In Chapter 2 we showed that flow disturbances can be decomposed into vorticity, entropy, and dilatational/acoustic fluctuations. The next two chapters focus on the evolution of vorticity in flows, and how vorticity in one region of the flow interacts with other regions of vorticity to influence hydrodynamic flow stability, leading to self-organization into concentrated regions of vorticity and flow rotation. Such large-scale structures, embedded on a background of acoustic waves and broadband, smaller-scale turbulence, dominate the unsteady flow fields in combustors. These large-scale structures play important roles in processes such as combustion instabilities, mixing and entrainment, flashback, and blowoff. For example, we will discuss vortex–flame interactions repeatedly in discussions of combustion instabilities in later chapters.

This book is about unsteady combusting flows, with a particular emphasis on the system dynamics that occur at the intersection of the combustion, fluid mechanics, and acoustic disciplines – i.e., on combustor physics. In other words, this is not a combustion book – rather, it treats the interactions of flames with unsteady flow processes that control the behavior of combustor systems. While numerous topics in reactive flow dynamics are “unsteady” (e.g., internal combustion engines, detonations, flame flickering in buoyancy-dominated flows, thermoacoustic instabilities), this text specifically focuses on unsteady combustor issues in high Reynolds number, gas-phase flows. This book is written for individuals with a background in fluid mechanics and combustion (it does not presuppose a background in acoustics), and is organized to synthesize these fields into a coherent understanding of the intrinsically unsteady processes in combustors.

This chapter presents the key equations for a multicomponent, chemically reacting perfect gas which will be used in this text [1]. These equations describe the thermodynamic relationships between state variables in a perfect gas, such as the interrelationship between pressure, density, and entropy. They also describe the physical laws of conservation of mass, which relates the density and velocity, the momentum equation, which relates the velocity and pressure, and the energy equation, which relates the internal and kinetic energy of the flow to work and heat transfer to the fluid.

Chapter 11 described the dynamics of flamelets forced by velocity or burning rate oscillations and illustrated the key physics controlling the spatiotemporal dynamics of the flame position. This chapter focuses on the impacts of these disturbances on the mass burning rate and/or heat release rate itself. For example, a key quantity of interest for the thermoacoustic instability problem is the heat release fluctuations that are induced by the flame disturbances. Section 12.1 gives an overview of the basic mechanisms through which flow disturbances lead to heat release oscillations, and differentiates between velocity coupling, fuel/air ratio coupling, pressure coupling, and acceleration coupling. Section 12.2 treats the effects of the flame configuration on its sensitivity to these disturbances, such as geometry or reactant premixing.

This chapter describes the processes associated with spontaneous (or “autoignition”) and forced ignition. The forced ignition problem is of significant interest in most combustors, as an external ignition source is almost always needed to initiate reaction. Two examples where the autoignition problem is relevant for flowing systems are illustrated in Figure 8.1 [1–10]. Figure 8.1(a) depicts the autoignition of high-temperature premixed reactants in a premixing duct. This is generally undesirable and an important design consideration in premixer design. Figure 8.1(b) depicts the ignition of a jet of premixed reactants by recirculating hot products. In this case, autoignition plays an important role in flame stabilization and the operational space over which combustion can be sustained. Although not shown, autoignition can also occur during the injection of a fuel, air, or premixed reactants jet into a stream of hot fuel, air, or products. For example, a vitiated H2/CO stream reacts with a cross-flow air jet in RQL combustors [11].

This section previews the structure and content of this book and provides suggestions for how readers of different backgrounds can use it most effectively. The bulk of Chapter 1 is dedicated to reviewing the basic equations to be used in this text. Then, the remainder of the book is divided into three main sections: Chapters 2–6, 7–9, and 10–12. The first section, Chapters 2–6, discusses flow disturbances in combustors. Chapter 2 details how different types of disturbances arise and propagate in inhomogeneous, reacting combustor environments. By introducing the decomposition of flow disturbances into acoustic, vortical, and entropy disturbances, this chapter sets the stage for Chapters 3–6 which delve into the dynamics of disturbances in inhomogeneous environments in more detail. Specifically, Chapters 3 and 4 focus on the evolution of vortical disturbances in combustor environments. Chapter 3 provides a general overview of hydrodynamic stability theory and details some general features controlling the conditions under which flows are unstable.

Chapter 8 considered ignition, and the processes associated with autoignition and forced ignition of a nonreactive mixture. In this chapter we focus on premixed and nonpremixed flames and the key physics controlling burning rates and extinction processes. Section 9.1 summarizes basic issues associated with the structure and burning rate of steady, premixed flames in homogeneous, one-dimensional flow fields. This includes discussions of the effects of pressure, temperature, and stoichiometry on burning rates. Section 9.2 then discusses how these results are modified by inhomogeneities in mixture composition, and the competition between autoignition waves and deflagration waves. Section 9.3 discusses how these one-dimensional characteristics are altered by inhomogeneities in the flow field relative to the flame, referred to as flame stretch. We then discuss how these lead to changes in burning rate and, for large enough levels of stretch, cause the flame to extinguish. Section 9.4 treats the effects of unsteadiness in pressure, fuel/air ratio, and stretch rate. Specifically, we discuss how the flame acts as a low-pass filter to disturbances in most cases, and that its sensitivity to disturbances diminishes with increasing frequency. These results have important implications for many combustion instability phenomena, where the flame is perturbed by time-varying flow and composition variations.

This chapter continues the treatment initiated in Chapter 3, focusing on specific flow fields. Hydrodynamic flow stability is a large, rich field and this chapter can only provide a brief introduction to the many fascinating instabilities that arise [1]. For these reasons, attention is specifically focused on high Reynolds number flows and several specific flow configurations of particular significance in combustor systems, including shear layers, wakes, jets, and backward-facing steps.

The final two chapters treat the response of flames to forced disturbances, both time-harmonic and random. This chapter focuses on local flame dynamics; i.e., on characterizing the local space–time fluctuations in flame position. Chapter 12 treats the resulting heat release induced by disturbances, as well as sound generation by heat release fluctuations. These two chapters particularly stress the time-harmonic problem, with more limited coverage of flames excited by stochastic disturbances. This latter problem is essentially the focus of turbulent combustion studies, a topic which is the focus of dedicated treatments [1–3].

Chapters 2–6 focused on disturbances in combustor environments and how they evolve in space and time. This chapter initiates the second section of this book, Chapters 7–9, which focus on reactive processes and their interactions with the flow. The flame acts as a volume/energy source that leads to rapid changes in flow properties or their derivatives, such as velocity, vorticity, or entropy. Wrinkling on the flame also leads to modification of the approach flow velocity field.

This chapter initiates the third section of the text, discussing transient and time-harmonic combustor phenomena. This particular chapter focuses on the transient phenomena of flashback, flame stabilization, and blowoff. Chapters 11 and 12 then focus on time-harmonic and broadband flame forcing.

This chapter discusses acoustic wave propagation in combustor environments. As noted in Chapter 2, acoustic waves propagate energy and information through the medium without requiring bulk advection of the flow. For this reason, and as discussed further in this chapter, the details of the time-averaged flow have relatively minor influences on the acoustic wave field in low Mach number flows. In contrast, vortical disturbances, which propagate with the local flow field, are highly sensitive to the flow details. For these reasons, there is no analogue in the acoustic problem to the myriad different ways in which vorticity can organize and reorganize itself as in the hydrodynamic stability problem. Rather, in low Mach number flows the acoustic field is insensitive to these details and is largely controlled by the boundaries and sound speed field.

This chapter follows Chapter 5 by treating the additional physical processes associated with sound wave propagation through an inhomogeneous, variable-area region with bulk flow. In the rest of this section we discuss four generalizations introduced by these effects: (1) wave reflection and refraction, (2) changes in disturbance amplitude and relative amplitudes of pressure and velocity disturbances.