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 mm 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.