Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-17T09:16:35.033Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected]
Get access Rights & Permissions [Opens in a new window]

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
Check for updates
Copyright
© 2019 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abramovich, G. N. 1982 On the deformation of the rectangular turbulent jet cross-section. Intl J. Heat Mass Transfer 25 (12), 1885–1894.Google Scholar
Ai, J. J., Yu, S. C. M., Law, A. W.-K. & Chua, L. P. 2005 Vortex dynamics in starting square water jets. Phys. Fluids 17 (1), 014106.Google Scholar
Amitay, M., Tuna, B. A. & Dell’Orso, H. 2016 Identification and mitigation of T–S waves using localized dynamic surface modification. Phys. Fluids 28 (6), 064103.Google Scholar
Bejan, A., Ziaei, S. & Lorente, S. 2014 Evolution: Why all plumes and jets evolve to round cross sections. Sci. Rep. 4 (4730), 1–5.Google Scholar
Betchov, R. 2012 Stability of Parallel Flows. Elsevier.Google Scholar
Bogey, C. & Bailly, C. 2006 Large eddy simulations of transitional round jets: influence of the Reynolds number on flow development and energy dissipation. Phys. Fluids 18 (6), 065101.Google Scholar
Bogey, C. & Bailly, C. 2007 An analysis of the correlations between the turbulent flow and the sound pressure fields of subsonic jets. J. Fluid Mech. 583, 71–97.Google Scholar
Bogey, C., Bailly, C. & Juvé, D. 2003 Noise investigation of a high subsonic, moderate Reynolds number jet using a compressible large eddy simulation. Theor. Comput. Fluid Dyn. 16 (4), 273–297.Google Scholar
Bridges, T. J. & Morris, P. J. 1984 Differential eigenvalue problems in which the parameter appears nonlinearly. J. Comput. Phys. 55 (3), 437–460.Google Scholar
Callegari, A. J. & Ting, L. 1978 Motion of a curved vortex filament with decaying vortical core and axial velocity. SIAM J. Appl. Maths 35 (1), 148–175.Google Scholar
Charru, F. 2011 Hydrodynamic Instabilities, vol. 37. Cambridge University Press.Google Scholar
Crow, S. C. & Champagne, F. H. 1971 Orderly structure in jet turbulence. J. Fluid Mech. 48 (3), 547–591.Google Scholar
Dini, P., Seligt, M. S. & Maughmert, M. D. 1992 Simplified linear stability transition prediction method for separated boundary layers. AIAA J. 3 (8), 1953–1961.Google Scholar
Drazin, P. G. & Reid, W. H. 2004 Hydrodynamic Stability. Cambridge University Press.Google Scholar
Frisch, U. 1995 Turbulence: The Legacy of AN Kolmogorov. Cambridge University Press.Google Scholar
Ghasemi, A., Pereira, A. & Li, X. 2017 Large eddy simulation of compressible subsonic turbulent jet starting from a smooth contraction nozzle. Flow Turbul. Combust. 98 (1), 83–108.Google Scholar
Ghasemi, A., Roussinova, V. & Balachandar, R. 2013 A study in the developing region of square jet. J. Turbul. 14 (3), 1–24.Google Scholar
Ghasemi, A., Roussinova, V., Balachandar, R. & Barron, R. M. 2015 Reynolds number effects in the near-field of a turbulent square jet. Exp. Therm. Fluid Sci. 61, 249–258.Google Scholar
Ghasemi, A., Roussinova, V., Barron, R. M. & Balachandar, R. 2016 Large eddy simulation of the near-field vortex dynamics in starting square jet transitioning into steady state. Phys. Fluids 28 (8), 085104.Google Scholar
Ghasemi, A., Tuna, B. A. & Li, X. 2018 Shear/rotation competition during the roll-up of acoustically excited shear layers. J. Fluid Mech. 119, 443–473.Google Scholar
Gohil, T. B., Saha, A. K. & Muralidhar, K. 2015 Direct numerical simulation of free and forced square jets. Intl J. Heat Fluid Flow 52, 169–184.Google Scholar
Grinstein, F. F., Gutmark, E. & Parr, T. 1995 Near field dynamics of subsonic free square jets. a computational and experimental study. Phys. Fluids 7 (6), 1483–1497.Google Scholar
Grinstein, F. F. 2001 Vortex dynamics and entrainment in rectangular free jets. J. Fluid Mech. 437, 69–101.Google Scholar
Grinstein, F. F. & Devore, C. R. 1996 Dynamics of coherent structures and transition to turbulence in free square jets. Phys. Fluids 8 (5), 1237–1251.Google Scholar
Gutmark, E. J. & Grinstein, F. F. 1999 Flow control with noncircular jets. Annu. Rev. Fluid Mech. 31 (1), 239–272.Google Scholar
Hashiehbaf, A. & Romano, G. P. 2013 Particle image velocimetry investigation on mixing enhancement of non-circular sharp edge nozzles. Intl J. Heat Fluid Flow 44, 208–221.Google Scholar
Ho, C.-M. & Gutmark, E. 1987 Vortex induction and mass entrainment in a small-aspect-ratio elliptic jet. J. Fluid Mech. 179, 383–405.Google Scholar
Ho, C.-M. & Huang, L.-S. 1982 Subharmonics and vortex merging in mixing layers. J. Fluid Mech. 119, 443–473.Google Scholar
Ho, C.-M. & Nosseir, N. S. 1981 Dynamics of an impinging jet. Part 1. The feedback phenomenon. J. Fluid Mech. 105, 119–142.Google Scholar
Hussain, A. K. M. F. & Zaman, K. B. M. Q. 1981 The preferred mode of the axisymmetric jet. J. Fluid Mech. 110, 39–71.Google Scholar
Hussain, F. & Husain, H. S. 1989 Elliptic jets. Part 1. Characteristics of unexcited and excited jets. J. Fluid Mech. 208, 257–320.Google Scholar
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69–94.Google Scholar
Kim, J. & Choi, H. 2009 Large eddy simulation of a circular jet: effect of inflow conditions on the near field. J. Fluid Mech. 620, 383–411.Google Scholar
Krothapalli, A., Baganoff, D. & Karamcheti, K. 1981 On the mixing of a rectangular jet. J. Fluid Mech. 107, 201–220.Google Scholar
Leonard, A. 1985 Computing three-dimensional incompressible flows with vortex elements. Annu. Rev. Fluid Mech. 17 (1), 523–559.Google Scholar
Lie, K. H. & Riahi, D. N. 1988 Numerical solution of the Orr–Sommerfeld equation for mixing layers. Intl J. Engng Sci. 26 (2), 163–174.Google Scholar
Margerit, D. & Brancher, J.-P. 2001 Asymptotic expansions of the Biot–Savart law for a slender vortex with core variation. J. Engng Maths 40 (3), 297–313.Google Scholar
Marxen, O., Kotapati, R. B., Mittal, R. & Zaki, T. 2015 Stability analysis of separated flows subject to control by zero-net-mass-flux jet. Phys. Fluids 27 (2), 024107.Google Scholar
Matsuda, T. & Sakakibara, J. 2005 On the vortical structure in a round jet. Phys. Fluids 17 (2), 025106.Google Scholar
Mi, J., Kalt, P., Nathan, G. J. & Wong, C. Y. 2007 PIV measurements of a turbulent jet issuing from round sharp-edged plate. Exp. Fluids 42 (4), 625–637.Google Scholar
Mi, J. & Nathan, G. J. 2010 Statistical properties of turbulent free jets issuing from nine differently-shaped nozzles. Flow, Turbul. Combust. 84 (4), 583–606.Google Scholar
Michalke, A. 1972 The instability of free shear layers. Prog. Aerosp. Sci. 12, 213–216.Google Scholar
Monkewitz, P. A. & Huerre, P. 1982 Influence of the velocity ratio on the spatial instability of mixing layers. Phys. Fluids 25 (7), 1137–1143.Google Scholar
Petersen, R. A. & Samet, M. M. 1988 On the preferred mode of jet instability. J. Fluid Mech. 194, 153–173.Google Scholar
Quinn, W. R. & Militzer, J. 1988 Experimental and numerical study of a turbulent free square jet. Phys. Fluids 31 (5), 1017–1025.Google Scholar
Saffman, P. G. 1992 Vortex Dynamics, Cambridge Monographs on Mechanics and Applied Mathematics, vol. 311, p. 368. Cambridge University Press.Google Scholar
Saffman, P. G. & Baker, G. R. 1979 Vortex interactions. Annu. Rev. Fluid Mech. 11 (1), 95–121.Google Scholar
Schmid, P. J. & Henningson, D. S. 2012 Stability and Transition in Shear Flows. vol. 142. Springer.Google Scholar
Sciacchitano, A., Neal, D. R., Smith, B. L., Warner, S. O., Vlachos, P. P., Wieneke, B. & Scarano, F. 2015 Collaborative framework for piv uncertainty quantification: comparative assessment of methods. Meas. Sci. Technol. 26 (7), 074004.Google Scholar
Tam, C. K. W. & Thies, A. T. 1993 Instability of rectangular jets. J. Fluid Mech. 248, 425–448.Google Scholar
Towne, A., Cavalieri, A. V. G., Jordan, P., Colonius, T., Schmidt, O., Jaunet, V. & Brès, G. A. 2017 Acoustic resonance in the potential core of subsonic jets. J. Fluid Mech. 825, 1113–1152.Google Scholar
Tsuchiya, Y. & Horikoshi, C. 1986 On the spread of rectangular jets. Exp. Fluids 4 (4), 197–204.Google Scholar
Vouros, A. P., Panidis, T., Pollard, A. & Schwab, R. R. 2015 Near field vorticity distributions from a sharp-edged rectangular jet. Intl J. Heat Fluid Flow 51, 383–394.Google Scholar
Westerweel, J. & Scarano, F. 2005 Universal outlier detection for PIV data. Exp. Fluids. 39 (6), 1096–1100.Google Scholar
Xu, M., Pollard, A., Mi, J., Secretain, F. & Sadeghi, H. 2013 Effects of Reynolds number on some properties of a turbulent jet from a long square pipe. Phys. Fluids 25 (3), 035102.Google Scholar
Yarusevych, S. & Kotsonis, M. 2017 Steady and transient response of a laminar separation bubble to controlled disturbances. J. Fluid Mech. 813, 955–990.Google Scholar
Yule, A. J. 1978 Large scale structure in the mixing layer of a round jet. J. Fluid Mech. 89 (3), 413–432.Google Scholar
Zaman, K. B. M. Q. 1996 Axis switching and spreading of an asymmetric jet: the role of coherent structure dynamics. J. Fluid Mech. 316, 1–27.Google Scholar
Zaman, K. B. M. Q. 1999 Spreading characteristics of compressible jets from nozzles of various geometries. J. Fluid Mech. 383, 197–228.Google Scholar

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