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

TL;DR

This study numerically investigates high Mach number compressible vortex rings generated in shock tubes, including the first simulation of supersonic vortex rings using hydrogen, and highlights the effectiveness of the DES turbulence model in capturing complex vortex phenomena.

Contribution

It reports the first numerical simulation of supersonic vortex rings (Mv > 1) using hydrogen and demonstrates the DES turbulence model's accuracy in replicating experimental vortex characteristics.

Findings

First simulation of supersonic vortex rings with hydrogen.

DES turbulence model accurately predicts vortex features.

High Mach number vortex rings exhibit multiple CRVRs and complex shear layers.

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-{\omega} 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 multiple CRVRs 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 (contd...)