## 1 Introduction
### Novelty and Theory  
In this work, a plain NACA 0012 is simulated, and COMSOLs automatic \"physics-controlled\" meshing is utilized with the SST turbulent flow model. The automated mesh is compared to a user-made mesh and to wind tunnel data from [PERSON] [15] and [PERSON] [3]. The airfoil is modified with a slotted flap and the performance differential is compared to the plain airfoil; additionally, different airspeeds are compared for the modified airfoil. The density and viscosity of a fluid are a function of the temperature, and, in turn, using an isothermal model means these material properties will not change due to temperature. The density and viscosity of the fluid are important properties of the air flowing around the airfoil. To investigate the validity of the constant temperature assumption, a non-isothermal model is compared to the isothermal model. The non-isothermal flow model is created by coupling the SST model to a heat transfer model in COMSOL. Finally, the stock NACA 0012 is extended into a 3D model; one 3D model has an airfoil spanning the entire domain and the other partially spans a larger domain, creating a wingtip. The 3D models are compared to the 2D model and to each other [16; 17; 18; 19].  
Based on airfoil theory, it is expected that the addition of a slotted flap will increase the \(C_{L}\) compared to the stock NACA 0012 airfoil, with larger increases at higher flap angles. However, the \(C_{L}\) slope with respect to the angle of attack should be largely unchanged. The addition of a flap will break up the streamlined shape of the airfoil, more so when the flap is angled, and, in turn, the \(C_{D}\) will be increased by the flap, and further increases in \(C_{D}\) should be present when the flap angle is larger. Finally, as the air velocity increases, so does the Reynolds number. As a consequence, a small decrease in \(C_{D}\) is expected [1; 20; 21]. The model should be able to reflect these changes in \(C_{L}\) and \(C_{D}\) stemming from the changing airfoil geometry and free-stream flow conditions.  
The extension of the 2D model to a 3D model with the wing spanning the domain effectively creates a wing of infinite span; as a result, the lift coefficient is expected to be similar to the 2D result for this mode. However, extending the domain beyond the span of the wing creates a wingtip around which air can flow. The wing now has a finite length, and the lift coefficient of the finite wing is dependent on the aspect ratio of the wing. Additionally, the flow around the wingtip introduces vortices which will trail behind the wing as it is moving through the air. Additionally, the trailing vortices persist for a significant amount of time and can be dangerous to following airplanes. This change in the lift and airflow profile should be visible between the two different 3D models [20]. Much research has gone into minimizing the loss of lift and reducing the trailing vortices, as they reduce the wing performance. This can be achieved by optimizing the aspect ratio of the wing and the wingtip. For example, the span can be increased to increase the lift coefficient; however, the structural integrity of the wing must be preserved.  
This work provides a comprehensive overview by considering additional aspects, such as the validity of an isothermal model, investigating the boundary layer profiles, and extending them to three dimensions. This work investigates the issue of whether the difference in performance resulting from modifying an airfoil with a high lift device, e.g., flaps, can be accurately modeled using CFD.