**2. Methods**

### **2.1 BPM model: trailing edge bluntness vortex shedding**

Flow around wind turbine blades can be considered often as incompressible and low Mach number for most utility scale wind turbines. Even though they operate in environments where the effects of air density and wind shear on power production are significant, aerodynamic noise generation from wind turbine blades becomes important when the blade tip speed range between 0.1 and 0.3 Mach number. As length of blade is increased, the sound radiation from blades depends not only upon aerofoil geometry, local angle of attack for the aerofoils but also the rotational speed of rotor. One of the noise mechanisms from blades occurs due to periodic vortex shedding from suction side of trailing edge surface when the turbulent boundary layer flow interacts with blade surface and contributes to a monotonic peak in high frequency region of noise spectrum. For a given flow condition i.e., Reynolds number and Mach number along the span wise direction of the blade strongly affects the overall noise levels as well as the tonal noise production. Typically, the noise amplitudes increase with increase in flow Mach number and Reynolds number of order 8 x 106 .

Vortex shedding is aerodynamic phenomenon observed on both streamlined and bluff bodies such as an aerofoil or a cylinder and becomes dominant when there exists an adverse pressure gradient within the boundary layer which causes a relative difference in the flow velocities between the surface and free stream flow conditions. According to BPM model, the trailing edge vortex shedding occurs when the turbulent boundary layer displacement thickness is at least 30% higher than characteristic dimension of source [6, 10]. In addition, flow conditions such as angle of attack, Reynolds number and Mach number affect the aerodynamic lift and drag force characteristics of an aerofoil. It can be noted that for low angle of attack and attached flows, vortex shedding from trailing edge occurs rapidly and produces unsteady lift which often result in higher noise generation [11]. The lift and drag coefficient at high angle of attack also increases rapidly but reach maximum values near stall angle of attack. For aerofoils with finite trailing edge thickness, and at stall angle of attack, the vortex shedding phenomenon is reduced due to turbulent boundary layer separation near the trailing edge. Beyond the stall angle of attack, significant reduction of lift can be observed and hence vortex noise from aerofoils is also reduced. BPM model predicts noise radiation from aerofoils using relative velocity and angle of attack as primary inputs and computes the turbulent boundary layer data for suction and pressure sides of aerofoil. This data varies according to the thickness of trailing edge of aerofoil as well as the chord length of aerofoil. As the thickness to chord increases, the turbulent boundary layer on the suction side of aerofoil becomes less stable and tend to shed vortices rapidly. For a rotating wind

turbine blade, the vortex shedding occurrence happens at faster rate which leads to the massive flow separation near the tip of blade due to centrifugal force action on the flow. The separated flow appears as wake which has lower velocity compared to free stream flow condition and contributes to aerodynamic noise. Further, according to this method, the strength of this source is approximated using the spectral functions, G4 and G5 which are functions of ratio of trailing edge thickness and average turbulent boundary layer displacement thickness from pressure and suction sides of aerofoil as given by Eq. (5). Hence, it is needed to compute the spectral functions G4 and G5 as given by Eq. (6)–(8). G4 represents the narrowband peak in spectra and G5 is used to determine the broadband overall shape of spectra which is dependent on Strouhal number, *St"'* and *St*peak*"'* .

The two spectral functions (G5)<sup>φ</sup> = 14 and (G5)<sup>φ</sup> = 0 are solid angles which are determined using the symmetric NACA 0012 aerofoil experiments and given by Eq. from (76) to (82) in (Brooks et al., 1989). As mentioned by [6, 10], the bluntness vortex shedding source appears as tonal peak in the overall noise spectra and becomes dominant near 10 kHz masking other self-noise mechanisms. It must be noted that the functional parameters in Eq. (1) are expressed in terms of the flow angle of attack, bluntness ratio h/δ\*, for aerofoil at moderate to high Reynolds number; at the same time, they show the dependence of Mach number, M5.5. The noise levels are also found to vary with the span segment length of aerofoil, *L* and inverse square of the distance between source and receiver, *r* 2 <sup>e</sup> as given in Eq. (1). The Strouhal number for this type of source is defined according to Eq. (2) where *h* is the height of trailing edge. It must be noted that at moderate Reynolds number and for subsonic Mach number flows, the chord Reynolds number and turbulent boundary layer thickness and displacement thicknesses for zero and non-zero angle of attack are evaluated using Eq. (5) and Eq. (16) given in [6]. The 1/3rd octave sound pressure for this source is approximated using the Eq. (1). The narrowband tonal peak is given by function G4 and expressed using Eqs. (6) and (7).

Function G5 is calculated using ratio of trailing edge thickness to average boundary layer displacement thickness and sloping angle, φ between 0° to 14° given by Eq. (78) and Eq. (79) found in [6] where φ is the angle between the sloping surfaces near trailing edge of aerofoil and δ\*p and δ\*s are the pressure and suction side turbulent boundary layer displacement thickness, and *h* is the trailing edge height. The empirical equations used to determine the pressure and suction side displacement thicknesses for zero and non-zero angle of attack for symmetric aerofoils are given in [6]. They are found to be dependent upon the local angle of attack and chord Reynolds number. For an aerofoil, it is expressed in terms of the turbulent boundary layer displacement thicknesses for the pressure and suction side. This source also uses the high frequency directivity function like turbulent boundary layer trailing edge noise and given by the Eq. (9).

$$\text{SPL}\_{\text{Blunt}} = 10 \log \frac{h \text{M}^{\text{5.5}} \text{LD}\_{\text{h}}}{r\_{\text{e}}^2} + G\_4 \left( \frac{h}{\delta\_{\text{avg}}^\*}, \rho \right) + G\_5 \left( \frac{h}{\delta\_{\text{avg}}^{\*\text{}}}, \rho, \frac{\text{St}^{\*}}{\text{St}\_{\text{peak}}^{\*}} \right), \tag{1}$$

$$\text{St}^{\*} = \frac{f\hbar}{U},\tag{2}$$

$$\text{St}\_{\text{peak}}^{\*} = \frac{0.212 - 0.0045\rho}{1 + 0.235\left(\frac{h}{\delta\_{\text{avg}}^{\*}}\right)^{-1} - 0.0132\left(\frac{h}{\delta\_{\text{avg}}^{\*}}\right)^{-2}}, \quad \text{for } \frac{h}{\delta\_{\text{avg}}^{\*}} \ge 0.2,\tag{3}$$

$$\text{St}\_{\text{peak}}^{\*} = 0.1 \left( \frac{h}{\delta\_{\text{avg}}^{\*}} \right) + 0.095 - 0.00243 \rho, \quad \text{for } \frac{h}{\delta\_{\text{avg}}^{\*}} < 0.2,\tag{4}$$

*Trailing Edge Bluntness Noise Characterization for Horizontal Axis Wind Turbines [HAWT]… DOI: http://dx.doi.org/10.5772/intechopen.99880*

$$
\delta^\*\_{\text{avg}} = \frac{\delta^\*\_{\text{p}} + \delta^\*\_{\text{s}}}{2},
\tag{5}
$$

$$G\_4\left(\frac{h}{\delta\_{\text{avg}}^\*}, \rho\right) = 17.5 \log \frac{h}{\delta\_{\text{avg}}^\*} + 157,5 - 1.114\rho, \quad \text{for } \frac{h}{\delta\_{\text{avg}}^\*} \le 5,\tag{6}$$

$$G\_4\left(\frac{h}{\delta\_{\text{avg}}^\*}, \rho\right) = 169.7 - 1.114\rho, \quad \text{for} \quad \frac{h}{\delta\_{\text{avg}}^\*} > 5,\tag{7}$$

$$\left(G\_{\sf S}\left(\frac{h}{\delta\_{\rm avg}^{\*}},\rho,\frac{\rm St}{\rm St}^{\*}\right)\right) = \left(G\_{\sf S}\right)\_{\rho=0^{\sf \*}} + \text{0.0714}\rho\left[\left(G\_{\sf S}\right)\_{\rho=14^{\sf \*}} - \left(G\_{\sf S}\right)\_{\rho=0^{\sf \*}}\right],\tag{8}$$

$$D\_{H}(\theta,\phi) = \frac{2\sin^{2}(\mathbf{1}/2\theta)\sin^{2}\phi}{(\mathbf{1}+\mathbf{M}\cdot\cos\theta)[\mathbf{1}+(\mathbf{M}-\mathbf{M}\_{\mathrm{C}})\cos\theta]^{2}},\tag{9}$$

where *θ*, *ϕ* are the directivity angles between the source and receiver line aligned to blade span and chord direction with respect to the receiver position. *M* is the Mach number and *Mc* is the convective Mach number. *h,* is the trailing edge height. The denominator term in Eq. (9) represents the Doppler effect and convective amplification of acoustic waves produced at the trailing edge of aerofoil [6, 10, 12, 13]. It has been proven that for high values of Strouhal number or for the order greater than 2, the flow is dominated by turbulent boundary layer thickness and results in small scale flow instabilities [6, 14–16].

The Strouhal number and the shape functions vary with the shape of aerofoil, inflow velocity conditions and local angle of attack. Experiments conducted by [6] used a reference chord length for test aerofoil which was 30.86 cm and boundary tripping was done with help of 2 cm wide strip or grit applied at 15% chord length. Tripping of boundary layer resulted in reduction of the noise levels in certain frequency regions of sound spectrum [7, 8, 17]. For the present analysis, tripping of turbulent boundary layer has not been taken into consideration.

The maximum trailing edge height in BPM model aerofoil experiments was 2.5 mm which is �0.8% of chord. For the present case of 38 m blade, it is 32.2 mm and corresponds to 1% chord, respectively.
