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The NACA0012 airfoil is one of the most common airfoils for airplane and other aircraft wings. It has a thickness of 12 % of the chord and a symmetrical shape, making it ideal for use on wings that must generate lift both up and down.
At low Reynolds numbers, i.e. At low air velocities, the NACA0012 airfoil behaves somewhat differently than at higher air velocities. In particular, at low Reynolds numbers, there is an increase in drag and a deterioration in the aerodynamic characteristics of the airfoil.
At low Reynolds numbers, i.e. At low air velocities, the NACA0012 airfoil can show unexpected properties, such as separation of the air flow from the airfoil surface and the occurrence of turbulence.
In this case, the wake behind the profile can be unstable and non-linear, with changes in the direction and speed of the air flow at different points in the profile. In addition, vortex structures and areas of increased resistance can occur, which can lead to loss of controllability and stability of the aircraft.
Commercial aviation has long been a primary focus of aerodynamic research, with much attention focused on high Reynolds number flows, as measured by chord length (Rec > 500,000). However, in recent decades, interest in low Reynolds number flows (10,000 < Rec < 100,000) has increased significantly due to their key role in the design and development of small unmanned aerial vehicles (UAVs). This category includes micro- (MAVs) and nano- (NAVs), which are being actively developed for monitoring, surveillance, and remote sensing applications [1].
Experimental studies of the NACA0012 airfoil by Wang et al. [2] showed that flow regimes at Rec < 10,000 and 10,000 < Rec < 30,000 can be classified as ultra-low Reynolds number and low Reynolds number regimes, respectively. Flow visualization results indicate that in the range from ultra-low to low Rec values, the flow structure is characterized by a sequence of transition, separation, and reattachment of the boundary layer, which significantly influences the formation of the airfoil wake. The combination of these processes leads to the formation of a laminar separation bubble (LSB), which is the reattachment of the flow after laminar separation due to turbulent mixing [3].
Since the presence of a laminar separation bubble negatively impacts airfoil aerodynamic performance, most research has focused on the mechanisms behind its formation and methods for controlling this phenomenon. However, Carmichael [4] and Gad-el-Haq [3] formulated a general rule according to which the formation of a laminar separation bubble is only possible for Rec > 50,000. Therefore, in the range of 10,000 < Rec < 50,000, the airfoil typically experiences laminar separation without subsequent flow reattachment. This atypical flow behavior is accompanied by sharp changes in the lift coefficient when transitioning from ultra-low to low Reynolds numbers [5], especially under conditions of developed flow separation.
Similar conclusions are presented in the work of Alam et al. [6], who analyzed the main flow characteristics at various angles of attack and demonstrated an increase in the lift coefficient over a wide range of Reynolds numbers – from Rec = 5300 to 360,000 [7]. Therefore, it can be argued that further research into the physics of flow around an airfoil and its wake in the range of 10,000 < Rec < 50,000 is necessary for a deeper understanding of complex flow mechanisms and the development of improved airfoil shapes for relevant engineering applications [8-11].
For mathematical modeling of the NACA0012 airfoil at low Reynolds numbers, the CFD (Computational Fluid Dynamics) computer simulation method can be used. CFD allows you to solve the Navier-Stokes equations that describe the movement of a fluid or gas inside a profile, and obtain data on pressure distribution, flow velocity and other parameters. To simulate the airfoil of NACA0012, you can use special programs such as ANSYS Fluent, OpenFOAM, STAR-CCM+, Comsol Multiphysics, etc. [12-14].
In recent decades, significant progress has been made in the development of high-precision numerical methods for solving the Navier-Stokes equations, which are used to model turbulent flows of practical significance. Computational approaches such as large-eddy simulation (LES) and direct numerical modeling (DNS) are currently being increasingly used to analyze turbulent flows. However, their practical application remains significantly limited by the high requirements for the spatiotemporal resolution of computational grids and, consequently, the significant computational costs. Therefore, the widespread adoption of these methods is directly linked to the further development of computing technology and, according to experts, is only possible in the distant future.
