Instability and localized turbulence associated with flow through an axisymmetric sudden expansion

Numerical simulations of flow through a sudden expansion were performed for various Reynolds numbers. Planar channel flow and axisymmetric pipe flow configurations are simulated with expansion ratios of 2:1 and Reynolds numbers ranging from 15 to 2500. Above a critical Reynolds number, a symmetry-breaking bifurcation occurs in the planar cases leading to asymmetry in the reattachment zone and a corresponding deviation between the planar and pipe configurations. For the planar flows, the variation of the reattachment length with the Reynolds number in the laminar and transitional regimes achieves excellent agreement with experimental data from literature. As the Reynolds number increases in the axisymmetric pipe cases, unsteadiness of the flow occurs as vortical disturbances begin in the core region along the pipe centerline and in the separated shear layer that forms downstream of the expansion. The disturbances convect downstream and rapidly amplify until a disturbance bursting event occurs wherein strong turbulent fluctuations are generated along the periphery of the core jet. The interaction between the shear layer instability and disturbance bursting events is studied via the instantaneous vorticity transport equation. The analysis suggests that bursting events are due to the rapid production of fluctuating vorticity through radial tilting of streamwise vortical disturbances by the fluctuating radial strain rates that are induced by the coherent azimuthal vortices. Once saturation of the shear layer instability is achieved, redistribution of fluctuating vorticity into small scales diminishes the radial strain rates and halts this vorticity production mechanism. Viscous effects lead to a gradual relaminarization of the flow, yielding a localized region of turbulent flow that remains fixed in a time-averaged sense near the reattachment point.