Chapter 3 - Transient growth and non-orthogonality of thermoacoustic eigenmodes

Abstract

Self-excited thermoacoustic instabilities could be triggered by transient growth of flow disturbances in a given combustor, which is associated with its non-normality. In this chapter, an open–open thermoacoustic combustor with different temperature configurations is modeled first to investigate its non-normality and the resulting transient growth. Both eigenmodes orthogonality and transient growth analysis are conducted by linearizing the acoustically compact flame model (G-equation) and recasting it into the classical time-lag (n-τ) formulation. Further studies are conducted by examining the effects of a choked outlet boundary and entropy waves on transient energy growth in triggering thermoacoustic instability. Finally, a choked combustor with spatially distributed heat sources is considered to evaluate the flame axial length and the mean heat input configurations on the combustor’s non-normality and the resulting maximum transient energy growth rate. In general, the recent researches on transient growth and non-orthogonality as well as non-normality features of a thermoacoustic combustor are overviewed and discussed.