Investigation of the Interaction Between Vorticity Confinement and Numerical Diffusion Effects for the Steady and Unsteady Flows Around NACA0012 Airfoil at Different Angles of Attack

The purpose of this article is investigating the simultaneous and mutual effect of numerical dissipations and vorticity confinement in the regions near and far from the surface. From one hand because of the numerical dissipations due to differencing method and truncation errors, the existence of artificial dissipation or diffusion property is inevitable. On the other hand vorticity confinement acts as a body force source term to the Euler equations, which this also add or subtract the amount of numerical viscosity. However, the effects of these properties are different and thus deeply consideration of these effects on each other and finally on the predictions and the speed of convergence seems to be necessary. The problem is set up for the compressible, two dimensional and steady and unsteady flow around the fixed and pitching NACA0012 airfoil at different angles of attack. From this point of view the attached and highly separated regions of the boundary layer are investigated. The overall goal is that, is it possible to achieve acceptable predictions using only Euler equations with vorticity confinement and suitable artificial dissipations with coarse grid meshes in comparison with Navier Stokes equations with turbulence models and very fine grids? The numerical predictions show that under these conditions with several try and errors satisfactory primary results could be obtained in much less running time.