# 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
This agrees well with other numerical predictions based on 2D analysis [14; 16; 17; 18], and is identified by the process of slow viscous T-S instability growth before reaching the separation point, followed by transformation of T-S instabilities into inviscid, fast-growing K-H instabilities sustained by LSB's separated sheared layer, and finally their nonlinear saturation through LSB and realization in the form of large-scale vortical rollers (Figure 16). From 2D analysis, such rollers sustain themselves nearly unchanged to the point of TE scattering into acoustic waves. In contrast, 3D results (more grid-sensitive) indicate a rapid decrease of RMS pressure amplitudes after reaching the peak levels, which is again related to the spanwise energy redistribution following the point of turbulent reattachment. Figure 16: Time snapshots of BL vorticity dynamics from 2D and 3D ILES simulations. NACA-0012 at 2\({}^{\circ}\) AoA, U = 25 m/s. (Adapted from [41]). The effect of upstream turbulence on the disruption of the AFL process was studied numerically in [42] for the same case study using the developed model of synthetic turbulence. In agreement with experimental findings of [14,15] (Figure 10), the high-turbulence results indicated suppression of prominent tones in the surface spectra downstream of the mid-chord location on the suction side, with much higher broadband levels. The analysis of the BL statistical moments indicated that for low-turbulence upstream flow conditions, the LSB was still preserved and flow reattachment occurred without subsequent fully turbulent transition, thus still enabling preservation of the coherent vortical modes and the AFL mechanism. For the high-intensity turbulence case, the much higher RMS disturbance levels were associated with the fully turbulent flow conditions reached on the suction side, with instabilities and the AFL process fully suppressed. In view of the relationships [9,10], the connection of the above discussed RMS perturbation dynamics with the modal stability analysis is apparent, and further elaborated in the majority of the reviewed studies, albeit primarily from the standpoint of the AFL frequency selection mechanism (discussed in the next section). In [18], the LSA analysis from Section 3.2.4 was applied in conjunction with parametric numerical analysis of NACA-0012 airfoil to investigate transition from tone-producing to no-tone-producing regimes in AOA-_Re_ plane (see Figure 4). By correlating different flow regimes with position and size of LSB on either side of the airfoil, it was determined that at low AoA, distinct tones were present and dominated the acoustics of the airfoil. However, the tones would disappear at higher AoA due to the LSB migration towards the LE and allowing sufficient time for the flow to transition to fully turbulent regime, thus suppressing the AFL mechanism. On the other hand, for a fixed AoA, the increase in flow velocity (_Re_) was associated with LSB shrinking on the suction side and an increasing dominant contribution of the amplified instabilities on the pressure side (Figure 18) driving the tonal noise production mechanism, which agrees with experimental findings of [PERSON] et al. [15] and [PERSON] et al. [22]. The results of LSA analysis [18] correlated with numerical predictions of separated regions for _Re_ = 144,000 and for _Re_ = 288,000 are illustrated in Figure 19.  
Figure 17: (a) Skin friction coefficient on suction sides. (b) Suction-side airfoil surface RMS pressure distribution. NACA-0012 at 2\({}^{\circ}\) AoA, U = 25 m/s. (Adapted from [41]).