Mathematical Sciences: Mathematial Modeling and Dynamics of Premixed Flames as Hydrodynamic Discontinuities

9400810 Bechtold The investigator proposes to study several fundamental aspects of premixed flame propagation. Of primary concern will be flames whose characteristic dimension is much larger than their thermal thickness so that the flame can be viewed as a hydrodynamic discontinuity. Such flames have taken on new significance in recent years due to their role in modeling turbulent combustion. In one phase of the project, hydrodynamic flame models will be used to study the dynamics and extinction characteristics of premixed flames in unsteady environments. The investigator also proposes to extend existing flame models that have employed one-step-chemistry approximations by considering a two-step mechanism that better captures the branching-recombination nature of flames. The methods that will be used include asymptotic and perturbation techniques together with numerical computations. This work will provide a better understanding of flame-flow interactions which are an important feature of turbulent combustion. Nearly all combustion devices of practical importance operate in a turbulent combustion regime. This includes spark-ignition engines, incinerators, rockets, forest fires, etc. The complexities inherent in each of these systems have prevented a deep understanding of turbulent combustion. However, a partial understanding of this topic can be achieved by first comprehending various fundamental aspects that are common in many of these systems. For example, a turbulent flow field is characterized by random spatial and temporal variations, and a flame situated in such a flow will get stretched and distorted. In addition, the heat released by the combustion process will affect the flow field. In this work the investigator proposes to study these interactions theoretically. There are two main themes: (i) to examine flame response in unsteady (time-dependent) flows; and (ii) to extend existing flame models to include additional eff ects due to chemical reaction. This work will provide a better understanding of flame-flow interactions which are an important feature of turbulent combustion.