## 3 Proposed Approach for the LG Far-Field Noise Prediction
### Acoustic Far-Field Computations for the LAGOON NLG  
The far-field acoustic noise is computed using the built-in 3D FW-H solver in ANSYS FLUENT. For each C-S, the outer surface is assigned as an acoustic source. The source extracted from each 2D near-field flow domain is extended into the third dimension. This extension, along the spanwise direction, is elongated up to the assumed SCL to perform the FW-H surface integration. It implies that the data used in the third direction is identical to the source data collected from the 2D CFD simulation. Finally, the far-field acoustic pressure is collected at the receiver located right above each bluff body at 6 m distance. Since the source zone is specified at the solid surface of each body, only the surface integral of the FW-H equation is computed. Thus, only the dipole acoustic source due to the unsteady surface pressure fluctuations is included. Note that, the nonlinearity of the near-field is maintained; however, the effect of reducing the dimensionality of the flow domain on the prediction of the far-field noise is investigated. The acoustic source of each resulting C-S is assumed to be acoustically compact. The compactness assumption is valid for L\({}_{a}<<\lambda\), where \(\lambda\) is the acoustic wavelength. To get an initial estimate of St, there are empirical formulas presented by [PERSON] [21] for a wide range of Re (from 47 to \(3.0\times 10^{5}\)) of flow past a stationary circular cylinder. For example, Equation (1) is utilized in this study to estimate the St for Sec.1 and Sec.2. \[\text{St}\ =\ 0.198\Big{(}1-\frac{19.7}{\text{Re}^{*}}\Big{)} \tag{1}\]  
The St magnitude is governed by [PERSON]'s requirement [26] when \(\text{St}\ll 1/(2\pi\text{M})\). For Sec.1 and Sec.2 with M = 0.23, St \(\ll 0.69\) to satisfy the compactness condition. It would be expected that the results captured at the main shedding tone (St \(\approx\) 0.2, from Equation (1)) and its harmonics would satisfy the [PERSON]'s requirement. In addition, the empirical formula for estimating the SCL presented in [21] is also used. Based on the calculated Re* for Sec.1 and Sec.2, as shown in Table 3, Equation (2) is used to calculate the SCL. \[\text{SCL}\ =\ \left[1.4\left(\frac{\text{Re}^{*}}{3.0\times 10^{5}}\right)^{ -2.7}\right]\text{L}_{a} \tag{2}\]  
For Sec.3, Sec.4, and Sec.5, the SCL is assumed based on the geometric features of the two wheels and the corresponding Re* of each C-S. The same number of acoustic pressure data is obtained for each C-S to calculate the total far-field noise. This corresponds to the unsteady pressure at the nodes of  
Figure 6: Schematic of possible flow instability modes occurring around: (**a**) the 3D LG model; (**b**) an isolated wheel; and (**c**) one wheel with axle component. the solid surface of each corresponding C-S. The total power spectral density (PSD) of all the noises propagated due to flow past those resulting C-S is calculated as:  
\[\text{PSD}_{Total}\ =\ 10\log_{10}\left(\sum_{i=1}^{n}10^{\text{PSD}_{i}/10}\right) \tag{3}\]  
where \(i\) is an index for the C-S number, and \(n\) indicates the total number of the C-Ss. The total computation time for the near-field flow domain is t = \(1.4010\times 10^{-1}\) s. However, the FW-H solver is started after \(20\times 10^{3}\) time steps, to ensure that the transient behaviour is settled, and run for further \(8.0\times 10^{3}\) time steps to collect the acoustic data. The noise spectrum for each corresponding simulation is produced based on a total number of 3960 samples. The number of samples is kept the same to perform the summation and calculate the overall PSD noise level. It is worth highlighting that although the flow that generates the noise is usually nonlinear, unsteady, and turbulent, the radiated sound field is typically linear. In general, the far-field acoustic pressure is less than the atmospheric pressure. This implies that the superposition principle is valid [15].