Bifurcations in bifurcations: a dynamical analysis of an impacting T-junction flow

ORAL

Abstract

Pipe bifurcations are a common flow configuration, for instance, in industrial systems and blood vessels. The impacting flow through a T-junction can cause corrosion, damage, and even aneurysms. To complement ongoing particle-laden flow physics research on this geometry, we perform a local bifurcation analysis of the steady-state Navier--Stokes solutions. We carry out numerical continuation on the Reynolds number, using a combination of linear extrapolation and the Newton-GMRES algorithm. A supercritical pitchfork (i.e., symmetry-breaking) bifurcation occurs at $Re \approx 410$, at which the pair of counter-rotating vortices in the outflow pipes becomes asymmetric. A supercritical Hopf bifurcation occurs at $Re \approx 540$, at which the asymmetric steady-state solution becomes unstable, and a stable periodic orbit grows out of this equilibrium.

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Authors

  • Kevin Chen

    Princeton University

  • Clarence Rowley

    Princeton University, Princeton University, Dept. of Mechanical and Aerospace Engineering

  • Howard A. Stone

    Princeton University, Princeton Universtiy, Department of Mechanical and Aerospace Engineering, Princeton University, Princeton University, Princeton, NJ, Department of Mechanical \& Aerospace Engineering, Princeton University

  • Daniele Vigolo

    Princeton University

  • Stefan Radl

    Graz University of Technology