Early onset of flow separation with rarefied gas flowing in a 90° bend tube

Abstract

This paper presents experimental and three-dimensional numerical study of early onset of separation with rarefied gas flow through a tube with single sharp 90° bend. Experiments are conducted for nitrogen gas flowing at low pressures in three conventional size tubes. The flow is dynamically similar to gas flow in a microchannel as the Knudsen number range (0.0003 < Kn < 0.0385) covers part of the continuum and the slip flow regime while maintaining the Reynolds number between 0.27 and 418.5. The static pressures along the inner, outer and top walls are measured for different mass flow rates and analyzed to understand the flow behavior. The static pressure measurement indicates adverse pressure gradient near the bend along the inner and outer walls of the tube at much lower value of Reynolds number as compared to conventional flow. The numerical solution of the Navier–Stokes equations with the Maxwell’s slip boundary condition shows good agreement with experimental data and helps bring out the complex flow behavior near the bend. The adverse pressure gradient, velocity profile, flow streamlines and velocity vectors in the bend plane clearly indicates secondary flows near the bend at as low a Reynolds number as unity. The flow acceleration and the presence of secondary flows near the bend causes a larger pressure drop as compared with a straight tube. Empirical correlations for Poiseuille number and additional pressure drop coefficient are proposed as part of this work. It is noted that limited experimental data exists in the literature for such flows; these results should therefore help enhance the fundamental understanding of gas flow in microchannels with bend.