| Περίληψη: | Two-phase fluid flows arise in a wide variety of industrial and scientific applications. Inherent feature of the two-phase flows is the topological evolution of the interface between the two fluids, which leads to the formation of various flow patterns or regimes that depend strongly on the properties of both fluids, the properties of the interface and the flow rate. Τhe detailed description of a moving interface remains challenging from physical and computational points of view due to the strong impact of surface tension and the discontinuity that arises in the stress and pressure field across the interface.
This Master thesis deals with the simulation of prototype two-phase flows via the phase-field model. Throughout the present work, the two fluids are supposed to be Newtonian, incompressible, immiscible and of matched densities. Thus, the Navier-Stokes equations along with the continuity equation, govern the flow of the two fluids, while the Cahn-Hilliard equation is used to describe the evolution of the interface as well as to produce an additional term in the Navier-Stokes equations representing the surface tension force acting only on the interfacial region.
Two novel numerical algorithms (NSCH) have been developed for accurate time integration of the governing equations; the first one is used for the simulation of moderate and high Reynolds number flows and the second one for the simulation of low Reynolds number flows. In both cases, the Cahn-Hilliard equation is always treated implicitly, while the modified NS equations are integrated explicitly in the first case and semi-implicitly in the second case.
The efficiency of the algorithm is verified on a set of problems. In particular, phase separation processes have been studied, to ensure the validity of the Cahn-Hilliard solver excluding flow effects. Then, the efficiency of the NSCH model is tested by tracking a fluid/fluid interface when it experiences large deformations due to an imposed vortex flow. We have validated the entire algorithm through simulations of two-phase flows and comparison to results found in the literature. Specifically, we studied the interfacial instabilities due to viscosity stratification in a planar Couette flow and the effects of inertia and capillarity on the deformation of liquid drops in simple shear flow.
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