Numerical investigation of three-dimensionally evolving jets under helical perturbations

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.

Dynamics and stability of lean-premixed swirl-stabilized combustion

“…In a high swirl number flow where the azimuthal velocity is comparable to the axial velocity, vortex breakdown may take place. Several important studies on swirling flow instabilities and coherent vortex motions, including experimental investigations [128][129][130][131][132][133], theoretical analyses [134][135][136][137][138], and numerical simulations [139][140][141][142][143][144], have been recently reported. Liang and Maxworthy [133] performed a notable experimental study of swirling jets, in which swirl is generated using a long rotating tube.…”

Nonlinear axisymmetric and three-dimensional vorticity dynamics in a swirling jet model

“…For the nonswirling top hat jet velocity profile it is known that axisymmetric and helical perturbations will result in the formation of vortex rings or helices, respectively, all of the same sign. 28,29 For purely swirling flow, on the other hand, Caflisch et al 21 demonstrated that axisymmetric perturbations lead to the emergence of counter-rotating vortex rings. By superimposing a top hat streamwise velocity profile upon the purely swirling flow, we hence expect a breaking of the symmetry exhibited by the purely swirling flow alone.…”

“…22,[28][29][30][31][32] It is based on the theorems of Kelvin and Helmholtz and follows the general concepts reviewed by Leonard 33 and Meiburg. 34 A detailed account of the technique is provided in these earlier references.…”

Vortical structure in forced unsteady circular jet: simulation by 3D vortex method

“…Cotke and Kusek 6] showed that the helical modes pair in the manner discussed by Cohen and Wygnanski 5]. The temporal evolution of a cylindrical jet-like mixing layer excited by axisymmetric and helical disturbances with an additional azimuthal disturbance is numerically studied by Martin and Meiburg 19,20].…”

“…As mentioned before, a temporally-evolving calculation such as Martin and Meiburg 19,20] does not include the e ect of feedback from the downstream vortex structures. We are in the opinion that the rapid development of the three-dimensional structures in the early part of the shear layer of the unforced jet (Figs.…”