Inverse Method-of-Characteristics Algorithms for Unsteady Gas Flows with Shifting Thermochemical Equilibrium

Abstract

Method of characteristics (MoC) algorithms were developed to evaluate quasi-one-dimensional, unsteady flows under thermochemical equilibrium. The effect of momentum losses were accounted through a simple, constant friction factor model. Heat losses were evaluated using the Reynolds analogy. For computational efficiency, changes in the gas state thermochemistry were evaluated through curvefits generated using the open-source toolkit Cantera. MoC algorithms developed here employed the inverse marching method and were capable of resolving various gasdynamic phenomena such as weak compression/rarefaction waves, contact surfaces and shock waves. These MoC algorithms were then used to develop reduced-order models representing the gasdynamics of two impulse facilities -- an expansion tube and a detonation-driven shock tube. Expansion tube calculations did not considered losses, so that they could be validated against an equilibrium Riemann solution. The detonation-driven shock tube model focused on the endwall loading in the damping section of an upstream mode detonation tube. For this case, losses were considered and thus experimental results were used to calibrate the friction factor and validate the MoC model.