Non-normality and nonlinearity in combustion-acoustic interactions in diffusion flames

In this paper, the role of non-normality and nonlinearity in flame-acoustic interaction in a ducted diffusion flame is investigated. The infinite rate chemistry model is employed to study unsteady diffusion flames in a Burke-Schumann type geometry. It has been observed that, even in this simplified case the combustion response to acoustic perturbations is non-normal and nonlinear. The above mentioned combustion model is then coupled with a linear model of the duct acoustic field to study the growth of acoustic perturbations. The one-dimensional acoustic field is simulated in the time domain using the Galerkin technique, treating the fluctuating heat release from the combustion zone as a compact acoustic source. It is been observed that the various modes interact due to the non-normality of the modes resulting in the exchange of energy from one mode to another. Further, the numerical simulations showed the occurrence of triggering; i.e., the thermoacoustic oscillations decay for some initial conditions whereas they grow for some other initial conditions. It is shown that triggering occurs due to the combined effect of non-normality and nonlinearity. As a result of the non-normal behavior, the solutions exhibit large transient growth, which could potentially trigger nonlinearities in the system when the amplitudes reach high enough values. For such a non-normal system, resonance or "pseudoresonance" may occur at frequencies far from its natural frequencies. They can be studied using pseudospectra, as eigenvalues alone are not sufficient to predict the behavior of the system.