Stall in a numerical wind tunnel

In this work, we introduce a new method for determining the behavior of the drag force. We have used this method in order to compare the drag and lift coefficients for a simple model of wing within numerical wind tunnels.
The inspiration comes from an experimental result: a small, light ball falls on air; its speed increases, reaches a maximum, decreases and finally stabilizes. This surprising behavior is due to the gradual formation of the so- called von K?rm?n street of vortices: while it is not completely formed, the transient drag force is smaller than the known steady state value and the ball can reach speeds higher than its final value. In building the numerical
wind tunnel we solved the Navier-Stokes equation by the finite difference method and successive relaxations. The initial condition is the flow around the obstacle immersed in an incompressible fluid with vanishing velocity (obeying the same equation for vanishing Reynolds number). At this moment, the wind tunnel is turned on with a constant, finite free stream speed (corresponding to a Reynolds number of the order of 1,000). After a transient time, we observe the formation of a street of vortices in the fluid portion behind the wing, the so-called von K?rm?n street. In particular, we investigated the relationship between the behavior of the coefficients and the attack angle. Our results suggest the manifestation in the wind tunnel of a well-known phenomenon in aviation, the stall crisis.