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# A predictive Livengood–Wu correlation for two-stage ignition

## Author(s): Pan, Jiaying; Zhao, Peng; Law, Chung K; Wei, Haiqiao

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 Abstract: 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. Publication Date: 2016 Citation: Pan, Jiaying, Peng Zhao, Chung K. Law, and Haiqiao Wei. "A predictive Livengood–Wu correlation for two-stage ignition." International Journal of Engine Research 17, no. 8 (2016): 825-835. doi:10.1177/1468087415619516 DOI: 10.1177/1468087415619516 ISSN: 1468-0874 EISSN: 2041-3149 Pages: 825 - 835 Type of Material: Journal Article Journal/Proceeding Title: International Journal of Engine Research Version: Author's manuscript

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