A Nonlinear Model for Combustion Instability: Analysis and Quenching of the Oscillations

Abstract

PreludeIt is a great pleasure for us to contribute to this book dedicated to Alberto Isidori on the occasion of his sixty fifth birthday. It is also, for the first author, the occasion to acknowledge a very long period of useful and pleasant exchange which started in 1973 (bilinear systems) and has continued through the years on various specific subjects.The important contributions of Albereto Isidori in the control of nonlinear systems have had a tremendous impact in the control community. Feedback linearization was one of the important subjects developed by Alberto. While the oscillatory nonlinear system considered in this contribution requires specific techniques for its analysis, still a feedback linearization is used for quenching the oscillations.

On the dynamics of flame images identified through computer vision and modal methods

“…Several researches had been undertaking the task of modeling the flame through an analytical standpoint. According to Landau et al [3], combustion instability phenomena can be explained, in most cases, by an unsteady flame that generates pressure waves by heat transfer process, then, these waves are reflected at the walls of the combustion chamber to interact back with the flame itself. In other words, it is a positive feedback coupling between the heat release process and acoustics of the chamber.…”

“…A particular model from a second-order ordinary differential equation that combines heat released by the flame and acoustic pressure generated by the combustion process inside the chamber received special attention over the last decades [3][4][5][6][7][8][9][10][11][12]. It is important to notice that the works of Bouziani et al [8][9][10] and Landau et al [3] culminated in an analytically tractable model with a Van der Pol-based formulation that could explain the coexistence of two distinct nonharmonic frequencies that were observed experimentally. Although these researches have brought remarkable results on proposing a model that could explain the dynamics of the flame, it is valid only for a narrow band of equivalence ratio values and there are some difficulties related to obtaining model's parameters that still limit its application.…”