# Recent Advances in Acoustics of Transitional Airfoils with Feedback-Loop Interactions: A Review
## 3 Laminar Separation Bubble and Acoustic Feedback Loop Process
### Numerical Approaches
#### 3.2.3 Numerical Implementation
The case study corresponds to the mean flow velocity of 16 m/s (\(M=0.0465\)) with uniform upstream flow and \(Re=140,\!000\) closely representing an experimental condition selected from tests conducted in [14; 15]. In Figure 13, the numerical predictions compare well with experiments as peak frequencies are accurately captured and broadband levels are of the same amplitudes at frequencies adjacent to the main tone. Note that 3D ILES results exhibit a near perfect match to experiment between 500-1500 Hz whereas 2D results slightly over-predict the broadband at lower frequencies. The comparison between 2D and 3D ILES results [18] is further elaborated in Figure 14 showing predicted time-averaged U-velocity contours. Overall, the latter are identical from LE to mid-chord due to the absence of separation and inherently laminar flow. As the flow convects past the mid-chord and travel towards the TE, the differences between the 2D and 3D results become more noticeable as the separation regions and wake structures appear larger from 2D simulations. Figure 15 further illustrates the differences by showing the predicted BL velocity profiles in comparison with experimental measurements [14; 15], for selected probe locations. Figure 12: Spectrogram (bottom plot) of the near-field pressure signal (top plot) producing the spectrum in Figure 11. (Adapted from [14]). Figure 14: Time-averaged U-velocity contours in 2D (**a**) and 3D LES (**b**). Baseline case for NACA-0012 at 0\({}^{\circ}\) AoA and U = 16 m/s [18]. Figure 13: Comparison of 2D (blue) vs. 3D (magenta) vs. measured (red) far-field pressure spectra [18]. Figure 15: Comparison of 2D (blue) and 3D LES (magenta) vs. measured (red) suction-side boundary layer profiles. Time-averaged U–velocity, NACA-0012 at 0\({}^{\circ}\) AoA and U = 16 m/s [18]. Overall, the above results confirm the validity of utilizing 2D analysis implemented in most AFL studies by revealing a good agreement both with 3D simulations and experimental data. Still, one needs to exercise caution. Figure 16 shows the time snapshots of BL vorticity dynamics based on the detailed 2D vs. 3D ILES comparison conducted in [41] for NACA-0012 airfoil at AOA of 2\({}^{\circ}\), with mean flow velocity of 25 m/sec (\(M\) = 0.072) and \(Re\) = 180,000. The results reveal a noticeably different vorticity dynamics on the airfoil suction side caused by the spanwise turbulent energy redistribution and appearance of fine-scale vortical structure in 3D analysis occurring towards the trailing edge. For the same case study, Figure 17 further illustrates the comparison in [41] by also examining grid sensitivity of numerical 2D vs. 3D predictions for two critical parameters: variation of skin friction coefficient \(c_{i}\) indicating suction-side LSB position in terms of BL separation point, and variation of suction-side RMS pressure coefficient (\(c_{p}\))\({}_{RMS}\) revealing dynamics of instability structures through and after LSB zone. In the fine-mesh (1285 \(\times\) 789) 2D calculations, the separated regions form between \(x\) = 0.5 c and \(x\) = 0.75 c starting with a very thin separated layer and followed by a near-reattachment point at \(x\) = 0.67, with a rather short LSB. The results deviate from predictions using the 2D base (643 \(\times\) 395) and both 3D meshes, all predicting delayed reattachments with slightly longer LSB zones. Correspondingly, Figure 17b shows that the 2D fine-mesh results predict the rise in RMS pressure slightly further upstream compared to all other computations. The RMS pressure distributions obtained from 2D simulations correspond well with one another and sustain the levels nearly to the trailing edge.