TABLE OF CONTENTS As briefly discussed in Section 1.2, chemical-reaction engineers recognized early on the need to predict the influence of reactant segregation on the yield of complex reactions. Indeed, the competitive-consecutive and parallel reaction systems analyzed in the previous section have been studied experimentally by numerous research groups (Baldyga and Bourne 1999). However, unlike the mechanical-engineering community, who mainly focused on the fluid-dynamics approach to combustion problems, chemical-reaction engineers began with a Lagrangian perspective based on the residence time distribution (RTD). In this section, we will review some of the simpler Lagrangian micromixing models with the perspective of relating them to chemical-source-term closures based on the joint composition PDF.
Perhaps the simplest Lagrangian micromixing model is the interaction by exchange with the mean (IEM) model for a CSTR. In addition to the residence time ?, the IEM model introduces a second parameter t m to describe the micromixing time. Mathematically, the IEM model can be written in Lagrangian form by introducing the age a of a fluid particle, i.e., the amount of time the fluid particle has spent in the CSTR since it entered through a feed stream. For a non-premixed CSTR with two feed streams, [100] the species concentrations in a fluid particle can be written as a function of its age as
| (5.244) |  |
where c ( n )(0) is the feed concentration vector for feed stream n, and ? c ? is the...
