Coherent Structure Transport in Turbulent Axisymmetric Pipe Expansions

Abstract

Turbulent separated flows in axisymmetric expansions can sustain fundamentally different transport organization despite nearly identical mean topology. Using stereo-PIV and time-resolved planar PIV, we compare abrupt $90^\circ$ (step) and gradual $45^\circ$ (wedge) axisymmetric expansions at step height Reynolds numbers of 25000 and 35000. Despite similar reattachment lengths, near-separation turbulence differs, with the wedge exhibiting higher turbulent kinetic energy over a broader shear layer, while the step confines production to a thinner region near the corner, where a secondary vortex weakens momentum and fluctuations. The spatial spectra reveal a pronounced spectral hump in the out-of-plane velocity fluctuations near separation. This feature is consistently observed across all cases and reflects the expansion effects on the redistribution of fluctuation energy associated with the interaction between the separating shear layer and the recirculating flow. Temporal spectra show no geometry-specific dominant frequencies, and space-time correlations indicate similar normalized convection velocities across all cases. The primary effect of geometry, therefore, does not lie in the characteristic scales or transport speeds, but in the spatial organization and persistence of coherence. The step cases exhibit stronger spectral concentration, longer local integral time scales, and a broader distribution of space-time correlations in convection velocities associated with momentum-depleted return flow. Finite-time Lyapunov exponent (FTLE) fields confirm that these differences extend to material transport, as the wedge produces larger and less fragmented deformation regions, while the step yields a more segmented pattern that persists downstream of reattachment.