It is of importance to first define deflagrations and detonations and give the characteristics that distinguish these two types of combustion waves. Since this book is concerned with a description of the detonation phenomenon, it is of value to first introduce the various topics that are concerned with detonations prior to their detailed description in later chapters. In this manner, a global perspective can be obtained and permit selective reading of the chapters for those who are already familiar with the subject.

In telling a story, it is natural to start from the beginning, and thus the presentation of the various topics follows more or less their historical development. However, no attempt is made here to discuss the extensive early literature. A historical chronology of detonation research covering the period from its first discovery in the late 1800s to the state of knowledge in the mid 1950s has been documented by Manson and co-workers (Bauer et al., 1991; Manson & Dabora, 1993). An extensive bibliography of the early works is given in these two papers for those who want to pursue further the history of detonations. This chapter is in essence a qualitative summary of the material covered in this book.

DEFLAGRATIONS AND DETONATIONS

Upon ignition, a combustion wave propagates away from the ignition source. Combustion waves transform reactants into products, releasing the potential energy stored in the chemical bonds of the reactant molecules, which is then converted into internal (thermal) and kinetic energy of the combustion products.

Explosives are highly energetic substances with fast reaction rates and can be in gaseous, liquid, or solid form. Chemical reactions can propagate through the explosive at high supersonic speeds as a detonation wave: a compression shock with an abrupt increase in the thermodynamic state, initiating chemical reactions that turn the reactants into products. This book is devoted to a description of the detonation phenomenon, explaining the physical and chemical processes responsible for the self-sustained propagation of the detonation wave, the hydrodynamic theory that permits the detonation state to be determined, the influence of boundary conditions on the propagation of the detonation, and how detonations are initiated in the explosive.

The book is concerned only with detonation waves in gaseous explosives, because they aremuch better understood than detonations in condensed phasemedia. There are many similarities between detonations in gaseous and in condensed explosives, in that the detonation pressure of condensed explosives is much higher than the material strength of condensed explosives and the hydrodynamic theory of gaseous detonations is applicable also to condensed phase detonations. However, material properties such as heterogeneity, porosity, and crystalline structure can play important roles in the initiation (and hence sensitivity) of condensed explosives.

It is perhaps impossible to be entirely objective in writing a book, even a scientific one. The choice of the topics, the order of their presentation, and the emphasis placed on each topic, as well as the interpretation of theoretical and experimental observations, are bound to reflect the author's views.

INTRODUCTION

Direct initiation refers to the instantaneous formation of the detonation without going through the predetonation stage of flame acceleration. By “instantaneous,” it is meant that the conditions required for the onset of detonation are generated directly by the ignition source rather than by flame acceleration, as in the transition from deflagration to detonation.

Direct initiation was first used to generate spherical detonations because, in an unconfined geometry, the various flame acceleration mechanisms are ineffective (or absent), and hence the transition from a spherical deflagration to a spherical detonation cannot generally be realized. In 1923, Lafitte (1925) used a powerful igniter consisting of 1 g of mercury fulminate to directly initiate a spherical detonation in a mixture of CS2 + 3O2. He also used a planar detonation emerging from a 7-mm-diameter tube into the center of a spherical flask containing the same mixture of CS2 + 3O2. With this method, Lafitte was not successful in initiating a spherical detonation. Using the same powerful igniter of mercury fulminate, spherical detonations were also initiated in 2H2 + O2 mixtures. From the streak photographs taken by Lafitte, the detonation is observed to form instantaneously by the igniter, without a noticeable predetonation period. The detonation of a condensed explosive charge generates a very strong blast wave that decays rapidly as it expands to form the CJ detonation (hence, this mode of initiation is also referred to as blast initiation).

INTRODUCTION

The detonation velocity from the Chapman–Jouguet (CJ) theory is independent of initial and boundary conditions and depends only on the thermodynamic properties of the explosive mixture. Experimentally, however, it is found that initial and boundary conditions can have strong influences on the propagation of the detonation wave. It is the finite thickness of the reaction zone that renders the detonation vulnerable to boundary effects. Thus, the influence of the boundary can only enter into a theory that considers a finite reaction-zone thickness. In the original paper by Zeldovich (1940) on the detonation structure, he already attempted to include the effect of heat and momentum losses on the propagation of the detonation wave. However, in the one-dimensional model of Zeldovich, the two-dimensional effect of losses at the boundary cannot be treated properly. It was Fay (1959) who later modeled boundary layer effects more accurately as a divergence of the flow in the reaction zone behind the shock front, resulting in a curved detonation front. Thus, heat and momentum losses become similar to curvature effects due to the lateral expansion of the detonation products in a two- or three-dimensional detonation. However, for small curvature this can be modeled within the framework of a quasi- one-dimensional theory.

INTRODUCTION

The heart of the detonation phenomenon is the structure where the detailed ignition and combustion processes take place. The Chapman–Jouguet (CJ) theory does not require any knowledge of the structure, as it is based on steady one-dimensional flow across the transition zone with equilibrium conditions on both sides. The CJ theory also assumes that the flow within the reaction zone itself is one-dimensional and steady. The details of the transition zone are provided by the Zeldovich–von Neumann–Döring (ZND) model for the detonation structure. The ZND model is explicitly based on a steady planar structure and is therefore compatible with the one-dimensional gasdynamic CJ theory. The excellent agreement between experimental values of the detonation velocity and the theoretical predictions from the CJ theory fortuitously confirm the validity of the steady one-dimensional assumption of the CJ theory and also, implicitly, the ZND model for the detonation structure.

Early experimental diagnostics lacked the resolution to disprove the steady one-dimensional ZND structure. The state of detonation theory in the early 1960s was best summarized in a remark by Fay (1962): “… the peculiar disadvantage of detonation research is that it was too successful at too early a date. The quantitative explanation of the velocity of such waves by Chapman and Jouguet has perhaps intimidated further enquiry.” However, it was during the late 1950s and early 1960s when overwhelming experimental evidence was produced to show that the detonation structure is neither steady nor one-dimensional.

INTRODUCTION

In the gasdynamic analysis of detonation waves discussed in Chapter 2, the conservation equations are based on the upstream and downstream equilibrium states only. The detailed transition through the structure of the detonation was not considered. For a given initial upstream state, the locus of possible downstream states is given by the Hugoniot curve. Although the transition from the initial to the final state follows the Rayleigh line, the intermediate states along the Rayleigh line need not be considered if only the relationships between upstream and downstream are desired. It suffices to have the final state correspond to the intersection of the Rayleigh line with the Hugoniot curve.

Because the gasdynamic theory of detonation is concerned with the relationships between the upstream and downstream equilibrium states only, shocks, detonations, and deflagrations can all be analyzed using the conservation equations across the front. The conservation equations do not require the mechanism for the transition across the wave to be specified. However, to describe this transition zone, a model for the structure of the detonation wave must be defined. The model specifies the physical and chemical processes that are responsible for transforming the initial state to the final state. Most of the early pioneers of detonation research proposed the mechanism responsible for the propagation of the detonation implicitly in their discussion of the phenomenon.

INTRODUCTION

For given initial and boundary conditions, the possible combustion waves that can be realized are given by the solutions of the steady one-dimensional conservation equations across the wave. Since the three conservation equations (of mass, momentum, and energy) and the equation of state for the reactants and products constitute only four equations for the five unknown quantities (p1, ρ1, u1, h1, and the wave velocity u0), an extra equation is required to close this set. For non-reacting gases, the solutions to the conservation equations were first investigated by Rankine (1870) and by Hugoniot (1887–1889), who derived the relationship between the upstream and downstream states in terms of a specified wave speed, pressure, or particle velocity downstream of the shock wave. Analysis of the solutions of the conservation equations also provided important information on the stability of shock waves and on the impossibility of rarefaction shocks in most common fluids. For reacting mixtures, similar analyses of the conservation laws were first carried out independently by Chapman (1889), Jouguet (1904), and Crussard (1907), but none of these investigators were aware of similar studies carried out by Mikelson (1890) in Russia. More thorough investigations of the properties of the solutions of these conservation laws were carried out later by Becker (1917, 1922a, 1922b), Zeldovich (1940, 1950), Döring (1943), Kistiakowsky and Wilson (1941), and von Neumann (1942). Their aim was to provide a more rigorous theoretical justification of the Chapman–Jouguet criterion.

INTRODUCTION

Self-propagating one-dimensional ZND detonations are unstable and hence not observed experimentally in general. However, a solution for the laminar structure of a ZND detonation can always be obtained from the steady one-dimensional conservation equations, irrespective of the activation energy, which controls the temperature sensitivity and thus the stability of the detonation. The use of the steady one-dimensional conservation equations excludes any time-dependent multidimensional solution that describes the instability of the detonation wave. The classical method of investigating the stability of a steady solution is to impose small multidimensional perturbations on the solution and see if the amplitude of the perturbations grows. The assumption of small perturbations permits the perturbed equations to be linearized and integrated, and thus the unstable modes to be determined. As with most hydrodynamic stability analyses, the dispersion relation is rather involved and cannot be expressed analytically, which obscures the physical basis of the stability mechanism.

An alternative method is to start with the time-dependent, nonlinear, reactive Euler equations and then integrate them numerically for given initial conditions. Stability is indicated when a steady ZND solution is achieved asymptotically at large times. Unlike linear stability analyses, direct numerical simulations have the advantage that the full nonlinearity of the problem is retained. Furthermore, stability in one, two, and three dimensions can be separately investigated, which facilitates the interpretation of the numerical results. Current numerical techniques and modern computers can readily handle the integration of the multidimensional, time-dependent, reactive Euler equations.

Effects of Compressibility in Free-Shear Flows. Observations

To understand and model compressibility-induced effects on turbulence is an important topic, as these effects are significant in many engineering applications, particularly in the fields of propulsion and supersonic aerodynamics, which are concerned with jets or wakes subjected to large velocity and density gradients. The compressible plane mixing layer is a generic problem for these applications, and explaining and modeling how compressibility reduces turbulent mixing in a shear layer has motivated the large research effort devoted to this topic during the 1980s and 1990s. Mixing usually refers to interpenetration of two streams. It is characterized by two scales: a length scale δ and a velocity scale ΔU, which evaluate the thickness of the interface and intensity of the fluctuations, respectively. The reduction of mixing by compressibility is illustrated in Fig. 10.1 in which δ is the previously mentioned thickness and Mc = ΔU/a is the convective Mach number, with a the average speed of sound.

There is now a consensus in the literature that the “intrinsic compressibility” (nonzero-velocity divergence in Mach-number-dependent flows) of a turbulent velocity field tends to reduce the amplification rate of turbulent kinetic energy produced by mean-velocity gradients, with respect to the solenoidal case.

Scope of the Book

Turbulence is well known to be one of the most complex and exciting fields of research that raises many theoretical issues and that is a key feature in a large number of application fields, ranging from engineering to geophysics and astrophysics. It is still a dominant research topic in fluid mechanics, and several conceptual tools developed within the framework of turbulence analysis have been applied in other fields dealing with nonlinear, chaotic phenomena (e.g., nonlinear optics, nonlinear acoustics, econophysics, etc.).

Despite more than a century of work and a number of important insights, a complete understanding of turbulence remains elusive, as witnessed by the lack of fully satisfactory theories of such basic aspects as transition and the Kolmogorov k-5/3 spectrum. Nevertheless, quantitative predictions of turbulence have been developed. They are often based on theories and models that combine “true” dynamical equations and closure assumptions and are supported by physical and – more and more – numerical experiments.

Homogeneous turbulence remains a timely subject, even half a century after the publication of Batchelor's book in 1953, and this framework is pivotal in the present book. Homogeneous isotropic turbulence (HIT) is the best known canonical case; it is very well documented – even if not completely understood – from experiments and simple models to recent 4096 full direct numerical simulation (DNS).

Description and knowledge of turbulent flows is advancing well, particularly with the increasing development of numerical resources (Moore's law) and detailed measurements using more and more particle image velocimetry (PIV), stereoscopic particle image velocimetry (SPIV), and particle tracking velocimetry (PTV). Well-documented databases are created that can support techniques of data compression using a dramatically reduced number of modes (POD, wavelet coefficients, master modes, etc.).

Behind this attractive show window, however, the advance of our conceptual understanding of turbulent flows is much less satisfactory. Advances in numerics, experiments, data-compression schemes, are first beneficial to applied studies, for instance those using a smart combination of techniques (often referred to as multiphysics, with hybrid RANS–LES methods, and many others). Turbulent flows are well reproduced in the vicinity of a well-documented “design-point,” but this modeling is questioned far from it (“far” in the parameter's space, or simply in elapsed time for unsteady processes). Efficiency of data-compression schemes, for instance, is ellusive because a low-dimension set of modes, identified and validated near the design-point, can lose its relevance far from it.

We hope that this book will contribute to an honest and up-to-date survey of turbulence theory, with the special purpose of reconciling different angles of attack.