Aspects of three-dimensional channel flow around a divider #

TD Dang

11:50 Monday in 4Q08.

Part of the Analysis of continuum mechanics session.

Abstract #

This study examines first the three-dimensional fluid flow in a channel which is rendered three-dimensional by means of a thin semi-infinite divider spanning from one wall to the other. The effect is thus that of a three-dimensional bifurcation. The relative flow rate as represented by the Reynolds number is assumed to be large. A combination of matched asymptotic expansions and numerical methods is used to interpret the behaviour of the boundary layer(s) near the divider and the channel walls, and the quasi-inviscid flow in the region between them. The length scale of the divider is $h$, taken such that $h/L \ll 1 $, where $L$ is the typical length scale along the channel. The model here is simulating laminar flow with the incident oncoming flow being steady plane Poiseuille flow ahead of the junction with the bifurcation. It is also assumed that there is no significant flow in the cross-plane geometry over the above length scales. The solution in the channel cross section immediately after the junction is in fact broken down into four different regions, where the fluid behaviour is determined by interaction with the channel walls, the divider, the corners at which the wall and divider meet and finally, the core flow. The core flow especially is studied using both analytical and numerical techniques with the results showing agreement. In the second part of the study, using many of the findings from the first part, the thin semi-infinite divider plate is replaced by a thin elliptical divider and the effects of flow far downstream from varying the ellipse’s thickness are studied. This aspect has connections with the classical Hele-Shaw configuration but, unlike most studies, the present work focusses on the regime where the inertial influence is a strong one.