Analysis of knock onset based on two-dimensional direct numerical simulation and theory of explosive transition of deflagration

In this study, we analyzed data from a two-dimensional (2D) direct numerical simulation (DNS) that reproduced the knocking experiment in order to elucidate the knocking phenomenon. First, it was confirmed that the reaction front behavior in 2D DNS could be reproduced as a one-dimensional (1D) laminar premixed flame simulation at extreme conditions. Furthermore, a detailed study using a 1D laminar premixed flame revealed a strong relation between the timing of knock onset and the flame propagation limit of the 1D laminar premixed flame at elevated temperature and pressure conditions. To clarify this relation, we introduced the theory of “explosive transition of deflagration.” This theory shows that when the Lewis number is unity, the time evolution of the normalized fuel mass fraction and temperature in a 0D homogeneous ignition is equal to the temporal evolution observed in a 1D laminar premixed flame, if the spatiotemporal transformation is properly applied. Furthermore, the rate at which the normalized fuel mass fraction decreases in the preheat zone was found to depend on the Lewis number, and when the Lewis number is greater than unity, no flame structure exists above a certain threshold temperature. Finally, the mechanism of knock onset was explained by considering the theory of explosive transition of deflagration and explosive transition boundary plotted on a pressure-temporal diagram.