A low order transient approach to modeling hot spots

A method of characteristics algorithm built on a four-equation Euler model coupled with one-step reaction chemistry has been developed to study one-dimensional, unsteady, reacting flows. The focus of the current research is in the progression of hot spots which are of particular interest due to their key role in the deflagration to detonation transition (DDT). When using a linear or super-elliptical model to simulate a hot spot’s initial temperature gradient and a simplified hydrogen-air combustion reaction, the initial progression of the flow can be followed until shock initiation, at which point the shock can be tracked in space and time along with the reaction front. Cases with 1) initial decoupling of the reaction front and leading compression wave, as well as cases with 2) initial coupling and 3) lasting coupling throughout the ignition process, can be explored with this model. The method of characteristics model allows for accurate tracking of small disturbances in the flow and preliminary comparisons between our model and CFD simulations show acceptable agreement.