Nonsteady flame spreading in two-dimensional ducts

Abstract

Nonsteady behavior of a flame stabilized at the center of a two-dimensional duct is studied using an integral technique. An exact representation of the irrotational flow field upstream of the flame is obtained by utilizing a suitable distribution of sources on the duct axis. Time-dependent solutions exhibit traveling wave patterns with significant amplification along the flame region. These solutions enable the calculation of the acoustic transmission and reflection properties of the flame region. HE control and elimination of combustion instability in systems of practical interest and the rational interpretation of subscale experiments require an understanding of the fundamental mechanism. In many instances response of the combustion processes to local pressure and velocity fluctuations is an important factor that feeds considerable energy into the system to sustain the oscillations. When the frequency is less than a few hundred hertz, the chemical reaction time delay is relatively unimportant, rather, the fluid mechanical adjustments of the flame region play the dominant role governing the detailed response of the system. As a result of fast chemical kinetics, flame fronts are usually very thin compared to length scales associated with combustion devices of practical interest. Therefore, in problems where detailed calculations of flame structure are not important, one often considers the flame front as a surface of discontinuity separating the cold fuel oxidizer mixture and hot combustion products. The flowfields on either side of the flame front are matched by relations analogous to the jump conditions across the shock discontinuities. Nonsteady behavior of a flame stabilized at the center of a two-dimensional duct is studied as a specific but typical example of the low-frequency behavior. Steady-state flame spreading of the confined premixed flames in two