Hysteretical behaviour of a NACA 0012 airfoil at ultralow Reynolds upon variation of the angle of attack

Reynolds's low numbers studies are necessary to understand the physics surrounding aerodynamics in larger Reynolds numbers where the phenomena they appear are becoming increasingly complex and it is very necessary to use mathematical models to model what is happening. Our scenario is described by a Reynolds of 5300 and for this configuration we find a case of aerodynamic hysteresis around the 7º angle of attack. We find the coexistence of two solutions for these values and we want to show that there is a third unstable solution that connects the other two. In order to do this we will have to use computational fluid dynamics in order to find a solution to the Navier-Stokes equations that govern our case and to be able to do the appropriate simulations. The method that we will use to determine the existence of this unstable solution is Edge Tracking. This method will allow us to determine what are the initial conditions necessary to fall to the unstable solution. The more accurate we are achieving with each iteration, the more time we will be able to be above the boundary of the unstable region before it is attracted to one of the stables. In addition, we will study the different solutions obtained and compare them with others in order to make a good description. We will compare the aerodynamic forces, but also two phenomena such as the detachment of the boundary layer or the vortex shedding, making the latter a frequency analysis using the Fourier transform. Finally, we have succeeded in demonstrating the existence of the unstable region for our study scenario