UC San Diego

The objective of this work is to investigate theoretically two different problems of interest in Combustion. First, autoignition in hydrogen-oxygen systems above crossover temperatures and under various conditions of pressure and composition is addressed computationally and by asymptotic methods. Different descriptions of the detailed chemistry are evaluated through comparison of computed and measured ignition times, and a balance between accuracy and simplicity is struck in selecting rate parameters to be used in investigating reduced chemistry. For isobaric, homogeneous, and adiabatic mixtures, only five elementary steps suffice to describe accurately ignition over the range of conditions addressed, which allows the derivation of explicit formulas for the induction time by neglecting heat release and reactants consumption. Further reduction of the chemistry to two overall steps, is used to include the effect of the energetics in the temperature-dependent initiation and branching rates. In this approach, an asymptotic analysis for high activation energy of the branching step is developed for predicting ignition times of branched-chain explosions on the basis of a criterion of thermal runaway. The second study addresses the vaporization of a droplet in rectilinear motion relative to a stagnant gaseous atmosphere for the limit of low Reynolds numbers and slow variation of the droplet velocity. A formal asymptotic analysis is performed, showing that, under the conditions addressed, there is an inner region in the vicinity of the droplet within which the flow is nearly quasisteady except during shorts periods of time when the acceleration changes abruptly and a fully time-dependent outer region in which departures of velocities and temperatures from those of the ambient medium are small. Matched asymptotic expansions, followed by a Greens-function analysis of the outer region enable expressions to be obtained for the velocity and temperature fields and for the droplet drag and vaporization rate. The results are applied to problems in which the droplet experiences constant acceleration, constant deceleration and oscillatory motion. The results, which identify dependences on the Prandtl number and the transfer number, are intended to be compared with experimental measurements on droplet behaviors in time- varying flows