A predictive Livengood-Wu correlation for two-stage ignition

The Livengood-Wu correlation has been widely used to predict the state of auto-ignition in internal combustion engines, although its application to two-stage ignition processes remains unresolved. In this study, the original Livengood-Wu integral is extended to such two-stage ignition process and applied to simulations of typical operations within homogeneous charge compression ignition engines. Specifically, based on recent understanding of the global and detailed kinetics of low-temperature chemistry leading to ignition, simplified Arrhenius-based global reaction expressions were developed for both stages of constant-state auto-ignition. It is shown that the original Livengood-Wu integral works well for the first-stage ignition delay, as demonstrated in previous studies. Furthermore, by also accurately describing the cool flame temperature and pressure increment at the end of the first-stage ignition, the second-stage ignition delay can in addition be coupled with the first-stage ignition and predicted satisfactorily with a second integral. This formulation is then applied to extensive homogeneous charge compression ignition engine operation conditions, showing satisfactory predictive capability.