This paper describes a numerical investigation of the generation and evolution characteristics of compressible vortex rings under varying pressure ratio conditions using the large-eddy simulation. The study primarily focuses on the influence of compressibility on the process of vortex ring evolution and the pinch-off mechanism. The results reveal that, as the pressure ratio rises, the number of trailing vortices increases significantly. Three typical vortex ring types are observed, namely shock-free vortex rings, vortex rings with an embedded shock, and vortex rings with an embedded shock accompanied by counter-rotating vortex rings. The formation number of compressible vortex rings, determined using both circulation-based and kinetic energy-based criteria, consistently falls within the range of 3.5 ± 0.5, closely aligning with the typical formation number observed in incompressible vortex rings. Moreover, a new method for calculating the dimensionless energy number α of compressible vortex rings is developed using the density-averaged value within the vortex core region. The values of α obtained from this method remain stable at around 0.33 under all pressure ratios, coinciding with the universal energy number previously reported for incompressible vortex rings. This consistency indicates that the proposed method effectively captures the underlying flow mechanisms of compressible vortex rings.
Liu et al. (2025) studied this question.