Friction Factor Correlations for Gas Flow in Slip Flow Regime

[+] Author and Article Information
Chungpyo Hong

Department of Mechanical Engineering, Tokyo Metropolitan University, Minami-Osawa, Hachioji, Tokyo, 192-0397, Japancphong@comp.metro-u.ac.jp

Yutaka Asako

Department of Mechanical Engineering, Tokyo Metropolitan University, Minami-Osawa, Hachioji, Tokyo, 192-0397, Japan

Stephen E. Turner

 Naval Undersea Warfare Center, Newport, Rhode Island, 02841

Mohammad Faghri

Department of Mechanical Engineering,  University of Rhode Island, 92 Upper College Road, Kingston, Rhode Island 02881

J. Fluids Eng 129(10), 1268-1276 (Apr 11, 2007) (9 pages) doi:10.1115/1.2776966 History: Received November 14, 2006; Revised April 11, 2007

Poiseuille number, the product of friction factor and Reynolds number (fRe) for quasi-fully-developed gas microchannel flow in the slip flow regime, was obtained numerically based on the arbitrary-Lagrangian-Eulerian method. Two-dimensional compressible momentum and energy equations were solved for a wide range of Reynolds and Mach numbers for constant wall temperatures that are lower or higher than the inlet temperature. The channel height ranges from 2 μm to 10 μm and the channel aspect ratio is 200. The stagnation pressure pstg is chosen such that the exit Mach number ranges from 0.1 to 1.0. The outlet pressure is fixed at atmospheric conditon. Mach and Knudsen numbers are systematically varied to determine their effects on fRe. The correlation for fRe for the slip flow is obtained from that of fRe of no-slip flow and incompressible theory as a function of Mach and Knudsen numbers. The results are in excellent agreement with the available experimental measurements. It was found that fRe is a function of Mach and Knudsen numbers and is different from the values by 96/(1+12Kn) obtained from the incompressible flow theory.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

A schematic diagram of problem

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Figure 2

Contour plot of (a) pressure, (b) temperature, and (c) velocity vector (Tw=350K, h=5μm, l=1mm, and pstg=600kPa)

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Figure 3

Pressure variation along the channel (h=5μm and l=1mm)

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Figure 4

Velocity profile

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Figure 9

ffRe as a function of x for Tw=350K

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Figure 10

Comparison of ffRe with experimental data: (a) No. 024 (b) No. 319

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Figure 5

fRe as a function of x for h=2μm: (a) Tw=250K (b) Tw=350K

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Figure 6

fRe as a function of Mach number for both Tw=250K and Tw=350K in the no-slip flow: (a) ffRe (b) fdRe

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Figure 7

Contour plot of ffRe for Tw=350K: (a) no-slip flow (b) slip flow

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Figure 8

fRe as a function of Ma and Kn for Tw=350K: (a) ffRe (b) fdRe



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