Real gas effect on ignition in ideal and non-ideal reactors

We studied the real gas effect on the ignition characteristics in chemical reactors with one-step irreversible reaction. The real gas effects were characterized by the inter-molecular attraction term (\(\alpha \)) and the finite molecular volume term (\(\beta \)). The Noble-Abel and van der Waals equations of state were employed to derive non-dimensional reactor models. In addition to ideal reactors, i.e., constant volume and constant pressure, non-ideal reactors that account for the non-ideal pressure variation in shock tube and rapid compression machine were also considered. For all reactors, low value of \(\alpha /\beta \) and high value of \(\beta \) (approximately \(\alpha /\beta <{{1.0}}\) and \(\beta >{{0.1}}\)) induce a decrease of the ignition delay-time, while high value of both \(\alpha /\beta \) and \(\beta \) (approximately \(\alpha /\beta >{{2.0}}\) and \(\beta >{{0.1}}\)) induces an increase of the ignition delay-time. The variations of the ignition delay-time induced by real gas effects are mainly related to the change of the fugacity coefficient with \(\alpha \) and \(\beta \). Additional contributions are due to the real gas heat capacity at constant pressure when considering a constant pressure reactor and to non-ideal volume variation when considering non-ideal reactors. The impact of various parameters was also investigated, including the heat capacity ratio of perfect gas, the reduced activation energy of the one-step reaction, and the heat content of the mixtures. Comparison with simulation performed with detailed reaction mechanisms and considering real gas models demonstrates that the present approach constitutes a rapid and simple, yet qualitatively or even quantitatively accurate method to assess the need of accounting for real gas effects to model chemical kinetics under high-pressure conditions.