A numerical method for two-phase fluid flows with particular application to planar jets

In modern paper making, the break-up of jets issuing from headboxes is responsible for a degradation in paper quality. Waves present on the jet surface are believed to initiate break-up. Numerical simulation of headbox flows and jets would allow prediction of surface waves and help control paper quality. The thesis objective is to significantly contribute to this task by adding two-phase flow capabilities into an existing finite-volume based fluid-flow solver. The solver is then used to numerically verify experimentally observed surface waves on planar water jets issuing from parallel channels. The Volume of Fluid method is used to reformulate the equations of motion of both the liquid and gas phases into equations for a single composite fluid that describe the behavior of both individual phases simultaneously. The phases are identified within the composite fluid by a indicator field known as the volume fraction. The composite fluid retains the incompressibility and Newtonian behavior of its constituent fluids. The fluid interface is replaced by a discontinuity in the physical properties of the composite fluid, and the reformulation satisfies all boundary conditions associated with standard two-phase flow problems. The reformulated equations are solved by standard finite-volume techniques, while the solution of the volume fraction equation requires special care. Several numerical two-phase techniques are presented and discussed. The CICSAM method is adopted for discretization of the volume fraction equation due to its impressive interface reconstruction abilities and its ease of compatibility with the existing code. The inclusion of surface tension is done through the Continuum Surface Force method, whereby a volumetric force mimicking surface tension effects is added to the momentum equations. These procedures are used in the existing solver and the behavior of the code is verified for a series of standard test cases. The solver exhibits very good quantitative and qualitative agreement with published results. The modified code is used to simulate jets under various conditions. Jet thicknesses are small compared to the breadth to allow two-dimensional simulations to be conducted. Results for jets in the absence of gravity or surface tension are in excellent agreement with available analytical results. The inclusion of gravitational effects poses no additional coni cerns. The addition of surface tension causes dramatic changes in jet interface profiles and increased difficulty in obtaining convergent results. A full two-dimensional simulation of water jets issuing from parallel channels with gravitational and surface tension effects is performed for domains of various downstream lengths. The experimentally observed surface waves cannot be reproduced by the tests performed in this study, due to an insufficient downstream grid length or possible three-dimensional effects. Suggestions for improvements relating to two-phase numerical routines and further simulations of planar jets are given.Applied Science, Faculty ofMechanical Engineering, Department ofGraduat

A fast numerical method for the interfacial motion of an electrically conducting bubble in a Stokes flow

There is a great need for efficient numerical methods when solving interfacial motion problems involving coupled physical processes. To this end, a fast numerical method is developed for tracking the motion of an electrically conducting fluid bubble in a Stokes flow subject to an electric field.The motion of a two-dimensional bubble immersed in an infinite expanse of viscous fluid is examined. The Stokes equations governing the fluid dynamics and Laplace\u27s equation governing the electrostatics are recast as integral equations. The electrohydrodynamic free boundary problem is reduced to the solution of integral equations along the bubble interface. The integral equations are discretized and solved with an iterative solver accelerated by the fast multipole method. Results from the numerical method are compared with published results of a simplified, analytical model and are found to be in good agreement