# Prediction and Control of Broadband Noise Associated with Advanced Air Mobility--A Review
## 3 Methods for Prediction of BBN
### BBN Prediction Models  
Semi-empirical model: The widely used and most successful model is the semi-empirical one developed by [PERSON] et al. [8], commonly known as the BPM model. This approach provided some boundary layer corrections using the NACA 0012 experimental test. The self-noise spectrum is the sum of all five self-noise mechanisms' spectra. Because the trailing-edge noise and separation/stall noise are generated from the trailing edge boundary layer, the equation names them as TBL-TE, \(G_{TBL-TE}(f)=G_{TBL-TE,p}(f)+G_{TBL-TE,s}(f)+G_{TBL-TE,s}(f)\), where \(G_{TBL-TE,p}(f)\) is the pressure side of the blade segment, \(G_{TBL-TE,s}(f)\) is from the suction side, and \(G_{TBL-TE,s}(f)\) is the TE separated flow noise. Each component is calculated as follows:  
\[G_{TBL-TE,p}(f)=\frac{\delta_{p}^{*}M^{5}L\overline{D}_{h}}{r_{e}^{2}}\cdot H _{p}\left(\frac{f\delta_{p}^{*}}{U},M,\text{Re}_{c},\text{Re}_{\delta_{p}^{*}}\right) \tag{1}\]  
\[G_{TBL-TE,s}(f)=\frac{\delta_{s}^{*}M^{5}L\overline{D}_{h}}{r_{e}^{2}}\cdot H _{s}\left(\frac{f\delta_{s}^{*}}{U},M,\text{Re}_{c}\right) \tag{2}\]  
\[G_{TBL-TE,s_{*}}(f)=\frac{\delta_{s}^{*}M^{5}L\overline{D}_{h}}{r_{e}^{2}}\cdot H _{s}\left(\frac{f\delta_{s}^{*}}{U},\alpha_{*},M,\text{Re}_{c}\right) \tag{3}\]  
\[G_{TBL-VS}(f)=\frac{\delta_{p}M^{5}L\overline{D}_{h}}{r_{e}^{2}}\cdot H_{l} \left(\frac{f\delta_{p}}{U},\alpha_{*},M,\text{Re}_{c}\right) \tag{4}\]  
\[G_{T\!P}(f)=\frac{M^{2}M_{\text{max}}^{3}l\overline{D}_{h}}{r_{e}^{2}}\cdot H _{l}\left(\frac{f_{l}}{U},\alpha^{\prime}_{T\!P}\right) \tag{6}\]  
Figure 9: Normalized time-averaged total velocity contour and SPL [17]. where \(\delta_{p}^{*}\), \(\delta_{s}^{*}\), and \(\delta_{avg}^{*}\) are boundary layer displacement thicknesses for the pressure, suction sides, and average, respectively. \(\delta_{p}\) is boundary layer thickness. \(h\) is the trailing edge thickness. \(M\) is the Mach number. \(L\) is the blade segment spanwise length. \(\overline{D}_{h}\) is the half-plane-baffled-type directivity term. \(r_{e}\) is the observer distance in retarded coordinates from the TE. \(\psi\) is the solid angle. \(M_{\text{max}}\) is the maximum velocity in or about the vortex near the TE. \(a^{\prime}_{Tip}\) is the effective blade angle at the blade tip. \(l\) is the spanwise extent. If \(|\alpha_{*}|>12.5^{\circ}\), the turbulent boundary trailing edge (TBL-TE) noise will be written as  
\[G_{TBL-TE}(f)=G_{TBL-TE,\alpha_{*}}(f)=\frac{\delta_{s}^{*}M^{5}L\overline{D}_ {l}}{r_{e}^{2}}\cdot H^{\prime}_{\alpha_{*}}\left(\frac{\ell\delta_{s}^{*}}{U },\alpha_{*},M,\text{Re}_{c}\right) \tag{7}\]  
The BPM model only considers self-noise, so to improve the accuracy of BBN, [PERSON] and [PERSON] [10] introduced the BWI noise to the BPM model. The BWI noise spectral contribution from the mnth blade segment was found to be the following:  
\[G_{BWI}(f)=\left(\frac{\omega z_{\tau}}{4\pi c_{0}\sigma^{2}}\right)^{2}G_{ LE\Delta p}(f)\cdot[bC]^{2}\Bigg{(}\frac{2L(\zeta\omega/U)}{\left(\zeta\omega/U \right)^{2}+\left(\omega y_{\tau}/c_{0}\sigma\right)^{2}}\Bigg{)} \tag{8}\]  
where \(\omega=2\pi f\). \(c_{0}\) is the speed of sound. \(G_{LE\Delta p}(f)\) is the auto-spectrum of the unsteady pressure differential near the leading edge. \(L\) and \(C\) are the span and chord length of a segment, respectively. \(b\) and \(\zeta\) are constant factors. \(\mathbf{r}\) indicates the retarded coordinates. The BPM model is well-regarded for its accuracy and easy application in predicting BBN noise. However, as a semi-empirical model, BPM relies on empirical data and assumptions, which may limit its accuracy or applicability outside the range of the conditions for which it was originally developed. Additionally, it may not be valid in all practical applications, particularly in cases involving unsteady or turbulent flow. Analytical model: The dominant noise component of broadband noise (BBN) is trailing-edge noise.