MME Seminar Series – Vortex-Breakdown and Wall-Separation States in Swirling Flows in Finite-Length Pipes

Abstract
The dynamics of inviscid-limit, incompressible and axisymmetric swirling flows in finite-length, long circular pipes
with varying geometries is studied through global analysis techniques and numerical simulations. The inlet flow is
described by fixed-in-time profiles of the circumferential and axial velocity together with a fixed azimuthal vorticity,
while the outlet flow is characterized by a state with zero radial velocity. A numerical algorithm based on the upwind
finite-difference method for the evolution of the circulation and azimuthal vorticity together with a Poisson solver for
the solution of the stream function in terms of the azimuthal vorticity is developed. The convergence of computed
results with mesh refinement is demonstrated. Moreover, a mathematical analysis that is based on the Squire-Long
equation (SLE) is formulated to identify steady-state solutions of the problem with special conditions to describe
states with separation zones. These solutions include the base columnar flow state, a decelerated flow along the
centerline, an accelerated flow along the centerline, a vortex-breakdown state and a wall-separation state. The
problem is then reduced to the columnar (axially independent) SLE, with centerline and wall conditions for the
solution of the outlet flow stream function. The numerical simulations realize the various flow states and show
correlation between time-asymptotic states and steady states predicted according to the SLE and the columnar
SLE problems. The simulations also shed light on the stability of the various steady states. Results show that pipe
divergence promotes the appearance of breakdown states at lower inlet swirl levels while pipe contraction delays
the appearance of vortex breakdown to higher swirl levels and promotes formation of wall-separation states. The
influence of various inlet swirling flow profiles on the manifold of steady states in a straight, finite-length pipe and
on flow dynamics is also investigated. Depending on the inlet profiles, flows may first exhibit vortex breakdown while
others wall-separation states.

MME Seminar_Flyer_Zhang_02.22.2019