The Eulerian description of dispersed two-phase flows results in a system of
partial differential equations describing characteristics of the flow, namely volume
fraction, density and velocity of the two phases, around any point in space over
time. When pressure forces are neglected or a same pressure is considered for both
phases, the resulting system is weakly hyperbolic and solutions may exhibit vacuum
states (regions void of the dispersed phase) or localized unbounded singularities (delta shocks) that are not physically desirable. Therefore, it is crucial to find a physical way for preventing the formation of such undesirable solutions in weakly hyperbolic Eulerian two-phase flow models.
This thesis focuses on the mathematical analysis of an Eulerian model for air-
droplet flows, here called the Eulerian droplet model. This model can be seen as the
sticky particle system with a source term and is successfully used for the prediction
of droplet impingement and more recently for the prediction of particle flows in air-
ways. However, this model includes only one-way momentum exchange coupling, and develops delta shocks and vacuum states. The main goal of this thesis is to improve this model, especially for the prevention of delta shocks and vacuum states, and the adjunction of two-way momentum exchange coupling. Using a characteristic analysis, the condition for loss of regularity of smooth solutions of the inviscid Burgers
equation with a source term is established. The same condition applies to the droplet
model. The Riemann problems associated, respectively, to the Burgers equation with
a source term and the droplet model are solved. The characteristics are curves that
tend asymptotically to straight lines. The existence of an entropic solution to the
generalized Rankine-Hugoniot conditions is proven. Next, a way for preventing the
formation of delta shocks and vacuum states in the model is identified and a new
Eulerian droplet model is proposed. A new hierarchy of two-way coupling Eulerian
models is derived. Each model is analyzed and numerical comparisons of the models
are carried out. Finally, 2D computations of air-particle flows comparing the new
Eulerian droplet model with the standard Eulerian droplet model are presented.
| Identifer | oai:union.ndltd.org:uottawa.ca/oai:ruor.uottawa.ca:10393/37907 |
| Date | 23 July 2018 |
| Creators | Keita, Sana |
| Contributors | Bourgault, Yves |
| Publisher | Université d'Ottawa / University of Ottawa |
| Source Sets | Université d’Ottawa |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf |
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