Numerical Simulations of 3D Compressible Vortex Ring

In this paper, the evolution and instability of compressible vortex rings at the open end of shock tube are investigated. Three-dimensional Navier-stokes simulations are performed to reveal the instability of circularcompressible vortex rings at different shock Mach numbers. Three shock Mach numbers M-s=1.26, 1.5 and 1.61 each corresponding to subsonic, moderately under-expanded, and highly under-expanded jet regimes, respectively are considered for simulations. It is observed that, in all the cases, the initial stable vortex ring becomes unstable to azimuthal disturbances. The azimuthal waves are seen to develop around the circumference of the vortex core and amplify with time, similar to incompressible vortex rings. At Ms=1.61, the results indicate that a counter-rotating vortex ring forms ahead of the primary vortex ring due to the roll-up of the slipstream vortices. With the presence of counterrotating vortex ring, the primary vortex ring is severely stretched and the azimuthal waves are seen to be amplified. Furthermore, a preliminary analysis on the number of waves (n) formed around the circumference of the vortex ring is presented. The results show that incompressible instability analysis under-predicts the value of n. However, by incorporating the compressibility correction, the value of n closely matches with the present simulation.