Formation and dynamics of compressible vortex rings generated by a shock tube

Abstract

Particle image velocimetry experiments were carried out to investigate the formation and dynamics of compressible vortex rings (CVRs) generated by a shock tube apparatus. Five shock Mach numbers ($$M_\mathrm{s}$$) including $$M_\mathrm{s}=\,1.28$$, 1.39, 1.48, 1.56, and 1.59 are designed to generate the three typical CVRs including shock-free CVRs, CVRs with embedded shock, and CVRs with embedded shock and counter-rotating vortex rings (CRVRs). Experimental results show that after the incident shock leaves the tube exit, CVRs roll up, grow in size, and then pinch off at a certain timescale. By referring to the idea of vortex formation time, CVRs are found to pinch off at the dimensionless formation number within the narrow range of $$F^*=3.5\pm 0.5$$ for the range of $$M_\mathrm{s}=\,1.28$$–1.59. When $$M_\mathrm{s}\ge 1.48$$, the embedded shock appears inside the CVRs and axially stretches the vortex core, therefore significantly affecting the dynamics of CVRs. The maximum axial velocity along the centerline, the non-dimensional mean core radius, and the propagation velocity of CVRs all increase with $$M_\mathrm{s}$$ when $$M_\mathrm{s}\le 1.48$$; however, they no longer increase when $$M_\mathrm{s}>1.48$$ owing to the effects of embedded shock. In addition, the propagation velocity estimated by the formula given by Moore (Proc R Soc Lond A 397:87–97, 1985) shows the better agreement with that obtained by experimental measurement for shock-free CVRs than CVRs with embedded shock and CVRs with CRVRs.