An introduction to far-reaching developments in theoretical combustion, with special emphasis on flame stability, a topic that has, to date, benefited most from the application of modern asymptotic methods.

Author: John David Buckmaster

Publisher: SIAM

ISBN: 161197027X

Category: Combustion

Page: 126

View: 120

An introduction to far-reaching developments in theoretical combustion, with special emphasis on flame stability, a topic that has, to date, benefited most from the application of modern asymptotic methods. The authors provide a modern view of flame theory, and a complete description of the longstanding ignition and explosion problems, including the solutions that were made available independently by Kapila and Kassoy through activation-energy asymptotics, the main theme of this monograph.

The description of reacting systems can be simplified when the so- called activation energy is large; the notion is an old one, but its full power is only released by modern singular perturbation theory.

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ISBN: OCLC:227586207

Category:

Page: 26

View: 804

The description of reacting systems can be simplified when the so- called activation energy is large; the notion is an old one, but its full power is only released by modern singular perturbation theory. More than forty years ago, Frank-Kamenetskii introduced approximations based on large activation energy to construct a thermal theory of spontaneous combustion, and we shall start there. His problem, which neglects the fluid-mechanical effects of main concern to us, focuses attention on the reaction and thereby acts as a precursor for the lectures that follow. The problem and its generalizations have been the happy hunting grounds of mathematical analysts for many years, but it was not until quite recently that a complete description of the ignition and explosion processes was made available of Kapila and Kassoy (working separately) through activation-energy asymptotics, the main theme of these lectures.

This is a formidable task that could fill a week of lectures by itself, most of which would not be of great interest to a mathematical audience.

Author: J. D. Buckmaster

Publisher:

ISBN: OCLC:227586211

Category:

Page: 24

View: 745

The problem of formulating the governing equations of combusion consists, as its simplest, in characterizing the flow of a viscous, heat-conducting mixture of diffusing, reacting gases. This is a formidable task that could fill a week of lectures by itself, most of which would not be of great interest to a mathematical audience. Mindful of this, we shall limit ourselves to a description, rather than a derivation, of the simplest equations that can be brought to bear on combustion problems. Only the most important assumptions normally used to justify the equations will be discussed; for a more extensive treatment the reader is referred to Buckmaster & Ludford (1982).

The material contained herein is the written version of ten lectures on mathematical combustion given during a CBMS-NSF Regional Conference held at Colorado ...

Author: John D. Buckmaster

Publisher: SIAM

ISBN: 9780898711868

Category: Science

Page: 126

View: 942

An introduction to far-reaching developments in theoretical combustion, with special emphasis on flame stability, a topic that has, to date, benefited most from the application of modern asymptotic methods. The authors provide a modern view of flame theory, and a complete description of the longstanding ignition and explosion problems, including the solutions that were made available independently by Kapila and Kassoy through activation-energy asymptotics, the main theme of this monograph.

Law has shown that the analysis of spherical diffusion flames is quite similar to that of counterflow diffusion flames, so that some explanation is needed for devoting a separate lecture to them. There are two good reasons.

Author: J. D. Buckmaster

Publisher:

ISBN: OCLC:227586232

Category:

Page: 27

View: 974

Law has shown that the analysis of spherical diffusion flames is quite similar to that of counterflow diffusion flames, so that some explanation is needed for devoting a separate lecture to them. There are two good reasons. First, the constant-density approximation has been used throughout these lectures in discussing all but plane flames, so there is room for a problem which does not neglect variations in density. (Plane diffusion flames have to be chambered, i.e. the reactants must be supplied at finite locations, which leads to distracting complications). Secondly, the spherical diffusion flame can lead to quite different (and unusual) responses. These arise in the technologically important application to the quasi-steady phase of fuel-drop burning, when a more realistic boundary condition than the conventional one is used. (Author).

The fundamental characteristic of diffusion flames is that the two reactants, fuel and oxidizer, are supplied in different parts of the combustion field, so that they must come together and mix by diffusion before reaction can take place.

Author: J. D. Buckmaster

Publisher:

ISBN: OCLC:227586230

Category:

Page: 25

View: 880

The fundamental characteristic of diffusion flames is that the two reactants, fuel and oxidizer, are supplied in different parts of the combustion field, so that they must come together and mix by diffusion before reaction can take place. Counterflowing streams provide one method of bringing them together; the resulting diffusion flames, whose main properties were established by Linan, is the subject of this lecture.

Steady, plane deflagration was introduced in the second lecture; here we shall consider infinitesimal perturbations of it and so examine its stability. We shall find two basic phenomena - the hydrodynamic and Lewis-number effects.

Author: J. D. Buckmaster

Publisher:

ISBN: OCLC:227586220

Category:

Page: 25

View: 607

Steady, plane deflagration was introduced in the second lecture; here we shall consider infinitesimal perturbations of it and so examine its stability. We shall find two basic phenomena - the hydrodynamic and Lewis-number effects.

For want of a complete analysis of multidimensional flows in preasymptotic days, it was natural to try to identify special characteristics that play particularly important roles in the understanding of flame behavior.

Author: J. D. Buckmaster

Publisher:

ISBN: OCLC:227586217

Category:

Page: 25

View: 864

For want of a complete analysis of multidimensional flows in preasymptotic days, it was natural to try to identify special characteristics that play particularly important roles in the understanding of flame behavior. Flame speed and temperature are examples of such characteristics that have already been identified; a more subtle characteristic, introduced by Karlovitz, is flame stretch. The authors start by discussing this concept, so as to have it available when we come to discussing general slowly varying and near-equidiffusional flames. (Author).

A mathematical framework in which to accommodate these is not obvious. (The first lecture dealt with special circumstances for which such variations were manageable).

Author: J. D. Buckmaster

Publisher:

ISBN: OCLC:227586214

Category:

Page: 22

View: 216

In the last lecture we examined the plane, steady, adiabatic, premixed flame and deduced an explicit formula for its speed. By using judicious choice of parameters this formula can be made to agree roughly with experiment; precision is not a reasonal goal, given the crude nature of our model. Noteworthy is the extreme sensitivity of the speed to variations in the flame temperature: an 0(1) change generates an exponentially large change in flame speed. Such variations in speed (caused, for example, by changes in mixture strength) are not excessive numerically (at least for fuels burnt in air), because activation energies and fractional changes in temperature are modest; but in an asymptotic analysis they present a potential obstacle to discussion of multidimensional and/or unsteady flames. Then signigicant variations, spatial and/or temporal, in the flame temperature can be expected and, if the sensitivity mentioned above is any guide, there will be correspondingly large spatial and/or temporal variations in the flame speed. A mathematical framework in which to accommodate these is not obvious. (The first lecture dealt with special circumstances for which such variations were manageable).

In section 5. it was found that plane NEFs to sufficiently large Lewis number are unstable. Since Im(a) 0 on the stability boundary, the instability is likely to result in either a pulsating flame or a flame that supports traveling waves.

Author: J. D. Buckmaster

Publisher:

ISBN: OCLC:227586225

Category:

Page: 28

View: 479

In section 5. it was found that plane NEFs to sufficiently large Lewis number are unstable. Since Im(a) 0 on the stability boundary, the instability is likely to result in either a pulsating flame or a flame that supports traveling waves. Such flames are the subject of this lecture.

Throughout these lectures we have ensured that the reaction terms vanish everywhere except in a thin (flame) sheet, whose location has to be found as part of the solution.

Author: J. D. Buckmaster

Publisher:

ISBN: OCLC:227586236

Category:

Page: 35

View: 660

Throughout these lectures we have ensured that the reaction terms vanish everywhere except in a thin (flame) sheet, whose location has to be found as part of the solution. So far this free boundary has been either a plane, a circular cylinder, a sphere, or a perturbation of one of these; we now consider problems with more complicated free boundaries. (Author).

Each line is a ridge of high curvature, convex towards the burnt gas. For a nominally flat flame these cells are very unsteady, growing and subdividing in a chaotic fashion; but curvature, for example, can make stationary.

Author: J. D. Buckmaster

Publisher:

ISBN: OCLC:227586222

Category:

Page: 31

View: 581

We shall now examine the left stability boundary that was uncovered in lecture 5 in our discussion of NEFs (figure 5.3). The boundary is associated with instabilities leading to cellular flames, i.e. flames whose surfaces are broken up into distinct luminous regions (cells) separated by dark lines. Each line is a ridge of high curvature, convex towards the burnt gas. For a nominally flat flame these cells are very unsteady, growing and subdividing in a chaotic fashion; but curvature, for example, can make stationary.

This monograph would never have come to fruition without the enthu siasm and drive of Dave Eberly-a former student, now collaborator and coauthor-and without several significant breakthroughs in our understand ing of the phenomena of blowup ...

Author: Jerrold Bebernes

Publisher: Springer Science & Business Media

ISBN: 9781461245469

Category: Science

Page: 178

View: 953

This monograph evolved over the past five years. It had its origin as a set of lecture notes prepared for the Ninth Summer School of Mathematical Physics held at Ravello, Italy, in 1984 and was further refined in seminars and lectures given primarily at the University of Colorado. The material presented is the product of a single mathematical question raised by Dave Kassoy over ten years ago. This question and its partial resolution led to a successful, exciting, almost unique interdisciplinary col laborative scientific effort. The mathematical models described are often times deceptively simple in appearance. But they exhibit a mathematical richness and beauty that belies that simplicity and affirms their physical significance. The mathe matical tools required to resolve the various problems raised are diverse, and no systematic attempt is made to give the necessary mathematical background. The unifying theme of the monograph is the set of models themselves. This monograph would never have come to fruition without the enthu siasm and drive of Dave Eberly-a former student, now collaborator and coauthor-and without several significant breakthroughs in our understand ing of the phenomena of blowup or thermal runaway which certain models discussed possess. A collaborator and former student who has made significant contribu tions throughout is Alberto Bressan. There are many other collaborators William Troy, Watson Fulks, Andrew Lacey, Klaus Schmitt-and former students-Paul Talaga and Richard Ely-who must be acknowledged and thanked.

Final report 30 Jun 81-29 Jun 82 , 83 : 12877 ( R ; US ) Activation Energy Lectures on mathematical combustion . Lecture 1. Pre - asymptotic combustion ...

J. D. Buckmaster and G. S. S. Ludford, 1983, Lectures on Mathematical Combustion, SIAM, Philadelphia. This is set of lecture notes which serves as an ...

Excerpt from Lectures on Combustion Theory This volume contains the elaborations of lectures at a seminar held at the Courant Institute in the spring of 1977 on the mathematical aspects of combustion.

Author: Samuel Z. Burstein

Publisher: Forgotten Books

ISBN: 1330236068

Category: Science

Page: 332

View: 487

Excerpt from Lectures on Combustion Theory This volume contains the elaborations of lectures at a seminar held at the Courant Institute in the spring of 1977 on the mathematical aspects of combustion. The purpose of the seminar was to put the achievements and problems of combustion theory into sharp focus and to bring them to the attention of the mathematical community, in the hope that, just as in the past, mathematical methods will shed light on these theories, and that mathematical ideas will lead to new and efficient computational procedures. The first half of the semester was devoted to subjects that were reasonably well understood as mathematics; the speakers were mathematicians. After the spring recess the seminar was devoted to subjects not yet mathematically digested; among the speakers there were engineers, chemists, and physicists with sympathy in their hearts for mathematics. The first part starts with a paper by Peter D. Lax which is a review of those numerical methods in fluid dynamics that are especially promising for reacting flows. This is followed by a report prepared by K. O. Friedrichs for the Navy in 1946, edited and presented by Gary A. Sod. The third paper by Peter D. Lax is a brief introduction to chemical kinetics, followed by papers by Alexandre Chorin, of the University of California at Berkeley, on reactive flows, by Gary A. Sod on a first step to modeling flows in an engine, and by Samuel Z. Burstein on combustion instability. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

These two volumes represent the culmination of the Special Year `84-'85 in Reacting Flows held at Cornell University.

Author: G. S. S. Ludford

Publisher: American Mathematical Soc.

ISBN: 0821896911

Category: Mathematics

Page: 512

View: 441

These two volumes represent the culmination of the Special Year `84-'85 in Reacting Flows held at Cornell University. As the proceedings of the 1985 AMS/SIAM Summer Seminar in Applied Mathematics, the volumes focus on both mathematical and computational questions in combustion and chemical reactors. They are addressed to researchers and graduate students in the theory of reacting flows. Together they provide a sound basis and many incentives for future research, especially in computational aspects of reacting flows. Although the theory of reacting flows has developed rapidly, researchers in the two subareas of combustion and chemical reactors have not communicated. The main goal of this seminar was to synthesize the mathematical theory and bring it to the interface with large-scale computing. All of the papers have high research value, but the first five introductory lectures should be especially noted.