Mathematical Modeling of Turbulent Reactive Flows

Doctoral thesis, 2005

The purpose of this thesis has been to study and develop mathematical models of non-premixed turbulent reacting flows. The models developed can be used both by the chemical process industry and for turbulent combustion applications. Furthermore, the models are general and not developed for any specific chemical or mechanical system. In the main parts of this thesis some of the most commonly applied models for turbulent reacting flows have been discussed. Emphasize has been put on presumed probability density function (PDF) methods applicable to Eulerian Computational Fluid Dynamics (CFD). The major contributions of this thesis are fourfold. (i) A model is developed for the rate of molecular mixing of a conserved scalar. The model is self-consistent with the transport equation for a conserved scalar in inhomogeneous flows and is a direct consequence of utilizing a presumed PDF of the conserved scalar. The model is a key development for consistent implementations of the conditional moment closure (CMC) that is a high level statistical model for chemical reactions in an Eulerian frame. (ii) A conceptually new approach for modeling of presumed PDFs, based on the fundamental theory of mapping closures, is suggested. Briefly it is suggested to use a presumed mapping function between a known reference field and the true scalar field, that indirectly will imply the PDF. Other commonly applied presumed PDFs models the shape of the PDF directly. The PDFs as implied by the PMF have been shown to give remarkable agreement with direct numerical simulations of both single and double scalar mixing layers. The PMF approach has also shown some very promising features for models of conditional statistics, important for existing reaction models, e.g. flamelet, CMC or large eddy simulations. Most importantly, the PMF approach allows for an algebraic expression of the counterflow mixing model. (iii) The first fully consistent CFD-implementation of CMC for inhomogeneous flows has been performed and (iv) an efficient implementation strategy for CMC has been suggested.