| Summary: | This thesis studies buoyant displacement flows with two miscible fluids in pipes and 2D channels that are inclined at an angle β measured from vertical changing from 0° to 90°. The focus is on inclination angles away from nearly horizontal since these flows are previously studied in full details in the literature. Detailed experimental, analytical and computational approaches are employed in an integrated fashion.
Both density stable (light fluid displacing heavy one) and density unstable (heavy fluid displacing light fluid) displacements are studied. For density stable flows the study is purely experimental in the limit of iso-viscous Newtonian fluids. The density stable configuration has been found to produce highly efficient displacements, with the bulk of the interface moving steadily at the mean velocity. The streamwise length of the stretched interface increases with the mean flow velocity, viscosity and inclination β from vertical, and decreases with density difference.
The rest of the thesis deals with density unstable configuration. From experimental point of view, the pipe displacement flows are studied for iso-viscous Newtonian and also viscoplastic fluids. In the Newtonian limit, completely different regimes than nearly-horizontal case are observed. As a first order approximation, different regimes are classified in a two-dimensional (Fr; Re cosβ/Fr plane) providing leading order correlations to transitions to different regimes. Similar regimes are found for channel geometry through numerical simulations of PELICANS code. For non-Newtonian fluids we have focused on industrially interesting cases of large yield stress fluids in the pipe. The two distinct flow regimes namely central-type and slump-type first observed in nearly horizontal angles were found to also persist over other inclinations. Completely new and exotic behaviors were also observed due to the effect of inclination angle and instabilities.
From mathematical and modeling point of view a two-layer weighted residual model for generalized Newtonian fluids has been developed. The model works for channel geometry and can be used to predict the displacement interface height, the front velocity and more importantly, the flow stability.
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