Control of two and three dimensional modes in the initial region of an axisymmetric jet

Kusek, S. M.; Corke, Thomas; Reisenthel, Patrick

doi:10.2514/6.1989-968

Cited by 6 publications

(3 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For m = rt 1, this would be most evident at the azimuthal locations of the helical-mode amplitude maxima. This in fact was brought out in our earlier work (Kusek, Corke & Reisenthel 1989). I n particular, when we introduced m = f 1 helical modes near their mostamplified frequency, and with sufficient initial amplitude so that they would dominate over other instability modes, flow visualization documented that downstream the streamwise wavelength of the helical mode would double compared to the initial value.…”

Section: Case Asupporting

confidence: 56%

Resonance in axisymmetric jets with controlled helical-mode input

Corke¹,

Kusek²

1993

J. Fluid Mech.

View full text Add to dashboard Cite

This work involves active control of fundamental two- and three-dimensional amplified modes in an axisymmetric jet by introducing localized acoustic disturbances produced by an azimuthal array of miniature speakers placed close to the jet lip on the exit face. The independent control of each speaker output allowed different azimuthal amplitude and phase distributions of periodic inputs. The types of inputs used in this study consisted of conditions to force helical mode pairs with the same frequency and equal but opposite azimuthal wavenumbers, m = ±1, separately, or with axisymmetric (m = 0) modes. Three forcing conditions were studied in detail. The first consisted of a weakly amplified helical mode pair which was essentially ‘superposed’ with the natural jet instability modes. This provided a reference to the second case which consisted of the same helical mode pairs along with an axisymmetric mode at the harmonic streamwise wavenumber. This combination led to the resonant growth of the otherwise weakly (linear) amplified subharmonic helical modes. A weakly nonlinear three-wave amplitude evolution equation with a coupling coefficient derived from the data was found to model the enhanced growth of the subharmonic helical modes well. The third case consisted of forcing only m = ±1 helical modes at a frequency which was close to the most amplified. This was compared to the results of Corke et al. (1991) who forced an axisymmetric mode at the same frequency and found it to lead to the enhanced growth of near-subharmonic modes, as well as numerous sum and difference modes. The helical modes had effects identical to the previous work and confirmed the resonant amplification of a near-subharmonic mode. The amplitude development was also well represented by the nonlinear amplitude equation, including the dependence of the streamwise amplification rate on the azimuthal change in the fundamental-mode initial amplitude. However, the coupling coefficient in this case was approximately one-third that with exact fundamental-subharmonic resonance. Finally we offer some explanation for the selection of the different mode frequencies in this case.

show abstract

Section: Case Asupporting

confidence: 56%

Resonance in axisymmetric jets with controlled helical-mode input

Corke¹,

Kusek²

1993

J. Fluid Mech.

View full text Add to dashboard Cite

show abstract

“…This motion was later numerically simulated by Martin, 16 who enforced a single fundamental helical mode plus an axisymmetric mode of 2 3 f on the axisymmetric jet and denoted the resulting motion as helical pairing. In the meantime, with an additional rst-harmonic axisymmetric mode to the m = §1 helical mode pair, Kusek et al 14 and Corke and Kusek 18 showed a similar vortex pairing motion to the one observed in this study, which was denoted as vortex pairing of helical modes. Especially in Ref.…”

Section: Flow Visualizationsupporting

confidence: 71%

Resonance in Axisymmetric Jet Under Controlled Helical, Fundamental, and Axisymmetric Subharmonic Forcing

2000

View full text Add to dashboard Cite

An axisymmetric jet is forced with two helical fundamental waves of identical frequency spinning in the opposite directions and an additional axisymmetric subharmonic wave. The subharmonic component rapidly grows downstream from resonant interaction with the fundamental, signi cantly depending on the initial phase difference between the subharmonic and the fundamental. The variation of the subharmonic amplitude with the initial phase difference shows a cusplike shape. The ampli cation of the subharmonic results in a vortex pairing of helical modes. Furthermore, the azimuthal variation of the ampli cation induces an asymmetric jet cross section. When the initial subharmonic is imposed with an initial phase difference close to a critical value, the jet cross section evolves into a three-lobed shape. The lobes are generated by vortex pairing. Therefore, the conclusion is made that the initial phase difference between the fundamental and the subharmonic plays an important role in controlling the jet cross section. Nomenclaturea s = subharmonic amplitude at jet exit [(u 0 s / U e )j x = 0 ] D = jet diameter f = fundamental frequency m = azimuthal wave number p = sound pressure Re D = Reynolds number based on jet diameter (U e D/ m ) r = radial coordinate r 0.1 = radial position, where U / U c = 0.1 Sr D = Strouhal number based on jet diameter ( f D/ U e ) U = streamwise mean velocity u = streamwise velocity uctuation x = streamwise coordinate c = azimuthal angle h = momentum thickness: Z r0.1 0 U U c 1 ¡ U U c´d rḿ = kinematic viscosity u d = local phase difference between the fundamental and the subharmonic (u f ¡ 2u s ) u de = initial phase difference between the helical fundamental mode pair and the axisymmetric subharmonic measured at x / D =0, r/ D =0.25, and c = 0 deg (u fe ¡ 2u se ) u f = local phase of the fundamental wave u fe = initial phase of the helical fundamental wave [Eq. (1)] u h = local phase of the rst-harmonic wave u s = local phase of the subharmonic wave u se = initial phase of the axisymmetric subharmonic wave [Eq. (3)] Subscripts c = jet center e = jet exit Presented as Paper 98-0783 at . Member AIAA. f = fundamental h = harmonic m = maximum value s = subharmonic Superscript 0 = rms

show abstract

“…Using large-scale vorticity peaks for the detection of organized motion, Tso & Hussain (1989) reveal the phase characteristics of axisymmetric and helical configurations and also observe a double helical pattern in the far field of a jet. Recently, Kusek, Corke & Reisenthel (1989) designed an apparatus which allows them to excite helical modes with azimuthal wavenumbers up to +/-6. Experiments conducted with jets seeded by + / -1 helical modes reveal a staggered vortical pattern.…”

Section: U ( R ) = ~ (1+r2)'mentioning

confidence: 99%

Numerical investigation of three-dimensionally evolving jets under helical perturbations

Martin

Meiburg

1992

J. Fluid Mech.

View full text Add to dashboard Cite

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.

show abstract

Control of two and three dimensional modes in the initial region of an axisymmetric jet

Cited by 6 publications

References 10 publications

Resonance in axisymmetric jets with controlled helical-mode input

Resonance in axisymmetric jets with controlled helical-mode input

Resonance in Axisymmetric Jet Under Controlled Helical, Fundamental, and Axisymmetric Subharmonic Forcing

Numerical investigation of three-dimensionally evolving jets under helical perturbations

Contact Info

Product

Resources

About