## 1 Introduction
### Acoustic Results Validation  
The effect of the grid densities on the Overall Sound Pressure Level (OASPL) is already investigated and presented in Table 1. It is noted that the OASPL value with SCL = 5.0\(D\) for all the three mesh sizes is in good agreement with the measured experimental data obtained by [PERSON] et al. [29]. [PERSON] [21] \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{2}{c}{**Flow Quantities**} & \multicolumn{1}{c}{**St**} & \multicolumn{1}{c}{\(\overline{C}_{d}\)1 **} \\ \hline \multicolumn{2}{c}{**Experimental Data**} & \multicolumn{1}{c}{**0.180–0.191 ([PERSON] [21])**} & \multicolumn{1}{c}{**1.0–1.4 ([PERSON] et al. [31])**} \\ \hline \multirow{4}{*}{**Turbulence Model**} & \multirow{2}{*}{**2D**} & \(k\)-\(\omega\) SST Orselli et al. [22] & 0.247 & 0.944 \\  & & \(k\)-\(\omega\) SST [PERSON] et al. [27] & 0.227 & 0.802 \\ \cline{1-1}  & & LES—Present study & 0.240 & 0.782 \\ \cline{1-1} \cline{2-4}  & \multicolumn{1}{c}{**3D**} & LES [PERSON] et al. [22] & 0.191 & 1.08 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of the obtained flow quantities with experimental, 2D, and 3D numerical results for a circular cylinder at \(\rm{Re}=9.0\times 10^{4}\). Figure 1: Pressure coefficient profile around the upper surface of the circular cylinder at \(\rm{Re}=9.0\times 10^{4}\). observed experimentally that the flow was fully correlated along \(\text{SCL}_{\text{Exp. }}\approx 3.16D\). This \(\text{SCL}_{\text{Exp. }}\) value was utilized by [PERSON] et al. [22] besides the other four values, \(2.5D\), \(5.0D\), \(10.0D\), and \(25.3D\). They concluded that the \(\text{SCL}=5.0D\) was in good quantitative agreement with the OASPL experimental data [29]. In the current study, the same observation is also noticed. Note that the acoustic data is extracted from the 2D near-field flow, while the acoustic source is coincident with the outer surface of the cylinder. Figure 2 presents the comparison of the predicted Sound Pressure Level (SPL) with the experimental data [29] and similar numerical acoustic results obtained from previous studies [27; 40]. In these studies, the near-field flow data were obtained using different CFD solvers. For example, [PERSON] et al. [27] used an in-house CFD code based on the SST turbulence model to collect near-field data, and the far-field noise is calculated using the FW-H analogy. However, [PERSON] et al. [40] obtained the acoustic results using the Curle acoustic analogy implemented in the OpenFOAM to predict the far-field pressure fluctuations. In the present study, the built-in FW-H acoustic solver in FLUENT is used to compute the far-field noise. As mentioned earlier, when the Re is high, the wake becomes fully turbulent, and thus, the fundamental motion of the von Karman vortex street can be visible. Nevertheless, this motion is superimposed by the spanwise velocity fluctuations characterized by different frequencies and phases. These fluctuations affect the surface pressure, which then influences the far-field noise signature by altering the spectral broadening of the tonal noise [21]. Although the vortex shedding frequency is over-predicted, the peak amplitude of the SPL of the present study has a better matching with the experimental data. Based on that, the 2D LES turbulence model can capture the essential flow characteristics compared to other turbulence models. Interestingly, the present 2D LES successfully reproduces the broadening of the tonal noise, as shown in Figure 2. Therefore, the LES turbulence model is utilized to solve all the 2D simulations in this work. In general, the turbulence model, acoustic analogy, and the assumed SCL highly influence the predicted far-field noise. This study provides insights to locate the C-Ss, and then the SCL is assumed accordingly to obtain the source data for the far-field noise calculations of the proposed approach.