On the spurious entropy generation encountered in hybrid linear thermoacoustic models

Abstract

This work demonstrates that a hybrid approach for linear thermoacoustic stability analysis that combines the Linearized Navier–Stokes Equations (LNSE) with a global Flame Transfer Function (FTF), generates spurious entropy waves when used to model acoustically forced premixed flames. The inability of the global FTF to account for the effects of flame movement is identified as the root cause of this unphysical behavior. Utilization of a local FTF, which resolves unsteady heat release on scales comparable to the reaction zone of the flame, suppresses the spurious entropy perturbations. This affirms that fine-grained resolution of the spatio-temporal distribution of heat release rate fluctuations in the combustion zone is required to model the movement of the flame front, even for acoustically and convectively compact flames. As an alternative to hybrid models, a Linearized Reactive Flow (LRF) approach is employed, which extends the LNSE by the linearized species transport equations as well as the reaction mechanism. Such a monolithic approach inherently accounts for the locally resolved flame dynamics, including the movement of the flame front, and does not require an external model for the flame-flow interaction. Thus the LRF eliminates the need for the cumbersome identification of a local FTF. Two configurations of lean premixed methane-air flames, i.e. a freely propagating 1D flame and a 2D flame anchored in a duct, are considered for validation. All results obtained with linearized modeling approaches and conclusions deduced thereof are validated against high resolution CFD results with excellent quantitative accuracy.