## 5 Conclusions  
The practical performance of the GEEO turbulence model for the RANS simulation of aeronautical flows of engineering significance was investigated. The specific application example concerned the mean turbulent flow around the realistic geometry of an innovative mid-range commercial aircraft in the cruise wing stall regime. The effect of varying the model coefficients of interest for the accurate prediction of the separated BL flow on the main wing was systematically examined. By means of the appropriate calibration, the generalized model was demonstrated to be able to reproduce the results of a more sophisticated (and more costly) scale-resolving turbulence modeling procedure.  
As a conclusion, the optimal selection of the model coefficients under examination resulted in using \(C_{\rm sep}=1\) while keeping the other coefficients at the prescribed default levels. The separation coefficient was found standing for the dominant parameter, which represents a very important outcome of the present study. Predictably, this coefficient will play an even more crucial role when simulating either take-off or landing aircraft configurations, where the deployment of high-lift surfaces leads to the presence of highly separated turbulent flow regions.  
Let us point out two facts suggested by the present study. First, the variation of the GEEO model coefficients provided a strong effect on the RANS predictions. This is not surprising, since the actual formulation of the turbulence model, which is integrated through the viscous sublayer, plays a crucial role in defining both the robustness and the accuracy of the solution, with the possible occurrence of undesired pseudo-transition. Second, in contrast to the similar analysis that was addressed in the original report [21] for two-dimensional simulations of airfoils, the present study examined the effect of varying GEEO coefficients for three-dimensional simulations of a realistic aircraft model. This way, the performance of the model fine-tuning procedure could be tested for a true industrial application.  
The present applied CFD work was intended as a proof-of-concept--namely, the preliminary testing of an industrial CFD-based prediction tool for the aerodynamic design of a new commercial aircraft. This study contributed to the development of affordable and reliable computational models, paving the way for ML-assisted optimization procedures for the generalized two-equation turbulence modeling of aeronautical flows based on experimental measurements and/or high-fidelity numerical data [15; 31]. In this regard, more sophisticated wavelet-based adaptive SRS methods for wall-bounded turbulent flows are under development [32; 33].  
Conceptualization, G.D.; methodology, G.D.; validation, V.R. and G.D.; investigation, V.R. and G.D.; resources, V.R. and G.D.; data curation, V.R.; writing--original draft preparation, G.D.; writing--review and editing, G.D.; visualization, V.R.; supervision, G.D. All authors read and agreed to the published version of the manuscript.  
This research received no external funding.  
Data Availability Statement: Not applicable. Conflicts of Interest: The authors declare no conflict of interest. Abbreviations  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} BL & Boundary layer \\ CFD & Computational fluid dynamics \\ DES & Detached-eddy simulation \\ FV & Finite volume \\ GEKO & Generalized \(k\)-\(\omega\) \\ HPC & High-performance computing \\ LES & Large-eddy simulation \\ MAC & Mean aerodynamic chord \\ ML & Machine learning \\ RANS & Reynolds-averaged Navier-Stokes \\ SBES & Stress-blended eddy simulation \\ SRS & Scale-resolving simulation \\ SST & Shear-stress transport \\ WT & Wind tunnel \\ \end{tabular}