Effects of channel geometry on buoyancy-driven mixing

Abstract

The evolution of the concentration and flow fields resulting from the gravitational mixing of two interpenetrating miscible fluids placed in a tilted tube or channel is studied by using direct numerical simulation. Three-dimensional ͑3D͒ geometries, including a cylindrical tube and a square channel, are considered as well as a purely two-dimensional ͑2D͒ channel. Striking differences between the 2D and 3D geometries are observed during the long-time evolution of the flow. We show that these differences are due to those existing between the 2D and 3D dynamics of the vorticity field. More precisely, in two dimensions, the strong coherence and long persistence of vortices enable them to periodically cut the channels of pure fluid that feed the front. In contrast, in 3D geometries, the weaker coherence of the vortical motions makes the segregational effect due to the transverse component of buoyancy strong enough to preserve a fluid channel near the front of each current. This results in three different regimes for the front velocity ͑depending on the tilt angle͒, which is in agreement with the results of a recent experimental investigation. The evolution of the front topology and the relation between the front velocity and the concentration jump across the front are investigated in planar and cylindrical geometries and highlight the differences between 2D and 3D mixing dynamics.

Miscible displacement flows in near-horizontal ducts at low Atwood number

“…We have also compared our results with those of Hallez & Magnaudet (2008) for exchange flow in a 2D channel over the range Ø = 60°90…”

“…The most comprehensive study of these eAEects is in the absence of the imposed flow, by Seon et al (2004Seon et al ( , 2005Seon et al ( , 2006Seon et al ( , 2007b using experimental methods. Three-dimensional computations have been performed by Hallez & Magnaudet (2008) and largely confirm the qualitative picture of Seon et al (2005Seon et al ( , 2006. The computations of Hallez & Magnaudet (2008) are focused mostly at inclinations away from horizontal and they consider mostly inertial flows.…”

“…Three-dimensional computations have been performed by Hallez & Magnaudet (2008) and largely confirm the qualitative picture of Seon et al (2005Seon et al ( , 2006. The computations of Hallez & Magnaudet (2008) are focused mostly at inclinations away from horizontal and they consider mostly inertial flows. They also study exchange flows in plane channels, concluding that the structure of buoyancy-inertia-driven flows is markedly diAEerent in 2D and 3D settings.…”

“…For example Hallez & Magnaudet (2008) studied pure exchange flows in pipes and channels in the inertially dominated regime, when the fluids mix, and have shown distinct diAEerences in the flow structures observed. Therefore, direct comparisons are only like to be valid in regimes where viscous forces dominate in balancing buoyant and imposed pressure drops.…”

Posicionamento De Tampões Em Poços De Petróleo: Uma Investigação De Escoamentos De Inversão Por Gravidade

“…Exemplos típicos são o posicionamento de tampão de cimento na indústria do petróleo (73), desgaseificação de vulcões (163), movimentação dos oceanos (8), ventilação em prédios (65) e propagação de fogo (87,178).…”