A study of the counter rotating vortex rings interacting with the primary vortex ring in shock tube generated flows

The formation and evolution of counter rotating vortex rings (CRVRs) appearing in shock tube-generated flows at high shock Mach numbers (M) have been studied numerically by solving ax symmetric Navier-Stokes equations and compared with experiments. The AUSM+ scheme is used for convective terms, and for time stepping a four-stage Runge-Kutta scheme is used. High-speed smoke flow visualizations and optical shadowgraph techniques are employed for verifying the numerical results. It is observed that the strong shear layer formed near the Mach disc in the axial region of the vortex ring plays a dominant role in CRVR formation. A series of CRVRs is formed for longer driver section and higher M as the shear layer persists for longer duration. The interaction of these CRVRs with the primary vortex and trailing jet vortices is studied for (i) different pressure-pulse durations at the open end keeping the amplitude constant, and (ii) varying pulse amplitude when the duration is fixed. Results are also presented comparing a high-amplitude case against a lower-amplitude one with a longer pulse duration. The maximum vorticity inside the first CRVR is found to be higher than the primary vortex ring during its formation.