Behaviour of rarefied gas flow near the junction of a suddenly expanding tube

Abstract

This paper presents an experimental study of isothermal rarefied gas flow through a tube with sudden expansion in the slip flow regime. The measurements reported here are for nitrogen flowing at low pressures in conventional tubes with sudden expansion area ratios of 1.48, 3.74, 12.43 and 64. The flow is dynamically similar to gas flow in a microchannel as the Knudsen number $(0. 0001\lt \mathit{Kn}\lt 0. 075)$ falls in the slip flow regime; the Reynolds number in the smaller section (${\mathit{Re}}_{s} $) ranges between 0.2 and 837. The static pressure along the wall is measured for different mass flow rates controlled by a mass flow controller and analysed to understand the flow behaviour. The velocity profiles are obtained through a momentum balance and using the pressure measurements. A discontinuity in the slope of pressure at the sudden expansion junction is noted and given special attention. The absence of flow separation is another key feature observed from the measurements. The streamlines are found to be concave near the junction. It is demonstrated that the flow ‘senses’ the oncoming sudden expansion junction and starts adjusting itself much before reaching the junction; this interesting behaviour is attributed to an increased axial momentum diffusion and wall slip. The additional acceleration of the central core of the gas flow causes an increase in the wall shear stress and a larger pressure drop as compared with a straight tube. These results are not previously available and should help in improving understanding of gaseous slip flows.

Low Mach number slip flow through diverging microchannel

“…The flow acceleration in zone III can be attributed to the sudden expansion downstream (channel outlet to reservoir) with expansion ratio of 4.3 for 4°, 1.3 for 16°channel. The sudden increase in cross section initiates gas expansion upstream away from the junction and continues with nonlinear pressure variation up to the junction [28]. The marginal flow acceleration can be noted in these cases (Fig.…”

“…The experimental facility is similar to that employed by Varade et al [28,45,46]. It consists of a vacuum system, inlet reservoir, outlet reservoir and mass flow controller as shown in Fig.…”

“…The kinetic energy of slip flow is negligible as compared to the driving pressure energy of the flow [28,30]. Therefore, any change in the kinetic energy due to a sudden change in the cross-section cannot influence the pressure gradient; and the flow separation is arrested.…”

“…Further, in the case of rarefied gas flow, the momentum diffusivity increases to a very large extent due to rarefaction as compared to continuum flow [28]. The larger momentum diffusivity causes the gas molecules to closely follow the surface just downstream of the microchannel inlet, unlike incompressible flow.…”

“…They noted that in the transition regime, the pressure ratio and length to diameter ratio of the passage strongly influence the discharge through sudden enlargements. In a recent experimental study involving flow through a sudden expansion, Varade et al [28] observed a discontinuity in the slope of pressure and absence of flow separation at the junction; in the slip regime. These measurements are qualitatively similar to the two-dimensional planar simulations of Agrawal et al [29].…”