AIRFOIL A

The Airfoil A is a profile designed by AEROSPATIALE in order to test some parameters influencing  wing aerodynamics. Otherwise, this airfoil is a theoritical one, meaning here that it never flyed and it will never fly.
We only run cases with the same mesh and with a Mach number of 0.3, and moreover in this case, the simulations are made with the Navier-Stokes equations. We made several runs with a variable incidence in order to calculate the polar.

DESCRIPTION OF THE MESH

We used an unstructured mesh.
Here is a global overview of the mesh:

Unstructured mesh

If we look closer, we can see that of course the mesh is strongly refined near the surface, and we can also observe a more refined zone just in the wake of the wing. This can be a clue for the following interpretation of the physical results.

Close-up of the mesh

THE ARTIFICIAL VISCOSITY

For the simu;ations with the airfoil A, we add some artificial viscosity in the code in order to have a better and faster convergence. Indeed, terms of artificial viscosity can be added in the residual in order to limitate instabilities in shock zones or for non-linear problems. This model of artificial viscosity allows to keep a good precision for unstructured meshes.

PROFIL A: SIMULATION FOR AN INCIDENCE OF 5 DEGREES

First of all, we can see that we obtain a quite good convergence (10^-5) for 5000 iterations. This result is probably due to the use of the artificial viscosity which allows to reduce the number of iterations necessary for the convergence.

Convergence for incidence 5 degrees.

Mach iso-lines, Profil A, incidence 5 degrees.

Velocity vectors, incidence 5 degrees.

PROFIL A: SIMULATIONS FOR DIFFERENT INCIDENCES

The following table present the different mach fields obtained for several incidences (from 0 to 25 degrees). We also indicate in this table the range of the mach number but if you want to see the entire picture with its legend, just click on the one you want to see.

 Incidence 0 Incidence 5 [Mmin, Mmax]=[0.0194-0.4003] [Mmin,Mmax]=[0.0180-0.3700]

 Incidence 10 Incidence 15 [Mmin,Mmax]=[0.0197-0.4061] [Mmin,Mmax]=[0.0207-0.4274]

 Incidence 25 [Mmin,Mmax]=[0.0194-0.4003]

We can observe that we don't observe the same Mach fields than for the NACA 12 airfoil, which is normal due to the fact that firstly, we are in a subsonic regime of flow (we are even just at the limit with incompressibility) and secondly, the airfoil is not symetric anymore. We can also see that there is a changing in the evolution of the field between 15 and 25 degrees. we can supposed that it is maybe due to te unhooking?? (cf following part).

PROFIL A: POLAR

We can see that in this case too, we don't observe any phenomenon of unhooking, despite the fact that we worked with Navier-Stokes equations. In fqct as we miss the value of the Cp coefficient for an incidence of 20 degrees, this curve doesn't mean anything. Indeed, as the unhooking is supposed to happen near an incidence of 20 degrees, the fact that the Cp coefficient is higher for an incidence of 25 than for 15 doesn't mean that the unhooking didn't happen between those two values.