The objective of this investigation has been to improve understanding of autoignition processes in nonpremixed flow fields of the types encountered in Diesel-engine ignition, through theoretical analyses that employ asymptotic methods of applied mathematics. The work was intended to develop formulas and equations that can be used in activities of applied research, such as code development, aimed atudproviding tools useful for the design of Diesel engines. The formulas may also be used directly for ignition estimates.Characteristic time scales were identified for these ignition problems. Their relative magnitudes were employed to define different regimes of ignition and to obtain simplified partial differential equations that describe ignition in these regimes. Effects of turbulence on ignition were addressed. Special attention was devoted to unsteady mixing layers, involving both variable strain and variable pressure, for which ignition-time formulas were derived. In addition, ignition analyses were completed for variable-volume chambers with arbitrary initial spatial variations of temperature and composition, to determine pressure histories produced by ignition-front propagation.udThese studies were based on one-step, Arrhenius approximations for the chemical kinetics and were restricted to ignition stages that precede ordinary flame propagation. Additional work considered triple-flame propagation that can odcur in mixing layers after ignition, with this same chemical-kinetic description, and asymptoticudanalysis of n-heptane ignition on the basis of a four-step, semi-empirical model for the chemical kinetics. In this latter study, the region of negative effective overalludactivation energy, between 800 K and 1100 K, was identified as exhibiting unusual ignition dynamics, and the asymptotic ignition-time formulas were shown to give good agreement with predictions of numerical integrations.udThis research has helped to strengthen the foundations of ignition theory for nonuniform media. It provided simplified descriptions of ignition processes that can beudemployed in studies of Diesel combustion that are oriented more towards development than are the present investigations. The asymptotic methods employed in this workudthus appear capable of providing quite useful results.
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