Counter-rotating vortex rings (CRVRs) are observed to form ahead of a primary compressible vortex ring that is generated at the open end of a shock tube at sufficiently high Mach numbers. In most of the earlier studies, the embedded shock strength has been asserted as the cause for the formation of CRVRs. In the present study, particle image velocimetry (PIV) measurements and high-order numerical simulations show that CRVRs do not form in the absence of a Mach disk in the sonic under-expanded jet behind the primary vortex ring. Kelvin–Helmholtz-type shear flow instability of the slipstream originating from the triple point of the Mach disk and subsequent eddy pairing, as observed by Rikanati et al. (Phys. Rev. Lett., vol. 96, 2006, art. 174503) in shock-wave Mach reflection, is found to be responsible for CRVR formation. The growth rate of the slipstream in the present problem follows the model proposed by them. The parameters influencing the formation of CRVRs as well as their dynamics is investigated. It is found that the strength of the Mach disk and its duration of persistence results in an exit impulse that determines the number of CRVRs formed.

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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. Highspeed 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.

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The present study focus on evolution of compressible vortex ring generated at the open end of a shock tube through accurate measurement of velocity field using Particle Image Velocimetry (PIV). To investigate the unsteady characteristics of embedded shock-free, low Mach number vortex rings, two cases (shock Mach numbers, M=1.27 and M=1.37) are considered for PIV measurements. Time-dependent variations of circulation, core and ring diameters, and ring velocity are calculated from the measured velocity field. Pinching-off process is investigated in detail for both cases. Formation time and the time of complete detachment of the vortex ring from the trailing jet are identified from the velocity and vorticity field. The ring formation is complete at about t *(= t U b/ D)=1.75 and 1.65 for M=1.27 and 1.37, respectively, where t is time, U b is fluid velocity behind the shock at exit, and D is tube diameter. Complete detachment of the vortex ring from the trailing jet is observed at [Formula: see text] and 2.9 for M=1.27 and 1.37, respectively.