1. Triggered longitudinal instabilities in a combustion chamber: role of acoustic and combustion nonlinearities.
- Author
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K. V., Swarnalatha and Rani, Sarma L.
- Abstract
Triggered instability is a nonlinear instability that may arise when finite-amplitude pulses are imposed on a combustor that is otherwise stable to infinitesimal perturbations. In this study, we investigate the role of acoustic and combustion nonlinearities in the occurrence of triggered longitudinal instabilities in a cylindrical combustion chamber. Using the Galerkin method of weighted spatial integration, we derive the nonlinear equations governing the time-dependent amplitudes of the longitudinal modes of the combustion chamber. The modal amplitude equations include quadratic and cubic acoustic nonlinearities, as well as combustion nonlinearities. The latter, arising from unsteady combustion processes, are represented using three separate models that include Crocco's pressure exponent–time lag model and two other nonlinear combustion response models. We first investigate whether a nonlinear instability may be realized when only the acoustic nonlinear terms are retained and the combustion nonlinearities are dropped. It is seen that large-amplitude pulses imposed on a stable fixed point can cause the system to evolve to another stable fixed point, with the implication that the acoustic nonlinearities indeed play a role in nonlinear instability. The inclusion of both acoustic and combustion nonlinearities did not significantly alter the nature of the nonlinear instability, at least for small values of the control parameter determining the magnitude of combustion nonlinearities. However, when both types of nonlinearities were included, perturbations of smaller magnitude were needed to trigger an instability than when only the acoustic nonlinearities were included. In addition to analyzing the two types of nonlinearities, we perform a systematic study of how their orders influence nonlinear instability. This entails retaining the quadratic or cubic acoustic terms in conjunction with the combustion nonlinearities from each of the three combustion response models. Nonlinear instability was observed when the quadratic acoustic terms were retained and cubic terms dropped, but no instability was obtained for the converse scenario. [ABSTRACT FROM AUTHOR]
- Published
- 2025
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