Secondary flow behavior in a double bifurcation

Abstract

Secondary flows in the form of multivortex structures can occur in bifurcation models as the result of upstream influence. Results from numerical modeling of steady inspiratory flows indicate that, for the case of a symmetric planar double bifurcation, four counter-rotating vortices develop in each of the grand daughter branches. In this paper, experimental visualization and verification is provided by particle image velocimetry measurements on a modified single bifurcation model. A splitter plate was positioned in the mother tube so that secondary vorticity was introduced into the fluid core. The axial velocity profile before the bifurcation junction resembles the M-shaped velocity profile commonly observed in bifurcated tube flows. The result of this manipulation is the development of a physically observable four-vortex configuration in the cross sections of the daughter branches, thus demonstrating the strong influence of upstream secondary vorticity. Through numerical visualization of vortex lines, it is shown that secondary vorticity is amplified by the extension of vortex lines due to secondary flow within the daughter tube. Order-of-magnitude arguments have been applied to the vorticity transport equation; and key dimensionless parameters have been obtained, accounting for curvature effects. Results indicate that the secondary vorticity goes through a maximum with increasing downstream distance, as a result of the interplay between vortex stretching and viscous effects.