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Interaction of an unstable planar jet with an oscillating leading edge

Published online by Cambridge University Press:  21 April 2006

Thomas Staubli  and
Donald Rockwell
Thomas Staubli
Affiliation:
Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA 18015, USA Present address: Sulzer Escher Wyss, Hydraulic Development, CH-8023 Zürich, Switzerland.
Donald Rockwell
Affiliation:
Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA 18015, USA
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Abstract

An inherently unstable jet impinges upon a leading edge oscillating at controlled frequency and displacement amplitude, giving rise to two coexisting instability waves in the jet: one at the self-excited frequency of the jet; and the other at the controlled frequency of the edge displacement. Correspondingly there is an unsteady loading of the edge at these two frequencies. Simultaneous edge pressure and jet velocity measurements allow insight into the upstream influence, arising from the edge loading, on the jet oscillations. This upstream influence initially distorts the jet at the nozzle exit and causes non-homogeneous phase variations along the streamwise extent of the jet. A simple superposition model which includes upstream-induced velocities and instability-wave velocities effectively simulates these distortions.

The jet oscillations synchronize with the frequency of the controlled edge oscillations for excitation frequencies close to those of the natural jet oscillations. Measurement of the pressure amplitudes on the edge surface shows resonance of the component at the excitation frequency within the synchronization range, and attenuation of the component at the self-excited frequency close to the synchronization range. Depending on the amplitude of edge displacement, synchronization is achieved either by quenching of the self-excited component or by phaselocking of the self-excited component to the excitation frequency. Phase measurements between edge displacement and surface pressure fluctuation allow determination of the direction of energy transfer between the flow and the edge.

Flow-visualization performed simultaneously with pressure measurements gives insight into the relation between impinging vortical structures and pressure fluctuations. Time-sequence photographs allow analysis of the modulation of the flow structure due to coexistence of the self-excited and the externally excited jet instabilities. Vortex coalescence involving vortices of like sense, as well as typical formations of pairs of counter-rotating vortices, are observed. Retardation of the development of the jet vortex pattern occurs when the energy transfer from the flow to the edge is a maximum. At high excitation frequency, the large-scale jet structure recovers to that occurring in absence of edge oscillations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 176 , March 1987 , pp. 135 - 167
Copyright
© 1987 Cambridge University Press

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