Chapters 2 through 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 through 9, which focus on reactive processes and their interactions with the flow. This particular chapter treats the hydrodynamic influence of the flame on the flow field in the thin flame limit. In this limit, the internal flame structure does not need to be considered. The flame acts as a volume/energy source that leads to discontinuities 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. Kinetically controlled phenomena are treated in Chapter 8, which treats ignition processes, and in Chapter 9 which treats premixed and non-premixed flames. This chapter focuses almost exclusively on premixed flames where the flame–flow coupling must be explicitly accounted for to describe many important phenomena. In contrast, the gas expansion induced by non-premixed combustion modifies the flow field, but its impact is more quantitative than qualitatative.

Section 7.1 works out the jump conditions across a thin, premixed flame and shows how flames modify flow vorticity and velocity. There is no specific section on non-premixed flame jump conditions, so we briefly note here that such jump conditions, based on one-step kinetics, stipulate that the diffusive fluxes of fuel and oxidizer into the reaction sheet occur in stoichiometric proportions (see Section 9.4 and Eq. (9.27) specifically) and that the jump in sensible enthalpy gradient on the fuel and oxidizer side is directly proportional to the fuel/oxidizer diffusive flux (i.e., the mass burning rate). The reader is referred to Section 5.5.1 in Law [1] or Section 3.1.5 in Williams [2] for these non-premixed flame derivations.