Merging flow in co-axial cylindrical pipes

Abstract

Independent high Reynolds number flows driven along two co-axial circular cylinders merge at the abrupt termination of the inner cylinder. The viscous mixing downstream of the trailing edge is discussed. The upstream response in the annular gap is governed by an interaction between the shear layers at the outer wall and the inner boundary, which occurs on a streamwise R1/7 lengthscale, where R is the Reynolds number. Downstream this is matched onto a long-scale similarity form which describes the subsequent development prior to the ultimate return to uni-directional flow. The central region within the inner cylinder suffers zero displacement at leading order, and in contrast to the outer gap the change in boundary conditions where the flows join has no significant effect upstream.