This work involves the development of new mathematical theories of flames in burning regimes not previously treated, namely at high, and extreme (supercritical) pressures, as well as a plan to use a combination of analytical and numerical strategies to investigate the nonlinear dynamics of such flames. Recent experiments suggest that there is a stronger interaction between large-scale (hydrodynamic) and small-scale (diffusion) effects at high pressure, as compared to atmospheric conditions. It is proposed to more fully account for these interactions by developing new asymptotic models that allow for merging of these scales through certain mild restrictions on the small scale structures, and selective use of numerical strategies to address these features in simplified configurations. It is also proposed to develop new mathematical models of flames in supercritical fluids, i.e. fluids whose pressure exceeds the thermodynamic critical point. The physical and thermal properties of supercritical fluids are fundamentally different from a liquid or an ideal gas, and only recently have some of the distinguishing traits been identified as essential ingredients to be incorporated in formal theories. Multi-scale analysis will be used to develop simplified asymptotic models that incorporate these features, most notably a novel transport mechanism.
The main thrust of this work is to develop new mathematical theories of flames in high-pressure environments. Many practical combustion devices operate at high pressures, including internal combustion engines, propulsion systems, turbines, furnaces, and incinerators. Given the growing global concerns about energy, efficiency, and pollution, theories describing the fundamental burning characteristics in these systems are likely to have a significant impact on many future experimentation and engineering applications. When a fluid is subjected to extremely high pressures, it displays very peculiar properties that are intermediate to a gas and a liquid. In recent years, the odd properties of these fluids, called supercritical fluids or SCF's, have been exploited in a number of emerging technologies, e.g. remediation of hazardous waste in supercritical water, the design of the next generation of motors, and as an agent for catalytic activity. The present work will produce new mathematical theories that describe how combustion occurs in such fluids. Given the broad applications for SCF's, it is expected that the theories to result from this work will be relevant to a number of technologies outside the field of combustion, including supercritical fluid extraction and chemical processing.
