## 4 Results
### log \(\gamma\)-SA Model Results  
In this subsection, we discuss the log \(\gamma\)-SA transition model. It is worth noting that in this paper, we developed and tested an implementation for incompressible flows within the OpenFOAM library. In such a context, we had to introduce the log \(\gamma\) formulation, following [PERSON] and [PERSON] (2019), in order to overcome the blow-up of the computations. Moreover, we also verified that, for \(\alpha\geq 6^{\circ}\), the Spalart and Garbaruk correction improves  
Figure 8: S809, \(\text{Re}=2\times 10^{6}\). Pressure coefficients.  
Figure 9: S809, \(\text{Re}=2\times 10^{6}\).  
the model behavior for medium Re numbers. On the other hand, for low Re configurations, this approach does not produce relevant effects; see Figure 9(a).  
[PERSON] et al. [13] did not report the implementation issues discussed above. However, it is important to note that they handled compressible flows through the SU2 code.  
In Figure 10, we represent the \(c_{p}\) distribution computed on SD/7003's surface at \(\text{Re}=6\times 10^{4}\). The same computational grid and numerical settings described in Section 4.1.1 were employed. The results obtained from the \(\log\gamma\)-SA model were not satisfactory for \(\alpha=4^{\circ}\) (see Figure 9(a)) and even nonphysical for \(\alpha=8^{\circ}\) (see Figure 9(b)). A similar behavior was obtained for other angles of attack, but not reported for compactness. Therefore, we cannot consider the \(\log\gamma\)-SA approach sufficiently reliable for low Re applications.  
The Eppler 387 airfoil at \(\text{Re}=2\times 10^{5}\) was studied for comparison with [PERSON] et al. [13]. The solutions reported in the following were computed using a structured C-shaped computational grid having about \(2.22\times 10^{5}\) cells. It was built by the authors and already successfully tested for the \(\gamma\)-\(\widetilde{\text{Re}_{\theta,t}}\)-SA model in [11,12]. The \(c_{p}\) data presented here (Figures 11 and 12) are globally very consistent with the experimental findings of [PERSON] et al. [36]. A particular mention has to be made for \(\alpha=8^{\circ}\). [PERSON] et al. [36] observed an LSB near to the leading edge at \(\alpha=8.5^{\circ}\), while a natural transition in the boundary layer was evidenced at \(\alpha=8^{\circ}\). This behavior may contribute to explaining the discrepancy between the numerical and experimental data, already discussed in [PERSON] et al. [11]. The force coefficients, shown Figure 13, confirm the very good consistency between \(\log\gamma\)-SA and experimental data prior to the stall region. However, it is important to highlight that the stall was not correctly predicted by \(\log\gamma\)-SA, different from what happens for the \(\gamma\)-\(\widetilde{\text{Re}_{\theta,t}}\)-SA technique. Furthermore, the \(\gamma\)-SA results published in [PERSON] et al. [13] reveal a dissimilar behavior if compared with the \(\log\gamma\)-SA implemented here.  
Lastly, the S809 airfoil outputs are not shown here since the \(\log\gamma\)-SA technique proved to be unable to correctly predict the transitional effect on this high Re problem.  
Figure 11: E387, \(\mathrm{Re}=2\times 10^{5}\). Pressure coefficients.  
Figure 12: E387, \(\mathrm{Re}=2\times 10^{5}\). Pressure coefficients.