• 대한기계학회논문집B
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• 제22권11호
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• pp.1610-1624
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• 1998

An axisymmetric jet is forced with two helical fundamental waves of identical frequency spinning in opposite directions and an additional axisymmetric sub harmonic wave. The subharmonic component rapidly grows downstream from subharmonic resonance with the fundamental, significantly depending on the initial phase difference. The variations of the subharmonic amplitude with the initial phase difference show cusp-like shapes. The amplification of the sub harmonic results in 'vortex pairing of helical modes'. Furthermore, azimuthal variation of the amplification induces an asymmetric jet cross-section. When the initial subharmonics is imposed with an initial phase difference close to a critical value, the jet-cross section evolves into a three-lobed shape. One lobe is generated by the enhanced vortex pairing and the other two lobes are generated by the delayed vortex pairing. Thus, it is confirmed that the initial phase difference between the fundamental and the subharmonic plays an important role in controlling the jet cross-section.

• 대한기계학회논문집B
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• 제21권10호
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• pp.1350-1362
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• 1997

An experimental study has been performed on vortex pairing under fundamental and subharmonic forcing with controlled initial phase differences through hot-wire measurements and a multi-smoke wire flow visualization. For the range of St$_{D}$ < 0.6, vortex pairing was controlled by means of fundamental and subharmonic forcing with varying initial phase differences. Much larger mixing rate was achieved by two-frequency forcing with a proper phase difference than one frequency forcing. As St$_{D}$ decreased, vortex pairing was limited to a narrow region of the initial phase difference between two disturbances and higher amplitudes of the fundamental and its subharmonic at the nozzle exit were required for more stable pairing. As the amplitude of the subharmonic at the nozzle exit increased for fixed St$_{D}$ and fundamental amplitude, the distribution of the subharmonic mode against the variation of the initial phase difference changed from a sine function form into a cusp-like form. Thus, vortex pairing can be controlled more precisely for the former case. For St$_{D}$ > 0.6, non-pairing advection of vortices due to the improper phase difference was sometimes observed in several fundamental forcing amplitudes when only the fundamental was applied. However, when its subharmonic was added, vortex pairing readily occurred. As the initial amplitude of this subharmonic increased, the position of vortex pairing moved upstream. This was thought to be due to the fact that the variation of the initial phase difference between the fundamental and its subharmonic has less effects on vortex pairing in the region of fundamental-only vortex pairing.pairing.