Triggered Instabilities in a Rocket Motor. Part II. One the Role of the Order of Acoustic and Combustion Nonlinearities

In the companion presentation, we demonstrated that triggered longitudinal instabilities can be realized when the governing equations containing only the acoustic nonlinearities were used to evolve finite-amplitude perturbations imposed on the base state of the combustor. We also identified the specific roles of acoustic and combustion nonlinearities in the occurrence of triggering. In the current study, we shift our focus toward understanding how the orders of the two types of nonlinearities influence stability. Three separate combustion response models are considered, which give rise to different functional forms and orders of combustion nonlinearities---fifth order being the highest. We perform a systematic analysis of the effects of including the quadratic and/or cubic acoustic terms in conjunction with the combustion nonlinearities arising from each of the three models. Triggering was observed when the acoustic quadratic terms were retained and the cubic terms dropped, but was not obtained for the reverse scenario. Triggering also arises when all acoustic and combustion nonlinearities are included. It is seen that that the stability behavior when considering all acoustic terms with the fifth order combustion model is only marginally different than with the third order model.