Cp COEFFICIENT AND POLARS
 

Cp coefficient

Two coefficients are particularly important in the study of an airfloil:  the lift coefficient and  the drag coefficient.
In the following part, the lift coefficient Cp is drawn as a function of x/c (c is the rope of the airfoil) for different meshes and for an incidence of 7 degrees.  then, they will be compared with the results provided in the MCIP course.

Cp coefficient as a function of x/c
Coarse Mesh
 

Cp coefficient as a function of x/c
Unstructured Mesh
 

Cp coefficient as a function of x/c
Fine Mesh

If we compare those results to the ones obtained by Marcello Manna in his thesis, we can see that they are quite good. They both start with a value of -1.4 for incidence 0 and rise up to an asymptote of approximatively 0.5.
Moreover, we can notice that there is a problem behind the airfoil, just at the edge. Indeed, the airfoil computed has a edge, whereas in reality, they is smoother. That's the reason why we notice that for the coarse and the fine meshes, the curves are not correct in the way that they join themselves at the end. Nevertheless, we have good results with the unstructured mesh wich seems to capture well this characteristic of the airfoil.
 

Polar

We plotted the polar for the NACA12 airfoil using the simulations made with the unstructured mesh.

We found in books that usually, this kind of airfoil unhooks at an angle of approximately 16 degrees. In consequence, we run simulations with an incidence degree included between 0 and 22. But we didn't observe the unhooking as expected (even if we can notice that the slope decreases for i=16). This is due to the fact that we are not working with Navier Stokes equations but with Euler's. In consequence, we don't have limit layer. As the interaction between  shock and limit layer can imply a 'decollement' of the limit layer and so a decrease of the lift.