Reduced-Order Model for Combustion Instability in a Two-Dimensional Duct with a Flameholder

Abstract

A reduced-order model for combustion instability in a two-dimensional duct with a flameholder is presented. A linear flame-response function for a premixed flame of arbitrary mean shape is derived using the G-equation approach. Perturbations consisting of coupled axial and transverse modes are superimposed on system mean flow conditions and analyzed for instability. Test cases involving variations of duct geometry, flameholder location, and mean flame shape are considered for evaluating the reduced-order model. Mean flow and temperature conditions andmean heat-release rate, needed as inputs to themodel, are obtained from highly resolved two-dimensional largeeddy simulation data for the same geometry. The pressure power spectrum from large-eddy simulation is available for two cases: 1) with the flameholder located symmetrically between the top and bottomwalls of the duct and 2) with the flameholder offset vertically by a small distance relative to the duct height. For the first case, the large-eddy simulation pressure power spectrum shows a dominant transverse instability mode that is also captured by the model. In the second case, large-eddy simulation shows that a small vertical offset damps the dominant transverse mode found in the zero-offset first case. The model also qualitatively supports this trend. For additional test cases in which large-eddy simulation data are not available, the model is seen to produce qualitatively consistent trends.