This research aims to investigate the nonlinear dynamics of the non-reacting jets and non-premixed lifted jet flames. The goal is to understand better how the flow system dynamics change over time and identify the path toward unwanted conditions such as flashback, extinction, or blowout to limit combustors' dynamical failure. The existence of these undesirable conditions is bound to the fluid's history, meaning that initiated perturbation may persist in the system for time scales comparable to large-scale flow timescales. Hence, the notion is to utilize jet and jet flames as a study test case to work out how the flow evolves dynamically with the hope of understanding how to limit occurrences of the chaotic unwanted condition. Initially, planar particle image velocimetry has been used for the development of the methodologies. I have used planar data to investigate the nonlinear dynamics of non-reacting turbulent jets, with a low-to-moderate Reynolds number using the single-trajectory framework and ensemble framework. I have used Lyapunov exponents to calculate the spectra of scaling indices of the attractor. Then, I used Lagrangian Coherent Structures (LCSs), which are defined as manifolds that are locally Euclidean and invariant, to study the relationship between Lyapunov exponent changes with flow topological features. These LCSs behave as hypersurfaces with maximally repelling or attracting properties. These various methodologies were used to investigate flame-turbulence interaction in lifted jet flames. The Lagrangian framework is shown to be effective at revealing the kinematics associated with flame-turbulence interaction. The LCSs' time history represents how eddy structures interact with the flame and highlight their role in the dynamics of the lifted jet flames. Finally, I have investigated the flame and turbulence interaction using high-speed luminosity imaging and simultaneous three-dimensional particle image velocimetry. The three-dimensional Lagrangian structures provide us a more detailed flow-flame interaction. It is shown that the flow features associated with attracting LCSs can create a barrier attracting the flame that makes the flame move upstream. In contrast, the presence of repelling LCSs near stationary flames breaks the balance between the gas velocity and flame propagation speed, causing the flame to become non-stationary and move downstream. It was also found that the repelling LCSs induce negative curvature on the flame surface whereas pushing the flame toward the products. However, the attracting LCSs induce positive curvature on the flame surface and draws the flame toward the reactants

This book focuses on developing strategies for ultra-lean combustion of natural gas and hydrogen, and contributes to the research on extending the lean flammability limit of hydrogen and air using a hot supersonic jet. The author addresses experimental methods, data analysis techniques, and results throughout each chapter and: Explains the fundamental mechanisms behind turbulent hot jet ignition using non-dimensional analysis Explores ignition characteristics by impinging hot jet and multiple jets in relation to better controllability and lean combustion Explores how different instability modes interact with the acoustic modes of the combustion chamber. This book provides a potential answer to some of the issues that arise from lean engine operation, such as poor ignition, engine misfire, cycle-to-cycle variability, combustion instability, reduction in efficiency, and an increase in unburned hydrocarbon emissions. This thesis was submitted to and approved by Purdue University.