Characteristics of shock tube generated compressible vortex rings at very high shock Mach numbers

Abstract

Compressible vortex rings, usually formed at the open end of a shock tube, often show interesting phenomena during their formation, evolution, and propagation depending on the shock Mach number (Ms) and exit flow conditions. The Mach number of the translating compressible vortex rings (Mv) investigated so far in the literature is subsonic as, the shock tube pressure ratio (PR) considered is relatively low. In this numerical study we focus on low to high vortex ring Mach numbers (0.31 < Mv < 1.08) cases with a particular focus on very high Mv cases that are not been reported in experiments as, it is difficult to obtain in laboratory. Using hydrogen as a driver section gas inside the shock tube, a supersonic compressible vortex ring (Mv > 1) is obtained for first time.It is established that the SST k-ω based DES turbulent model replicates the experimental observation better than the previously published results at different stages of development of the vortex ring. DES, which is an inbuilt hybrid of LES and RANS approaches is evoked that can automatically switch to the sub-grid scale (SGS) model in the LES regions (i.e. with different scale vortical structures) and to a RANS model in the rest of the region (i.e. where the grid spacing is greater than the turbulent length scale). The DES model can predict characteristics of the shear layer vortices as well as counter-rotating vortex rings (CRVRs) as reported in the experimental measurements. Formation of multiple triple points and the corresponding slip-stream shear layers and thus multipleCRVRs behind the primary vortex ring at different radial locations, in addition to the usual CRVRs, appears to be a unique characteristic for high Mach number vortex rings. For high PR, H2, case during formation stage, a vortex layer of reverse circulation (that of primary vortex ring) is formed from the outer wall of the shock tube, whose instability formed another series of opposite circulation vortices which interfere with the primary vortex ring considerably. Also, near the central zone, a near stationary slipstream vortex and multiple, fast moving tiny vortices of opposite circulation to slipstream vortex are observed. Mechanisms for formation of these complex vortex structures are identified. The implications of these phenomena on vortex rings' geometric and kinematic characteristics such as ring diameter, core diameter, circulation, translational velocity as well as vortex Mach number are discussed in detail illustrating their differences with low PR cases.

Vortex Ring Formation Following Shock Wave Diffraction in Low-Pressure Environments

“…Compressible vortex rings, as a common phenomenon in aerospace engineering, have been studied intensively for decades, both experimentally and numerically, in the atmosphere (Elder and De Haas 1952;Baird 1987;Hillier 1991;Brouillette and Hebert 1997;Kontis et al 2006;Murugan et al 2012;Dora et al 2014;Zhang et al 2014;Poudel et al 2021). Understanding compressible vortex ring evolution is fundamental to thrust control improvement (Cao et al 2021) and avoiding contamination and impingement on sensitive surfaces (Martinez and Worthy 2020).…”

Shock wave formation from head-on collision of two subsonic vortex rings

“…Vortex rings can form not only in air, such as in rocket nozzles and wing tips of airplanes or out the end of a shock tube, but also in water in cavitation bubbles, the wake of a boat and waterspouts 1 , 2 . Cavitation bubbles can turn into vortices as they travel, and upon impact with the propeller or wall of a ship, break and create shock waves that damage the vessel 14 .…”