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Curvature-induced deformations of the vortex rings generated at the exit of a rectangular duct

Published online by Cambridge University Press:  01 February 2019

Abbas Ghasemi Open the ORCID record for Abbas Ghasemi [Opens in a new window] ,
Burak Ahmet Tuna  and
Xianguo Li Open the ORCID record for Xianguo Li [Opens in a new window]
Abbas Ghasemi
Affiliation:
Department of Mechanical and Mechatronics Engineering, University of Waterloo, 200 University Avenue West, Waterloo, ON N2L 3G1, Canada
Burak Ahmet Tuna
Affiliation:
Department of Mechanical and Mechatronics Engineering, University of Waterloo, 200 University Avenue West, Waterloo, ON N2L 3G1, Canada
Xianguo Li*
Affiliation:
Department of Mechanical and Mechatronics Engineering, University of Waterloo, 200 University Avenue West, Waterloo, ON N2L 3G1, Canada
*
†Email address for correspondence: Xianguo.Li@uwaterloo.ca
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Abstract

Rectangular air jets of aspect ratio $2$ are studied at $Re=UD_{h}/\unicode[STIX]{x1D708}=17\,750$ using particle image velocimetry and hot-wire anemometry as they develop naturally or under acoustic forcing. The velocity spectra and the spatial theory of linear stability characterize the fundamental ($f_{n}$) and subharmonic ($f_{n}/2$) modes corresponding to the Kelvin–Helmholtz roll-up and vortex pairing, respectively. The rectangular cross-section of the jet deforms into elliptic/circular shapes downstream due to axis switching. Despite the apparent rotation of the vortex rings or the jet cross-section, the axis-switching phenomenon occurs due to reshaping into rounder geometries. By enhancing the vortex pairing, excitation at $f_{n}/2$ shortens the potential core, increases the jet spread rate and eliminates the overshoot typically observed in the centreline velocity fluctuations. Unlike circular jets, the skewness and kurtosis of the rectangular jets demonstrate elevated anisotropy/intermittency levels before the end of the potential core. The axis-switching location is found to be variable by the acoustic control of the relative expansion/contraction rates of the shear layers in the top (longer edge), side (shorter edge) and diagonal views. The self-induced vortex deformations are demonstrated by the spatio-temporal evolution of the phase-locked three-dimensional ring structures. The curvature-induced velocities are found to reshape the vortex ring by imposing nonlinear azimuthal perturbations occurring at shorter wavelengths with time/space evolution. Eventually, the multiple high-curvature/high-velocity regions merge into a single mode distribution. In the plane of the top view, the self-induced velocity distribution evolves symmetrically while the tilted ring results in the asymmetry of the azimuthal perturbations in the side view as the side closer to the acoustic source rolls up in more upstream locations.

JFM classification

Wakes/Jets: Jets Turbulent Flows: Shear layer turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 864 , 10 April 2019 , pp. 141 - 180
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Copyright
© 2019 Cambridge University Press 

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Ghasemi et al. supplementary movie 1

Iso-surfaces of the instantaneous Qp-criterion during the phases (Φ = 0°, 120°, 240°) for the acoustic forcing at HFHA. Vortical structures are coloured by the vorticity component corresponding to the roll-up sense of rotation.

Download Ghasemi et al. supplementary movie 1(Video)
Video 3.5 MB

Ghasemi et al. supplementary movie 2

Iso-surfaces of the instantaneous Qp-criterion during the phases (Φ = 0°, 120°, 240°) for the acoustic forcing at HFMA. Vortical structures are coloured by the vorticity component corresponding to the roll-up sense of rotation.

Download Ghasemi et al. supplementary movie 2(Video)
Video 3.3 MB

Ghasemi et al. supplementary movie 3

Top view (TV: near the y/a = 0.5 edge) or the x-z plane coloured by the phase-averaged streamwise velocity. The TV plane is passed through the local vortex loop demonstrated by the yellow-coloured iso-surface of the instantaneous Qp-criterion. The vortex loop is isolated from the longer side of the initially rectangular vortex ring. Instantaneous snapshots are presented for the acoustic forcing at HFHA during the phases (Φ = 0°, 60°, 120°, 180°, 240°, 300°).

Download Ghasemi et al. supplementary movie 3(Video)
Video 3.7 MB

Ghasemi et al. supplementary movie 4

Phase-averaged streamwise velocity spikes characterizing the curvature-induced velocity. Instantaneous information are extracted from the top view (TV: near the y/a = 0.5 edge) or the x-z plane. Instantaneous snapshots are presented for the acoustic forcing at HFHA%"during the phases (Φ = 0°, 60°, 120°, 180°, 240°, 300°).

Download Ghasemi et al. supplementary movie 4(Video)
Video 1.2 MB

Ghasemi et al. supplementary movie 5

Side view (SV: near the z/a = 1 edge) or the x-y plane coloured by the phase-averaged streamwise velocity. The plane is passed through the local vortex loop demonstrated by the iso-surface of the instantaneous Qp-criterion. The vortex loop is isolated from the shorter side of the initially rectangular vortex ring. Instantaneous snapshots are presented for the acoustic forcing at HFHA during the phases (Φ = 0°, 60°, 120°, 180°, 240°, 300°).

Download Ghasemi et al. supplementary movie 5(Video)
Video 2.3 MB

Ghasemi et al. supplementary movie 6

Phase-averaged streamwise velocity spikes characterizing the curvature-induced velocity. Instantaneous information are extracted from the side view (SV: near the z/a = 1 edge) or the x-y plane. Instantaneous snapshots are presented for the acoustic forcing at HFHA during the phases (Φ = 0°, 60°, 120°, 180°, 240°, 300°).

Download Ghasemi et al. supplementary movie 6(Video)
Video 1.5 MB