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.

A key focus of this text is to relate the manner in which fluctuations in flow or thermodynamic variables propagate and interact in combustion systems. In this chapter, we demonstrate that combustor disturbances can be decomposed into three canonical types of fluctuations – acoustic, entropy, and vorticity disturbances. This decomposition is highly illustrative in understanding the spatial/temporal dynamics of combustor disturbances [1]. For example, the velocity field can be decomposed into acoustic fluctuations, which propagate at the speed of sound with respect to the flow, and vorticity fluctuations, which are advected by the flow. This decomposition is important because, as shown in Chapters 11 and 12, two velocity disturbances of the same magnitude can lead to very different influences on the flame, depending on their phase speeds and space–time correlation. Section 2.9 further emphasizes how this decomposition provides insight into behavior measured in a harmonically oscillating flow field.