Revisiting a Model for Combustion Instability Involving Vortex Shedding

We revisit a simple reduced order model (Matveev, K. and Culick, F. E. C, (2003) "A Model for Combustion Instability Involving Vortex Shedding", Combust Sci. and Tech., 175, 1059-1083) and re-examine its implications in the light of the non-normal and nonlinear nature of combustion acoustic interactions. One-dimensional linear acoustics is used to model the acoustic field in an open-open duct. The Galerkin technique is used to expand the acoustic pressure and velocity fluctuations in terms of the natural acoustic modes. The coupled thermoacoustic system is shown to be non-normal and nonlinear. This leads to complicated, but interesting physics which were not examined in the earlier study. Examples showing triggering and bootstrapping in an initially decaying system are then presented. It is also shown that a vortex based combustor reaches different limit cycle amplitudes for the same system parameters, when subjected to different initial conditions. Further, the effect of damping on the non-normal behavior of the system is studied. Pseudospectra analysis reveals that for a lightly damped system, an increase in damping might lead to higher nonnormal interaction of modes.