| The focus of this dissertation is on modeling and analysis of prototype problems of reacting flows interacting with surfaces or in porous media. In particular, flammability limits of gaseous and condensed fuels, complex nonlinear dynamics of flames, and deposition of thin membranes within porous substrates have been studied.; The regime of self-sustained methane-air combustion has been first identified in the parameter space of strain rate-fuel flow rate, for a gaseous diffusion flame. Additionally, the regime of absolute stability, where heat losses at the surface do not extinguish a flame, has also been mapped. It has been found that the critical extinction mass pyrolysis rate is insensitive to thermo-transpo-kinetic details at high values of modified Damköhler numbers, whereas is very sensitive at low values. Selected comparisons with experimental results have been made to validate our numerical predictions.; The regime of oscillatory instabilities in hydrogen-air combustion was systematically mapped for the first time for premixed and diffusion flames. It has been demonstrated that premixed hydrogen-air flames exhibit complex dynamics including chaos at high pressures. The interplay of autocatalytic chemistry with transport, reaction exothermicity, and flow, inherent to distributed flames, has been identified to be the cause for the observed chaotic dynamics.; Finally, a multiscale computational framework for deposition of films within porous substrates is developed and applied to the opposed flow geometry. The model captures transport of reactants through the pores described by the dusty gas model, homogeneous reaction of the organometallic precursor producing an intermediate species, nucleation (treated stochastically), and growth of the film as a moving boundary problem. Adaptive mesh refinement is used to resolve length scales varying from nanometers to one millimeter. The numerical results provide insight into how to confine thin films within substrates and control their thickness. For example, it has been found that the location of the metal deposit within the porous substrate is essentially determined by the relative concentrations of H2 and the organometallic precursor. Additionally, it is shown that the interplay of nucleation and growth kinetics determines the morphology of the deposit at short time scales. |
