## 4 Conclusions  
Two- and three-dimensional models of an NACA 0012 were studied in COMSOL under different regimes and analyzing the different physics involved. * A first numerical conclusion of this study is that the COMSOL physics-controlled meshing settings are not suitable for this airfoil simulation as they are either unable to converge or give results that do not match those of experiments. User-controlled meshes are required to yield good results. * The SST turbulence flow model with a user-controlled mesh shows good agreement with experimental \(C_{L}\) results. The \(C_{D}\) results need to be considered carefully when trying to apply it to real life wings, as the flow model assumes turbulent flow across the entire airfoil. The degree to which this assumption is valid will depend on the wing roughness. The modified airfoil has increased \(C_{L}\) and \(C_{L}/C_{D}\) values compared to the stock NACA 0012. Increasing the flap angles further increases \(C_{L}\) and \(C_{D}\). The free stream velocity has a minor impact, with a very slightly higher \(C_{L}\) and slightly higher \(C_{D}\) at higher velocities. Overall, the simulated results correspond well to what is expected from theory and real-life experiments. * No significant difference was found in \(C_{L}\) or \(C_{D}\) between the isothermal and non-isothermal models. In turn, the use of a non-isothermal model is not required for good results in these simulations. * The 3D model shows some interesting avenues for future research, but the current results are limited and more verifications are necessary. Figure 31: Pressure slice of the 3D NACA without a wingtip. The slice is positioned at 0.15 chord lengths from the leading edge (\(yz\) plane). Figure 30: Pressure slice of the 3D NACA with a wingtip. The slice is positioned at 0.15 chord lengths from the leading edge (\(yz\) plane). For instance, a large eddy simulation (LES) model could be evaluated, especially at higher angles of attack near or at stalling. Different high lift devices could be used to modify the NACA 0012 and compare their performance, for example, a slat at the front. Combinations of these devices could be made to further optimize the airfoil, for example, an additional flap or a combination of a flap and a slat. The shape of the main body could be altered, for example, by using the NASA supercritical (SC) airfoils used in commercial jets. The span could be increased, and this would be especially interesting for the model with a wingtip. Similar modifications which have already been made or suggested for the 2D model could be made for the 3D model. Methodology; software; validation; formal analysis; investigation; writing--original draft preparation, B.S. Project administration; conceptualization; resources; writing--review and editing; visualization; supervision, P.D. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. B.S. thanks the University of Groningen for providing the COMSOL Multiphysics software. P.D. thanks to [PERSON] for her valuable comments about this paper. The authors declare no conflict of interest. The following abbreviations are used in this manuscript: \begin{tabular}{l l} CFD & Computational Fluid Dynamics \\ LES & Large Eddy Simulation \\ NACA & National Advisory Committee for Aeronautics \\ RANS & Reynolds-Averaged Navier-Stokes \\ SA & Spalart-Allmaras \\ SST & Shear-Stress Transport \\
**Nomenclature** \\ A & Area (m\({}^{2}\)) \\ c & Speed of sound (m/s) \\ C\({}_{D}\) & Drag coefficient (-) \\ C\({}_{L}\) & Lift coefficient (-) \\ F\({}_{D}\) & Drag force (N) \\ F\({}_{L}\) & Lift force (N) \\ k & Specific heat ratio (-) \\ P & Pressure (Pa) \\ \(R_{p}\) & Particular gas constant (J/kg \(\cdot\) K) \\ T & Temperature (K) \\ \([u,v,w]\) & Fluid velocity field (m/s) \\ Greek Letters & \\ \(\alpha\) & Angle of attack (\({}^{\circ}\)) \\ \(\rho\) & Fluid density (kg/m\({}^{3}\)) \\ \(\mu\) & Phase viscosity (mPa \(\cdot\) s) \\ \end{tabular}   
**Figure A4.