Aeroacoustic noise prediction for wind turbines using

J. Wind Eng. Ind. Aerodyn. 145 (2015) 17–29

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Journal of Wind Engineering and Industrial Aerodynamics journal homepage: www.elsevier.com/locate/jweia

Aeroacoustic noise prediction for wind turbines using Large Eddy Simulation Sahan H. Wasala a, Rupert C. Storey b, Stuart E. Norris b, John E. Cater a,n a

Department of Engineering Science at The University of Auckland, New Zealand The University of Auckland, Department of Mechanical Engineering, Auckland 1142, New Zealand

b

art ic l e i nf o

a b s t r a c t

Article history: Received 14 November 2014 Received in revised form 6 May 2015 Accepted 18 May 2015

Noise disturbance is one of the major factors considered in the development of wind farms near urban areas, and therefore an accurate estimate of the noise levels generated by wind turbines is required before production and installation. Horizontal-axis wind turbines are the most popular type of turbines and the aeroacoustic noise generated by their rotating blades is known to be the most significant noise source. The region of the turbine blade that produces the strongest acoustic sources has been identified in published acoustic camera measurements. In the present work, a Large Eddy Simulation (LES) of this region is carried out using an annular computational domain, which leads to a significant reduction of computational expense compared to full blade simulations. The Ffowcs-Williams and Hawkings (FW–H) acoustic analogy is then used to predict the far field sound. Numerical results for a simulation of the CART-2 wind turbine show good agreement with the available experimental data. & 2015 Elsevier Ltd. All rights reserved.

Keywords: Wind turbine noise Large Eddy Simulation Aeroacoustics

1. Introduction The wind is a renewable energy resource with the potential to supplement and replace some fossil fuel based energy sources. In an increasingly urbanised world, it is often attractive to site wind farms near human settlements. Noise exposure is one of the main concerns when siting new farms near dwellings (Wolsink, 2000) and as a consequence, it is important to estimate and mitigate wind turbine noise levels before installation. There are two sound general generation mechanisms for wind turbines: mechanical noise and aerodynamic noise. Mechanical noise is mainly generated by moving parts inside the gearbox and the generator (Pinder, 1992). This source can be reduced through technologies such as high precision gear tooth profile designs and acoustic insulation of the nacelle (Tong, 2010). However, the aerodynamic noise sources (also called aeroacoustic sources) are more complex and not easy to control. Aeroacoustic sources can be classified as monopoles, dipoles and quadrupoles. Monopole and dipole sources originate near surfaces and are strong radiators of acoustic energy (Ffowcs-Williams and Hawkings, 1969b). Quadrupole sources originate away from surfaces and are weak radiators (Lighthill, 1952). The flow around a wind turbine is highly n

Corresponding author. E-mail addresses: [email protected] (S.H. Wasala), [email protected] (R.C. Storey), [email protected] (S.E. Norris), [email protected] (J.E. Cater). http://dx.doi.org/10.1016/j.jweia.2015.05.011 0167-6105/& 2015 Elsevier Ltd. All rights reserved.

turbulent and the aerodynamically generated noise from a wind turbine is due to the unsteady flow over the surface of the wind turbine blade, resulting in strong dipole sources. Schlinker and Amiet (1981) identified blade trailing edge noise as the main noise source from a horizontal-axis turbine. Brooks and Schlinker (1983) formulated two main aeroacoustic broadband noise generation mechanisms for rotating aerofoil sections in order to simplify understanding of these complex sources, and to implement models in a semi-empirical noise prediction code. The first mechanism is turbulent ingestion noise, which is a function of the inflow turbulence. It has been shown that the power at the low frequencies in the acoustic noise spectrum is mainly due to the turbulent inflow (Wagner et al., 1996), and these amplitudes are difficult to determine using a semiempirical method because of the non-linear character of the turbulence. The second noise mechanism is the aerofoil self-noise which is a function of the blade geometry. Aerofoil self-noise generation can be further divided into turbulent boundary layer trailing edge noise, laminar boundary layer vortex shedding noise, separation and stall noise, trailing edge bluntness and vortex shedding noise and tip vortex noise. A detailed explanation of these mechanisms can be found in Brooks et al. (1989). Moriarty (2004) developed a semi-empirical wind turbine noise prediction method based on work by Brooks et al. (1989), however the predicted noise levels differed significantly from the experimental data at both low and high frequencies. An additional noise mechanism is due to the interaction between the rotating

18

S.H. Wasala et al. / J. Wind Eng. Ind. Aerodyn. 145 (2015) 17–29

blade wake and the turbine tower. This mechanism has a tonal character where the tones are integer multiples of the blade passing frequency of the rotor (McAlpine and Kingan, 2012). An alternative to empirical methods is to resolve the aeroacoustic sources using Computational Fluid Dynamics (CFD) and Computational Aeroacoustics methods (CAA). An accurate estimate of the noise generation from a wind turbine requires wellresolved transient flow field data, particularly near the surface of the blade (Arakawa et al., 2005). Methods such as Direct Numerical Simulation (DNS) or Large Eddy Simulation (LES) can be used for calculation of an unsteady turbulent flow field. These methods are computationally expensive because they require a fine computational grid around the surface of the blade (Storey et al., 2014). The fine grid also leads to high temporal resolution requirements for transient simulation in order to avoid numerical instability. LES is computationally less expensive than DNS, and to date has shown reasonable results for aeroacoustic simulations (Wagner et al., 2007). Recent studies by Mo and Lee (2011) used LES to predict the aeroacoustic noise from the NREL Phase VI wind turbine. However, the maximum frequency resolved was 500 Hz; this is not within the range of 1–5 kHz where the human ear is most sensitive (Gelfand and Levitt, 1998). The effects of the tonal noise due to the blade passing frequency were not quantified, even though the whole wind turbine including the tower was modelled. The acoustic data has also not been validated with experimental data. Arakawa et al. (2005) simulated the noise from the WINDMELIII wind turbine using LES and a finite difference method. However, the results largely differ from far field experimental noise measurements due to insufficient span-wise grid resolution. The acoustic camera measurements of Oerlemans et al. (2001) suggest that the majority of the noise sources are located at the 75–95% span section of the wind turbine blade, where the local flow velocities are relatively high. Further analysis of Oerlemans's data shows that at span-wise locations below approximately 75% the dominant noise sources are frequencies below 1 kHz, and beyond this location, most of the acoustic power is radiated at higher frequencies. Therefore, it is proposed that the noise generated at the inboard region of the blade can be neglected when considering noise disturbance and does not need to be modelled. Zahle (2009) suggested that at high tip speed ratios (TSR), when the turbines are noisiest, the outboard region of the blade has a flow field of a tangential nature. Simulating only the outboard region of the blade, assuming there is no radial flow, reduces the computational cost compared to a full wind turbine simulation and may produce sufficient acoustic source data for accurate far field noise prediction. In the present work, a non-rotational domain with a symmetric NACA0012 aerofoil is initially simulated using LES with ANSYS Fluent (Ansys Inc.) to establish suitable mesh distribution requirements and boundary conditions. Thereafter, a hybrid computational mesh of the rotational annular section of the 75– 95% span of the CART-2 wind turbine blade is simulated. The Ffowcs-Williams and Hawkings (FW–H) acoustic analogy is used to calculate the acoustic pressure at a far field receiver location and the results obtained are compared with experimental data.

2. Methodology

being modelled using a sub-grid scale turbulence model. The filtered mass continuity equation is

∂ρ ∂ + (ρu¯i ) = 0. ∂t ∂xi

(1)

The filtered incompressible unsteady three-dimensional Navier– Stokes equations are

∂τij ∂ ∂ ∂ ∂p¯ (ρu¯ i ) + (ρu¯ i u¯ j ) = (σij ) − − , ∂t ∂x j ∂x j ∂xi ∂x j

(2)

where u¯ i is the mean velocity component, ρ is the density of the fluid, p¯ is the pressure, τij is the sub-grid scale stress tensor, and sij is the stress tensor due to molecular viscosity given by

⎛ ∂u¯ ∂u¯ j ⎞ i ⎟⎟. σij ≡ μ ⎜⎜ + ∂xi ⎠ ⎝ ∂x j

(3)

Here, the dynamic viscosity of the fluid is μ. The sub-grid scale stress tensor is normally modelled as (Smagorinsky, 1963),

τij = − 2Cs Δ¯2 |S˜|S¯ij,

(4)

where Cs is the Smagorinsky constant, Δ is the sub-grid filter width and |S¯| = 2S¯ij S¯ij , where S¯ij is the rate of strain tensor. However, the optimum Cs value varies from flow to flow and has to be reduced near solid walls in order to reduce the numerical dissipation introduced by the sub-grid scale model, particularly for the present work where the surface fluctuations are assumed to be the main acoustic sources. Therefore, the dynamic Smagorinsky method of Germano et al. (1991) is used. Here, an extra filter level, which is known as the test filter, is used in combination with subgrid scale filter level, in order to estimate the value of Csnew , which is a function of time and space. Germano's identity in Eq. (5) explains the relationship between the two filter levels:

^ L ij = ui˜u j − u˜ i u˜ j = Tij − τij.

(5)

Here, the stress tensor at the sub-grid level (τij) and at the test filter level (Tij) are modelled in the same way as in the Smagorinsky model where

Tij = − 2Cs Δ˜2 |S¯˜|S¯˜ij,

(6)

and the test filter has a filter width of Δ˜ , which is twice that of the 1

grid filter width Δ. In the present calculations Δ = V 3 , where the local cell volume is V. Lîj can be calculated using the values from the resolved large eddy field using

^ L ij ≈ 2Csnew ΔMij,

(7)

where

Mij = (Δ˜ /Δ)2|S˜ |S˜ij . The model coefficient

(8) Csnew

is assumed to be independent of the

filter (Csnew = Cs2). A stable expression for Csnew was introduced by Lilly (1992) which increased the stability during the dynamic procedure

Csnew Δ2 =

L ij Mij Mij Mij

.

(9)

2.1. Large Eddy Simulation 2.2. Acoustic simulation Large scale turbulence in a flow can have a complex and anisotropic structure. However, small scale eddies may be assumed to be isotropic. In LES, a low-pass filter is used to filter the Navier– Stokes equations, with length scales smaller than the filter width

The earliest approach to formulate the aeroacoustic noise was that of Lighthill (1952, 1954), where the Navier–Stokes equations were rearranged into an inhomogeneous wave equation given by


The loading contribution (pL′ ) is

∂ 2Q ij 1 ∂ 2p′ , − ∇2p′ = 2 2 ∂xi ∂x j c0 ∂t

(10)

where p′ = c02 ρ′ and c0 is the ambient speed of the sound. The right hand side represents the source term, where Lighthill's stress tensor is Qij. The left hand side of Eq. (10) describes the propagation of the acoustic wave in both the spatial and temporal domains. The original purpose of this equation was to predict aircraft jet noise, which was a significant concern when civil aviation becomes a common form of transportation. Lighthill considered quadrupole sources, however Ffowcs-Williams and Hawkings (1969a) (FW–H) extended Lighthill's equation to allow for the prediction of noise from a moving surface. The FW–H equation has two extra source terms which represent monopole and dipole sources, shown in the following equation:

⎧ ⎫ ⎪ ⎪ 1 ′ ⎨ − ∇2p′ = Q ij H (f ) ⎬ ⎪ ⎪ 2 2 ∂xi ∂x j ⎩ c0 ∂t ⎭ ∂ 2p

∂2

⎧ ⎫ ⎪ ∂ ⎪⎡ ⎨ ⎣ρ 0 vn + ρ (un − vn ) ⎤⎦ δ (f ) ⎪ ⎬. ⎪ ∂t ⎩ ⎭

(11)

Lighthill's stress tensor can be expressed as

Q ij = ρui u j + Pij − c02 (ρ − ρ 0 ) δij,

(12)

and the compressive stress tensor is

Pij = p′δij,

(13)

where ui is the fluid velocity in the i direction, vi is the surface velocity in the i direction, ni is the unit vector in the i direction, un is the fluid velocity normal to the surface (f¼ 0), vn is the surface velocity normal to the surface (f ¼0), δ (f ) is the Dirac delta function, H (f ) is the Heaviside delta function, p′ is the acoustic pressure at the far field and f is the mathematical surface of the moving body. Solving the FW–H equation at every grid point in the domain requires a fine computational grid and is computationally expensive (Farassat, 1981). However, the solution at a receiver location can be calculated analytically using generalised function theory and the free space Green's function. The total acoustic pressure at a far field receiver location is given by

p′ = pT′ + pL′ ,

(14)

where the thickness contribution (pT′ ) is

4πpT′ (x, t ) =

+

⎡ ρ (U ̇ + U ) ⎤

∫f = 0 ⎢⎢ r0(1 −n M )n2 ⎥⎥ ⎣

r

⎦ret

ds

⎡ ρ U {rṀ + c (M − M 2)} ⎤ 0 r r 0 n ⎥ ds . 2 (1 − M )3 ⎥⎦ r ⎣ r ret

∫f = 0 ⎢⎢

4πpL′ (x, t ) =

1 c0

⎡

r

⎡

+

⎤

∫f = 0 ⎢⎣ r 2 L(1r −− LMM )2 ⎥⎦ r

+

1 c0

⎡

(15)

M r is the Mach number of a point on the moving surface and r is the distance to the observer. The subscript ret denotes that the integrals are computed at the corresponding retarded times, tret = t − r /c0 , where t is the observer time. The dot above a variable represents the source-time derivative of that variable.

⎤

̇

∫f = 0 ⎢⎣ r (1 −L rM )2 ⎥⎦

ds

ret

ds

ret

̇

r − M ∫f = 0 ⎢⎢⎣ L r {rMrr 2+(1c−0 (M M )3 r

2)} ⎤

⎥ ds . ⎥⎦ ret

(16)

Here,

Ui = vi +

ρ (ui − vi ), ρ0

L i = Pij δij n j + ρui (un − vn ).

⎧ ⎫ ⎪ ∂ ⎪⎡ ⎨ ⎣Pij n j + ρui (un − vn ) ⎤⎦ δ (f ) ⎪ ⎬ − ⎪ ∂xi ⎩ ⎭

+

19

(17)

(18)

The detailed derivation of Eqs. (15) and (16) can be found in Farassat (2007). The Doppler effect due to a uniform free stream flow is accounted for in the present simulations. The acoustic pressure data at a far field receiver location, obtained using the above method was post-processed using a Fast Fourier Transform (FFT) algorithm with a Hamming windowing function (Welch, 1967). Finally, the 1/3 octave spectra were constructed for comparison to experimental data. The Sound Pressure Level (SPL) is obtained with respect to the reference acoustic pressure pref = 2 × 10−5 Pa where

⎡ p′ ⎤ SPL = 20 log10 ⎢ rms ⎥. ⎢⎣ pref ⎥⎦

(19)

The method assumes that there are no obstacles between the source and the receiver that could disturb the acoustic wave. The acoustic wave is also assumed to exert no forces on the fluid flow. In this simulation, the quadrupole sources are neglected from the calculation, as they are assumed to have no significant acoustic contribution to a far-field receiver. Tonal noise due to the wake– tower interaction is also neglected in the present study in order reduce the computational cost. The WOPWOP and PSU WOPWOP (Brentner, 1986) codes have demonstrated this method for prediction of noise generation from helicopter rotors. 2.3. NACA0012 validation 2.3.1. Mesh generation The aeroacoustic simulation methodology was initially tested on a NACA0012 aerofoil in a rectangular domain and validated with experimental data from Brooks et al. (1989). The NACA0012 is a symmetric aerofoil developed by the National Advisory Committee for Aeronautics (Jacobs et al., 1933). It has been widely used in the aerospace industry for experimental purposes due to the simplicity of the geometry. The final two digits represent the maximum thickness of the aerofoil with respect to the chord, in this case 12%. The simulation domain used is shown in Fig. 1. The domain is scaled such that the blockage ratio, which is the ratio of the cross sectional area of the onset wind to the front projection area of the NACA0012 blade, is less than 1%. The chord length used is C ¼0.3048 m to match the experimental data. The span used is 0.1143 m which is 1/4 of the experimental span (S) used by Brooks et al. (1989). This reduced span gave acceptable acoustic results with reduced computational cost and was obtained by a series of preliminary studies where the span was varied from S to 1/8S. The

20


Fig. 1. Rectangular domain used for the initial NACA0012 aeroacoustic simulations showing the boundary conditions. The chord length of the aerofoil is C and the span is 1/4 S.

distance from the main inlet boundary to the leading edge of the blade is 6C and the distance from the leading edge to the main outlet boundary is 12C. The 3D geometry of the NACA0012 and the hybrid computational grid was created using ANSYS ICEM CFD (Ansys Inc.). The mesh is structured near the blade and unstructured in the far field. The blade is simulated with a sharp trailing edge, since the wind tunnel experiment had a trailing edge thickness of less than 0.016% of the chord. The boundary layer thickness at the trailing edge was initially estimated using the Blasius equation and is spanned by 12 structured prism layers. The first grid point near the wall has a y+ value of order one (Wagner et al., 2007). The span-wise and chordwise surface grid sizes are equal (Δx = Δz ), so that the acoustic sources will be consistently resolved across the surface of the blade. A mesh resolution study was performed in order to obtain a solution independent mesh and the results showed that a minimum number of 152 nodes along the chord of the blade was required for a converged solution. Beyond the structured prism mesh, another 5 uniform sized tetrahedral layers were included. In the far field mesh, the maximum cell size was limited to be less than 1/3 of the width of the computational domain. The resulting complete mesh contained approximately 3 million cells. 2.3.2. Boundary conditions Velocity inlet and pressure outlet boundaries are used to simulate the far field flow locations. The two inlet boundaries had prescribed velocities of u = U∞ cos (α ), v = U∞ sin (α ) and w = 0, where U∞ = 71.3 m/s and α is the angle of attack if the aerofoil. A free stream velocity 71.3 m/s yields a Reynolds number of 1.5 × 106 based on the chord length. The free stream turbulence intensity at the anechoic wind tunnel in NASA Langley research facility is low and is assumed to be I∞ ¼0.4% (Moreau and Roger, 2007) and this is the value used at the inlet in the simulation. The spectral synthesiser method was used to generate velocity fluctuations at the inlet in order to simulate the transient turbulent flow field. The turbulence length scale is estimated based on the boundary layer thickness, where l = 0.4δ . In an initial study, the turbulence length scale was increased by up to two orders of magnitude and the spectral response showed an increase of less than 2 dB in the SPL at the low frequencies. Therefore, it is assumed that the turbulence length scale does not have a significant effect on the acoustic spectra and the initial value is used for later simulations. The two outlet boundaries have zero gauge pressure prescribed. A symmetry boundary condition is used to simulate the remaining boundaries

where the normal velocity and normal velocity gradient on the symmetry surface are zero. Both periodic and symmetry boundary conditions were tested on these boundaries, however no significant differences were observed in the acoustic results. Finally, the NACA0012 aerofoil surface is specified as a no-slip wall. 2.3.3. Steady flow field A steady state RANS (Reynolds-Averaged Navier–Stokes) solution has been used for the initial flow field for the LES simulation. In this way the transient flow field reached a quasi-steady state more rapidly than initialising the flow field with a uniform velocity, significantly reducing the computational cost of the LES calculation. The RANS solution was calculated with the SIMPLE (Semi-Implicit Method for Pressure Linked Equations, Patankar and Spalding, 1972) algorithm, using third order spatial differencing with a convergence criteria of 10 6 for all residuals. 2.3.4. Transient flow field The iterative PISO algorithm (pressure implicit with splitting of operator (Issa, 1986) was used for the transient LES, with the pressure and momentum equations solved using a second order central differencing scheme. A Green–Gauss node-based method is used to evaluate the pressure gradient (Raisch et al., 1991). The optimal time step size was found with a temporal resolution study. A time step size of 10 6 s provided a stable solution by limiting the maximum Courant number throughout the domain to less than 0.3. The simulation became quasi-steady after a single flow domain pass-through and data from a subsequent pass-though was used for post-processing. 2.3.5. Validation of the CFD results In order to validate the simulations, the coefficients of lift and pressure were compared with experimental data from two separate sources. The lift coefficient can be obtained using

CL =

L , 1 2 ρ∞ U∞ S 2

(20)

where L is the total lift force and ρ∞ is the free stream fluid density. The pressure coefficient can be obtained using

Cp =

p − p∞ , 1 2 ρ∞ U∞ 2

(21)


21

Gregory and O'Reilly (1973) and shows close agreement. At α = 0°, Cp is slightly lower than the experimental value. This difference could be due to the higher Reynolds number of the experimental data. However, at high α this difference is not visible. At α = 0°, the numerical results show a data point above C p = 1. According to Norris (2011) this is due to a numerical error at the stagnation point near the leading edge. At α = 5.4° the Cp results near the leading edge are slightly lower than the experimental data on the suction side. This could be due to the slightly higher angle of

where p∞ is the ambient pressure. The time-averaged lift coefficient has been evaluated for LES calculations at four different angles of attack as shown in Fig. 2, and agrees well with the experimental data of Abbott and VonDoenhoff (1959). Fig. 3 compares the time-averaged pressure coefficient data obtained using LES with the closest available experiment data by 1.6 1.4 1.2

CL

1 0.8 0.6 0.4 0.2 0

0

2

4

6

8

10

12

14

16

Fig. 4. Instantaneous isosurface of vorticity at 2500 1/s on the suction side of the NACA0012 aerofoil coloured by the velocity magnitude. α ¼ 0 °. The inlet velocity is constant at 71.3 m/s and the inflow turbulence intensity is 0.4%. (For interpretation of the references to colour in this figure caption, the reader is referred to the web version of this paper.)

α, degrees Fig. 2. CL LES results of NACA0012 blade ( from Abbott and Von-Doenhoff (1959) (◊).

) compared with experimental data

α = 0°

α = 5.4° −3

−0.5

−2

0

−1 C

Cp

p

−1

0.5

0

1

1

1.5

0

0.2

0.4

0.6

0.8

2

1

0

0.2

0.4

0.6

x/c

x/c

α = 10.8°

α = 14.4°

−6

0.8

1

0.8

1

−10 −8

−4

−2

Cp

C

p

−6 −4 −2 0 0 2

0

0.2

0.4

0.6

0.8

2

1

0

0.2

0.4

x/c

0.6 x/c

106

Fig. 3. LES results of the pressure coefficient Cp for the NACA0012 aerofoil, at Re = 1.5 × mental data by Gregory and O'Reilly (1973) at Re = 2.88 × 106 and α = 0°, 5° , 10°, 14° ( ).

and α = 0°, 5.4°, 10.8°, 14.4° (

) are compared with closest available experi-

22


attack of the numerical data. The results at α = 10.8° and 14.4° do not show any significant difference to the experiments. The velocity curl (vorticity) describes the local rate of rotation, and instantaneous coherent vortex structures suggest locations where rapid pressure fluctuations can occur that lead to the generation of acoustic sources. Fig. 4 shows the instantaneous

isosurface of vorticity at 2500 1/s on the NACA0012 blade at α = 0°. The isosurface is relatively smooth on the leading edge surface, however, there appear to be large vortex structures just in front of the stagnation point, which are thought to be related to the onset turbulence. There are also complex vortex structures at the trailing edge which are related to the trailing edge noise.

Fig. 5. Instantaneous surface strain rate contours for the NACA0012 aerofoil at α = 0° (a), α = 5.4° (b), α = 10.8° (c) and α = 14.4° (d). The inlet velocity is constant at 71.3 m/s and the inflow turbulence intensity is 0.4%.

Fig. 6. RMS values of the instantaneous surface time derivatives of static pressure for the NACA0012 aerofoil at α = 0° (a), α = 5.4° (b), α = 10.8° (c) and α = 14.4° (d). The inlet velocity is constant at 71.3 m/s and the inflow turbulence intensity is 0.4%.


The RMS values of the static pressure time derivative (p¯s ), as defined in equation (22), are the sources used in the FW–H equation to calculate the far field noise:

p¯ s =

1 N

N

⎛ dp ⎞2 ⎟ dt ⎠

∑ ⎜⎝ 1

(22)

Fig. 5 shows the instantaneous surface rate of strain contours for α = 0–14.4°. The surface strain rates closely correlate with the value of p¯s in Fig. 6. At angles of attack greater than 5°, the strain rates near the suction side of the leading edge are relatively high compared to the lower angles of attack. Similarly, p¯s values at the trailing edge also increase with increasing angle of attack. Fig. 6 shows the values of p¯s on the surface of the blade. In all cases, there are high values of p¯s at the trailing edge of the aerofoil indicating the existence of turbulent boundary layer trailing edge noise. When the angle of attack increases, the most significant noise sources shift towards the leading edge. Simultaneously, the magnitude of the trailing edge noise sources also increase. Brooks et al. (1989) concluded that the trailing edge is the most significant noise source based on measurements at 0° angle of attack. 2.3.6. Validation of the acoustic results An acoustic receiver was located at a point in the mid-span plane 1.2 m from the trailing edge of the aerofoil perpendicular to

the chord line to match the position of the microphone in experiments. The acoustic pressure was recorded during 1.5 complete pass-throughs of the transient flow through the domain after the simulation has become quasi-steady. The 1/3 octave spectra of the data are compared with the experimental data of Brooks et al. (1989). The results of this comparison are shown in Fig. 7. All numerical spectra show good agreement with the experimental data. At α = 0°, local maxima are evident in frequency bands at 800 Hz and 1.6 kHz. These are assumed to be associated with tonal components; at high angles of attack they are not apparent. However, as angle of attack increases, the SPL increases at frequencies below 2 kHz, with a low frequency hump from 600 Hz to 1 kHz. The amplitudes above 2 kHz are almost the same regardless of the angle of attack; this shows that the high frequency noise generated by the aerofoil is not a strong function of the angle of attack. However, at α = 0° the numerical model slightly over-predicts the SPL in the 3–6 kHz range. The numerical model correctly predicts the increasing energy at low frequencies with respect to the angle of attack. This can be also explained using the strain rate data shown in Fig. 5, where increasing strain rates near the leading edge at high angles of attack contribute to the low frequency component of the acoustic power spectrum. At α = 10.8°, frequencies above 8 kHz and below 700 Hz are over-predicted with a maximum error of 3 dB. At α = 14.4° the numerical method has under-predicted the noise

°

°

Alpha = 5.4

80

80

70

70

1/3

SPL , dB

SPL1/3, dB

Alpha = 0

60

50

40

60

50

3

40

4

10

10

10

3

Frequency, Hz °

4

°

Alpha = 14.4

80

80

70

70

1/3

SPL , dB

SPL1/3, dB

10 Frequency, Hz

Alpha = 10.8

60

50

40

23

60

50

3

4

10

10 Frequency, Hz

40 10

3

10

4

Frequency, Hz

Fig. 7. Anechoic wind tunnel acoustic measurement data for NACA0012 aerofoil at α ¼0°( ) 5.4° ( ) 10.8° (◊) and 14.4°( ). Numerical results are shown with open symbols.

24


Fig. 8. Acoustic directivity for the NACA0012 aerofoil at , , α = 10.8° and receiver locations on a circle of radius 4C from the trailing edge at the mid-plane of the aerofoil.

calculated using the LES data. OASPL is calculated at 36

directions. This shows the contribution of the low frequency sources near the leading edge to the overall noise. These data may be used to estimate the directivity of the noise from a wind turbine as it is expected that the downwind and upwind noise levels from a wind turbine would be higher than in the plane of rotation. Additionally, higher sound levels will be recorded by a ground-based receiver when a blade is rotating towards to the ground, compared to when it is moving away from the ground. These initial observations agree with the study by Oerlemans et al. (2001) which was based on acoustic camera measurements and will be used for validation of a rotating wind turbine blade in the next section. 2.4. CART-2 wind turbine simulation

Fig. 9. CART-2 wind turbine photograph by Lee Fingersh, NREL 16387.

level with a 2 dB maximum error. Overall, the method is regarded as satisfactory for the prediction of the far field noise. The OASPL was calculated using the receiver placement discussed above, with an additional 35 receivers placed around the aerofoil in a 1.22 m radius as shown in Fig. 8. At all frequencies, the receivers located perpendicular to the chord experience the highest noise level with respect to all the other receivers, approximately 12–18 dB louder than the noise in the plane of the chord. Additionally, in the leading edge direction the OASPL is 5–6 dB higher compared to the trailing edge direction. When the angle of attack increases from α = 0° to 5.4°, OASPL increases in the chord plane, however there are no significant changes at directions perpendicular to the chord. When the angle of attack is further increased to α = 10.4° and α = 14.8°, OASPL increases for all

The two bladed Control Advanced Research Turbine (CART-2), shown in Fig. 9, is located at the National Wind Technology Centre (NWTC) in Boulder, Colorado, and is a Westinghouse 600 kW horizontal axis wind turbine with a 42 m rotor diameter (D) and 36.6 m hub height (H). The CART-2 wind turbine blade consists of a modified LS(1)-04XX aerofoil section, which was initially used in General Aviation, where the chord and the aerofoil maximum thickness vary with respect to the span. The thickness, chord and twist data for the blade were obtained from drawings provided by NREL. However, the trailing edge thickness used in the present work is the default for LS(1)-04XX aerofoil, as the actual geometry of the blunt blade as built was not available. An initial study of the NACA0012 trailing edge thickness demonstrated that doubling the trailing edge thickness had no significant effect on the acoustic spectrum. Acoustic measurements of this wind turbine have been made by Moriarty (2004) according to the IEC61400-11 standard, where the receiver was located at ground level at a distance of H + D/2 in the downwind direction. The simulation was conducted for the case where the blade pitch angle is 3°. The mean inlet velocity at hub height is 10.81 m/s and the upwind turbulence intensity is 10.3%. The CART-2 wind turbine has a rated output of 660 kW at


25

Fig. 10. A section of the CART-2 blade in an annular domain. −2.5

−2

−1.5

C

p

−1

−0.5

0

0.5

1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

x/c

Fig. 11. The pressure coefficient at the mean chord location (C ¼1.013 m) for the CART-2 blade section, which is located at a radius of 17.416 m. The local angle of attack is α ≈ 6°.

Fig. 12. Instantaneous iso-surface of vorticity at 2500 1/s on the suction side of the CART-2 blade section coloured by the velocity magnitude. The blade section is viewed with the radius increasing in the positive Y-direction. (For interpretation of the references to colour in this figure caption, the reader is referred to the web version of this paper.)

26


41.7 rpm (Bossanyi et al., 2010). The measurements by Moriarty (2004) were conducted at the rated rotational speed, where the tip speed ratio (TSR) is 8.5, which is relatively high. Therefore, it is assumed that the flow at the outboard region of the blade is primarily tangential (Zahle, 2009). 2.4.1. Mesh generation and boundary conditions The dimensions of the domain used for the CART-2 simulations are normalised with the chord length at the tip, as shown in Fig. 10. Two velocity inlet boundaries and two pressure outlet boundaries are defined to simulate the free stream flow. The velocity inlets have constant u = v = 0 m/s and w ¼10.8 m/s, so that U∞ ¼10.8 m/s and the turbulence intensity at the inlet is defined as I∞ = 10.3% using the spectral synthesiser method, where the velocity fluctuations are generated as a summation of Fourier harmonics. A rotational reference frame with a constant

angular velocity of 41.8 rpm is used to simulate the rotation of the blade, giving an apparent onset velocity that varies with the radial distance across the inlets. The mesh is generated with the same cell distribution method described in Section 2.3.1. The number of grid points per chord length is maintained at 152, but the cell height is reduced from the NACA0012 simulation in order to maintain y+ values of approximately 1. Since the cell size is normalised by the chord length, the x+ and z + of the cells on the surface have increased with respect to the surface cells in the NACA0012 simulations. The total number of cells in the domain is approximately 15.8 million. The simulations used the second order central differencing scheme for spatial discretisation. Therefore, the maximum frequency resolved is reduced to 4.5 kHz (Wagner et al., 2007). The simulation was stable at a transient time step of 5 × 10−6 s, and ran for a total simulated duration of approximately 0.3 s. The final 30° of rotation

Fig. 13. Instantaneous surface rate of strain for the CART-2 blade section, suction surface (top) and pressure side (bottom). The onset wind is in the X-direction.

Fig. 14. Surface static pressure time derivative RMS values for the CART-2 wind turbine blade section. The suction surface is facing upwards, with the leading edge on the left-hand side.


has been used for the acoustic calculations. This simulation took approximately 10 days running in parallel on 128 computer cores. In the present simulation, only a single rotational blade section was numerically simulated using LES. However, the CART-2 turbine has two blades, therefore the final noise calculation has to take into account sources from both blades. The noise from the second blade is simulated by placing an extra identical source at the relative location of the second blade. Summing the sound pressure levels will give a time averaged approximation of the noise due to both of the blades, assuming that the acoustic sources are incoherent, and thus that there is no noise cancellation due to the phase difference. A full rotation of 360° is simulated by placing 36 receivers in a plane parallel to the turbine plane with a radius of H, 58 m downwind.

3. Results and discussion 3.1. CFD results Fig. 11 shows the average pressure coefficient at the mean chord location for the CART-2 turbine blade section. The local

27

apparent angle of attack at that section is approximately 6° and the apparent velocity is 76 m/s. Comparing the α ≈ 6° CART-2 section with the α ¼ 5.4° NACA0012 simulation, there is a lower pressure coefficient on the suction side. This indicates that the LS(1)-04XX aerofoil produces more lift than the NACA0012 aerofoil. The LS(1)04XX has relatively high loading across the blade unlike the NACA0012 shape, where lift is generated mostly near the leading edge of the aerofoil (McGhee and Beasley, 1973). An instantaneous vorticity iso-surface is shown in Fig. 12 at ω = 2500 1/s and the iso-surface of vorticity is coloured by the velocity. The vorticity iso-surface shows complex 3D structures, particularly near the leading edge of the blade. The rotational case has a gradient of inlet velocity along the span so that the highest velocity is observed mainly on the suction side near the leading edge of the blade, and increases near the tip. The mean apparent velocity increases from approximately 68 m/s to 88 m/s from 75% to 95% along the span of the blade due to rotation. The turbulence intensity is inversely proportional to the mean apparent velocity. For the rotational blade the apparent velocity varies with radius, and therefore so will the apparent turbulence intensity. The apparent turbulence intensity was calculated using

Fig. 15. Surface static pressure time derivative RMS values for the CART-2 wind turbine blade. The pressure side is facing upwards, with the trailing edge on the left-hand side.

100

SPL1/3, dB

80

60

40

20

0 1 10

10

2

3

10 Frequency, Hz

10

4

10

5

Fig. 16. Comparison of simulated CAA results for the CART-2 wind turbine (◯), with the acoustic field measurements by Moriarty (2004) (◊ ), and the semi-empirical model from the same work (solid line).

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the relationship Ia = I∞ U∞/u¯ a , where u¯ a is the mean apparent velocity at the particular location along the span. Using this estimate the apparent turbulence intensity varies along the span from 1.6% to 1.3%. This is still a relatively high value compared to the NACA0012 simulations presented. In other simulations for the same geometry, increasing the upwind turbulence intensity above 2% showed a significant increase in the acoustic pressure at the far field receiver location. Vorticity and strain rate play a role in noise generation as observed in the NACA0012 case. The strain rate distribution shown in Fig. 13 is relatively high on the suction side of the blade where the local velocities are high. For CART-2, unlike the NACA0012 results, there is a very low strain rate region at the leading edge of the aerofoil near to the stagnation point. This is because the leading edge of the LS(1)-04XX aerofoil is thicker than that of the NACA0012. For CART-2 there is also a region of relatively high strain-rate along the trailing edge of the blade. Fig. 14 shows high values of p¯s on the suction side near the leading edge of the blade that increases towards the blade tip. There is also a region of high p¯s along the trailing edge of the blade in Fig. 15, which is the main source of trailing edge noise. It is observed that p¯s values at the trailing edge at 75% span are higher than at the leading edge, but this situation is reversed at 95% span. This indicates that the trailing edge noise becomes less dominant towards the tip where the local onset velocities are higher. It is also observed that the instantaneous strain rate distribution on the blade surface shown in Fig. 13 correlates closely with the contours of the fluctuating static pressure in Fig. 14. 3.2. Acoustic results The acoustic results for the CART-2 wind turbine model are presented in Fig. 16, compared with the data from Moriarty (2004). The acoustic power spectrum of the numerical simulation is in good agreement with the experimental data. However, the peak at approximately 100 Hz is not evident in the numerical results. Moriarty (2004) suggested that this peak could be due to mechanical noise, which may account for the observed discrepancy. Fig. 17 shows the acoustic footprint data at a 58 m radius at ground level around the wind turbine, first as selected frequency bands, and secondly as OASPL. This is an indication of the directivity of acoustic wave propagation. The rotational plane of the

turbine shows the minimum noise levels and this agrees with the predicted acoustic noise footprint from the semi-empirical code by Moriarty (2004). However, the noise levels in the upwind direction are slightly higher than for downwind, particularly at high frequencies. This differs from the results of the semi-empirical code and is due to the Doppler effect caused by the onset wind. The present FW–H calculations include convective effects so that the propagation velocity of the acoustic wave upstream is slower than downstream. Therefore, the acoustic spectrum upstream is shifted to higher frequencies and the SPL of related individual bands increases. Conversely, in the downstream direction, there is a shift to slightly lower frequencies. At high frequencies the directivity pattern exhibits the expected dipole pattern. At lower frequencies the directivity gradually changes to a more omni-directional shape.

4. Conclusions A Large Eddy Simulation of the CART-2 wind turbine blade section in an annular domain has been performed to estimate the far field noise due to unsteady aerodynamic loading. The choice of an annular domain is based on a the acoustic field measurement by Oerlemans et al. (2001). The initial results are compared with field measurement data by Moriarty (2004) and show good agreement. This shows that acoustic noise estimates can be made with less computational expense than by performing full wind turbine simulations, and with higher accuracy than using semiempirical noise prediction codes. Additionally, this work suggest that the assumption of zero radial flow is valid for calculating the far field noise at high tip speed ratios. Leading edge noise is shown to be the predominant noise source for a rotating wind turbine blade in a highly turbulent environment at high angles of attack. The most intensive noise sources are not located at the trailing edge of the blade near the tip region. This is where the local apparent velocities are relatively high. The Doppler effect due to the onset flow velocity is shown to change the directivity pattern, particularly at high frequencies. At high frequencies the directivity has a typical dipole shape but at low frequencies it is more omni-directional. Observers in the rotational plane are shown to experience the lowest overall noise levels.

Fig. 17. (L) Directivity of CART-2 wind turbine noise at a receiver location on the ground 58 m from the hub at (R) OASPL integrated from 100 Hz to 4 kHz. The results of the semi-empirical model are presented as a solid line.

,

,

,

, (…) 4 kHz.


Acknowledgements The authors wish to acknowledge Dr. Patrick Moriarty, the University of Auckland Doctoral Scholarship and the contribution of the NeSI high-performance computing facilities and the staff at the Centre for eResearch at the University of Auckland. New Zealand's national facilities are provided by the New Zealand eScience Infrastructure (NeSI) and funded jointly by NeSI's collaborator institutions and through the Ministry of Business, Innovation and Employment's Infrastructure programme. URL http:// www.nesi.org.nz.

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