Identification of heat transfer dynamics for nonmodal stability analysis of thermoacoustic systems

A systematic approach to study the nonmodal stability analysis of the thermoacoustic systems is proposed. The heat source is obtained using unsteady computational fluid dynamics in combination with correlation based linear system identification. The time domain simulation of the full system is obtained from a Galerkin expansion technique and the heat source is modeled as a compact element in the system. The eigenvalues of the resulting system are obtained from the discretization of the solution operator. The maximum growth factor is estimated from the pseudo spectra using Kreiss' theorem. The approach is illustrated in a simple Rijke tube configuration. For modeling the heat source, the King's law which is widely used in hot wire anemometry and the heat source model obtained from CFD and linear identification are used. The sensitivity of the eigenvalues near the zero of the real axis in a pseudospectra diagram for different perturbations for the same set of parameters show different behavior for different heat source models and hence different non-normal behaviors. The maximum growth factor for the system with King's law heat source model is more sensitive to the change in the heat source location than that of the CFD model heat source.