7R54. Turbulent Combustion. - N Peters (Institut fur Technische Mechanik, RWTH, Aachen, Germany). Cambridge UP, Cambridge, UK. 2000. 304 pp. ISBN 0-521-66082-3. \$69.95.

Reviewed by AM Kanury (Dept of Mech Eng, Oregon State Univ, Corvallis OR 97331-6001).

Written by an author who is well-known in the field, this handsomely produced book is intended for researchers and students of engineering and applied mathematics as an introduction to turbulent combustion. Before examining the details of its content, let us consider the following background setting of the field of turbulence without and with combustion.

Most of the fluid flows are turbulent, be they reacting or non-reacting, and be they in nature or in manmade devices. The fundamental character of turbulence remained elusive over much of the last century. It has been said quite a while ago, “…there is a problem that is common to many fields, that is very old, and that has not been solved…in spite of its importance to (its) sister sciences. It is the analysis of …turbulent fluids… we ought to solve some day,…” [The Feynman Lectures on Physics, Vol 1, p. 3.9, Addison-Wesley, (1963)].

Even in flows which are simpler due to absence of chemical reactions, once fluctuations in the flow are found to give rise to the Reynolds stresses, the resultant closure problem occupied much of the researchers’ attention through the decades. Progress was tenuous in topics such as eddy diffusivity analyses, mixing length hypotheses, statistics of turbulence intensity, coherent structures and strange attractors. Prediction schemes proliferated, often with multiple fitting constants which bore little or no physical meaning. Only over the very recent years did the advances in speed and capacity of computation make possible substantial progress. Predominant carriers of energy in the flow are sought to be identified through techniques using probability distribution functions, orthogonal decompositions, direct numerical simulations and large eddy simulations.

In the field of turbulent reactive flows, ie, in combustion science, one of the sisters, the story is much the same. Damko¨hler’s classical 1940 measurements of the dependency of turbulent flame speed on the flow Reynolds number got hashed and rehashed for decades. So also has been his explanation that turbulence enhances mixing/transport at low Reynolds numbers and increases the flame surface area at the high. Again, an intense research activity into the nature of turbulent flames has been inspired only in the last two decades by the advent of laser-based non-intrusive flame diagnostics coupled with high-speed computation for modeling and data processing. Roughly only in the last two decades too, the asymptotic theory of flames has been devel- oped to answer certain previously unanswered important questions.

In the book presently being reviewed, Peters sets down the resultant progress in an elegant, methodical, and unified framework. The writing style is uniformly excellent. The title Turbulent Combustion, however, does not quite correctly convey the fact that almost all of this book deals only with gas flames. (“Turbulent Flames” or “Turbulent Combustion of Gases” would probably have been better.)

The book is composed of four chapters. Chapter 1 is 65 pages long and is an excellent overview of modeling approaches for turbulent flows and of asymptotic flame theory. Chapters 2, 3, and 4 are 103, 66, and 24 pages long, respectively. They deal with the three distinct cases of flames in premixed, nonpremixed, and partially-premixed $fuel+oxidant$ gases. At the end is given a valuable two-page Epilogue recapitulating the restrictions under which one can combine the methodologically disparate turbulence theory on one hand and the asymptotic flame theory on the other. The exhaustive Bibliography (with over 500 entries) is a strong feature in that each entry is complete with the title of the paper. This is something pleasing to this reviewer and something unusual in a world where, sadly, it is not uncommon for an author to cite a reference without ever having read it. Finally, the volume ends with an extensive author index and a short subject index.

Given in Chapter 1 is a brief review of statistical description of turbulent flows. Application of the fluctuations in the flow quantities is demonstrated to lead through the Navier-Stokes equations to the notion of the Reynolds stress tensor. Concepts useful in modeling to estimate the stresses are brought to the fore. These include: turbulent kinetic energy, viscous dissipation, the Taylor length and the Kolmogorov scales of length and time. A discussion of the energy and species conservation equations of the reactive flow forms the basis of identifying the conserved scalar which plays a major role in the models of Chapter 3. The asymptotic flame theory has then been presented briefly in order to define the spatial regions of preheating, fuel consumption, and oxidation across a flame in a $fuel+oxidant$ gas mixture. Also introduced here are the various available combustion models to be encountered in future chapters.

Chapter 2 begins with a nice introduction to the fundamental flame speed of a given combustible gas mixture, flame thickness, and turbulent burning speed. A diagram is presented to show the different conditions required for combustion to occur in a laminar flame, wrinkled flamelets, corrugated flamelets, thin reaction zones, and broken reaction zones. The rest of the chapter deals with several modeling approaches to describe these different sorts of turbulent flames. Of special importance is the prediction of the flame surface area and thereby the turbulent burning speed as dependent on turbulence intensity. In the large scale turbulence regime where corrugated flamelets prevail, the model shows that the product of fundamental flame speed and gradient of the conserved scalar turns out to be independent of the molecular properties so that it can be calculated in terms of the viscous dissipation and turbulent kinetic energy. In the small scale turbulence regime where a thin reaction zone prevails, on the other hand, the model shows that the product of diffusivity and square of the gradient of the conserved scalar ought to be independent of the molecular properties so that it too can be calculated in terms only of the dissipation and kinetic energy. Both of these results, quite consistent with the explanations of Gerhard Damko¨hler, are compared with newer measurements. The chapter ends with numerical calculations of one- and multidimensional flames.

Chapter 3 is on turbulent flames arising when the fuel and oxidant gases are admitted into the combustor separately, ie, diffusion flames. In these flames, whose characteristics are independent of the very fast chemistry, all scalars such as temperature, species concentrations, and density are uniquely related to a conserved scalar known as the mixture fraction. This is illustrated for the: classical problem of Burke and Schumann; candle flame; counterflow diffusion flame; and one-dimensional unsteady laminar mixing layer. Here, too, a map is presented to show the different conditions (pertaining to the mixture fraction distribution, its root mean square fluctuation and the scalar dissipation rate) which would result in flames that are either contiguous reaction zones or separated flamelets. The mixture fraction distribution is obtained in a model for a turbulent jet diffusion flame. (A one-page-long discussion of the length of a buoyant turbulent gas jet diffusion flame seems to serve a purpose none other than simply interrupting the important exposition on the mixture fraction distribution.) Experimental measurements of composition and temperature as functions of the mixture fraction are presented. The chapter is concluded with modeling of laminar and turbulent flamelets, predictions of reactive scalar fields for pollutant formation, and quick surveys of modeling gas turbine combustion, burners and diesel engines.

Chapter 4, the shortest and most qualitative one in this book, is on turbulent combustion of partially premixed gases. Here alone, and quite passingly, liquid fuel vaporization and combustion is mentioned. When a liquid fuel is injected into a combustion chamber and vaporized, the $fuel+oxidant$ mixture in the vicinity of the injector port is neither premixed nor nonpremixed but is highly nonuniform in composition. Another situation in which the mixture is partially premixed arises in the lift-off (and stabilization at the lift-off height) of turbulent jet diffusion flames. Combustion in these mixtures of nonuniform composition poses special practical, modeling and computational challenges. This chapter is, in the main, made up of the topics of: triple flames in ignition and stabilization of lifted turbulent jet diffusion flames; scaling and numerical simulation of lift-off heights; and modeling turbulent flame propagation in mixtures of nonhomogeneous mixtures. The coverage on these topics seems to be done in strokes of a rather broader brush, briefer, and mathematically less detailed than that on other topics in the earlier chapters.

The unavailability of a nomenclature makes reading of this book a bit difficult. Topical indexing is less than adequate. This book probably will have only a limited use as an advanced graduate textbook, for it does not appear quite helpful for someone seeking freshly to be introduced to the science of gas flames. The scope and level of its contents make it an excellent repository of important developments in a difficult topical area. Every library must have a copy of it. People who are deeply involved in studying turbulent combustion of gases, and those who already know the material fairly well will enjoy and benefit from it. Being the result of a marriage of turbulence to combustion, it is bound to become an exciting addition to an applied mathematician’s bookshelf. Having said all the good things and some minor not-so-good things about it, this reviewer believes that Turbulent Combustion will probably be counted among the most significant steps of progress in turbulence—progress for which Feynman so fondly longed. It will serve as a thorough, ready, and reliable reference for all combustion experts and modelers.