# Leading Edge Blowing to Mimic and Enhance the Serration Effects for Aerofoil +
## 3 Results
### Acoustic Results  
This section will show the acoustical results when the leading edge of the aerofoil is subjected to both the serration and blowing treatments, respectively. By examining the Sound Pressure Level SPL as a function of non-dimensional frequency \(f\)'(=\(\!\! Here, \(\Delta\)SPL is defined as the difference in SPL between the acoustic spectra generated by the baseline and treated leading edges (either serration or blowing). A positive \(\Delta\)SPL denotes noise reduction by the treated aerofoil, while a negative \(\Delta\)SPL denotes noise increase. The following discussion focuses on the aeroacoustical performances by the serrated leading edge only. As demonstrated in Figure 7a,b, the most effective serration configuration for the turbulence-leading edge broadband noise reduction is the combination of the smallest \(\lambda\) and largest \(A\), although a slight noise increase at high frequency can also be detected. The \(A\) exerts a more dominant factor on the noise reduction compared to the \(\lambda\), which has also been reported in [14; 15]. Repeating the same set of serrated leading edges across a wider range of \(U\) essentially returns the same positive outcomes, as shown in Figure 8.  
The next discussion concerns one of the most important outcomes of this paper. Facilitating different levels of \(Q\)'on the leading edge could produce very interesting aeroacoustical performances. The turbulence-leading edge broadband noise reduction by leading edge blowing can indeed be achieved. In some cases, \(\Delta\)SPL as high as 10 dB can be achieved by one of the leading edge blowing configurations. However, it is important to stress that the noise reduction can only be achieved over a rather narrow range of blowing rate \(Q\) '. When the blowing rate is outside of this optimal range, no significant noise reduction can be observed. From the acquired dataset, a selection of the acoustic spectra subjected to leading edge blowing within the range of 6.14 \(\leq\)\(Q\)'\(\leq\) 6.41 L/minute is presented here. Figure 9a shows the acoustic spectra produced by the leading edge blowing for the \(\lambda\)'10Q '6.14, \(\lambda\)'10Q '6.22, \(\lambda\)'10Q '6.32, and \(\lambda\)'10Q '6.41 at \(U\) = 45 ms\({}^{-1}\). Acoustic spectra produced by the \(\lambda\)10\(A\)15 and \(\lambda\)10\(A\)30 serrated leading edges are also included for comparison. Note that the comparison between the serrated and blowing leading edges is based on the matching value of \(\lambda\) and \(\lambda\)', respectively. In order to provide a clearer picture of the comparison, the mean-difference in the SPL level between the baseline and treated aerofoil is defined below:  
\[\overline{\Delta\text{SPL}}(f)=\ n^{-1}.\sum_{i=1}^{n}\text{SPL}_{(\text{ baseline})}(f)-\text{SPL}_{i\ (\text{serrated})}(f),\ n\ \
i\ \{\lambda 10A15,\,\lambda 10A30\} \tag{5}\]  
\[\overline{\Delta\text{SPL}}(f)=\ N^{-1}.\sum_{i=1}^{N}\text{SPL}_{(\text{ baseline})}(f)-\text{SPL}_{i\ (\text{blowing})}(f),N\
i\ \{\lambda 10Q\,^{\prime}6.14,\,\lambda 10Q\,^{ \prime}6.22,\,\lambda 10Q\,^{\prime}6.32,\,\lambda 10Q\,^{\prime}6.41\} \tag{6}\]  
Similarly, a positive value in the \(\overline{\Delta\text{SPL}}\) denotes that noise reduction is achieved against the baseline, and vice versa. An examination of Figure 9b can easily identify strong similarities in the noise reduction trend at \(f\)' < 8. This is a clear evidence that the leading edge blowing can indeed mimic the serrated leading edge. Above this frequency, however, cumulative jet noise produced by the orifices becomes dominant and overtakes the aerofoil noise radiation. As a result, negative value of \(\overline{\Delta\text{SPL}}\) (i.e., noise increase) can be produced. It should also be noted that the optimised \(Q\)' values listed above for the broadband noise reduction are slightly higher than the optimised \(Q\)' in the \(\text{C}_{\text{L}}\) distributions (see Figure 5), which was performed under different \(U\) and \(Tu\) domains.