# Prediction and Control of Broadband Noise Associated with Advanced Air Mobility--A Review
## 3 Methods for Prediction of BBN
### BBN Prediction Models
Turbulence ingestion noise model: Turbulence ingestion noise presents significant challenges in prediction due to the need to account for both turbulence and unsteady loading models, or the development of new noise prediction models. [PERSON] and [PERSON] [42] and [PERSON] [7] approached this by assuming that turbulence ingestion noise could be treated as leading-edge noise resulting from vertical gusts. The spectrum of an airfoil in rectilinear motion, as described in their work, is given by the following:  
\[G_{TBL-TE,s_{*}}(f)=\frac{\delta_{s}^{*}M^{5}L\overline{D}_{h}}{r_{e}^{2}}\cdot H _{s}\left(\frac{f\delta_{s}^{*}}{U},\alpha_{*},M,\text{Re}_{c}\right) \tag{3}\]0  
where \(L\) is the effective lift that can be derived from the Sears function [43] and \(\Phi_{ww}\) is the wavenumber spectrum of the airfoil surface pressure replaced by the von Karman spectrum, \(\Phi_{ww}\big{(}k_{x},k_{y},k_{z}\big{)}=\frac{E(k)}{4\pi^{2}}\big{(}1-k_{z}^{ 2}/k^{2}\big{)}\). The rotating frame spectrum equation is the same as the Equation (13). [PERSON] [44] mentioned that if the ingested turbulence is chopped by more than one blade, the noise will tend to be narrowband at blade passage frequency, while if there is only one blade, there is no blade-to-blade correlation. Thus, for the no blade-to-blade correlation form, \(S^{\prime}_{pp}(\underline{x},\omega_{0},\gamma)=\omega/\omega_{0}S_{pp}( \underline{x},\omega_{0},\gamma)\), which is the same as \begin{table}
\begin{tabular}{c c c} \hline \hline
**Models** & \(k\) & \(C\) \\ \hline DH & 2 & 36.7 \\ SKM & 2 & 42.9 \\ SG & 1.66 & 39.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: \(k\) and \(C\) of different empirical models [33]. the no turbulence ingestion, while the blade-to-blade correlation form with the introduced Equation (20) can be written as follows:  
\[S^{\prime}{}_{pp}(\omega)=\left(\frac{\omega bz\rho_{0}}{c_{0}\sigma^{2}}\right)^ {2}\pi ULd\omega/\omega_{0}|L(K_{x},\lambda,M)|^{2}\overline{u^{2}}b^{2}{\sum }_{n=-\infty}^{\infty}\Phi_{ww}(\lambda,K_{y},K_{z}^{(n)})\frac{2\pi}{u^{2}b^{2 }Z} \tag{21}\]  
[PERSON] and [PERSON] [45] derived frequency-domain models from the wave equation by rapid distortion theory and a potential mean flow. They utilized the [PERSON] turbulence model coupled with the unsteady blade force solution developed by [PERSON] [46] to solve the wave equation. [PERSON] et al. [47] conducted similar frequency-domain model research, deriving their model from the loading noise predictions of the FW-H equation. Like [PERSON] [7], they employed the Sears function to model the unsteady force acting on the blade. For modeling turbulence, they assumed anisotropic turbulence and utilized the Kerschen and Gliebe [48] model, which accommodates the directional dependence of turbulence effects. This approach allowed them to capture the complex interactions between the turbulent flow and the blade, providing a more accurate prediction of the resulting noise. [PERSON] et al. [49] reported that the frequency domain model was numerically slower due to the Bessel functions. Furthermore, characterizing turbulence through its wavenumber spectrum posed challenges, as it was often difficult to model the entire wavenumber range. To address these issues, they investigated a time-domain method derived from the loading noise predictions of the FW-H equation. This method was coupled with the Sears function to model unsteady forces, offering a more practical approach for capturing the intermediate turbulence ingestion noise while avoiding the limitations of frequency-domain analysis.