Simulations of inviscid swirling flows in pipes with various geometries

Numerical simulations of the dynamics of high-Re swirling flows in pipes with varying geometries is a challenging computational problem, specifically when vortex-breakdown or wall-separation regions naturally evolve in the flows. The paper describes a simulation scheme of the evolution of inviscid-limit, axisymmetric and incompressible swirling flows in expanding or converging pipes. Integration in time of the circulation and azimuthal vorticity uses an explicit, first-order accurate finite-difference scheme with a second-order accurate upwind difference formulation in the axial and radial directions. A Poisson solver for the spatial distribution of the stream function uses a second-order accurate over-relaxation difference scheme. The solver provides the natural evolution of flows including the dynamics to states with slow-speed recirculation zones along the pipe centerline or attached to the wall. The simulations show convergence of results with mesh refinement for various swirl levels and pipe geometry variations. Results of time-asymptotic states also present agreement with available theoretical predictions of steady vortex flows in diverging or contracting pipes. Results support theoretical predictions and clarify the nature of high-Re flow evolution.