## 3 Proposed Approach for the LG Far-Field Noise Prediction
### The 2D CFD Setup for the LAGOON NLG  
After the number of C-Ss is set for the different components and configurations, the dimensions are obtained using CAD software accordingly. The full 3D LAGOON NLG is modelled using SolidWorks to facilitate extracting the dimensions of each C-S. Then, the flow computational domain is designed separately for each C-S using ANSYS Workbench. Figure 4 shows the dimensions and boundary conditions applied to the circular geometry of Sec.1 and Sec.2. However, in Sec.3, Sec.4, and Sec.5, half of their characteristic lengths are used to reduce the size of the domain. Figure 5 illustrates the mesh configurations of the 2D computational domain, where the hybrid mesh method is utilized, as mentioned earlier. The unstructured mesh is used to discretize the entire domain, while the structured mesh is used around the contour of each C-S to capture the BL and flow separation. The flow conditions used in all the simulations are based on the anechoic open wind tunnel [10]. The flow density, \(\rho_{0}\) = 1.18 kg/m\({}^{3}\), the static pressure, \(P_{0}\) = 9.67723 \(\times\) 10\({}^{4}\) Pa, and the inlet velocity, U\({}_{\text{in}}\) = 78.99 m/s, which corresponds to M = 0.23. The LES turbulence model is used for all the simulations. The solution is performed in the time domain by using an implicit second order scheme. Figure 4: Schematic of the 2D computational domain size and boundary conditions for Sec.1 and Sec.2. Figure 5: Mesh configurations of the LG C-Ss at: (**a**) Sec.1 or Sec.2; (**b**) Sec.3; (**c**) Sec.4; and (**d**) Sec.5. To enhance the solution accuracy and accelerate the simulations, the non-iterative time advancement scheme is used. The \(\Delta\)t is set to \(5.0\times 10^{-6}\) s throughout the simulations to ensure numerical convergence and stability. In the case of the LES model, \(\Delta\)t size is governed by the time scale of the smallest resolved eddies. Thus, the Courant-Friedrichs-Lewy (CFL) number is maintained close to one. Based on this \(\Delta\)t, the highest frequency is 100 kHz. It is important to ensure that the flow exhibits a quasi-stationary behaviour before extracting the source data for the acoustic analysis. Table 3 presents the summary of the location of each 2D C-S, all the calculated flow parameters, and their mesh properties. The Re* for each C-S is determined based on the corresponding L\({}_{\text{a}}\). The LAGOON NLG has an inner cavity with side-to-side spacing, S = 198 mm, and the wheel diameter, \(D_{\text{w}}\) = 300 mm [10]. For the full 3D LG model, the Re = \(1.56\times 10^{6}\) is calculated based on the wheel diameter since it has the largest dimension in comparison to other components. Consequently, the flow behaves in the upper transition regime. In this study, the calculated Re* has a wide range of flow regimes from critical lower transition to upper transition, including supercritical. Note that the aspect ratio (AR), \(l_{\text{c}}\)/\(D_{\text{c}}\), where, \(l_{\text{c}}\) and \(D_{\text{c}}\) are the cylinder length and diameter, respectively, is calculated only for Sec.1 and Sec.2. Both circular cylinders have larger aspect ratios than the wheel component. For the other C-Ss, each wheel also has a cylindrical geometry but with a shorter aspect ratio compared to the upper struts and with different orientation with respect to the incoming flow. In addition, these wheels are not smooth/continuous bluff bodies due to the inner and outer cavities. Thus, the aspect ratios of Sec.3 and Sec.4 are not computed, as illustrated in Table 3.  
For each wheel body, the flow instabilities may occur in two different modes, lateral and longitudinal, as illustrated in Figure 6. The lateral perturbation could be generated due to the flow oscillation around the wheel along the Y-axis. The second longitudinal mode could be possibly generated due to the oscillatory motion of the flow around the Z-axis because of the wheel curvature.