Acoustic Modes in Combustors with Complex Impedancesand Multidimensional Active Flames

Abstract

two approaches for solving the corresponding nonlinear eigenvalue problem are proposed. The first one is based on an asymptotic expansion of the solution, the baseline being the acoustic modes and frequencies for a steady (or passive) flame and appropriate boundary conditions. This method allows a quick assessment of any acoustic mode stabilitybutisvalidonlyforcaseswherethecouplingbetweenthe flameandtheacousticwavesissmallinamplitude. The second approach is based on an iterative algorithm where a quadratic eigenvalue problem is solved at each subiteration. It is more central processing unit demanding but remains valid even in cases where the response of the flametoacousticperturbationsislarge.Frequency-dependentboundaryimpedancesareaccountedforinbothcases. A parallel implementation of the Arnoldi iterative method is used to solve the large eigenvalue problem that arises fromthespacediscretization ofthe Helmholtzequation.Several academicandindustrial testcasesareconsideredto illustrate the potential of the method.