Turbulent nonpremixed combustion with local extinction and reignition is an important fundamental phenomenon that has many practical implications. The objective of the research reported in this thesis is to identify and understand the mechanisms that govern extinction and reignition by studying the kinematics of the stoichiometric mixture fraction isosurface (i.e., the flame surface). The configuration, area and the behavior of the flame surface can quantitatively describe the interaction of the flame with turbulent flow and thus the flame surface kinematics has a strong influence on the properties of the reactive scalars. One particular property of importance is the mean flame surface density [signma]. This study contributes to the determination of [sigma] by proposing three approaches for its measurement through the use of direct numerical simulations (DNS) data for the case of incompressible and isotropic turbulence. These direct and indirect approaches proposed for the computation and modeling of the time evolution of [sigma] are 1) direct numerical measurement, 2) theoretical prediction from the concept of level crossings with the application of Rice's theorem\cite{S.O.Rice1}, which leads to 3) two separate modeling approaches using statistical definitions and by balance equation of isoscalar surface area density. These approaches allow us to follow the growth of the surface due to local surface stretching by turbulence and its ultimate decrease due to molecular destruction. The statistical model fairly accurately predicts the evolution of [sigma]. We are also able to determine values of the principal terms in the evolution equation for [sigma], including the surface stretching term and the molecular destruction term. We find that the stretching and destruction term are approximately statistically independent of the isoscalar value of the surface. The difficulties in modeling of local flame extinction and reignition are demonstrated by evaluating the application of the steady-state flamelet (SFL) model. The transient effects (i.e., the lag of flame quenching behind fluctuations in the stoichiometric scalar dissipation rate X[subscript st] ) and the time lag of reignition relative to the relaxation of X[subscript st] are not considered by the SFL model. These are demonstrated by showing the mixing and reactive quantities along the stoichiometric mixture fraction contour lines. With the knowledge of the flame surface evolution and its properties, the mechanisms of local extinction and reignition can be directly investigated by the dynamics of flame hole (i.e., an extinguished flame surface) expansion and collapse. The flame surface is first resolved as a mesh of triangular surfaces within the three-dimensional DNS volume that represents the stoichiometric surface. A criterion is developed on this flame surface mesh to identify instantaneously local quenched regions and distinguish these from burning surface regions. Next, a new methodology is developed to numerically identify contiguous extinguished stoichiometric surface elements such that the size of a single flame hole can be identified. The new methodology is tested and found to be accurate. This numerical algorithm can provide rich geometric information on local flame hole structure and along with knowledge of the local reacting properties for each individual flame hole. The statistics of the geometric properties of the flame holes are then obtained. During the reignition process, the area size distribution of flame holes was found to be roughly invariant with time which results in an approximate time invariant average hole area. This appears to be due to the loss of small flame holes with time while larger holes become smaller. To first order, this process appears to approximate a self-preserving size distribution.

Lean burning of premixed gases is considered to be a promising combustion technology for future clean and highly efficient gas turbine combustors. Yet researchers face several challenges in dealing with premixed turbulent combustion, from its nonlinear multiscale nature and the impact of local phenomena to the multitude of competing models. Filling a gap in the literature, Fundamentals of Premixed Turbulent Combustion introduces the state of the art of premixed turbulent combustion in an accessible manner for newcomers and experienced researchers alike. To more deeply consider current research issues, the book focuses on the physical mechanisms and phenomenology of premixed flames, with a brief discussion of recent advances in partially premixed turbulent combustion. It begins with a summary of the relevant knowledge needed from disciplines such as thermodynamics, chemical kinetics, molecular transport processes, and fluid dynamics. The book then presents experimental data on the general appearance of premixed turbulent flames and details the physical mechanisms that could affect the flame behavior. It also examines the physical and numerical models for predicting the key features of premixed turbulent combustion. Emphasizing critical analysis, the book compares competing concepts and viewpoints with one another and with the available experimental data, outlining the advantages and disadvantages of each approach. In addition, it discusses recent advances and highlights unresolved issues. Written by a leading expert in the field, this book provides a valuable overview of the physics of premixed turbulent combustion. Combining simplicity and topicality, it helps researchers orient themselves in the contemporary literature and guides them in selecting the best research tools for their work.

The combustion of fossil fuels remains a key technology for the foreseeable future. It is therefore important that we understand the mechanisms of combustion and, in particular, the role of turbulence within this process. Combustion always takes place within a turbulent flow field for two reasons: turbulence increases the mixing process and enhances combustion, but at the same time combustion releases heat which generates flow instability through buoyancy, thus enhancing the transition to turbulence. The four chapters of this book present a thorough introduction to the field of turbulent combustion. After an overview of modeling approaches, the three remaining chapters consider the three distinct cases of premixed, non-premixed, and partially premixed combustion, respectively. This book will be of value to researchers and students of engineering and applied mathematics by demonstrating the current theories of turbulent combustion within a unified presentation of the field.

This thesis utilizes time-resolved particle image velocimetry (PIV) measurements to provide a detailed statistical characterization of the kinematic properties from a set of standard non-premixed flames, which serve as benchmark test cases within the turbulent combustion community. The flames under consideration are the well-characterized DLR CH4/H2/N2 jet flames operating at two Reynolds numbers, DLR A (Re = 15,200) and DLR B (Re = 22,800), where DLR A represents a robust flame condition and DLR B represents a flame near blowout with high degrees of local flame extinction. A qualitative and quantitative comparison between DLR A and DLR B is presented to understand the effect of Reynolds number variations and local flame extinction on turbulence statistics. Detailed data processing techniques to analyze the time-resolved, 2D PIV data have been developed and presented in this work. Radial profiles of the mean and RMS fluctuations of the velocity are presented and results from DLR A agree with previous point-based measurements giving confidence in the measurements and analysis. While the DLR flames are highly utilized test cases, no published velocity data from the DLR B flames is available and thus the current measurements extend the existing data set available for modelers.