Theoretical analysis on detonation initiation induced by thermal nonuniformity in a supersonic flow

Detonation initiation in a supersonic reactive flow constitutes a crucial problem in fundamental combustion research and meanwhile receives great attention in the application of detonation-based propulsion systems. In this paper, we conduct theoretical analysis on detonation initiation induced by thermal nonuniformity. The underlying mechanism for detonation initiation is attributed to the self-strengthening coupling between the reaction front and the induced shock wave. A detonation initiation factor is introduced to quantify the capability of the thermal nonuniformity in causing detonation initiation. The initiation factor changes nonmonotonically, with the temperature difference describing the thermal nonuniformity. We find that there exist three regimes of detonation initiation. A threshold temperature difference of the thermal nonuniformity below which detonation initiation cannot take place is identified. Additionally, it is found that the temperature profile of the thermal nonuniformity has a substantial impact on detonation initiation. The creation of an additional induced shock wave on the reaction front due to the downward convex temperature profile significantly improves the initiation condition for weak thermal nonuniformities with relatively small temperature difference. Moreover, two-dimensional analysis is also conducted, considering the convective transport in the transverse direction. It is shown that the transverse heat transfer reduces the curvature of the reaction front, which promotes (inhibits) detonation initiation for strong (weak) thermal nonuniformity with large (small) temperature difference. In the present analysis, we provide useful insights into detonation initiation in a supersonic reactive flow.