**2.2 Shape function and trailing edge thickness approximation proposed by Wei et al**

As mentioned previously, trailing edge bluntness vortex shedding model was developed based on the experiment data obtained from NACA 0012. To account for the effects of vortex shedding noise levels, the geometry near the trailing edge requires an interpolation function essentially to approximate the height of trailing edge sloping surfaces. Standard solid angle was specified as ψ = 14o for a NACA 0012 aerofoil while for a flat plate it is ψ = 0<sup>o</sup> . However, it must be noted that a wind turbine blade has finite thickness and varying camber along span direction. This led to erroneous predictions of the trailing edge noise levels. Hence [9] used a modified interpolation function for the trailing edge bluntness noise source and corrected the Eq. (1) using two additional functions viz. *S1* and *S2*. *S1* is the shape function that is equivalent to the actual G5 function and *S2* is the correction function for aerofoil thickness variation along the span wise direction of the blade given by Eqs. (10) and (11)

$$\begin{split} \text{SPL}\_{\text{Blunt}} &= 10 \log\_{10} \frac{h \text{M}^{\text{S},7} L D\_{\text{h}}}{r\_{\text{e}}^{2}} + 20 \left( 1 + \text{M}^{2} \right) \log\_{10} \left( \frac{h}{\delta^{\*} \text{avg}} \right) + \text{S}\_{1} \left( \frac{h}{\delta^{\*} \text{avg}}, \frac{\text{St}}{\text{St}\_{\text{peak}}} \right) \\ &+ \text{S}\_{2} \left( \frac{t}{c} \right) + K\_{0} \end{split} \tag{10}$$

$$\text{S}\_2 = 654.43 \left( \frac{t}{c} \right)^3 - 652.26 \left( \frac{t}{c} \right)^2 + 58.77 \left( \frac{t}{c} \right) \tag{11}$$

Where, the constant, *Ko* is taken as 150 for h/δ\* < 0.2 otherwise *Ko* is approximated as 150–20(h/δ\* -0.2)0.25. The Eq. (10) was modified in such a way that noise levels are not dependent of the solid angle formed at the trailing edge surfaces rather expressed as function of the bluntness height *h,* Mach number, *M,* and average of the boundary layer displacement thickness between suction and pressure sides of airfoil, δ\* avg. Further, in the modified BPM for trailing edge bluntness, the sound pressure level is proportional M5.7 instead of M5.5. This change also demonstrates that the sound pressure for trailing edge bluntness source is sensitive to flow Mach number increments.

### **2.3 Modified thickness approximation using regression curve fitting**

In the present study the basic shape function for the trailing edge angle is taken as from the original BPM model. However, for the shape function, G5 the trailing edge angle is varied continuously between the blade root and tip section to account for differences in blade geometry. Since, the trailing edge sloping surfaces are proportional to the trailing edge height, a change in trailing edge angle parameter is retained in present noise computations while correction function for airfoil thickness, *S2* is modified in terms of thickness to chord ratio for each span segment of the blade similar to that proposed by [9]. One must note that coefficients in the modified function for thickness are obtained by regression and given by Eq. (12)

$$S\_2 = -0.02158 \left(\frac{t}{c}\right)^3 + 0.9518 \left(\frac{t}{c}\right)^2 - 13.38 \left(\frac{t}{c}\right) + 61.4 \tag{12}$$
