Thermoacoustic Stability of Quasi-One-Dimensional Flows—Part II: Application to Basic Flows

In this paper, applications of a previously developed numerical formulation (Prasad, D., and Feng, J., 2004, “Thermoacoustic stability of Quasi-One-Dimensional Flows—Part I: Analytical and Numerical Formulation,” J. Turbomach., 126, pp. 636–643. for the stability analysis of spatially varying one-dimensional flows are investigated. The results are interpreted with the aid of a generalized acoustic energy equation, which shows that the stability of a flow system depends not only on the nature of the unsteady heat, mass and momentum sources but also on the mean flow gradients and on the inlet and exit boundary conditions. Specifically, it is found that subsonic diffusing flows with strongly reflecting boundary conditions are unstable, whereas flows with a favorable pressure gradient are not. Transonic flows are also investigated, including those that feature acceleration through the sonic condition and those in which a normal shock is present. In both cases, it is found that the natural modes are stable. Finally, we study a simplified ducted flame configuration. It is found that the length scale of the mean heat addition affects system stability so that the thin-flame model commonly used in studies of combustion stability may not always be applicable.