Abstract: Vortex ring is the fundamental structure in three dimensional fluid field. Three dimensional Navier-Stokes simulations are performed through finite volume method to reveal the compressible effect on axial symmetry vortex ring generated at the open end of a shock tube. Local Mach number and vortex Mach number can characterize the compressibility quantificationally. Compressibility vortex ring can be classified into three categories which correspond to subsonic, transonic and supersonic. The parameters related to vortex ring structure are also affected by compressibility. As the increase of compressibility, the vorticity profile in vortex core deviates from Gaussian distribution and the concentrated vorticity fields in the vortex core diminishes; the radius of vortex ring increase with the increasing compressibility; the radius of vortex core increase first then decrease slightly due to the embedded shock wave. The velocity of vortex ring is proportional to the compressibility. The theoretical velocity obtained from simulation agrees well with the calculated value obtained by vortex Mach number, which indicates that the formula is suitable to all three kinds of compressible vortex rings.

Key words: compressible vortex ring; shock tube; shock Mach number; local Mach number; vortex Mach number; velocity of vortex ring