Thermal Explosion E-Book

Vasily B. Novozhilov

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Serie: Wiley-ASME Press Series
• Sprache: Englisch

Seitenzahl: 504

Veröffentlichungsjahr: 2025

Beschreibung

Thermal Explosion

A full review of thermal explosion theory featuring a new universal notation as a framework to develop and report research results

Summarizing all significant and notable developments made in the field over nearly 100 years, Thermal Explosion provides a single, authoritative source of information on the subject that connects the theory with examples from practical applications. After opening with an introduction to prerequisite technical information, the book goes on to cover the mathematical theory behind thermal explosion, with detailed explanations of how thermal explosion can develop in different media and under different conditions and strategies and techniques that can be used to prevent thermal explosion.

Readers will learn how to recognize thermal explosion hazards within technical designs and operation procedures, including for lithium ion batteries, biofuels, biomaterials, and microcombustors, predict the circumstances that may cause a thermal explosion in a particular design or process, and develop optimal mitigating strategies for these risks. Each chapter is supported by extensive example problems that introduce readers to a universal notation that can be used as a framework for developing and reporting their own research results.

Topics covered in Thermal Explosion include:

• Steady-state theory: the Semenov formulation and planar, cylindrical, and spherical symmetry cases in the Frank-Kamenetskii formulation
• Generalized boundary conditions, dynamical regimes, thermal explosion in a region of arbitrary shape, and nonsteady thermal explosion theory
• Thermal explosion in two-phase porous systems and spotted, diffusion, and conjugate thermal explosion
• One- and two-variable thermal explosion models of fire flashover
• Thermal explosion prevention through management of cooling flows and other passive methods, inertization, and cooling one- and two-phase media injections

Thermal Explosion is an essential, up-to-date reference on the subject for engineering researchers and professionals, along with mathematicians and other scientists working in related fields. The book is also an excellent learning aid within an academic setting for graduate-level researchers or as supplemental reading in upper-level courses.

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Thermal Explosion: Theory and ApplicationVasily B. Novozhilov

This Work is a co‐publication between John Wiley & Sons Ltd. and ASME Press

Thermal Explosion

Theory and Application

Vasily B. Novozhilov

Honorary Research Professor in MathematicsVictoria UniversityMelbourne, Victoria 8001Australia

and

N.N. Semenov Federal Research Centre for Chemical PhysicsRussian Academy of Sciences119 991 Moscow, Russia

This edition first published 2026© 2026 John Wiley & Sons Ltd

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Cover Design: WileyCover Images: Designed by Inga Novozhilov

TO MY TEACHERS

Igor Fedorovich Sharygin, in mathematicsandBoris Vasilievich Novozhilov, in physics

About the Author

Professor Vasily B. Novozhilov

Professor Vasily B. Novozhilov was born in 1963 in Moscow. He graduated with an M.Sc. in Applied Mathematics from the Russian State University of Oil and Gas in 1986. He later received a PhD in Physical and Mathematical Sciences (with a specialization in Mechanics of Fluid, Gas and Plasma) from the Moscow Aviation Institute in 1993.

Professor V.B. Novozhilov has held research positions at the Russian Academy of Sciences (the Institute of Physics of the Earth and the Institute for Problems in Mechanics) and the University of Sydney (Australia). Furthermore, he has held academic appointments at Nanyang Technological University (Singapore), as a Professor in Fire Dynamics at the University of Ulster (UK), and as a Professor of Mathematics at Victoria University (Australia). From 2014 to 2017, he was the Director of the Centre for Environmental Safety and Risk Engineering at Victoria University, Australia.

Major research interests of Professor V.B. Novozhilov are mathematical methods in mechanics, heat and mass transfer and chemical physics.

He is a leading expert in theoretical and computational methods in the areas of combustion and fire research, in particular, Computational Fluid Dynamics modelling of compartment fires. He has also made important contributions to the application of dynamical system methods in fire dynamics. Professor V.B. Novozhilov has also been greatly involved with analytical methods in heat transfer theory, including applications to ultra‐fast heat transfer processes.

He is the author of 69 journal papers and 4 book chapters. He co‐authored (together with Professor B.V. Novozhilov) the monograph ‘Theory of Solid‐Propellant Nonsteady Combustion’, published by Wiley in 2020.

He was Colloquium Co‐Chair at the Thirty Sixth International Symposium on Combustion (2016) and a Keynote Speaker at the Sixty‐Eighth International Astronautical Congress (2017).

Currently, Professor Vasily B. Novozhilov is an Honorary Research Professor in Mathematics at Victoria University in Melbourne, Australia. He also has a research affiliation with the N.N. Semenov Federal Research Centre for Chemical Physics of the Russian Academy of Sciences in Moscow, Russia.

Preface

In 2028, one hundred years will have passed since the publication of the N.N. Semenov’s paper (Semenov 1928a), which laid the foundation for the thermal explosion theory. It has been fascinating to see how the approach of this study, essentially amounting to a single first‐order ordinary differential equation, has been influential in establishing new research directions on the subject and attracting the attention of generations of scientists. The reasons for this, nearly one hundred years after the publication, are clear.

First, Semenov's theory captures the very physical essence of the problem, explaining it and making predictions in a succinct mathematical form. Owing to these virtues, Semenov's theory became classical. Second, since the proposed approach was very simple and involved a number of assumptions, the theory allowed for generalizations.

The present book reviews, along with the Semenov's theory itself, its major logical extensions. There is still no monograph written on the subject, and making such a monograph available has been the primary aim of the development of the present book.

Originally, the theory was practically applied to identify safe conditions for storage or chemical processing of various chemically reactive substances.

Consequently, the major generalizations have been concerned with traditional reactive systems (in particular, gas mixtures and solid energetic materials) and developed primarily in two main directions: (1) consideration of complicated heat transfer regimes between the system and its surroundings, and (2) effects of complicated chemical kinetics.

Several examples of the first stream of developments may be mentioned here.

One practical problem related to civil explosives is their application for underground works. In these circumstances, an explosive substance is being subjected to increased ambient temperature and, while being inert at the ground‐level temperature, may unintentionally explode in the process of transportation into deep wells. It is well known that temperatures in the wells of up to 8 km depth may reach 350 °C, or up to 400 °C in more deeper wells.

A similar problem arises upon studying thermophysical and kinetic properties of solid substances in specifically designed laboratory experiments, applying the technique of Thermogravimetric Analysis (TGA). In these experiments, samples are heated in such a way that their temperature increases linearly (or less often, according to some other law, e.g. parabolic, exponential, etc.).

It is essential that the sample maintains integrity during heating. The onset of a thermal explosion may result in the destruction of the sample. Besides, knowledge of the conditions causing thermal explosion allows the accuracy of the experiment under different heating rates to be estimated. Therefore, the possibility of thermal explosion needs to be taken into account when designing such laboratory experiments.

The next example is the concept of conjugate thermal explosion, proposed and further developed by the author. In this problem, conjugate heat transfer between different chemically reacting materials needs to be investigated. Analysis of the problem leads to the prediction of conditions under which such type of thermal explosion occurs. These conditions are significantly different from the analogous conditions of the classical thermal explosion theory.

Examples of the second major line of developments, identified above, are modern Computational Fluid Dynamics (CFD) simulations of thermal explosion, which take into account very detailed chemical kinetic mechanisms, and are often performed for complicated regimes (e.g. turbulent flows of reactive media).

As time has passed, it has gradually become apparent that manifestations of thermal explosion are much more diverse than were assumed traditionally. Thermal explosion may occur in different media and at a very wide range of circumstances. It has become especially evident with industrial developments which occurred later in the twentieth and at the beginning of the twenty‐first century. Indeed, whilst chemical processing and storage of reactive materials is still highly relevant, a number of modern technologies have emerged which, whether in traditional or new forms, inevitably use chemical energy sources. In various circumstances, these technologies are prone to thermal explosion.

These technological advancements brought up new and challenging applications of the thermal explosion theory. Their overview provided the second motivation for writing this book.

There are at least three areas of such developments.

The first one, that has emerged over the last few decades, concerns the handling of new types of chemical and biological substances. The increasing use of environmentally friendly fuels, combined with their low (compared to traditional energy sources) calorific values, results in the need to store, transport and burn them in very large quantities. This circumstance presents a significant challenge from a safety point of view. Storages of such fuels (various biosolids, wood chips, Refuse Derived Fuels (RDF), Refuse Paper and Plastic Fuels (RPF) and similar substances) have been known to be a source of fires, accompanied by casualties and very difficult to extinguish. The ignition of such fires is caused by a thermal explosion in the system. Development of a thermal explosion in such substances has peculiar features (e.g. the presence of microbiological activity that initiates chemical reactions with more substantial heat release) that are still not completely understood quantitatively.

As the application area of these fuels widens, there will be a greater need for a more reliable prediction of thermal explosion conditions, and for the development of safe fuel handling procedures.

The theory of thermal explosion is capable of predicting to what extent storage sizes and ranges of storage conditions must be limited in order to avoid catastrophic accidents.

The second area of development is related to the application of new generations of electric batteries and other innovative devices utilizing chemical energy. The most remarkable example of these recent technologies is lithium‐ion electric batteries of various capacity. The accidents involving Boeing 787 and Samsung Galaxy Note 7 lithium‐ion batteries are most commonly known. The cause of these accidents is still the same, that is thermal explosion developing in electric batteries in a quite specific way. The same safety concern applies to other devices such as fuel cells and microcombustors.

The development of the above technologies is expected to continue, demanding an understanding of their thermal explosion scenarios and efficient means to prevent them.

A very different and important third area where considerations of thermal explosion have recently proved to be very helpful is fire protection design. It has become apparent over the last two decades that the most severe, dangerous and most often resulting in fatalities type of compartment fire (the so‐called Fire Flashover) is a very specific form of thermal explosion. The problem has become more severe in recent years with a fundamental shift of combustible load in compartments towards plastics and similar highly flammable materials. The available data suggests that the time to flashover (which is effectively the time available to occupants to leave the property) has decreased in modern compartments by several times, or perhaps even up to an order of magnitude.

Understanding the flashover mechanism from the point of view of thermal explosion theory, and the application of respective quantitative models, can play a vital role in identifying scientifically justified ways towards safer building designs.

There are also other areas where the application of methods of the thermal explosion theory will be important, for example in handling and storage of highly energetic propellants of the new generation (metalized propellants).

There are some, probably inevitable, limitations to the scope of the book. Thus, multi‐phase systems are not considered (except for explosion prevention application in Chapter 9). Extension of the analysis to multi‐phase case in any context, not just related to thermal explosion, results in a dramatic increase in complexity. Correspondingly, it would require a considerable increase of the volume of the book.

The author's own scientific preferences are also reflected in the scope, predominantly via noticeable attention given to applications for fire safety.

It should be noted, finally, that while the book is essentially confined to the analysis of chemical sources of energy generation, the phenomenon of thermal explosion may also be considered in a more broad sense. Some very interesting and important manifestations of identical behaviour have been found in systems where energy generation progresses due to physical mechanisms, such as in some processes related to the mechanics of polymers.

Thus, the theory of thermal explosion provides a unified and powerful framework for understanding, prediction and practical handling of phenomena in very different fields of human activity. This fact emphasizes the strength and vitality of the theory created almost one hundred years ago.

This book is organized into nine Chapters.

The first chapter is introductory. It seeks to provide very general exposition of the subject. It introduces the concept of Thermal Explosion, provides an informal description of this phenomenon in relation to other similar processes and discusses its definition adopted in the present book. It presents historical remarks and also provides a necessary discussion on terminology. Prerequisite facts concerning chemical kinetics are also briefly reviewed in this chapter.

The second chapter presents classical mathematical results of the thermal explosion theory, obtained in the two major formulations: (i) Semenov formulation (uniform temperature of the mixture), and (ii) Frank‐Kamenetskii formulation (distributed system where the temperature distribution in the vessel, for subcritical conditions, forms part of the problem solution). Critical conditions for thermal explosion are derived in the three basic cases possessing particular types of symmetry. Both steady‐state and nonsteady versions of the theory are considered. The chapter also discusses other important properties of thermal explosion, such as an induction period. Comparison between the Semenov and the Frank‐Kamenetskii approaches is presented at the end of the chapter.

The third chapter provides an extensive discussion of the major results obtained in the mathematical theory of thermal explosion. In particular, it considers several specific topics, such as generalized boundary conditions, dynamical regimes, stability of solutions of the thermal explosion theory and critical conditions of thermal explosion in regions of arbitrary shape. The chapter also investigates and discusses mathematical connections of the theory with the theory of catastrophes and control theory. Some results are discussed in a very detailed way, while the rest are reviewed so that the reader can obtain the full knowledge of the facts established in the theory of thermal explosion up to the present moment.

The fourth chapter concerns the further extensions of the theory. Importantly, the problems considered here are confined to a quiescent medium, with the absence of any dynamical effects, for example related to internal flow. Manifestations of thermal explosion in such situations are versatile. Most important results obtained for various media and in various formulations are presented in this chapter. A very important topic considered in this chapter is effects of chemical kinetics. Several other considered problems describe conjugate thermal explosion (controlled by heat exchange between reactive systems with different properties), diffusion thermal explosion (where reactants are separated initially) and the so‐called spotted thermal explosion (originating from a hot spot of limited size in the mixture). Finally, experimental validation of the theory of thermal explosion is discussed.

In contrast to the preceding chapter, the fifth chapter presents an extensive treatment of the dynamical regimes of thermal explosion. The distinctive feature of such regimes is that chemical transformations are accompanied by the flow of the reacting mixture. At the beginning of the chapter thermal explosion development in a flow reactor is considered. In subsequent sections, major emphasis is put on the analysis of the two major types of flow conditions, that is (i) natural convection and (ii) forced convection. The influence of such conditions on the development of thermal explosion is discussed in detail using specific examples of both types of flow regimes.

The following chapter is devoted to discussion of dynamical models of compartment fire flashover, developed within the framework of the thermal explosion theory. The chapter starts with a description of the phenomenon of fire flashover, and a discussion of its mechanism. Consideration of fire flashover as a specific form of thermal explosion is justified. The models considered here are constructed using the widely known zone approach to fire modelling and differ essentially by the number of variables describing the state of the system (i.e. by the dimension of their phase space). Major attention is paid to one‐ and two‐variable models. Attempts to develop models with a higher dimension of phase space, as well as some other recent flashover model developments are also discussed.

The seventh chapter discusses several very specific practical applications of the concept of thermal explosion. The major aim of this chapter is to emphasize the possibility of thermal explosion development in some modern industrial processes and devices, and to review quantitative models that allow such dangerous developments to be predicted. The starting section of this chapter provides an exposition of available experimental data. Then, the three major classes of reactive media are considered, namely granular media, biosolid fuels and electric batteries. The major focus of the discussion in the latter case is lithium‐ion batteries.

The last two chapters deal with the theoretical and practical considerations related to the prevention of thermal explosion.

The eighth chapter discusses potential approaches theoretically. Here, several control problems in the theory of thermal explosion are formulated. The major question considered in this chapter is how external conditions for a particular reactive system need to be changed so that thermal explosion in the system is prevented. Investigation of this question leads to the proposition of several control strategies. The first of them is an instantaneous change of parameters, in the simplest case, the ambient temperature. The second strategy is a smooth control, that is a continuous change of control parameters in the course of thermal explosion development. Smooth control may be exerted in two forms: autonomous and non‐autonomous (the mixed type is not considered) reflecting the type of the relevant differential equation. For both these types of control analytical solutions, providing rigorous estimations of the system evolution under control conditions are obtained.

The final, ninth chapter discusses some practical approaches to the prevention of thermal explosion. The active prevention strategies follow the theoretical developments of Chapter 8. It is shown that the problem of thermal explosion control is closely related to the concept of thermal management. Control methods are classified into passive and active, and definitions of both types are presented. Further sections provide examples of passive and active methods. As far as active methods are concerned, the strategies of reacting system inertization and dilution with cooled media are considered, along with their basic mathematical models. The third active method, prevention of fire flashover, is considered in greater detail. In particular, analytical solutions describing heat exchange between water spray and the fire‐generated hot smoke layer are obtained. These solutions are then used in the flashover development model in order to predict critical water flow rates required to suppress flashover.

It is necessary to make remarks regarding some format conventions.

Predominantly, non‐dimensional variables are used throughout the book. To indicate dimensional variables, these are typed with the wave as an ascent.

Formulae are numbered consecutively within each chapter. This results in double‐digit notation, with the first digit being the chapter number.

Definitions and Theorems are numbered consecutively within each chapter, that is the first digit in their numbers being the respective chapter number.

In conclusion, it is my pleasure to acknowledge the significant contribution of the people who invaluably helped in the preparation of this book.

I am greatly indebted to the Wiley Editorial staff for their patience in the course of the book preparation, and for their encouragement and advice.

Special thanks are given to Inga Novozhilov. It is certain that without her careful and dedicated work, the manuscript could not have been adequately prepared. She kindly provided a number of figures used in the book, including the cover image, and also assisted in the preparation of the text.

Finally, I would like to thank my wife, Natalia Golubnichaya, for her love, patience and continuous support throughout the project.

Vasily B. Novozhilov

Melbourne2020–2025

1Introduction

1.1 Informal Description of Thermal Explosion

The notion of explosion is familiar to everyone. Explosions for high‐rise building demolition, accidental domestic gas explosions, volcano eruptions and nuclear explosions are just few examples.

In everyday’s perception, explosion power and its consequences are primary questions of interest. Most noticeable explosions are indeed accompanied by sound, thermal and/or shock waves, emission of electromagnetic impulses, radiation, etc., causing significant destruction.

Scientific perception is, however, different. In scientific investigation, the cause and mechanism of explosion and the analysis of conditions that lead to explosion take the center stage.

It is clear that, essentially, explosion is a quick release of a significant amount of energy. However, the mechanisms of such release may be vastly different. Moreover, phenomena that are intrinsically of explosive nature may not cause significant damage. As such, scientifically, in the notion of explosion, the intrinsic properties of the phenomenon and its mechanisms are of importance, rather than its appearance and consequences.

Thermal explosion is a good example. This term refers to explosion that is progressively driven by energy generation, which occurred at earlier stages of the explosion development. Energy, needed for explosion to progress, must be contained within the system, i.e. no external energy supply is required for such explosion to occur. Moreover, energy release is quickly self‐accelerating. Self‐acceleration means that the rate at which energy is being generated within the system is increasing as the total amount of energy that has been released increases. This is a very important necessary condition for thermal explosion.

Such self‐acceleration may only occur in strongly non‐linear physical or chemical systems. It should be noted, though, that before the rapid self‐accelerating stage there may exist the so‐called induction period of thermal explosion (in some cases, very long) during which energy accumulation in the system is very slow.

The present book is confined to the analysis of the very specific mechanism of energy generation in a thermal explosion, that is to the release of energy via exothermic chemical reactions. Heat generated in such reactions causes the reaction rate to grow rapidly, providing a positive feedback mechanism and causing reaction self‐acceleration. The exact mechanism of such reaction rate self‐acceleration (Arrhenius dependence of the reaction rate on the mixture temperature) will be clarified below.

It should be understood that, of course, in such a process, energy would also be lost from any real system. However, under certain circumstances, the rate of energy dissipation would become less than the rate of energy accumulation. Under such conditions, which are called critical conditions of thermal explosion, the progressive accumulation of energy would proceed.

Thermal explosion may be observed in laboratory conditions, in relatively small‐scale vessels containing mixtures of reacting gases. Therefore, the damage caused by such explosions may in some cases be minimal.

This is not to say that the opposite cannot occur. Thermal explosions can be very severe. Some of these occasions have been well documented.

Such was the Texas City disaster that occurred on April 16, 1947 (Fire Prevention and Engineering Bureau of Texas and The National Board of Fire Underwriters 1947). It is believed to be the deadliest industrial accident in the United States history and one of the largest non‐nuclear explosions in history with 581 deaths and more than 8,000 victims. The accident, which was a chain of different fires and explosions, started with a detonation of 2,300 tons of ammonium nitrate in the ship (S.S. GRANDCAMP) cargo due to thermal explosion.

Destructions were overwhelming. S.S. GRANDCAMP exploded violently, and there were reports of secondary explosions. An immense tidal wave flooded the vicinity of the explosion. The area was quickly filled with dense smoke from burning chemical facilities and oil refineries. Shock waves were easily felt 10 ml away. Shocks were able to shake buildings and shatter glass windows over wide areas.

Apart from fatalities and casualties, there was widespread property damage. The most extensive damage was sustained by Monsanto Chemical Company and Texas City Terminal Railway Company; however, many more businesses were affected.

Figure 1.1 is an artist's impression of the Texas City Disaster.

Another example is the thermal explosion of dinitolmide (or zoalene) which was used as a poultry feed additive, in a dryer at King's Lynn (Health and Safety Executive 1976) on 27 June, 1976. There was one death and extensive damage to the plant and adjacent buildings.

Figure 1.1 An artist's impression of the Texas City Disaster on April 16, 1947.