Average Friction Factor for Laminar Gas Flow in Microtubes

Abstract

The average friction factor in micro tubes will help the design engineers to estimate

the pressure loss in micro flow devices. The aim of the present study is to obtain

numerically average Darcy and Fanning friction factors and Mach numbers between

the inlet and outlet of gas flows through adiabatic microtubes. This paper presents

the average Poiseuille numbers, (fdRe)ave & (ffRe)ave, between the inlet and outlet,

those are obtained from numerical results for laminar gas flow in microtubes with

diameters of 50, 100 and 150 m and aspect ratios (i.e. length/diameter) of 100, 200

and 400, respectively. Axis-symmetric compressible momentum and energy

equations were solved with the Arbitrary-Lagrangian-Eulerian (ALE) method. The

stagnation pressure was chosen in such a way that the outlet Mach number ranged

from 0.1 to 1.0. The outlet pressure was fixed at atmospheric condition. As a result,

the average Darcy and Fanning friction factors between the inlet and outlet were

obtained and compared with Moody’s chart. The (fdRe)ave and (ffRe)ave were also

obtained and presented as a function of average Mach number and were compared

with the local fRe correlations proposed in the previous study.