Hot spot ignition: The Newtonian limit (Q2748114)

Initiation of gaseous detonations (a problem of evident practical interest) is analysed analytically for a one-dimensional confined domain with a smooth thermal gradient. Euler equations with chemical source terms corresponding to one-step chemistry with Arrhenius kinetics are considered. The high-temperature regions lead to local hot spots that preferentially promote ignition. In this paper, the ignition onset is studied through a combination of high activation energy asymptotics and the Newtonian limit \(p\) to \(g M- 1,\) in which a reaction front is born. The front is seen to be associated with a spatially evolving logarithmic singularity of temperature and pressure, corresponding to the local ignition time. The speed of the front remains supersonic, although the front decelerates rapidly as it crosses the exponentially thin zone away from the initiating hot spot. Explicit results for the flow field and the singularity path are obtained and are found to agree well with full numerical calculations for specific initial temperature profiles.