Reduced-order modeling of transversal and non-compact combustion dynamics

A low-order methodology to perform linear and nonlinear stability analysis of transversal thermoacoustic modes is presented. The mathematical basis of such an analysis is formed by a Reduced Order Model of a large-scale system given by a Finite Element discretization of the Linearized Euler Equations. Linearized Euler systems are capable of describing aeroacoustic wave propagation and damping in non-uniform mean flow environments - as occurring in real engineering systems - i.e. gas turbine combustors. The derivation methodology of the Reduced Order Model based on a large-scale system is outlined, conducted on, and its reproduction capabilities successfully validated against a choked nozzle benchmark test case. In order to demonstrate the concept of the novel thermoacoustic modeling approach, an analysis of a generic configuration is carried out. Specifically, this thermoacoustic analysis consists of two parts: (1) Linear stability analysis in frequency domain, which features the consideration of non-compact heat release couplings. (2) Nonlinear dynamical analysis in time domain to model transversal mode dynamics governed by nonlinear saturation of heat release fluctuations and stochastic forcing due to turbulent combustion noise. Thereby, the randomly changing standing and rotation transversal mode behavior - as observed in experiments - are reproduced via simulations.