18. Characterization of Turbulent Combustion Systems Using Dynamical Systems Theory

Turbulent combustion which is ubiquitous in all real engines in power and propulsion industries has inspired the combustion community to a great extent in recent years. Turbulence being the most significant unresolved problem gets more complicated by the interaction with combustion as combustion involves a large number of chemical reactions occurring at different time scales. A researcher often focuses on some specialized problems of turbulent combustion as it has many different aspects to investigate. One such challenging aspect of turbulent combustion is combustion dynamics. Many such facets of combustion dynamics have been understood through modelling, simulation and experiments. The present chapter proposes a survey of combustion dynamics which has been addressed under the parlance of dynamical systems theory. More recently, combustion instability in turbulent combustors such as modern low-\(NO_x\) gas turbine has gained a lot of attention. The stable state is generally characterized by combustion noise which is generated by turbulent reactive flow. A transition occurs from combustion noise to combustion instability through a dynamical regime called intermittency. Combustion instability is, in general, detrimental for all combustion systems except pulse combustors where combustion instability is deliberately maintained for better performance. The dynamical transition in pulse combustor has also been analyzed both theoretically and experimentally. The analysis of a nonlinear analytical model using dynamical systems theory reveals the regime of limit cycle oscillations, Hopf bifurcation, period-doubling bifurcations and so on. A case study of numerical continuation in pulse combustor model will be explained in detail at the end of this chapter.