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We study the emergence of precessing vortex core (PVC) oscillations in a swirling jet experiment. We vary the swirl intensity while keeping the net mass flow rate fixed using a radial-entry swirler with movable blades upstream of the jet exit. The swirl intensity is quantified in terms of a swirl number $$S$$ . Time-resolved velocity measurements in a radial–axial plane anchored at the jet exit for various $$S$$ values are obtained using stereoscopic particle image velocimetry. Spectral proper orthogonal decomposition and spatial cross-spectral analysis reveal the simultaneous emergence of a bubble-type vortex breakdown and a strong helical limit-cycle oscillation in the flow for $$S>S_{c}$$ where $$S_{c}=0.61$$ . The oscillation frequency, $$f_{PVC}$$ , and the square of the flow oscillation amplitudes vary linearly with $$S-S_{c}$$ . A solution for the coherent unsteady field accurate up to $$O(\unicode[STIX]{x1D716}^{3})$$ ( $$\unicode[STIX]{x1D716}\sim O((S-S_{c})^{1/2})$$ ) is determined from the nonlinear Navier–Stokes equations, using the method of multiple scales. We show that onset of bubble type vortex breakdown at $$S_{c}$$ , results in a marginally stable, helical linear global hydrodynamic mode. This results in the stable limit-cycle precession of the breakdown bubble. The variation of $$f_{LC}$$ with $$S-S_{c}$$ is determined from the Stuart–Landau equation associated with the PVC. Reasonable agreement with the corresponding experimental result is observed, despite the highly turbulent nature of the flow in the present experiment. Further, amplitude saturation results from the time-averaged distortion imposed on the flow by the PVC, suggesting that linear stability analysis may predict PVC characteristics for $$S>S_{c}$$ .
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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 $$\varLambda$$ 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 $$S^*_C$$ .
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- Award ID(s):
- 1916979
- PAR ID:
- 10330993
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 936
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2022.18
