Shallow Mixing Layer Downstream from a Sudden Expansion

Abstract

The present paper aims at investigating the mixing layer located at the interface between the free stream and the recirculation zone downstream an open-channel, sudden, lateral expansion. Specific attention is paid on the interaction of the shallowness of the flow, characterized by the bed friction number, with the lateral confinement, due to the side wall. The velocity field for four flows, with the same geometry but very different bed friction numbers, is measured in detail in order to characterize the mean velocity fields and Reynolds stresses across the mixing layers and to evaluate the width of the mixing layers and their growth rates along with the typical oscillation frequencies. In the upstream region of the recirculation zone, the mixing layer characteristics for our configurations are analogous to the ones of classical-laterally unbounded-mixing layers. In this region, the shallowness modifies the shape of the streamwise velocity profiles, extends the mean velocity gradient magnitudes, lowers the Reynolds stress terms but hardly affects the mixing layer expansion rate. On the other hand, in the region near the flow reattachment, the mixing layer adopts a very different behavior, with an abrupt drop of the mixing layer expansion. This change in behavior is linked to the dynamics of the 2D vortices within the mixing layer. It is not due to a damping effect of the bed friction on these vortices as the local bed friction numbers remain much lower than the critical values reported in the literature. It is rather due to the interaction of the coherent structures with the side wall, the characteristics of this interaction being itself influenced

Measurement of mass exchange processes and coefficients in a simplified open-channel lateral cavity connected to a main stream

“…Note that a decrease of α and thus of  indicates that the typical sizes of the coherent turbulent structures advected along the mixing layer are of reduced transverse (along y) extent (see Mignot et al, 2016) and thus that the efficiency of passive scalar transfer through turbulent diffusion across the interface also decreases. The fact that decreasing the water depth tends to decrease the horizontal extension of the coherent turbulent structures was recently observed by Han et al (2017).…”

Mixing layer and coherent structures in compound channel flows: Effects of transverse flow, velocity ratio, and vertical confinement

“…It corresponds to a streamwise integral length scale Λ x of quasi‐2‐D structures that is several times higher than δ . This is not surprising as a ratio Λ x / δ ∼ 3.5 was measured by Uijttewaal and Booij [] for shallow mixing layers, Λ x / δ ∼ 3 at the boundary of recirculating flow area [ Han et al ., ], and Λ x / δ ∼ 4–8 in compound channels with rough FP [ Dupuis et al ., ].…”

On modeling subgrid-scale macro-structures in narrow twisted channels

“…Second, topographic dissipation caused 792 by near-wall velocity gradient is not parametrized. The separation of the advection and recirculation zones in V eff implies that the mixing layer 794 between the two zones and the associated turbulent mixing processes are 795 neglected ( Han et al, 2017 ). Furthermore, for simplicity the size of V eff 796 in any cell is a constant that is independent of the local velocity, which there, experimental data (e.g.…”

“…The high velocities are observed around the channel centerlines and away from the macro-structure, low velocities are observed in the recirculation zone. The expected physical result is stronger momentum transport around the centerline (conveniently referred to as the "advection zone ") accompanied by weaker momentum transport in the recirculation zone and turbulent mixing at the interface of the two zones( Han et al, 2017 ). For illustrative purposes, we can ignore the turbulent mixing layer and consider frictionless inviscid flow in two distinct zones (advection and recirculation zones) in a coarse grid cell, as shown inFig.…”