Investigation of the Livengood-Wu integral for modelling autoignition in a high-pressure bomb

The reaction progress variable, which is widely used in premixed and diffusion combustion studies, comprises a set of pre-selected intermediate species to denote reaction progress. Progress towards autoignition can also be traced by the Livengood–Wu (LW) integral. Autoignition occurs when the LW integral attains a value of unity. This concept is further explored by applying it to an inhomogeneous mixture scenario, to determine the time and place of autoignition occurrence. A semidetailed mechanism (137 species and 633 reactions) for n-heptane/iso-octane/toluene is used in this study. Two numerical schemes based on the LW integral are proposed and incorporated into a computational fluid dynamics platform, to model autoignition in a 3D configuration, when a spray is injected into a constant volume bomb under diesel engine conditions. Tabulated chemistry, a traditional method of modelling autoignition using information from pre-calculated igniting diffusion flames, is also used for comparison purposes. The associated predicted pressure profiles are compared with experimental measurements.