Numerical computation and bifurcation analysis of reacting flow systems

The main focus of this work is to develop theoretical understanding of reacting flow systems. In Part I, we elucidate the challenges involved in the computation of reacting flows and provide guidelines to compute solutions that are qualitatively correct and accurate. We have examined various one parameter dispersion models (axial dispersion, cell, recycle, and two-phase) and show that the exit concentrations predicted are in good agreement for only slow reactions defined by 0 ≤ Da|f '(cN)| < Da*. Our results imply that for fast reactions (Da|f '(cN)| > Da*), the mesh that solves the flow field or the convective diffusion equation without the reaction term may give spurious solutions and inaccurate exit concentrations. A formula for determining the mesh size needed for fast reactions so that spurious solutions are avoided is also determined.; In Part II, we analyze the models that describe reacting flow systems using techniques from bifurcation theory. For the case of two-phase catalytic reactor model, the analysis predicts ten qualitatively different bifurcation diagrams of solid temperature versus residence time. Using the results from this analysis we have developed new criteria to determine when pseudohomogeneous models describe the qualitative behavior of catalytic reactors. We have demonstrated that the widely used literature criterion can lead to erroneous conclusions. The effect of heat and mass transfer coefficients dependence on velocity, on the bi-furcation features of the catalytic reactors is demonstrated using the two-phase well-mixed model. The bifurcation analysis of a coupled homogeneous and heterogeneous reactions model is also presented. We show that the behavior of this model is a two-state variable bi-furcation problem when B * > B and Lep < 1. Our results indicate that the number of qualitatively different bifurcation diagrams is rather large (>30). The analysis demonstrates the possibility of using an exothermic catalytic reaction to drive an endothermic homogeneous reaction.; We have also developed an approach based on the theory of dynamical systems to derive rigorously effective or pseudohomogeneous type models for catalytic reactors. Our results indicate that the mathematical form of the effective model is substantially different from the standard pseudohomogeneous models used in the literature. It is also shown that the effective dispersion coefficients depend on the reaction parameters and formulas are derived for this dependence.