The inverse marching method-of-characteristics algorithm was extended to account for flows where finite-rate chemical reactions occur. The governing equations for an unsteady, inviscid, quasi-one-dimensional chemically reacting gas flow were reduced to ordinary differential equations using the method-of-characteristics. Utilizing these simplified ordinary differential equations, two inverse marching type algorithms—commonly known as interior point and outflow algorithms—were developed. The former resolves continuous regions in the flowfield representing rarefaction and weak compression waves. The latter, as the name implies, resolves outflow conditions at the exit of a computational domain. These algorithms incorporated an in-built subroutine to resolve the thermochemical state of the gaseous mixture and to evaluate the species source function while integrating the species continuity equation along pathlines. The reaction rates in the chemical source term were evaluated using a modified Arrhenius type relation, while the thermophysical properties of individual species were modeled using polynomial curvefits commonly used in the literature. The method-of-characteristics algorithms were then used to develop models of steady-state chemically reacting flows for which validation models exist in the literature. Validation cases reported here include supersonic combustion of stoichiometric oxyhydrogen in a one-dimensional duct, Lagrangian flow behind a strong normal shock wave traveling in air and gasdynamic expansion of air through a reflected shock tunnel nozzle. Results show that the new method-of-characteristics algorithms capture the chemically reacting flowfield in all these cases.
Jayamani et al. (Thu,) studied this question.