due to variations of turbulent kinetic energy and length scale along the altitude can

be identified The steady wind speed profile along altitude level is obtained under the assumption that the averaged wind speed at a height of 10 m and the ground roughness z0 are 6 m/s and 0.05

m, respectively To predict aerodynamic characteristics of wind turbine blades subject to this wind,

FIG 2 Spectrum of unsteady wind history at a height of 50 m computed by using the statistical model in Eq ( 1 ) in the case

of the averaged wind speed of 6 m /s at a height of 10 m and a ground roughness of 0.05m.

incident flow condition on sectional blades which is a function of time and space are computed by interpolating these unsteady wind data Resultant unsteady wind has spectral profile of decaying rate proportional to -5/6 which closely follows the decaying rate of low pass filter in Eq (5), as shown in Fig.2

III LOWSON ACOUSTIC ANALOGY

Lighthill derived a method to deal with aerodynamic noise generated by sources in rectilinear uniform motion As an extension of Lighthill’s study, Lowson derived formulas to describe the acoustic fields due to various types of sources: loading, simple source, and acoustic stress in arbitrary motion.19The equation employed in this study from Lowson’s acoustic analogy is

`

where `ρ is density fluctuation in sound field, and the subscripts ‘t’, ‘ f ’, and ‘n’ denote the total, far-field, and near-field terms, respectively The far- and near-field density fluctuations correspond-ing to the loadcorrespond-ing are respectively expressed in the forms

`

ρf =



(xi−yi) 4πa3

0r2(1 − Mr)2

∂Fi

∂t +

Fi

1 − Mr

∂Mr

∂t

 







and

`

ρn=



1 4πa2

0r2(1 − Mr)2

 Fi(xi−yi) r

 1 − M2

1 − Mr



− FiMi

 







where a0is the speed of sound, Fiis the force exerted on the source, M is the Mach number of the moving source, xiindicates the location of the observer, yirepresents the location of the source and

r is the distance between the source and the observer From Eqs (10) and (11), each contribution from the loading sources can be related to specific physical behavior The acoustic field due to point loading sources in rotational motion is found to consist of superposition of acoustic pres-sures represented by five terms: Doppler shift,(1−Mr); unsteadiness of force, ∂Fi/∂t ; acceleration from source to observer, ∂ Mr/∂t; geometric(spherical) spreading of the wave, Fi(xi−yi)/4πr; and convection of the source, FiMi In the case of an application using the far-field formula of Eq (10), even though force is steady, ∂Fi/∂t=0, an acoustic field can be generated from the acceleration term For instance, a rotating source of constant force and angular velocity generates acoustic pres-sure through its relative acceleration with respect to an observer’s fixed position If the sources are

in rectilinear motion with constant velocity, Eq (10) indicates that acoustic pressure in the far-field

is only due to unsteadiness of the source, as described in Lighthill’s analogy The near-field terms include spherical wave-spreading and convection terms The latter represents acoustic pressure generated by relative motion of the sources compared to a fixed observer while the former simply represents spherical wave-spreading if the sources are fixed

To validate the acoustic code developed using Lowson’s acoustic analogy, aerodynamic noise generated by a small vertical type of wind turbine is predicted and compared with the prediction obtained using the commercial code based on the FW-H equation.20Figure3shows the geometry of the target turbine The diameter and height of the turbine are 0.54 m and 0.75 m, respectively The turbine is assumed to rotate at a speed of 16.36 rad/s and to be subject to inflow wind at a speed

of 9 m/s First, the flow field around the rotating vertical turbine is simulated using a commercial CFD code, Fluent 14.5 The RANS solver with Shear-Stress-Transport (SST) k-ω model21in Fluent

is utilized Then, acoustic pressures at a specific location are predicted using two methods: the FW-H equation provided in Fluent and the present in-house code based on Lowson’s analogy Both methods used the same source data obtained from the flow simulation results by Fluent, which is the static pressure on the blade

Figures4and5show the acoustic pressure and its spectrum at near field, r/λ1st<< 1, and far field, r/λ1st>> 1, respectively, where r is distance from the center of turbine to an observer and

FIG 3 Geometrical shape of target turbine.

FIG 4 Comparison of acoustic predictions for a vertical wind turbine between the commercial code (acoustic module

in Fluent) and the present Lowson code at near field, r /λ 1st << 1; (a) time-varation of acoustic pressure and (b) its corresponding spectrum.

FIG 5 Comparison of acoustic predictions for a vertical wind turbine between the commercial code (acoustic module in Fluent) and the present Lowson code at far field r /λ 1st >> 1; (a) time-variation of acoustic pressure and (b) its corresponding spectrum.

TABLE I Specifications of the target HAWT for the field measurements

λ1stis the wavelength corresponding to the first BPF Good agreement is observed between the two methods, confirming the validity of the present method based on Lowson’s acoustic analogy

IV MEASUREMENT OF INFRA- AND LOW-FREQUENCY NOISE FROM A HAWT

One-third octave band levels are measured in the frequency range of 1 to 40 Hz at wind speeds of 6 and 7 m/s The specifications of the target HAWT are briefly summarized in TableI Measurement instrumentation and procedures based on the IEC61400-11 (2002) standard were used

to evaluate the ILF noise emission from the turbines Noise measurements were taken downstream

of the wind turbine using a microphone positioned on a circular rigid board The board was placed

on the ground to reduce wind noise generated at the microphone and to minimize the influence due

to variations in the soil type Previous studies by Lee et al.13and Jung et al.12can be refered to for further details on the experimental procedures

According to the IEC61400-11, measured sound levels must be corrected to assess the influ-ence of background noise by using the following equation:

Ls= 10 log10

100.1(LS+n)− 100.1(Ln )

(12) where Lsis equivalent continuous sound pressure level during the operation of a wind turbine alone,

Ls+nis the equivalent level of wind turbine noise with background noise, Lnis the background noise Figure 6 shows the measured SPLs with relative contributions of background noise in the relevant frequency bands The IEC61400-11 requests that, if the difference between Ls+nand Ln is larger than 6 dB, Lsis computed by Eq (12) to assess apparent sound power level, and in the case for the difference between 3 to 6 dB, Ls+nis corrected by subtraction of 1.3 dB, but the corrected data are indicated with mark of an asterisk, “*”.11In the case where the difference is under 3 dB, the measured band levels need not to be reported

For higher wind speed 7 m/s at the height of 10 m, it is seen that effect of the background noise

on the measured noise is stronger in the frequency range under 40 Hz, while at the wind speed of

6 m/s only two band levels are valid Similar difficulties are reported in other studies Leventhall reported that the noise radiating from the wind turbine of 1.5 MW capacity could be separated from the background in the frequency range only above about 40 Hz, where the measurements were

FIG 6 1 /3 octave band level L s of wind turbine operating alone estimated by using IEC61400-11: (a), L s for V 10 = 6 m/s; (b) L for V = 7 m/s.

FIG 7 Comparisons between predicted and measured powers according to wind speeds.

conducted at 65 m apart from the turbine.15The contamination by background noise becomes more serious for higher wind speeds,16as confirmed in Fig.6(b) The measurement taken in the case of

V10= 6 m/s is, therefore, chosen to validate the predictions

V VALIDATIONS OF CURRENT NUMERICAL METHODS

In this section, the ILF noise of the HAWT is predicted using the hybrid CAA methods based

on Lowson’s acoustic analogy and the stochastic wind speed model The predicted results are compared with the measured data to validate the method, and then possible underlying mechanisms responsible for generating the ILF noise of HAWTs are discussed

As described above, an empirical constant has been used to define the standard deviation of the fluctuating wind speed components The wind speed and its standard deviation can be modeled by

FIG 8 Comparisons of 1 /3 octave band levels among measurements and predictions using mean and stochastic wind speed: (a) V = 6m/s and (b) V = 7m/s.

FIG 9 Comparison of iso-contours of averaged pressure on the blade surface, computed by using the mean 3 (solid lines) and stochastic (dash-dot-dot lines) wind models for V 10 = 6 m/s.

using the measured wind speeds at the target site Nichita et al have applied the following equation

to estimate the standard deviation instead of using the measured data:

where kσ, vis a proportionality constant between the standard deviation and mean wind speed distri-bution along the altitude This parameter can be determined empirically by considering geometric conditions around the target site where the wind turbine is installed For example, at the coast and offshore sites where the influence of the site’s topography is weak, kσ, vis considered to be small, i.e., 0.1 to 0.15 All of the following computations to predict the fluctuating wind speed components are conducted using Eq (13) with kσ, v= 0.15

Prior to computing acoustic wave propagation, the aerodynamic characteristics of the pressure distribution on the surface of the rotating blade must be computed as acoustic source input data The XFOIL code is utilized to compute the pressure distribution on each section of the wind turbine blades Aerodynamic prediction is validated by comparing the predicted power of the turbine with the measured data, as shown in Figure 7 It is seen that the predicted power for the target wind turbine agrees well with measurements

Figure8compares predictions with measurements in the frequency range under 40 Hz When only the averaged wind profiles are considered, there are significant discrepancies between the pre-dicted results and the measured data Predictions using the averaged wind profiles can give only BPF harmonic contributions, and thus no contributions above 10 Hz are identified The predictions using the statistical wind speed model show much better agreement to the measurements, though differences

FIG 10 Iso-contours of fluctuating surface pressure on the blade computed by using the mean (a) and stochastic (b) wind models for V = 6 m/s.