Abstracts

Chapter 1. Introduction
This chapter sets out the goals and objectives of the book, which are principally to develop the theory and modeling approaches that facilitate understanding, design, and optimization of chemically reacting flow processes. The scope of the book is explained and differentiated from previous works. Several illustrative examples of chemically reacting flow simulations are given.

Chapter 2 Fluid Kinematics
This chapter develops the Reynolds transport theorem and the general fluid-mechanical stress--strain-rate relationships that form the fundamental underpinnings of the conservation equations. A number of fundamental concepts, such as the relationship between a system and a control volume, are defined and used. The Stokes postulates are introduced, quantitatively connecting the velocity field to the stress field. The derivations are presented in cylindrical coordinates and in general vector-tensor form.

Chapter 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. Transport properties (viscosity, thermal conductivity, and diffusion coefficients) are introduced and discussed. The conservation-equation derivations use both three-dimensional cylindrical coordinates and general vector formalisms. The mathematical characteristics of partial differential equations are classified and discussed.

Chapter 4 Parallel Flows
This chapter concentrates on the broad class of parallel flows, in which there is only one velocity component. Although these flows are often solvable by analytic techniques, this chapter uses parallel flows to introduce basic computational algorithms. The use of dimensionless variables and equations is introduced. The chapter uses specific problems to reinforce the fundamental, but general, concepts developed in the previous chapters. Specific flow situations discussed include Couette flow, Poiseuille flow, Stokes problems, and the Graetz problem.

Chapter 5 Similarity and Local Similarity
This chapter discusses certain two- and three-dimensional flow fields whose mathematical solution can be greatly simplified by recognizing special symmetry or similarity behavior. The similarity reduction, especially in a nondimensional setting, can provide the vehicle to develop general correlations of the flow. A number of examples illustrate how the similar behavior can be exploited in the design and operation of practical reactors. This chapter also introduces the use of general curvilinear coordinate systems.

Chapter 6 Stagnation Flows
This chapter considers a class of boundary-layer flows called stagnation flows. Although the flow field is described by two, or three, velocity components, the temperature and species fields are a function of only one independent variable. Thus the conservation equations are reduced to an ordinary-differential-equation boundary-value problem. Such flows are prominent in materials-processing applications like semiconductors and other high-value thin films. Computational solution algorithms are developed and used.

Chapter 7 Channel Flow
This chapter develops the general concepts of internal-flow boundary layers, in which certain terms in the conservation equations become negligibly small in the limit of certain physical-parameter combinations (e.g., Reynolds number). The focus is on internal flow in channels and ducts. These flows are prominent in a number of chemical processes, including chemical-vapor-deposition reactors and catalytically active honeycomb monoliths. The governing equations can be represented as differential-algebraic equations. The method of lines is introduced as a computational solution algorithm.

Chapter 8 Statistical Thermodynamics
Formulation and solution of chemically reacting flow problems requires thermochemical properties (e.g., specific heats, enthalpies, and entropies) for every species in the system. Quite often these properties may not be known and thus require estimation. After reviewing fundamental results from kinetic theory, statistical mechanics, and quantum chemistry, the chapter develops techniques to calculate thermodynamic properties of species using techniques from statistical thermodynamics.

Chapter 9 Mass Action Kinetics
The rate of progress of chemical reactions is described by mass-action kinetics. This chapter summarizes the equations of mass-action kinetics in a general manner suitable for implementation in a computational setting. The Gibbs free energy is discussed as the driving force for chemical reaction, and it is further related to the reaction equilibrium constant. Pressure-dependent unimolecular and bimolecular chemical activation reactions are summarized.

Chapter 10 Reaction Rate Theories
This chapter describes the fundamental theoretical basis for the rates of chemical reactions. In particular it discusses the factors that determine the magnitude of reaction rate constants. The reaction rate theories discussed include simple collision theory, transition-state theory, and the Lindemann and Hinshelwood theories of unimolecular reactions. QRRK theory is discussed in some detail as a means of calculating pressure-dependent unimolecular and bimolecular chemical activation reaction rate constants.

Chapter 11 Heterogeneous Chemistry
Heterogeneous reaction at the interface between a solid surface and the adjacent fluid is central to many chemical processes. This chapter develops a general, flexible framework for describing complex reactions between gas-phase, surface, and bulk phase species. Many common surface-reaction-rate forms (e.g., expressions for Langmuir adsorption isotherms, competitive adsorption, dissociative adsorption, Langmuir-Hinshelwood kinetics) are given and the analogous rate forms in terms of mass-action kinetics are shown. Thermodynamics of heterogeneous reactions are discussed. The rates of production and destruction of species at reactive surfaces form boundary-condition constraints in reacting flow simulations; the relevant governing equations are summarized.

Chapter 12 Molecular Transport
In addition to thermodynamic properties, transport properties (e.g., viscosity, thermal conductivity, and diffusion coefficients) are also needed to describe chemically reacting flow processes. A general introduction to transport properties is given. Practical techniques to estimate needed properties are presented and discussed. The rigorous kinetic theory expressions appropriate for calculating transport-properties in a reacting flow simulation are summarized.

Chapter 13 Reaction Mechanisms
Sets of individual chemical reactions progressing in concert determine the net species production rates. The chapter summarizes the characteristics of complex reaction mechanisms. There is discussion of elementary versus multi-step reactions, reaction order, chain reactions, and parallel versus serial reactions. Experimental techniques for probing chemical-reaction mechanisms are discussed, and useful sources of information are provided.

Chapter 14 High Temperature Chemistry
This chapter presents an overview of several high-temperature chemistry systems that may be represented by elementary reaction mechanisms. These include hydrogen oxidation, carbon monoxide oxidation, hydrocarbon oxidation, pyrolysis, nitrogen chemistry, sulfur chemistry, and chlorine chemistry. These systems have important applications in combustion and chemical processing. The objective is to illustrate the complex chemical interactions that occur in elementary reaction mechanisms.

Chapter 15 Numerical Solution of Stiff Equations
When complex chemistry is involved in a flow simulation, the governing equations are usually highly nonlinear and stiff. Differential equations are characterized as stiff when they are characterized by vastly disparate time or length scales. Owing to severe stability restrictions, explicit numerical algorithms are inappropriate for solving stiff problems and implicit methods must be used. This chapter discusses the stability behavior of explicit and implicit algorithms. Numerical techniques are discussed for solving initial and boundary value problems. These methods are specifically adapted to be efficient and accurate for complex chemistry problems.

Chapter 16 Zero- and One-Dimensional Systems
The primary objective of this chapter is to develop low-dimensional representations of chemically reacting flow situations. Specifically these include batch reactors, plug-flow reactors, perfectly stirred reactors, and one-dimensional flames. Even for systems with highly complex fluid dynamics, where the flow cannot adequately be approximated by a single chemical reactor, a network of ideal reactors may form the basis of a useful approximation.

Chapter 17 Two Dimensional Systems
Abstract: This chapter addresses computational simulation of chemically reacting flows in two dimensions. Examples are drawn from stagnation-flow chemical-vapor-deposition reactors, stagnation flames, opposed-flow diffusion flames, premixed counterflow flames, and flow in catalyst monoliths.

Appendices
Five appendices provide useful supplemental information to accompany the main text. Appendix A summarizes many vector and tensor operations in cartesian, cylindrical, and spherical coordinates. Appendix B presents alternative formulations of the Navier-Stokes equations in a general vector form, and in cartesian, cylindrical, spherical and orthogonal curvilinear coordinate systems. Appendix C discusses the general characteristics of boundary-layer behavior. Appendix D illustrates the solution of several different types of differential equations using Microsoft Excel. Appendix E outlines the Chemkin software approach to solution of chemically reacting flow problems.