Type
Text
Type
Dissertation
Advisor
Li, Xiaolin | Glimm, James | Jiao, Xiangmin | Qin, Hong.
Date
2014-12-01
Keywords
front tracking, high-order algorithms, parallel triangular mesh, Taylor-Couette flow, turbulent fluid flow mixing | Applied mathematics
Department
Department of Applied Mathematics and Statistics.
Language
en_US
Source
This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree.
Identifier
http://hdl.handle.net/11401/76615
Publisher
The Graduate School, Stony Brook University: Stony Brook, NY.
Format
application/pdf
Abstract
We develop a front tracking method based on the hydrodynamic library FronTier for the solution of the governing equations of motion for two-phase micromixing of incompressible, viscous, liquid-liquid solvent extraction processes. The method is used for accurate simulation of the turbulent micromixing dynamics of an aqueous and an organic phase exposed to intense centrifugal force and shearing stress. The onset of mixing is the result of the combination of the classical Rayleigh-Taylor and Kelvin-Helmholtz instabilities. We demonstrate verification and convergence results for one-phase and unmixed, two-phase flows. For mixed, two-phase flow a mixing environment that emulates a sector of the annular mixing zone of a centrifugal contactor is used with the mathematical domain small enough to allow for resolution of the individual interfacial structures and large enough to allow for an analysis of their statistical distribution of sizes and shapes. Such a statistical picture provides the information needed for building a consistent coarsened model applicable to the entire mixing device. We reach a stable two phase configuration as a statistically steady state in late time after going through a fully mixed transient chaotic flow regime with a high surface area. To handle problems introduced by the extreme complexity of interfaces, a new parallel triangular mesh library called HiProp is implemented which serves as the basis for high-order mesh algorithms. The new library keeps a full list of parallel information for each point and triangle so that each element has a unique master processor and global ID. No floating point comparison is needed after the parallel information is built. The utilities for building ghost triangles while keeping the parallel information updated based on either connectivity or domain decomposition are implemented for applying different high-order mesh algorithms. We develop parallel high-order mesh smoothing, parallel high-order normal and curvature calculation and point propagation based on the new structure. A novel high-order functional mesh propagation algorithm is also developed for propagating local polynomial patches instead of separate points to get high-order results not only for point positions but also for higher order differential quantities such as normals and curvatures. To have a complete mesh propagation package, we also implement tangle detection algorithm and with the I/O interface between FronTier and Hiprop we only go back to FronTier for untangling the self-intersection. It minimizes the time for transferring data between two libraries. In the future a more accurate untangling algorithm would be developed based on the new structure and the data transfer could be entirely eliminated. | 164 pages
Recommended Citation
Zhou, Yijie, "Front Tracking Method with High-Order Enhancement and Its Application in Two-Phase Micromixing of Incompressible Viscous Fluids" (2014). Stony Brook Theses and Dissertations Collection, 2006-2020 (closed to submissions). 2505.
https://commons.library.stonybrook.edu/stony-brook-theses-and-dissertations-collection/2505