A statistical framework for modeling and simulation of direct initiation

Prediction of direct initiation (DI) of detonation in a fuel-air mixture is hindered by the probabilistic nature of the outcome, which is a function of many variables including composition, temperature, pressure, and ignition energy. This paper presents a statistical surrogate model of the probability of direct initiation as a function of the latter three variables for stoichiometric mixtures of ethylene and air. An idealized 2D piston-driven detonation tube was simulated at different conditions and diaphragm burst pressures and the database of DI outcomes was used to train a radial basis function neural network (RBFNN). The surrogate model identified the manifold of 50% DI probability and expressed the fundamental outcome variability near the threshold. The necessary ignition pressure showed a negative exponential dependence on temperature and a complex dependence on pressure. The reaction speed and detonation cell size were also obtained at every case for validation and verification, and a variation of the Cellpose-SAM neural network was used to automatically identify the detonation cells in 355 numerical soot foils. The corresponding detonation cell sizes were several times smaller than predicted by empirical correlations, indicating that numerical underprediction of cell size also results in underprediction of critical energy. The results also show that critical energy does not correlate with detonation cell size when compared at different pressures. The framework used in this study is generalizable to other variables that influence DI and can be used to study and optimize variations in composition and configuration of the ignition system. This paper presents the first effort to use numerical simulation and machine learning to predict the probability of detonation in a complex configuration. The probabilistic forecast reflects the intrinsic variability of detonation and offers a more repeatable prediction than simulations of individual events. The rigorous data-driven approach also enables identification of trends and quantification of accuracy.