Application of a Generalized Instability Model to Industrial Annular Combustion Chambers

This study presents a method of analyzing the stability of annular combustion chambers using a physics based generalized instability model (GIM). This analytical model is used to study combustion instabilities using the solution of an inhomogeneous pressure wave equation by a modified Galerkin method and allows the combination of geometric and flow effects along with unsteady heat response functions to parametrically study the thermoacoustic stability of a given system. GIM has been extensively validated and utilized for cylindrical geometries to determine the mode shapes, frequencies, and stability of these simplified models. The current work extends the applicability of GIM to annular geometries by incorporating both the ordinary Bessel and Neumann functions into the solution of the cylindrical wave equation, as well as a generic unsteady heat release model. This extension allows for the solution of annular geometries to determine the frequencies and linear growth rates of these systems. Results are given for a set of generic annular geometries and verified against finite element solutions in which the effects on frequency from changes in geometry and mean flow properties are investigated. GIM is then used to predict frequencies measured during engine operation as well as stability trends.