Analyzing the effects of temperature on soot formation with a joint volume-surface-hydrogen model

The intent of the current work is to present and further validate a new tri-variate model for the formation of soot particles, to apply this model in analyzing the effects of temperature on the formation and growth of soot, and to compare the findings with the present understanding derived from numerous experimental studies. In this novel model, a particle is represented as a fractal shaped aggregate and is described by three independent quantities: the volume, the surface area, and the number of hydrogenated sites (or active sites) on the surface. The introduction of this third variable allows for a better description of the surface reactivity at high temperatures. This approach is extended by a model for the total carbon-to-hydrogen (C/H) ratio of the particle. The model is validated first in high temperature premixed ethylene flames, premixed benzene flames, an acetylene counterflow diffusion flame, and toluene pyrolysis in shock-tubes. Then, the soot volume fraction is computed for a series of atmospheric laminar ethylene premixed flames with varying flame temperatures. The soot model is shown to reproduce the well known bell-shaped temperature dependence of soot volume fraction, which was found in many experiments. It is observed that nucleation is the largest contributor to soot volume fraction at low temperatures while growth by surface reactions is more important at higher temperatures. The surface reactivity and the volumetric carbon-to-hydrogen ratio (C/H) are also computed as a function of temperature. The surface reactivity is found to depend not only on the temperature but also on the particle size and the residence time in the flame. Finally, as observed experimentally, the C/H ratio is found to be essentially constant and close to unity for low temperature flames and increases with residence time in high temperature flames.