Local Pipe Friction Factor of Compressible Laminar or Turbulent Flow in Micro-Tubes

Abstract

Laminar/turbulent flows of compressible fluid in micro-tubes were simulated to investigate the effect of compressibility on local pipe friction factor. The numerical procedure based on arbitrary-Lagrangian-Eulerian method solves compressible momentum and energy equations. The Lam-Bremhorst Low-Reynolds number turbulence model was adopted to calculate eddy viscosity coefficient and turbulence energy. The computations were performed for a wide range of Reynolds number and Mach number including laminar/turbulent choked flows. It was found that in laminar regimes the ratio of the Darcy friction factor to its conventional (incompressible flow's) value is a function of Mach number. The same thing is observed for the Fanning friction factor. On the other hand, in turbulent regimes, the ratio is still a function of Mach number for the Darcy friction factor but takes about unity for the Fanning friction factor. These facts can be seen in choked flows. The correlation between Darcy friction factor and Fanning friction factor was found to be a function of only Mach number, when adiabatic flow is assumed. Prediction of static pressure distribution and Reynolds number (mass flow rate) using modified one dimensional theory is introduced.