Combustion is a fascinating phenomenon coupling complex chemistry to transport mechanisms and nonlinear fluid dynamics. The combustion of reactive mixtures, frozen far from chemical equilibrium, is an irreversible process in which the approach to equilibrium proceeds through the propagation of nonlinear waves in the form of sharp fronts exhibiting complex geometrical forms. These waves were discovered in the nineteenth century, but the understanding of their structure and dynamics is quite recent. In gaseous mixtures, the rate of chemical heat release is small compared with the rate of elastic collisions, so that combustion is described by the macroscopic equations for the conservation of mass, species, momentum and energy, assuming local equilibrium (except for the inner structure of shock waves). The full system of equations is complicated and is not useful to describe each of the elementary phenomena, separate from the others. Even the coupling of two phenomena, as for example a quasi-isobaric flame and acoustic waves, is represented by simplified equations. The major advances have resulted from analytical studies of simplified models performed in close relation to carefully controlled laboratory experiments. A systematic reduction of the complexity of the basic equations, validated by the confrontation with experiments, is the key to understanding. It is also the most difficult step. The analytical and numerical solutions of simplified equations of relevant models can be completed in a second step by direct numerical simulations of a more detailed system of equations.

The book is written along this line and attention is focused on fundamental aspects. It is meant to be a survey of the nonlinear dynamics of combustion waves, which now constitute a mature scientific field. A similar approach is used to improve the understanding of other types of waves such as ablation fonts in inertial confinement fusion. The approach is also tentatively extended to the explosion of stars at the end of their lifetime, the famous supernovae. A large variety of phenomena is presented. The purpose is to provide a wide view of the physical problems involved in different domains that can benefit from cross-fertilisation. The most important scientific results are reported, ranging from the pioneering works of the last century to the advanced research of the last decade.

Brief Historical Introduction

Fire, Humanity and Civilisation

Combustion has played a decisive role in the development of mankind and civilisation. At the present time it is the principal source of energy and the main support of economic development. Mastering the use of fire was the first major step in the development of humanity and marked a decisive step in its evolution. The oldest traces of the use of fire, limited to the occasional use of naturally occurring embers, date back to more than one million years, after the emergence of Homo erectus. However, the first fireplaces in dwellings appeared much later in Eurasia, about 450000 years ago. Neanderthal man had well mastered the art of fire, greatly improving living conditions through the ability to create light after sunset, to fight against cold, and to cook food. The first technical uses of fire were limited to hardening the points of wooden arrows and spears. Small lamps made of stone, bone or shells burning animal fat or vegetable oil, and dating back to the upper Palaeolithic 35000 years ago, can be directly associated with the development of parietal arts.

The development of other technologies using fire appeared with the advent of farming and a more sedentary existence in the Neolithic era and the early Bronze Age, some 10 000 years ago. At this time, fire was used to transform clay into pottery, and ore into metals. Because of its capacity to transform and purify(?) or destroy matter and its dancing flames, source of light and heat, fire quickly acquired a mystical dimension as attested by the central place of fire in the Vedic ritual and in the legends of antique Greece. Let us cite, for example, the legend of Prometheus, a Titan who stole fire from Zeus and gave it to the mortals, as did his Hindu counterpart, Pramatha, the hero who brought civilising fire to earth. The holders of the secrets of fire were at the same time priests and scientists, as for example the ‘Guild of Chinese Blacksmiths’ (eighth century BC), which was at the origins of Taoism at the time of Laozi (sixth century BC). From this stems the Taoist alchemy, more than one and a half millenniums before the alchemy of the Middle Ages, whose esoteric gnosis reserved a major role for the sacred fire.