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Friction Factor Correlations of Gas Slip Flow in Concentric Micro Annular Tubes

[+] Author Affiliations
Chungpyo Hong, Koichi Suzuki

Tokyo University of Science, Noda, Chiba, Japan

Yutaka Asako

Tokyo Metropolitan University, Hachioji, Tokyo, Japan

Paper No. ICNMM2009-82089, pp. 407-415; 9 pages
doi:10.1115/ICNMM2009-82089
From:
  • ASME 2009 7th International Conference on Nanochannels, Microchannels, and Minichannels
  • ASME 2009 7th International Conference on Nanochannels, Microchannels and Minichannels
  • Pohang, South Korea, June 22–24, 2009
  • Conference Sponsors: Nanotechnology Institute
  • ISBN: 978-0-7918-4349-9 | eISBN: 978-0-7918-3850-1
  • Copyright © 2009 by ASME

abstract

A concentric micro annular passage is a basic and important micro-geometry of micro-fluidic-systems from simple heat exchangers to the most complicated nuclear reactors. Therefore, the product of friction factor and Reynolds number (f·Re) for quasi-fully developed high speed and slip flow in a concentric micro annular tubes of Re<1000 and Ma<1.0 was obtained numerically. The numerical methodology was based on the Arbitrary-Lagrangian-Eulerian (ALE) method. The compressible momentum and energy equations with slip boundary conditions were solved for both isothermal flow and no-heat conduction flow conditions. The outer tube radius ranged from 5 to 40 μm with the radius ratios of 0.2, 0.5 and 0.8. The ratio of length to hydraulic diameter was 100. The stagnation pressure was chosen in such a way that the exit Mach number ranged from 0.1 to 1.0. The outlet pressure was fixed at the atmospheric pressure. The value of f·Re for compressible slip flow in concentric micro annular tubes were obtained. The detail of the incompressible slip f·Re is documented and its value defined as a function of r* and Kn is represented. The results show that in the case of fast flow, the values of f·Re for compressible slip flow is higher than those for incompressible slip flow due to compressibility effects. Also, the f·Re correlation for compressible slip flow is obtained from that of compressible no-slip flow and incompressible slip flow as a function of Mach and Knudsen numbers and radius ratio. In addition, a f·Re correlation from the values of f·Re obtained for micro-channel, micro-tube, and micro annular tube referred in author’s previous works that is applicable to micro-geometries whose cross-sections are parallel, rectangular, circular and annular, is proposed.

Copyright © 2009 by ASME
Topics: Friction , Slip flow

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