The main goal of this work is to propose, implement, test, and refine numerical methodologies for computer simulations of two-fluid flows. These methodologies fall into the category of volume tracking methods, with piecewise-linear interface calculation (PLIC). The scope of this work is limited to the laminar, incompressible flow of immiscible, non-reacting Newtonian fluids, without phase change, in planar two-dimensional geometries. / The following new or enhanced procedures are proposed: a parallelogram scheme for multidimensional advection of the volume fraction field, that rigorously conserves mass; a circle fit technique for the orientation of the interface segments and the calculation of curvature; a novel contact angle treatment; and a staggered formulation for volumetric body forces that can accurately balance pressure forces in the vicinity of the interface. In addition, surface-tension-derived and hydrostatic-derived pressure corrections are introduced as a novel means of calculating accurate pressure forces in cells that contain the interface, thereby virtually eliminating parasitic currents, or the non-physical flows that afflict many available volume tracking methods. / A total of six test problems are presented. The first three test problems do not involve surface tension, and are used to demonstrate the ability of the proposed method to accurately simulate two-fluid flows with complex interface deformations. These test problems involve pure advection flows, a collapsing water column, and a Richtmyer-Meshkov instability. The last three test cases are employed to check the effectiveness of the surface tension modelling. Simulations of a static drop indicate that the proposed curvature calculation procedure is of reasonable, but not very high, accuracy, and it is quite successful at maintaining a smooth, high fidelity interface. Next, it is shown that the proposed method can accurately simulate an oscillating bubble. In the final test case, the formation of a meniscus between two parallel plates is simulated. The equilibrium meniscus shape is in good agreement with the analytic meniscus solution. Overall, the proposed method is shown to be capable of accurate and stable simulations of the two-fluid flows considered in this work.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.36935 |
| Date | January 2000 |
| Creators | Garrioch, Stephen Hugh. |
| Contributors | Baliga, B. R. (advisor) |
| Publisher | McGill University |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Format | application/pdf |
| Coverage | Doctor of Philosophy (Department of Mechanical Engineering.) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | alephsysno: 001807223, proquestno: NQ70027, Theses scanned by UMI/ProQuest. |
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