Propagation of Fronts in Porous Media Combustion

This research project is focused on mathematical analysis of the propagation and stability of fronts in a porous medium. The project is motivated by recent theoretical advances that revealed a number of new effects and regimes in porous media combustion, such as low-velocity (subsonic) detonation, deflagration to detonation transitions, and various types of instabilities. This work studies a model for combustion in porous media consisting of three degenerate parabolic equations for temperature, concentration of the deficient reactant, and pressure. The project investigates the long-time behavior of the combustion fronts, their stability, and bounds on propagation velocity. Stability will be explored by a combination of numerical and analytical tools. The project also studies the so-called high activation energy limit, as well as the transition from slowly propagating deflagration to detonation. Premixed gas combustion is the combustion of gaseous reactants that are perfectly mixed prior to ignition. The most distinctive feature of premixed combustion is its ability to assume a self-sustained reaction front propagating subsonically or supersonically at a well-defined speed. Combustion fronts constitute a truly fascinating dynamical system, displaying an amazingly rich variety of phenomena, such as non-uniqueness of possible propagation regimes, their birth (ignition) and destruction (extinction), chaotic self-motion and fractal-like growth, and various hysteretic transitions. The current project is concerned with the mathematical analysis of combustion front dynamics in a porous medium, involving evaluation of the propagation velocity, its limits, stability, and the transition from deflagrative to detonative combustion. The results of the work have potential application to engineering design of propulsion systems.