Modeling Hypergolic Ignition Based on Thermal Diffusion for Spherical and Cylindrical Geometries

A linear model for predicting the ignition delay time of hypergolic ignition is presented based on thermal diffusion theory. The heat released by the hypergolic reaction is assumed to diffuse through a given length scale while being governed by a heat source in the form of an Arrhenius equation. A linearized approach is used to reach analytical expressions for the ignition delay times, defined when the temperature change at the reactants interface drastically increases, diverges, or tends toward infinity. Ignition delay times for three different geometries, cartesian, cylindrical, and spherical, are derived and compared. The results show that, for spherical coordinates, the ignition depends on a critical condition, which is based on material and chemical properties and geometry. A prediction of the ignition condition for all cases where one of the reactants is a droplet/particle is given. The ignition process is analyzed based on non-dimensional parameters in order to understand the behavior of the temperature change during ignition. The results obtained are consistent with results presented in the literature. In addition, a prediction for ignition delay times is provided.