Publication Date:
2017-08-03
Description:
The flow induced by the combined torsional and transverse oscillations of a sphere with amplitude ratio α and phase difference β in a concentric spherical container is examined. Analytical solutions of the leading-order flow field and shear stress profiles have been obtained. Steady streaming flows are also analysed not only for the case of unrestricted Womersley number lMl, but also in the low-frequency (lMl " 1) and high-frequency (lMl » 1) limits. At high frequency, the flow field has been divided into three regions: two boundary layers and the outer region. The streaming flow field is determined for the limiting case of the streaming Reynolds number Rs " 1. The results are compared with those of single torsional or transverse oscillation, and found to match very well. The amplitude ratio α and phase difference β, in determining the streaming, are also discussed. The number and direction of steady streaming recirculation on the r-θ plane depend on value of the amplitude ratio α. The phase difference β plays a dominant role in the azimuthal velocity u(s) 1 of steady streaming. When β is approximately (2n + 1)/2, u(s) 1φ vanishes under low-frequency oscillation, while steady streaming has a recirculation on the r-θ plane under higher-frequency oscillation. © 2017 Cambridge University Press.
Print ISSN:
0022-1120
Electronic ISSN:
1469-7645
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
,
Physics
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