Chaotic modelling and control of combustion instabilities due to vaporization

In this paper, a state of the art LES algorithm is employed to validate an evaporation model to be employed in predictive modelling regarding combustion instabilities. Good agreement between the numerical predictions and experimental data is achieved. Additionally, transient sub-critical droplet evaporation is investigated numerically. In particular, a numerical method is proposed to capture the extremely important pressure–velocity–density coupling. Moreover, a discrete dynamic model accounting for both combustion and vaporization processes is developed. In terms of different bifurcation parameters relevant to either combustion or evaporation, various bifurcation diagrams are presented. As part of the nonlinear characterization, the governing process Lyapunov exponent is calculated and employed to analyze the stability of the particular dynamic system. The study has shown conclusively that the evaporation process has a significant impact on the intensity and nonlinear behaviour of the system of interest, vis-à-vis a model accounting for only the gaseous combustion process. Furthermore, a particular nonlinear control methodology is adopted to control the chaotic behaviour displayed by the particular aperiodic motions observed. This algorithm is intended to be implemented for control of combustion instability numerically and experimentally to provide a rational basis for some of the control methodologies employed in the literature.