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Vortex breakdown in variable-density gaseous swirling jets

Published online by Cambridge University Press:  07 February 2022

Benjamin W. Keeton Open the ORCID record for Benjamin W. Keeton [Opens in a new window] ,
Jaime Carpio ,
Keiko K. Nomura Open the ORCID record for Keiko K. Nomura [Opens in a new window] ,
Antonio L. Sánchez Open the ORCID record for Antonio L. Sánchez [Opens in a new window]  and
Forman A. Williams
Benjamin W. Keeton*
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, CA 92093–0411, USA
Jaime Carpio
Affiliation:
Departamento de Ingeniería Energética, E.T.S. Ingenieros Industriales, Universidad Politécnica de Madrid, 28006 Madrid, Spain
Keiko K. Nomura
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, CA 92093–0411, USA
Antonio L. Sánchez
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, CA 92093–0411, USA
Forman A. Williams
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, CA 92093–0411, USA
*
†Email address for correspondence: [email protected]
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Abstract

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 $S^*_C$.

JFM classification

Vortex Flows: Vortex breakdown Wakes/Jets: Jets
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 936 , 10 April 2022 , A1
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

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