Friction Factor Correlations for Compressible Gaseous Flow in a Concentric Micro Annular Tube

Abstract

Compressible momentum and energy equations were solved numerically for concentric micro annular tubes with slip velocity and temperature jump wall boundary conditions. The results were expressed in the form of the product of friction factor and Reynolds number (f · Re) for a quasi-fully developed condition and for the ranges of Re < 1000 and Ma < 1. The numerical methodology was based on the Arbitrary-Lagrangian-Eulerian (ALE) method. The outer tube radius ranged from 5 to 40 µm with radius ratios of 0.2, 0.5, and 0.8. The length to hydraulic diameter ratio was more than 100. The stagnation pressure was chosen in such a way that the exit Mach number ranged from 0.1 to 1.0, and the outlet pressure was fixed at the atmospheric pressure. For the case of incompressible slip flow, f · Re is calculated as a function of radius ratio and Knudsen number. For high speed flows, the values of f · Re for compressible slip flow were higher than those for incompressible slip flow due to compressibility effects. Also, f · Re correlation for compressible slip flow was obtained from compressible no-slip flow and incompressible slip flow as a function of Mach and Knudsen numbers and radius ratio. In addition, a correlation for microchannel, microtube, and micro annular tube was obtained from the authors' previous work.