Vortex breakdown in variable-density gaseous swirling jets

Theoretical predictions and numerical simulations are used to determine the transition to bubble and conical vortex breakdown in low-Mach-number laminar axisymmetric variable-density swirling jets. A critical value of the swirl number S for the onset of the bubble (S-B*) and the cone (S-C*) is determined as the jet-to-ambient density ratio Lambda is varied, with the temperature dependence of the gas density and viscosity appropriate to that of air. The criterion of failure of the slender quasi-cylindrical approximation predicts S-B* that decreases with increasing values of Lambda for a jet in solid-body rotation emerging sharply into a quiescent atmosphere. In addition, a new criterion for the onset of conical breakdown is derived from divergence of the initial value of the radial spreading rate of the jet occurring at S-C*, found to be independent of Lambda, in an asymptotic analysis for small distances from the inlet plane. la maintain stable flow in the unsteady numerical simulations, an effective Reynolds number Re-eff, defined employing the geometric mean of the viscosity in the jet and ambient atmosphere, is fixed at Re-eff = 200 for all Lambda. Similar to the theoretical predictions, numerical calculations of S-B* decrease monotonically as Lambda is increased. The critical swirl numbers for the cone, S-C*, are found to depend strongly on viscous effects; for Lambda = 1/5, the low jet Reynolds number (51) at Re-eff = 200 delays the transition to the cone, while for Lambda = 5 at Re-eff = 200, the large increase in kinematic viscosity in the external fluid produces a similar trend, significantly increasing S-C*.