Examination of mode shapes in an unstable model combustor

The coupling between the fluid dynamics, heat addition, and the acoustics of a combustor system determine whether it is prone toward combustion instability. This paper presents results from a benchmark study of the eigenmodes in an unstable experimental combustor. The axisymmetric combustor configuration is representative of a number of practical systems and comprises an injector tube, geometric expansion into a combustion chamber, and a short converging nozzle. Instability limit cycle amplitudes ranged from 5% to nearly 50% of the mean 2.2 MPa pressure. Multiple harmonics were measured for the highly unstable cases. The model combustor was designed to provide a fairly comprehensive set of tested effects: sonic vs subsonic inlets; oxidizer tube lengths that were either quarter-wave, half-wave, or off-resonant acoustic equivalents to the combustion chamber; a significant injector mean flow with Ma∼0.4; and a varied combustion chamber length. The measured mode shape data were analyzed and reduced to provide comparison with results from a linearized one-dimensional Euler model, which included the effects of real boundary conditions, entropy generation, area change, and heat and mass addition, but did not include a model for unsteady heat addition. For low-amplitude instabilities, the measured resonance frequencies agreed with those calculated by the model for the injector tube-combustion chamber system. Resonance frequencies for the high-amplitude oscillation cases corresponded to the first longitudinal frequency of the combustion chamber and its integer multiples. Good quantitative agreement was obtained between computed and measured phase difference profiles, and mode envelopes agreed qualitatively. These results provide a basis for subsequent combustion response studies on the effects of unsteady heat addition.