Search for: All records

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 $$\varLambda$$ 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 $$\varLambda$$ 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 $$\varLambda$$ , in an asymptotic analysis for small distances from the inlet plane. To 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 $$\varLambda$$ . Similar to the theoretical predictions, numerical calculations of $$S^*_B$$ decrease monotonically as $$\varLambda$$ is increased. The critical swirl numbers for the cone, $$S^*_C$$ , are found to depend strongly on viscous effects; for $$\varLambda =1/5$$ , the low jet Reynolds number (51) at $$Re_{eff}=200$$ delays the transition to the cone, while for $$\varLambda =5$$ at $$Re_{eff}=200$$ , the large increase in kinematic viscosity in the external fluid produces a similar trend, significantly increasing $$S^*_C$$ .