Bifurcation of vortex dipole in the viscous incompressible flow around an airfoil

Abstract

The viscous incompressible flow around a NACA0012 airfoil at angle of attack equal to 5° and Reynolds numbers (Re) of 5 000, 10 000, and 30 000 is considerd. The Navier-Stokes equations written in terms of stream function and vorticity are solved by a finite-difference predictor-corrector algorithm. Distinctive feature of the algorithm is the strict fulfilment of pressure uniqueness condition in the stream. Special attention is paid to displaying the dispersion properties in the computed viscous flow. Development of the flow separation on the airfoil, surface vorticity waves (streaming waves) which intensify in the separation region and, especially, at the trailing edge (TE), leads to strong vortex-pressure (acoustic) transition in vicinity of TE, to generation of vortex spots and to bifurcation of vortex dipole at the leading (LE) and TE. The complex vortex disturbances are perturbed which partly are emitted from LE into upstrearnfiow, and partly merge into velocity-pressure disturbances and surface vorticity waves. Found are the physical grounds for inevitable development of dispersion in the vorticity fields at Re > 10 000. The vortex dipole bifurcation is clearly defined as the main reason for dispersion impulse formation.