Numerical and Theoretical Analysis of Beam Vibration Induced Acoustic Streaming and the Associated Heat Transfer
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Date
2004-02-23
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Abstract
The purpose of this research is to numerically and analytically investigate the acoustic streaming and the associated heat transfer, which are induced by a beam vibrating in either standing or traveling waveforms. Analytical results show that the beam vibrating in standing waveforms scatters the acoustic waves into the free space, which have a larger attenuation coefficient and longer propagating traveling wavelength than those of the plane wave. In contrast to a constant Reynolds stress in the plane wave, the Reynolds stress generated by such acoustic wave is expected to drive the free space streaming away from the anti-nodes and towards nodes of the standing wave vibration.
The sonic and ultrasonic streamings within the channel between the vibrating beam and a parallel stationary beam are also investigated. The acoustic streaming is utilized to cool the stationary beam, which has either a heat source attached to it or subjected to a uniform heat flux. The sonic streaming is found to be mainly the boundary layer streaming dominating the whole channel while the ultrasonic streaming is clearly composed of two boundary layer streamings near both beams and a core region streaming, which is driven by the streaming velocity at the edge of the boundary layer near the vibrating beam. The standing wave vibration of the beam induces acoustic streaming in a series of counterclockwise eddies, which is directed away from the anti-nodes and towards the nodes. The magnitude of the sonic streaming is proportional to ω²A while that of the ultrasonic streaming is proportional to Ω[superscript 3/2]A². Numerical results show that the acoustic streaming induced by the beam vibrating in either standing or traveling waveforms has almost the same cooling efficiency for the heat source and the heat flux cases although the flow and temperature fields within the channel are different.
The hysteresis of the ultrasonic streaming flow patterns associated with the change of the aspect ratio of the channel is numerically investigated. Present research is also extended to a cavity which is driven by a vibrating lid. The ultrasonic streaming induced in the cavity reveals some interesting interactions among the primary eddies, which have never been observed in the classical driven cavity problem.
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standing wave, traveling wave, driven cavity, bifurcation, hysteresis, acoustic streaming, ultrasound, boundary layer
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Degree
PhD
Discipline
Mechanical Engineering
