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Numerical investigation of three-dimensionally evolving jets under helical perturbations

Published online by Cambridge University Press:  26 April 2006

J. E. Martin  and
E. Meiburg
J. E. Martin
Affiliation:
Center for Fluid Mechanics, Division of Applied Mathematics, Brown University, Providence, RI 02912, USA Department of Aerospace Engineering, University of Southern California, Los Angeles, CA 90089, USA.
E. Meiburg
Affiliation:
Department of Aerospace Engineering, University of Southern California. Los Angeles, CA 90089, USA
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Abstract

We study the three-dimensional evolution of a nominally axisymmetric jet subject to helical perturbations. Our approach is a computational one, employing an inviscid vortex filament technique to gain insight into the vorticity dynamics of jets dominated by helical vortices. For the case of a helical perturbation only, the streamwise vorticity forming in the braid is of the same sign everywhere, with the vortex helix representing streamwise vorticity of opposite sign. Owing to the helical symmetry, concentrated structures do not form in the braid. By introducing an additional periodic perturbation in the azimuthal direction, the helical symmetry is broken and we observe the emergence of concentrated streamwise braid vortices all of the same sign, in contrast to the counter-rotating braid vortices of ring-dominated jets. A Kelvin—Helmholtz-like instability of the braid vorticity layer plays a significant role in their generation. We furthermore find that the initial evolution of the braid vorticity is strongly dependent upon the ratio between the helical and azimuthal perturbation amplitudes. Smaller azimuthal perturbation amplitudes slow down the concentration process of the braid vorticity. However, we find that the long-time strength of the streamwise braid vortices should not depend on the amplitudes of the streamwise and azimuthal perturbation waves, but rather on their wavenumbers. The evolution of the helical vortex varies with the ratio between jet radius R and shear-layer momentum thickness θ. While for a jet with R/θ = 22.6 and azimuthal wavenumber five, the emerging helix continuously rotates and thereby avoids instability, we observe in a jet with R/θ = 11.3 the reduction of this rotation and the near exponential growth of waves on the helical vortex, characteristic of vortex helix instability.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 243 , October 1992 , pp. 457 - 487
Copyright
© 1992 Cambridge University Press

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