The applicability of stochastic turbulent transport models in strongly non-homogeneous and non-stationary flows
Karvounis, Evangelos Artemios
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https://hdl.handle.net/2142/19790
Description
Title
The applicability of stochastic turbulent transport models in strongly non-homogeneous and non-stationary flows
Author(s)
Karvounis, Evangelos Artemios
Issue Date
1996
Doctoral Committee Chair(s)
White, Robert A.
Department of Study
Mechanical Science and Engineering
Discipline
Mechanical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Mechanical
Language
eng
Abstract
The objective of this work has been to assess the applicability of the direct-pdf method for the modeling of turbulent-transport processes inside reciprocating engines. The research can be divided in two phases.
In the first phase, a Monte-Carlo solution algorithm for the joint-scalar pdf has been implemented. A three-dimensional extension of the Langevin model was adopted for the closure of the turbulent-diffusion-flux term and a stochastic-mixing model for the closure of the molecular-mixing term. The results have shown that the most severe limitation of the implementation resulted from the inconsistency of the Langevin closure with the thermodynamic constraint in the presence of inhomogeneity. Remedies which have been suggested in the literature have been evaluated and were found to be inadequate in flows as complex as the in-cylinder flow. An alternative method was devised and was shown to maintain the consistency of the stochastic model with the thermodynamic constraint at all times.
In the second phase, the mathematical foundation of random-flight models of turbulent diffusion was revisited and the origins of their limitations were investigated. It was shown that linearized-motion approximations of fluid kinematics in general can not meet the requirements of the thermodynamic constraint even in the absence of a random-displacement component. Then, it was shown that random-displacement models which are based on a single-point velocity pdf in general can not have the same divergence properties as the mean-velocity field. Mathematically, the problem was connected to the classical Ito-Stratonovich dilemma. From the physical point of view, it has been argued, in contrast to the solutions which are typically suggested in the literature, that restrictions such as the thermodynamic constraint are related to the two-point correlation and their enforcement to a single-point-pdf model is an ill-posed problem.
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