• Transactions of the Korean Society of Mechanical Engineers B
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• v.21 no.10
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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.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.27 no.8
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• pp.1023-1032
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• 2003

The effect of local forcing on the separated flow over a backward-facing step is investigated through hot-wire measurements and flow visualization with multi-smoke wires. The boundary layer upstream of the separation point is laminar and the Reynolds number based on the free stream velocity and the step height is 13800. The local forcing is given from a slit located at the step edge and the forcing signal is always defined when the wind tunnel is in operation. In case of single frequency forcing, the streamwise velocity and the reattachment length are measured under forcing with various forcing frequencies. For the range of 0.010〈S $t_{\theta}$〈0.013, the forcing frequency component of the streamwise velocity fluctuation grows exponentially and is saturated at x/h = 0.75 , while its subharmonic component grows following the fundamental and is saturated at x/h = 2.0. However, the saturated value of the subharmonic is much lower than that of the fundamental. It is observed that the vortex formation is inhibited by the forcing at S $t_{\theta}$ = 0.019 . For double frequency forcing, natural instability frequency is adopted as a fundamental frequency and its subharmonic is superposed on it. The fundamental frequency component of the streamwise velocity grows exponentially and is saturated at 0.5 < x/ｈ < 0.75, while its subharmonic component grows following the fundamental and is saturated at x/ｈ= 1.5 . Furthermore, the saturated value of the subharmonic component is much higher than that for the single frequency forcing and is nearly the same or higher than that of the fundamental. It is observed that the subharmonic component does not grow for the narrow range of the initial phase difference. This means that there is a range of the initial phase difference where the vortex parring cannot be enhanced or amplified by double frequency forcing. In addition, this effect of the initial phase difference on the development of the shear layer and the distribution of the reattachment length shows a similar trend. From these observations, it can be inferred that the development of the shear layer and the reattachment length are closely related to the vortex paring.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.22 no.11
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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.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.26 no.3
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• pp.423-431
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• 2002

An experimental study is conducted to investigate the effect of two-frequency forcing on turbulent flow behind a backward-facing step at the Reynolds number of 27000 based on the step height. The forcing is provided from a thin slit located at the edge of the backward-facing step to increase mixing behind the backward-facing step and consequently to reduce the reattachment length. With single frequency forcing, the minimum reattachment length is obtained at the non-dimensional forcing frequency (F) of St$\_$h/ = 0.29. With two-frequency forcing, a subharmonic frequency (F/2) or biharmonic frequency (2F) is combined with the fundamental frequency (F), i.e. (F, F/2) or (F, 2F) forcing is applied. In the case of (F, F/2) forcing, the reattachment length is not much sensitive to the phase difference between F and F/2. However, the reattachment length significantly depends on the phase difference between F and 2F in the case of (F, 2F) forcing. At a certain range of the phase difference, the reattachment length becomes smaller than that of the single frequency forcing.

• Journal of applied mathematics & informatics
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• v.8 no.2
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• pp.613-625
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• 2001

In this paper, we investigate a simplified model of a particle suspended elastically from two towers by two nonlinear elastic springs, with a restoring force similar to Hooke’s law under extension and with no resistance to compression. Numerical results are presented, showing the solutions can be either of the same period oscillation the forcing term, can be a subharmonic response of multiple period, or can be noisy periodic which is apparently chaotic. Multiplicity of periodic solutions for certain physical parameters are demonstrated.

• Journal of the Korean Society of Propulsion Engineers
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• v.1 no.2
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• pp.32-40
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• 1997

The velocity and turbulent intensity of the jet core are affected by the vortices around jet. By the control of vortex acoustically, we can expect the changes of the flow and heat transfer characteristics of free and impinging jets. On this paper, we studied the effects of vortex forcing. If vortex pairings are promoted by acoustic excitation, the turbulent intensity is increased and the high heat transfer coefficients are obtained at the small nozzle to plate distance. On the other hand, it has low turbulent intensity at the center of jet. However due to increase of potential core length, it is more effective at the large nozzle to plate distance. Therefore the excited frequency, especially its subharmonic frequency, has an important role to control the jet flows.