Shock tracking in unsteady, reacting flows using the method of characteristics

Using the method of characteristics, a 1-dimensional model has been developed to examine unsteady, reacting flow properties in the subsonic, transonic, and supersonic regions with second order accuracy. A four-equation Euler model with a superelliptic approach to temperature variation, previously explored by Reinbacher and Regele (2017) is being utilized with a one-step hydrogen-air combustion reaction to examine the flow’s local Mach number, pressure, and temperature as the combustion advances in time. The method of characteristics allows us to determine the location and time where a shock appears in the 1-D flow and subsequently track its propagation through the flow. By adjusting dimensionless parameters that include the Damkohler number and dimensionless reaction enthalpy within the model as well as maximum temperature and initial fuel concentration, the formation of the shock can be tracked in time and space. Our initial results show agreement between this low order method when compared to CFD results that appear in the literature.