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https://hdl.handle.net/2142/85951
Description
Title
Applications of Lie Groups in Turbulence Modeling
Author(s)
DeMers, Louis Joseph
Issue Date
2000
Doctoral Committee Chair(s)
Axford, Roy A.
Department of Study
Nuclear Engineering
Discipline
Nuclear Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Applied Mechanics
Language
eng
Abstract
Group analysis is applied to the general two-dimensional k-epsilon turbulence model. Symmetry algebras for the k-epsilon turbulence model have been calculated by Khor'kova. and Verbovetsky. This systematic approach is applied to the specific flow problem of turbulent submerged free plane jets. Similarity solutions obtained through Lie group analysis of the zero-equation turbulence model are equivalent to those obtained through traditional mathematical techniques. Lie groups are then applied to the k-epsilon turbulence model's PDEs for submerged free plane jets. A numerical simulation is performed on the subsequent system of ODEs obtained from this model. The results for the turbulent properties obtained from the numerical computation are in good agreement with the similarity profiles obtained from the zero-equation model. These properties include the axial and transverse velocities, stream function, vorticity and transverse eddy viscosity.
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