EFFICIENT CALCULATION OF THERMOACOUSTIC MODES UTILIZING STATE-SPACE MODELS

This paper describes a framework for the efficient computation of thermoacoustic modes in annular combustors. It is based on state-space models for coupling both the linearized acoustics and the flame dynamics. The state space models for the acoustics are exported from COMSOL Multiphysics. The Finite Element Method for the linearized Euler equations yields very sparse system matrices. The acoustic and the flame models are connected by network model routines. Due to the state-space modeling, thermoacoustic modes can be computed by solving a generalized non-Hermitian linear eigenvalue problem instead of a nonlinear eigenvalue problem. The Arnoldi algorithm is used to calculate selected eigenvalues in case the systems are too big to compute a direct solution for all the eigenvalues. Validation is carried out for a plenum-burner-chamber configuration with four burners. Simplistic n-t models are chosen for the flame-acoustic interaction, which are represented in state space form utilizing an advection equation for representing the time delay. The results show good agreement with a full three-dimensional Finite Volume Helmholtz solver in mode shape, frequency and growth rates. Coupling between the plenum and the chamber is observed to be dependent on the interaction index and the characteristic time delay of the flame models.