Forced Response II – Heat Release Dynamics

Abstract

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 wrinkling processes described in Chapter 11. Section 12.1 overviews basic mechanisms through which flow disturbances lead to heat release oscillations, and differentiates among velocity coupling, fuel/air ratio coupling, pressure coupling, and acceleration coupling. These are quantitatively analyzed in the linear regime in Section 12.2. Key questions addressed in this section are the gain and phase responses of the unsteady heat release in response to different types of disturbances. For example, given a disturbance velocity fluctuation of magnitude ɛ, what are the magnitude and phase shift of the resulting unsteady heat release, Q̇(t)? This phase shift has profound implications on thermoacoustic instability limits in particular. We also detail how these gain and phase shifts are functions of the flame configuration, such as its length and spreading angle, as well as the frequency. Nonlinear effects are discussed in Section 12.3. As detailed in Section 6.7.2.2, the amplitude dependence of the flame response is critically important in controlling the limit cycle oscillations in self-excited instabilities.