Instability Mechanisms in Straight-Diverging-Straight Channels

Abstract

The linear instability mechanisms of two-dimensional flows through straight-diverging-straight channels with variable angle of divergence, α and expansion ratio κ = D/d, have been studied here. The extreme limits of this problem are compared to those of the plane Poiseuille flow (α = 0o) and the sudden expansion flows (α = 90o). The base flow obtained by direct numerical simulations shows two picthfork type of bifurcations. At very low Reynolds numbers (Re) the flow is steady and symmetric with two symmetric separated regions at the walls. With an increase in Re the symmetric flow evolves into an asymmetric flow with separated regions of unequal lengths. The linear stability analysis on symmetric base flows confirms the primary instability to be a symmetry-breaking type thus leading to a picthfork bifurcation. With a further increase in Re the steady asymmetric flow develops into a base state with ‘tertiary’ separated region. The appearance of the tertiary separated region is a bifurcation of the flow, but is not related to an instability. The Re beyond which the tertiary flow develops is characterized for the various parameters and compared with literature for the sudden expansion flows (α = 90o). A fairly good comparison is observed for the higher expansion ratios (κ). While the sudden expansion flows have been studied extensively, very little is known about the straight-diverging-straight channels. Thus, the instability mechanisms including the primary and secondary bifurcations have been studied in detail for the intermediate α to derive a link between the plane Poiseuille flow and the sudden expansion flows.