A model of dispersion in the unsteady separated shear flow past complex geometries

Abstract

Separated flows past complex geometries are modelled by discrete vortex techniques. The flows are assumed to be rotational and inviscid, and a new technique is described to determine the streamfunctions for linear shear profiles. The geometries considered are the snow cornice and the backward-facing step, whose edges allow for the separation of the flow and reattachment downstream of the recirculation regions. A point vortex has been added to the flows in order to constrain the separation points to be located at the edges, while the conformal mappings have been modified in order to smooth the sharp edges and let the separation points be free to oscillate around the points of maximum curvature. Unsteadiness is imposed on the flow by perturbing the vortex location, either by displacing the vortex from equilibrium, or by imposing a random perturbation with zero mean on the vortex in equilibrium. The trajectories of passive scalars continuously released upwind of the separation point and trapped by the recirculating bubble are numerically integrated, and concentration time series are calculated at fixed locations downwind of the reattachment points. This model proves to be capable of reproducing the trapping and intermittent release of scalars, in agreement with the simulation of the flow past a snow cornice performed by a discrete multi-vortex model, as well as with direct numerical simulations of the flow past a backward-facing step. The simulation results indicate that for flows undergoing separation and reattachment the unsteadiness of the recirculating bubble is the main mechanism responsible for the intense large-scale concentration fluctuations downstream.