Incompressible multiphase flows: Issues and algorithms

Xu Wang, Purdue University

Abstract

This thesis focuses on the issues and algorithms for motion of mixture of multiple immiscible incompressible flows, which consists of two parts: 1. The scheme for incompressible multiphase flows with contact-angle boundary conditions.2. The pressure-correction scheme for incompressible two-phase flows with open boundary conditions. In the first part, we study the effects of the static contact-angle boundary conditions in multiphase flow system, especially when the system contains more than two fluids. With the phase field framework and existing algorithm for simulating the motion of a mixture of multiple fluids, we propose an extensive algorithm to address static contact-angle boundary conditions issue for wall-bounded flows of N immiscible incompressible fluids, with N ≥ 3. We also provide various numerical tests and experiments to demonstrate the capabilities of our multiphase contact-angle scheme for actual simulations.A wide range of numerical examples under different settings are presented to demonstrate the spatial and temporal convergence characteristics. With different combinations of number of phases and contact angles, parallel and restart tests are also provided. Furthermore extensive physical simulation results show that such scheme is effective for real incompressible multiphase contact-angle problems. In the second part, we assume that N = 2. Two-phase outflows refer to situations where the interface formed between two immiscible incompressible fluids passes through open portions of the domain boundary. We have proposed several new formulations of open boundary conditions for two-phase outflow system based on the phase field approach. Additionally, a new algorithm, used to numerically deal with those open boundary conditions, is presented based on the rotational pressure-correction framework. One novelty of this algorithm is that all coefficient matrices associated with discretized formulation could be pre-calculated and pre-processed after temporal and spatial discretization, which are irreverent to physical properties such as fluid density, viscosity and surface tension between two fluids. Furthermore, the physical accuracy is demonstrated by making comparison between simulation results with the theoretical values or the experimental data. In this thesis, extensive physical simulations are presented to demonstrate the capabilities of long-term stability of our algorithm, in situations where large density contrast, large viscosity contrast, and backflows are present at the two-phase outflow/open boundaries.

Degree

Ph.D.

Advisors

Dong, Purdue University.

Subject Area

Applied Mathematics

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