Vortex dynamics in a pipe T-junction: Recirculation and sensitivity

Abstract

In the last few years, many researchers have noted that regions of recirculating flow often exhibit particularly high sensitivity to spatially localized feedback. We explore the flow through a T-shaped pipe bifurcation—a simple and ubiquitous, but generally poorly understood flow configuration—and provide a complex example of the relation between recirculation and sensitivity. When Re ≥ 320, a phenomenon resembling vortex breakdown occurs in four locations in the junction, with internal stagnation points appearing on vortex axes and causing flow reversal. The structure of the recirculation is similar to the traditional bubble-type breakdown. These recirculation regions are highly sensitive to spatially localized feedback in the linearized Navier–Stokes operator. The flow separation at the corners of the “T,” however, does not exhibit this kind of sensitivity. We focus our analysis on the Reynolds number of 560, near the first Hopf bifurcation of the flow.