A multi-stage inverse integral method for deriving ignition delay correlation from autoignition experimental measurements

This work introduces a multi-stage inverse integral method to derive steady-state ignition delay time (IDT) correlations directly from transient experimental measurements, circumventing reliance on detailed chemical kinetic mechanisms. By inverting the conventional Livengood–Wu integral framework, the proposed method constrains the parameters of a physics-based, multi-stage IDT correlation model directly against experimentally measured non-reactive pressure/temperature histories and ignition times. A sequential optimization strategy is employed to efficiently extract correlation parameters from key experimental features, including first-stage pressure rise and multi-stage ignition delay times. The method is demonstrated for isooctane, yielding a global correlation that captures low-to-high temperature autoignition behaviour well, including negative temperature coefficient and two-stage ignition characteristics, across a wide range of pressures, temperatures, equivalence ratios, and dilution levels. This approach provides a robust, mechanism-independent pathway for developing high-fidelity IDT correlations tailored for autoignition predictions.