EG 552 Chemically Reacting Flow

 

This is a graduate-level course on advanced fluid mechanics. It was delivered for the first time in the Fall 1998 semester. The course material is based on a book that is now in draft form. The book chapters are summarized below.

Theory and Modeling of Chemically Reacting Boundary Layers
Robert J. Kee, Laxminarayan L. Raja, and Michael E. Coltrin

1. Introduction

2. Fluid Kinematics
This chapter develops the generalized fluid-mechanical stress-strain relationships that are the fundamental underpinning of the Navier-Stokes equations. The derivations are presented in cylindrical coordinates and in general vector-tensor form.

3. The Conservation Equations
This chapter presents derivations of the conservation equations for mass continuity, momentum (Navier-Stokes), energy and thermal energy, and species continuity. The development and discussion use both three-dimensional cylindrical coordinates and general vector formalisms.

4. Parallel Flows
This chapter concentrates on the broad class of Òparallel flows,Ó in which only one velocity component. In many cases, these flows are solvable by analytic techniques. However, the chapter uses parallel flows to introduce basic computational techniques and discusses how spreadsheets can be used to program solutions. The chapter also uses specific problems to reinforce the fundamental, but general, concepts developed in the previous chapters.

5. Stagnation Flows
This chapter is devoted to a class of boundary layers called stagnation flows, which are reduced to ordinary-differential-equation boundary-value problems. Even though the flow field is described by two, or three, velocity components, the temperature and species fields are a function of only one independent variable. The governing equations are exact reductions of the Navier-Stokes equations, rather than approximations that are asymptotically exact in the limit of some parameter. Such flows are prominant in materials-processing applications like semiconductors and other high-value thin films.

6. External Boundary Layers and Ducts
This chapter develops the general concepts of boundary layers, in which certain terms become vanishingly small as physical parameters vary. After reviewing and discussing the general apporaches for external flows, the focus is on internal flow in channels and ducts. These flows are prominant in a number of chemical processes, including chemical vapor deposition reactors and catalytically active honeycomb monoliths.

7. Numerical Methods for Stiff Systems
To this point in the book, equations have been derived in general settings and then reduced for application to specific flow configurations. While complex chemical reaction has been included in general formalisms, specific problems have neglected chemistry. Without complex chemistry, numerical solution can be accomplished with straightforward techniques. Once complex chemistry is introduced, the computationl techniques must handle a phenomena called stiffness. This chapter presents numerical techniques for solving initial and boundary value problems that are specifically designed to be efficient and accurate for complex chemistry problems.

8. Chemical Thermodymanics and Thermochemical Properties
Formulation and solution of chemically reacting flow problems requires therochemical properties (e.g., specific heats, enthalpies, and entropies) for every species in the system. Quite often these may not be known and require estimation. After reviewing fundamental concepts in kinetic theory, statistical mechanics, and quantum chemistry, the chapter develops techniques to estimate thermodynamic properties for use in chemically reacting flow simulation.

9. Molecular Transport and Transport Properties
In addition to thermodynamic properties, transport properties (e.g., viscosity, thermal conductivity, and diffusion coefficients) are also needed to describe chemically reacting flow processes. This chapter takes a kinetic-theory and statistical-mechanics approach to develop the formalism for transport-property description. It also develops techniques to estimate needed properties.

10. Chemical Kinetics and Reaction Rates
This chapter reviews the general concepts of chemical reaction theory. It considers both gas-phase homogeneous chemistry as well as heterogeneous chemistry at surfaces. It discusses the use and validity of ab-initio quantum-chemical approaches, although the techniques themselves are outside the scope of this book. Nevertheless, the intent is to equip the reader to incorpoate and use the results ab-initio rate-expression estimation in chemically reacting flos simulation.

11. Chemically Reacting Stagnation Flows
This chapter returns to stagnation flows (introduced in Chapter 5) to incorporate complex chemistry and transport. It uses specific examples from semiconductor processing and combustion to illustrate fundamental issues in problem formulation and solution. These problems bring together all the fluiid-mechanical and chemical concepts developed in earlier chapters. The problems also serve to introduce and use important concepts like the identification of rate-limiting processes.

12. Chemically Reacting Duct Flows
This chapter continues in the spirit of the previous chapter, but focuses attention on internal boundary layers. Examples are drawn from channel-flow chemical-vapor-deposition reactors, flow reactors for chemical processing, and flow in catalyst monoliths.

A. Examples of Spreadsheet Solution to Boundary-Layer Problems

B. General Vector-Tensor Relationships