Steady and time-dependent laminar flames are computed using a damped, modified Newton's method. Research efforts are focused on two main areas:​ simulating time-dependent laminar flames with detailed chemistry and transport, and advancing the understanding of soot modeling in laminar flames. Toward an end goal of simulating sooting time-dependent flames, a modified fluid-dynamical formulation is developed and tested on steady flows, the sensitivity of a sectional soot model to transport effects is studied, and nonsooting time-dependent flames are computed and validated against experimental data.

A modification is introduced to the vorticity-velocity formulation, and, using the case of non-reacting steady incompressible pipe flow, it is shown that the modified formulation is better at conserving mass than the unmodified formulation. The modified formulation is applied to a steady laminar methane/air diffusion flame and to a periodically-forced time-dependent methane/air diffusion flame, and comparisons are made with experimental data to validate the model. Very good agreement is seen between numerical predictions and experimental measurements for temperature and major species.

A comparative study follows in which three different transport models are implemented for a variety of sooting ethylene/air flames. This study specifically investigates how transport modeling can affect predictions of soot concentration in counterflow and coflow ethylene/air flames using a sectional representation for spheroid growth. The transport models are applied to diffusion and partially premixed counterflow flames for a range of strain rates, and to a coflow diffusion flame with varying fuel/air ratios, and their effects on soot volume fraction predictions are quantified. It is shown that for some combustion regimes, higher-order transport modeling is necessary to predict soot volume fraction accurately.

The work culminates with a distributed-memory parallel computation of a sooting, time-dependent coflow diffusion flame, in which a periodic fluctuation is imposed on the fuel velocity for four different amplitudes of modulation. Due to the computational intensity of the problem, which would be intractable on a serial computer, the solution proceeds in parallel using strip domain decomposition over 40 CPUs. A full set of numerical predictions of time-resolved temperature, soot volume fraction, and species that contribute to the soot model is presented, and the effect of the oscillating fluid field on soot volume fraction is characterized.