Analysis of Flow Separation Using a Local Frame Axis: Application to the Open-Channel Bifurcation

Abstract

The motivation for the present work comes from the fact that a few recent publications describing separation flows report a counter-gradient diffusion phenomenon (CDP) along the separating streamline. This CDP is related to (1) a change of sign of the Reynolds shear stress near the separating point and (2) an opposite sign between the Reynolds shear stress and the mean shear rate, leading to a negative eddy-viscosity coefficient. Such CDP is only reported for configurations where the angle between the separating streamline and the main flow is large (referred to as group 1), whereas no CDP was reported for low angle configurations (referred to as group 2). All these flows were analyzed using Cartesian or curvilinear frame axes. The aim of the present paper is to propose a more intuitive frame for analysis, namely the Serret-Frenet frame axis based on the local flow direction, for which the CDP disappears for group 1 flow configurations and that highly improves the characterization of the mixing layer. The recirculation zone occurring in the lateral branch of an open-channel bifurcation is chosen as a separating flow configuration belonging to group 1 and measured using particle image velocimetry (PIV). The characteristics of the mean flow and of the horizontal Reynolds stress are first analyzed using a Cartesian frame axis, to retrieve the CDP, for which extension is enhanced compared with the literature cases. Then, the local Serret-Frenet frame axis is introduced and used for a second analysis of the data. The flow characteristics at the interface between the main flow and the recirculation zone accurately match the characteristics of the well-documented mixing layers available in the literature. Moreover, the eddy-viscosity concept nicely applies using this Serret-Frenet frame axis. A simple geometrical analysis is finally performed to confirm that the negative eddy-viscosity coefficient obtained when using a Cartesian frame axis is only attributable to a nonadequate frame of analysis.