# Prediction and Control of Broadband Noise Associated with Advanced Air Mobility--A Review
## 3 Methods for Prediction of BBN
### BBN Prediction Models
Consequently, [PERSON] and [PERSON] [29] proposed an improved version, Formulation 2B. Despite its enhancements, Formulation 2B was not recommended for discrete-frequency noise prediction of a propeller/rotor due to its reliance on numerical differentiations and the calculation of retarded times, which are computationally expensive and complex. The time domain model is recognized as the most accurate approach for predicting broadband noise (BBN), which relies on high-fidelity simulations. This high level of accuracy, however, comes with a significant computational cost. A refined region is crucial to capturing detailed acoustic phenomena. This refinement, while essential for enhancing the accuracy of BBN predictions, further escalates the computational expense. Empirical model: Analytical or semi-empirical methods are computationally expensive. Equation (17) provides a basis to represent three empirical broadband noise models with different values for \(k\) and \(C\): [PERSON] and [PERSON] [30], [PERSON] [31], and [PERSON] [32], which were derived from different helicopter rotor experimental tests. \[G_{TBL-TE,s}(f)=\frac{\delta_{s}^{*}M^{5}L\overline{D}_{h}}{r_{e}^{2}}\cdot H _{s}\left(\frac{f\delta_{s}^{*}}{U},M,\text{Re}_{c}\right) \tag{2}\]6  
where \(\theta_{0}\) is an observer elevation angle, \(s_{0}\) is the distance from the rotor hub to the observer, \(C_{T}/\sigma\) is blade loading, and \(\Omega R\) is blade tip speed. The distinct constants employed by the models are shown in \[G_{TBL-TE,s}(f)=\frac{\delta_{s}^{*}M^{5}L\overline{D}_{h}}{r_{e}^{2}}\cdot H _{s}\left(\frac{f\delta_{s}^{*}}{U},M,\text{Re}_{c}\right) \tag{2}\]7  
Earlier empirical broadband noise prediction models have constraints when applied to AAM and were based on a limited number of noise experiments conducted with larger and high tip-speed helicopter rotors. Recently, a new empirical BBN prediction model for AAM was developed by [PERSON] and [PERSON] [33]. They expanded their noise data sets to cover all size propeller/rotors, including small drone rotors, medium-sized propellers, and larger helicopter rotors, such as the CH-53A and CH-3C. This broader data inclusion enhances the model's accuracy and applicability across a wider range of rotorcraft types, as detailed in Equation (18). They also developed the one-third octave band spectral model by \"Gene Expression Programming\", as presented in Equation (19). \[G_{TBL-TE,s}(f)=\frac{\delta_{s}^{*}M^{5}L\overline{D}_{h}}{r_{e}^{2}}\cdot H _{s}\left(\frac{f\delta_{s}^{*}}{U},M,\text{Re}_{c}\right) \tag{2}\]8  
\[G_{TBL-TE,s}(f)=\frac{\delta_{s}^{*}M^{5}L\overline{D}_{h}}{r_{e}^{2}}\cdot H _{s}\left(\frac{f\delta_{s}^{*}}{U},M,\text{Re}_{c}\right) \tag{2}\]9  
where \(\Delta=fc/V_{t}-\left(\sigma\log_{10}C_{T}+0.9M_{t}\sigma(M_{t}+3.82)\log_{10 }\sigma\right)\). Some code: The popular NASA code, ANOPP [34], adopts the BPM model [4] to predict several types of broadband noise: turbulent boundary layer trailing-edge noise (TBL-TE), trailing-edge separation/stall noise (angle dependence of TBL-TE), bluntness vortex shedding noise (BTE), and laminar boundary layer vortex shedding noise (LBL-VS). For the tip vortex formation noise, the code applied the [PERSON] [35] model. ANOPP also provides alternative models, such as [PERSON]'s [36] for the trailing-edge-bluntness vortex-shedding noise and [PERSON]'s [23] for TBL-TE and angle dependence of TBL-TE. Similarly, the UCD-QuietFly code [37] is designed to predict broadband noise for urban air mobility (UAM) applications. This program utilizes [PERSON]'s [23] model for trailing-edge noise and incorporates the semi-empirical BPM model [4] to predict trailing-edge bluntness noise and stall noise. Time-domain programs, such as PSU-WOPWOP [38; 39] and ASSPIN [40], use [PERSON]'s Formulation 1A [26]. Recently, NASA released ANOPP2 [41], which employs the Ffowcs-Williams and Hawkings (FW-H) equation to enhance noise prediction capabilities.