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Renewable Energy 36 (2011) 1902e1912 Contents lists available at ScienceDirect Renewable Energy journal homepage: www.elsevier.com/locate/renene Numerical prediction of wind turbine noise A. Tadamasa*, M. Zangeneh Department of Mechanical Engineering, University College London, Torrington Place, London WC1E 7JE, United Kingdom a r t i c l e i n f o a b s t r a c t Article history: Received 18 June 2009 Accepted 29 November 2010 Available online 26 January 2011 This paper develops and validates the first principle based numerical method for predicting the noise radiated from the rotating Horizontal-Axis Wind Turbine (HAWT) blades. The noise radiated to the farfield was predicted by the code based on Ffowcs WilliamseHawkings (FWeH) equation, using both original non-permeable formulation and permeable formulation. A commercially available CFD solver, ANSYS CFX 11.0, was used to calculate the flow parameters on and around the blade surface that are required for FWeH codes. A capability of the solver for modelling the flow field around the wind turbine blades was validated by comparing with the experimental results of NREL phase VI wind turbine blades. The FWeH codes were validated using acoustic results of UH-1H helicopter rotor in hover and Hartzell aircraft propeller in forward motion, which were measured in anechoic wind tunnel facility. Then the developed FWeH acoustic codes were applied to calculate the noise radiated from NREL Phase VI wind turbine blades. Ó 2010 Elsevier Ltd. All rights reserved. Keywords: Wind turbine noise FWeH equation NREL Phase VI blade 1. Introduction In recent years, the generations of power by wind energy are obtaining a considerable attention as an alternative to conventional fossil, coal or nuclear sources. This is due to a serious problem of air pollution from these conventional energy sources leading to global warming. At present, less than 1% of the electricity comes from wind energy in UK. Their development is known to contribute greatly for accomplishing the government’s target of obtaining 20% of electricity from renewable energy sources by 2020 [1,2]. However, wind energy also has several disadvantages, which are hindering its global use. One of its major problems is noise, especially aerodynamic noise, emitted from the wind turbine blades. The aerodynamic noise emitted from the wind turbine blades can be broadly classified as discrete frequency (tonal) noise and broadband noise. The tonal noise is generally low frequency and due to the disturbance in the flow caused by the movement of rotating blade (thickness noise) and associated pressure field (loading noise). The broadband noise is higher frequency and due to various types of turbulent flow interaction with the blades [3,4]. The semi-empirical models are widely used for calculating the noise radiated from the wind turbine blades. Most popular semi-empirical approach for calculating the broadband noise is the one developed by Brooks, Pope and Marcolini for a blade aerofoil [5]. This model is derived by fitting a scaling law of Ffowcs Williams and Hall to the wind tunnel measurements of noise from two-dimensional NACA0012 aerofoil. The inputs required for * Corresponding author. Tel.: þ44(0)20 7679 3997. E-mail address: [email protected] (A. Tadamasa). 0960-1481/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.renene.2010.11.036 this semi-empirical method is a simple geometry such as chord and blade span length, operational conditions and the boundary layer parameters at the trailing edge. These semi-empirical methods have limitations in capturing the 3D effects. As the generation and propagation of aerodynamic noise is governed by the conservation laws of fluid dynamics, it could be solved by the Computational Fluid Dynamics (CFD) solver. The advance in CFD field has made it possible to simulate the flow field around the rotating blade accurately, which takes into account the 3D effects. However, with current computer powers, it is still difficult to fully calculate both noise source and its propagation to the far-field. Arakawa et al. (2005) [6] performed the first direct noise simulation of full wind turbine blade using LargeEddy Simulation (LES) based CFD solver on Earth simulator, which was the fastest supercomputer at the time research was done. However, it requires very fine computational meshes and hence large amounts of computational resources so that it could only be used for an observer in very near-field. The main aim of the paper is to develop and validate a numerical methodology for predicting the noise radiated from the wind turbine blades to the far-field. The hybrid methodology is used where Reynolds-averaged NaviereStokes (RANS) based CFD solver is used to calculate the aerodynamic noise sources and its propagation to the far-field is calculated using Ffowcs WilliamseHawkings (FWeH) equation [7]. There are two types of FWeH approaches for predicting far-field noise. In the original FWeH approach the sources of flow perturbations on the solid surfaces of the blades are considered. The usual formulation of this approach is to use a surface integral on the blade to estimate the so-called loading noise and thickness noise. However, this approach fails to predict the quadruple noise as in this A. Tadamasa, M. Zangeneh / Renewable Energy 36 (2011) 1902e1912 case the sources of noise require volume integration. In the alternative permeable wall approach, proposed by Di Francescantonio [12], the surface integral is considered on a flow permeable surface which include the major the blade and the major sources of noise. In such an approach, depending on the fidelity of the CFD computation (Steady RANS, Unsteady RANS, LES, or DNS) the total noise at far-field (including the quadruple noise) can be computed. The source of noise considered on this approach is stated to include both periodic discrete frequency noise and broadband noise since broadband noise can be considered as unsteady loading noise [4]. However, in order to capture the broadband noise well, time-accurate LES solver will be necessary for the noise-generating region and hence it will increase CPU cost. This paper uses RANS based CFD solver to calculate the inputs for FWeH codes which are pressure on the blade surface for original FWeH code and pressure, density, velocities on the control surface that surrounds the blade for permeable FWeH code. Both solid and permeable formulation of FWeH equations is implemented and validated by using available experimental data related to helicopter rotor and propeller fan. Since as yet no detailed and open experimental data for wind turbine noise is available to use for validation purposes. The methods are then used to study the contribution of different types of noise radiated from the wind turbine rotor. The paper also shows the study of the variation of each type of noise with variation in operating conditions. Also the influence of rpm and wind speed on the far-field noise are investigated numerically. The ultimate aim of the study is to use the proposed methodology for a multi-objective optimisation of the wind turbine blades considering their power and noise. 2. Background theory 2.1. FWeH equations The original FWeH equation was developed in 1969 from Lighthill’s acoustic analogy [8] by including the effect of the moving solid body [7]. This equation is a rearrangement of continuity equation and NaviereStokes (NeS) equations into an inhomogeneous wave equation with sources of sound. It is first derived by representing the blade surface as a moving control surface, which introduces discontinuity in the unbounded fluid domain. The shape ! and the motion of the control surface is defined byf ð x ; tÞ ¼ 0 , with f < 0 for its interior and f > 0 for its exterior. It has been assumed that the flow inside this control surface have the same fluid state as the undisturbed medium and outside as the real state including the influence from the body [4]. The FWeH equation is derived by obtaining the equation that can be applied in the entire unbounded domain, both inside and outside the control surface. This is done by using the generalised functions to describe the flow field. The generalised variables (shown with tilde on the top of the variable) for density, momentum and compressive stress tensor respectively can be written as [9] 9 > = ~ r ¼ r0 Hðf Þ þ r0 r~u~ i ¼ rui Hðf Þ ; ~ ¼ p0 Hðf Þ þ p0 d > p ij ij (1) ij  1 f >0 where H(f) is Heaviside function, Hðf Þ ¼ if . 0 f <0 Subscript, 0, define the value in undisturbed medium and the primed value represents difference between the value in real state and in undisturbed medium ðe:g: r0 ¼ r  r0 Þ. The generalised variables (1) are substituted to ordinary continuity equation to obtain the generalised version of the equation [10], 1903   ~ v~ ru~ i vr vf vf dðf Þ; ¼ r0 þ rui þ vt vxi vt vxi (2) where v=vt indicates generalised differentiation. d(f) is Dirac’s delta function, which is the derivative of Heaviside function, vHðf Þ ¼ dðf Þ vf  where dðf Þ ¼ N f ¼ 0 if 0 f s0 Similarly, the generalised conservation of momentum equation is obtained by substituting the generalised variables into the ordinary equation,   ru~ i u~ j þ p~ij v ~ ~u ~ vr i ¼ þ vxj vt !  vf vf  0 rui þ rui uj þ pij dðf Þ: vt vxj (3) vf =vxi and vf =vt in the Eqs. (2) and (3) are replaced by n i and vn respectively, wheren i is the unit vector in the direction normal (outward) to the control surface and vn is the velocity of control surface in the normal direction. Then, these equations are combined and rearranged, by assuming no fluid flow through the control surface, to give differential FWeH equation [11],  1 v2 p0 v v v2  2 0 r d d V p ¼ v Þ ðf Þ  ½l ðf Þ þ T Hðf Þ ; ½ð n i 0 vt vxi vxi vxj ij c20 vt 2 (4) where c0 is the speed of sound in undisturbed medium, li ¼ p0ij n j is the local force vector components exerted by the surface on fluid, p0 is the acoustic pressure where p0 ¼ c20 ðr  r0 Þ and Tij ¼ rui uj þpij c20 rdij is the Lighthill stress tensor. A first term on the right hand side of Eq. (4) represents the source that is proportional to the local rate of mass injection into the exterior of control surface and thickness noise can be represented by this type of source. A second term represents the source proportional to the local force intensity and the loading noise can be represented by this type of source. A third term represents quadrupole type source. As first 2 terms has d(f) function, which is zero for all f except at the control surface, f ¼ 0, they can be determined as surface sources. Similarly the third term has H(f) function, which is equal to unity only in the region exterior to the surface, it can be determined as a volume source. Due to the complexity of volume integral calculation, the third term is often assumed negligible. However, Di Francescantonio [12] developed a permeable type FWeH equation, which can include the quadrupole source without this complex volume integral calculation (explained later in Section 2.3). The main advantage of FWeH equation is being able to separate each source terms and can determine which type of noise is dominant. The different characteristics of these sources can also determine the frequency and directional characteristics of the generated sound field. This can help to arrive at useful guidelines for the design of reduced noise wind turbine blades. 2.2. Solution of FWeH equation The integral form of FWeH Eq. (4) is obtained by using Green’s function of wave equation in unbounded three-dimensional space; * * Gð x; t; y; sÞ ¼  0 dðgÞ 4pr s>t ; st (5) where g ¼ s  t þ r=c0 ; r ¼ jxi  yi j is the distance between the noise source (yi) and the observer (xi), s is time when noise source is emitted, and t is time when noise reach observer. 1904 A. Tadamasa, M. Zangeneh / Renewable Energy 36 (2011) 1902e1912 Only the surface source terms are considered and the integral form of FWeH equation is obtained as [4], v * p0 ð x; tÞ ¼ vt Zt ZN N N Zt v  vxi r0 vn dðf ÞdðgÞ * d yds 4pr ZN N N li dðf ÞdðgÞ * d yds: 4pr (6) The changes of variables are required for integrating the delta functions. First, integration over s is performed. As the coordinates frame fixed relative to the blade surface is used, d(f) is unaffected by s. Therefore, dg dg dsh ¼ : jdg=dsj j1  Mr j (7) Secondly, the integrating over one space dimension is performed. It has been assumed f ¼ y3 and S describe surface on (y1, y2) plane. This gives relation A permeable FWeH differential equation is derived similar manner to the original equation but the fluid is allowed to pass across the control surface, 1 v2 p0 v  V2 p0 ¼ f½r0 vn þ rðun  vn Þdðf Þg vt c20 vt 2 i o  v nh 0 v2   pij n j þ rui ðun  vn Þ dðf Þ þ T Hðf Þ vxi vxi vxj ij where un is the fluid velocity in direction normal to control surface and vn is the control surface velocity in direction normal to control surface. The solution of permeable FWeH equation can be rearranged to give same format as the original FWeH equation for the comparison and computational simplicity. The third term on the Eq. (11) is a quadrupole source outside the control surface and this can be assumed small compared with the quadrupole source inside the control surface and can be neglected. Z " 4pp’ðx; tÞ ¼ f ¼0 * dy dy df d yh 1 2 ¼ dSdf : jdf =dy3 j (8) þ After the integration of the delta functions, the retarded-time formulation of FWeH equation is obtained, 4pp0T ðx; tÞ ¼ " Z f ¼0 þ # r0 v_ n þ vn_ 4pp0L ðx; tÞ ¼ 1 c0 þ " Z f ¼0 Z þ dS r 2 ð1  Mr Þ3 f ¼0 _l r i i f ¼0 (9) # rð1  Mr Þ2 ret " # lr  li Mi 1 c0 Z " L_ r r 2 ð1  Mr Þ3 # rð1  Mr Þ2 f ¼0 # Z " Lr  Li Mi f ¼0 dS r 2 ð1  Mr Þ3 dS rð1  Mr Þ2 ret   Z "r Un rM r þ c Mr  c M 2 # 0 0 i i 0 dS ret dS ret dS r 2 ð1  Mr Þ2 ret f ¼0   Z "Lr rM r þ c Mr  c M 2 # 0 0 i i 1 þ c0 r 2 ð1  Mr Þ3 ret dS ret where dS r 2 ð1  Mr Þ2 ret f ¼0   Z "lr rM r þ c Mr  c M2 # 0 0 i i 1 c0 þ dS # r0 U_ n þ U n_ f ¼0 þ rð1  Mr Þ2 ret   Z "r vn rM r þ c Mr  c M2 # 0 0 i i 0 dS (10) ret where PT is thickness noise, PL is loading noise and Mr is the relative Mach number in radiation direction. This is the most common solution to the FWeH equation and called Farassat’s formulation 1A. This formulation gives time history of the acoustic pressure. Due to the existence of Doppler factor, 1=ð1  Mr Þ , this formulation is limited to the subsonic cases. The wind turbine works, in general, at low Mach number below 0.3 and this formulation will be applicable. 2.3. Permeable FWeH equation Di Francescantonio [12] has developed a new formulation called permeable FWeH equation to distinguish it from original impenetrable FWeH Eq. (4). In the original FWeH equation, the control ! surface, f ð x ; tÞ ¼ 0 , was taken to coincide with the blade surface but in the new permeable FWeH equation, the control surface is taken at a fictitious surface at some distance from the blade surface enclosing the blade and the entire noise-generating region. As the flow can pass through the control surface, it is called permeable FWeH equation. This new equation has advantage of including the quadrupole noise as surface source, without complex volume integral calculation. (11) Fig. 1. Unstructured computational mesh of NREL Phase VI model. (12) A. Tadamasa, M. Zangeneh / Renewable Energy 36 (2011) 1902e1912 1905 Fig. 2. Pressure coefficient distribution of NREL blade at wind speed of 7 ms1 at (a) 30% (b) 46.6% (c) 63.3% (d) 80% and (e) 95% of blade span.  Ui ¼ and 1 r r0  vi þ rui ; r0 Li ¼ Pij n j þ rui ðun  vn Þ: (13) (14) 3. Validation and results 3.1. Validations of CFD tool The commercially available CFD solver, ANSYS CFX 11.0, has been used to calculate the aerodynamic flow parameters, required as an input to the FWeH equations. The RANS (Reynolds-Averaged NaviereStokes Simulation) approach was used with Shear Stress Transport (SST) k-u based turbulence model. The validation of the flow solver has been performed on NREL Phase VI HAWT wind turbine blade. This wind turbine blade model is widely used for validating the numerical codes for predicting the aerodynamics performances due to the availability of experimental data at various operating conditions [14,15]. The NREL Phase VI wind turbine is two-bladed which has 10.06 m diameter with power rating of 20 kW and they are stall-regulated wind turbine with full-span pitch control. The blade has S809 aerofoil cross-section, which is designed especially for use in the wind turbine blade. It is linearly tapered 1906 A. Tadamasa, M. Zangeneh / Renewable Energy 36 (2011) 1902e1912 Fig. 3. Pressure coefficient distribution of NREL blade at wind speed of 11 ms1 at (a) 30% (b) 46.6% (c) 63.3% (d) 80% and (e) 95% of blade span. from 0.737 m chord length at the blade root section to 0.356 m chord length at the blade tip section. It is nonlinearly twisted from 20.05 at the blade root to 2.00 at the blade tip (detailed blade geometry can be obtained in [13]). In this paper, the cases where operating in upwind and no yaw condition were chosen for the comparison with the experimental data. The blade is also pitched so that the tip chord is 3 towards the feather (towards wind direction) from the rotor plane. The tower height of NREL Phase VI wind turbine is 12.03 m. In the upwind configuration, the influences of tower and nacelle on the rotor aerodynamics can be assumed to be negligible [14]. A model and the meshes were created using Pointwise Gridgen V15.0. Only one blade has been created and a periodic boundary condition has been applied to model the second blade. The no-slip wall boundary condition was applied on the blade surface. The computational domain was created from two regions; an inner region containing the blade which is rotating with 72 RPM A. Tadamasa, M. Zangeneh / Renewable Energy 36 (2011) 1902e1912 1907 Fig. 4. Pressure coefficient distribution of NREL blade at wind speed of 15 ms1 at (a) 30% (b) 46.6% (c) 63.3% (d) 80% and (e) 95% of blade span. and outer region which is stationary. The unstructured mesh was used for the whole region with 1158423 tetrahedral meshes in inner region and 880261 tetrahedral meshes in outer region. The frozen rotor conditions were used for the interface between the inner and outer region. The inlet and outlet was located at 10 m and 50 m respectively from the rotor plane. Fig. 1 shows the computational mesh of NREL Phase VI model. The comparison was done for surface pressure distributions at five different wind velocities, 7, 9, 11, 13, and 15 m/s at five blade spanwise sections at 30, 46.6, 63.3, 80 and 95% of the blade span. The surface pressures are expressed in non-dimensional form, coefficient of pressure. Figs. 2e4 shows the results from wind velocities of 7, 11 and 15 m/s respectively At 7 m/s, the results from the solver agree very well with the experimental results. However, at higher velocity, the discrepancies appeared. As the discrepancies were seen only on the suction surface of the blade, it can be assumed that the errors are caused by the separation prediction. It was seen that the flow becomes unsteady and the stall region start to occur in the inner sections of the blade. With the current turbulence models, it is still difficult to accurately simulate the highly separated flow field. However, considering overall results, it can be concluded that CFD simulation 1908 A. Tadamasa, M. Zangeneh / Renewable Energy 36 (2011) 1902e1912 Fig. 7. FWeH calculation for UH-1H rotor at M ¼ 0.80. can predict fairly well the flow field of the wind turbine blade. They were used to calculate the input, which is the noise sources, required for FWeH codes to calculate the noise radiated to the observer in a far-field. 3.2. Validation of FWeH codes As suitable wind turbine noise measurements which can be used for the validation of FWeH code were not available, it has been validated using the acoustic measurements of other types of propellers; UH-1H helicopter rotor in hover and Hartzell aircraft propeller in forward motion. Fig. 5. Surface pressure of UH-1H model at (a) M ¼ 0.80 and (b) M ¼ 0.85. Fig. 6. Control surface shape. 3.2.1. Case1: UH-1H helicopter The experimental data of a 1/7th scale model of UH-1H helicopter rotor, obtained in an anechoic environment, was used for the comparison with the predicted results [16,17]. The UH-1H rotor has two simple straight blades with NACA0012 aerofoil cross-section. The 1/7th scale of the rotor has a radius of 1.045 m with a chord length of 7.62 cm (blade aspect ratio is 13.7). For the validation, a case where the rotor is non-lifting in hover with the observer in the rotor plane located at 3.09 rotor radius from the centre of rotation has been considered [17]. A case for two tip Mach numbers at M ¼ 0.80 and 0.85 have been used for the validation, corresponding to rotational velocity of 2491 and 2644.8 RPM respectively. First of all, aerodynamics calculation was performed on the model using CFD solver. The blade surface pressure distributions at 70 and 94% of the blade span are shown in Fig. 5 Fig. 8. FWeH calculation for UH-1H rotor at M ¼ 0.85. A. Tadamasa, M. Zangeneh / Renewable Energy 36 (2011) 1902e1912 1909 Fig. 9. 2D cross-sections of Hartzell propeller. The thickness noise and loading was obtained using original FWeH code and the total noise was obtained using permeable FWeH code. A sensitivity study of the control surface shape was performed before deciding the final shape of the control surface to be used in permeable FWeH code. In this study, the control surface shape for permeable FWeH code was chosen to have the same aerofoil profile as the blade section, NACA0012 profile for this case, and the chord length was varied to twice and three times the blade chord length. The control surface shape was also varied in blade spanwise direction. From the study, the final shape of the control surface was chosen to have twice the chord length of the blade and the spanwise length was extended 11.5% of blade radius from the blade tip as shown in Fig. 6. The thickness and total noise predicted from FWeH codes at Mach number of 0.80 and 0.85 respectively are shown in Figs. 7 and 8. As UH-1H rotor is symmetrical and non-lifting, the loading noise at in-plane observer was small and is not shown in the figures. For M ¼ 0.80 case, the total noise predicted from permeable FWeH code agrees well with the experimental results [16] for the negative peak. Same for M ¼ 0.85 case when compared with the experimental results in [17]. The thickness noise calculated shows at the observer position chosen in this study, they are the dominant noise source. By comparing the Figs. 7 and 8, increasing the rotational velocity by 6% increases the noise radiation more than twice. The FWeH codes were further validated using much more complicated case of Hartzell aircraft propeller. Fig. 10. Surface pressure distribution for Hartzell propeller. Fig. 11. Acoustic results of Hartzell propeller obtained from FWeH code. Fig. 12. Acoustic result from NREL blade rotating at 72 RPM, wind speed of 7 m/s. 3.2.2. Case 2: Hartzell propeller The acoustic result of full-scale two-bladed Hartzell aircraft propeller conducted at German Dutch Wind Tunnel (DNW) was used for the validation [18]. The propeller is 2.03 m diameter and has round-shape at the blade tip section. This blade is nonlinearly twisted, tapered and swept as shown in Fig. 9. The blade was pitched 20.8 . The case where it is rotating at a rotational velocity of 2700 RPM and moving with forward velocity of 69.5 m/s was used for the validation. The relative tip Mach number of this case is 0.87. Noise was measured at in-plane and 4 m from the centre of the rotation. Fig. 13. Acoustic result from NREL blade at various wind speed. 1910 A. Tadamasa, M. Zangeneh / Renewable Energy 36 (2011) 1902e1912 positive peak was underpredicted. This could be due to the location or the size of the control surface. As Hartzell propeller is rotating at high speed, some of the quadrupole sources lie outside the control surface. At high Mach number, it is known that the quadrupole sources must be taken into account up to 2 rotor radii at least, which will be in supersonic region [19]. As the retarded-time formulation of FWeH equation is used, they are not capable of solving the sources in supersonic region. The other type of formulations known as collapsing-sphere and emission-surface formulations are required to be used for the supersonic cases. However, the wind turbine is known to work in low Mach number (currently less than 0.3) that they will not be used in this research due to the complexity of its use. 4. NREL wind turbine noise prediction Fig. 14. Acoustic result from NREL blade rotating at 210 RPM, wind speed of 7 m/s. First of all, aerodynamics calculation was performed using CFD solver and the blade surface pressure distribution at 30, 75 and 90% of the blade span was computed as shown in Fig. 10. The control surface location for permeable FWeH code was chosen in a similar manner to the UH-1H rotor case. The spanwise length of the control surface was extended 14.8% of the blade radius from the blade tip. The thickness, loading and total noise calculated using FWeH codes is shown in Fig. 11. The time history of the total noise radiated from the blade calculated using permeable FWeH codes were compared with the experimental result [18]. The shape of the FWeH result agrees well with the experimental result especially negative peak. However, The noise radiated from the NREL Phase VI wind turbine blades were calculated using FWeH codes. They were converted to frequency domain using Fast Fourier Transform (FFT) code. The noise radiation of the case where it is rotating at 72 RPM under wind speed of 7 m/s is shown in Fig. 12. Thickness and loading types of noise were obtained using original FWeH code and the total noise was calculated using permeable FWeH code. The observer was located at a reference observer location specified by international standard, which is at on-axis with 17 m (rotor diameter/ 2 þ tower height) from the rotor and at the bottom of the tower. As this wind turbine is operating at blade tip Mach number of approximately 0.12, which is much smaller than the real operating wind turbine conditions, the noise radiation is small. At this Fig. 15. Thickness and Loading noise from NREL blade at various RPM. A. Tadamasa, M. Zangeneh / Renewable Energy 36 (2011) 1902e1912 Fig. 16. Total noise from NREL blade at various RPM calculated using permeable FWeH code. operating condition and observer location, the loading noise is the dominant noise source. The difference between total noise calculated from permeable FWeH code and addition of thickness and loading noise (TL) indicates that quadrupole noise is not important at this tip Mach number. Fig. 13 shows the effect of increasing wind speed on the total noise radiation with rotational velocity fixed at 72 RPM. The variation observed in the total noise radiation with increase in wind speed was mainly due to the increase in loading noise. 1911 Fig. 18. Acoustic results of 2 operating conditions having same tip-speed-ratio. As the operating condition at tip Mach number of 0.12 is unrealistic, they were increased to more realistic value of 0.3 by increasing the rotational velocity to 210 RPM. Fig. 14 shows the acoustic result at this operating condition. At this operating condition, thickness noise becomes the dominant noise source and the quadrupole noise also increased. To see the effect of the rotational velocity on the noise radiation, the rotational velocity was varied from 30 RPM (M z 0.05) to 210 RPM (M z 0.3) with wind speed fixed at 7 m/s. Thickness, loading and total noise variation with the variation in rotational velocity are shown in Figs. 15 and 16 respectively. Fig. 15 shows that the thickness noise increases continuously with increase in rotational velocity. However, there are not significant variations in loading noise from 55 to 130 RPM. The results also show that until about 130 RPM loading noise is the dominant noise source, but for higher RPM the thickness noise becomes dominant. Fig. 17 shows the power and power coefficient of NREL blade against a tip-speed-ratio. The Tip-speed-ratio is a ratio of blade tip speed to wind speed. Its value can be varied by varying wind speed or varying rotational velocity. A various range of tip-speed-ratio was obtained by varying wind speed with fixed rotational velocity and varying rotational velocity with fixed wind speed. The result shows power coefficient is same for different operating conditions as long as they have a same tip-speed-ratio. The NREL Phase VI wind turbine has an optimum power coefficient at tip-speed-ratio between 6 and 7, which is lower than the actual two-bladed wind turbine operating in the field [20]. Fig. 18 shows the acoustic result from two operating conditions, where one is operating with rotational velocity of 72 RPM at wind speed of 9 m/s and the other with rotational velocity of 55 RPM at wind speed of 7 m/s. They both have a same tip-speed-ratio of approximately 4.2. As expected, former operating condition produces larger power and radiates higher noise. 5. Conclusions Fig. 17. Power and Power coefficient of NREL blade against tip-speed-ratio. Both impenetrable and permeable form of the Ffowcs WilliamseHawkings (FWeH) equations have been used to predict thickness, loading and total noise radiated from the rotor blades. The aerodynamic flow parameters required on and around the blade surfaces for the FWeH codes were obtained using Reynoldsaveraged NaviereStokes (RANS) based computational fluid dynamics (CFD) solver. The predicted results from FWeH codes for helicopter and aircraft rotor agreed very well with the measurement obtained in the anechoic wind tunnel facility. The FWeH codes were applied to the wind turbine rotor blades to study the contributions of different types of noise at various operating conditions. In future, these codes can be used for designing the acoustically improved wind turbine blades. 1912 A. Tadamasa, M. Zangeneh / Renewable Energy 36 (2011) 1902e1912 Acknowledgements The authors wish to thank Dr. Scott Schreck from NREL for providing the experimental data of the NREL Phase VI Rotor Nomenclature c0 f H li M Mr _r M ni p pij ri ri S Tij t ui vi xi yi Speed of sound, ms1 Function defining location of control surface Heaviside function Local force vector components exerted by the surface on fluid, N Mach number relative Mach number in radiation direction, Mr ¼ Mi $r i 1st derivative of relative Mach number with respect to emission time Normal unit vector Surface pressure (static), Pa Compressive stress tensor, Pa radiation vector between observer and source at emission time, r i ¼ (xi  yi), m Component of unit vector in radiation direction, r i ¼ ri =r Surface area Lighthill stress tensor, Pa Observer time, s luid velocity, ms1 Control surface velocity, ms1 Observer location, m Source location, m Greek symbols dij Kronecker Delta function r Density, kg m3 s Source emission time, s Subscripts L Loading value n Component in surface normal direction r Component in radiation direction T Thickness value 0 Undisturbed condition Superscripts w Generalised value 0 Fluctuated value Abbreviations CFD Computational Fluid Dynamics FWeH Ffwocs WilliamseHawkings HAWT Horizontal-Axis Wind Turbine References [1] The national energy foundation [accessed May 2007] http://www.nef.org.uk/ greenenergy/wind.htm. 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