Numerical simulation of high speed chemically reacting flows

A single step second-order accurate flux-difference-splitting method has been developed for solving unsteady quasi-one-dimensional and two-dimensional flows of multispecies fluids with finite rate chemistry. A systematic method for incorporating the source term effects into the wave strength parameters of Roe's linearized approximate Riemann solver is presented that is consistent with characteristic theory. The point implicit technique is utilized to achieve second-order time accuracy of the local area source term The stiffness associated with the chemical reactions is removed by implicitly integrating the kinetics system using the LSODE package. From the implicit integration, values of the species production rates are developed and incorporated into the flux-difference-splitting framework using a source term projection and splitting technique that preserves the upwind nature of source terms.; Numerous validation studies are presented to illustrate the capability of the numerical method. Shock tube and converging-diverging nozzle cases show the method is second order accurate in space and time for one-dimensional flows. A supersonic source flow case and a subsonic sink flow case show the method is second order spatially accurate for two-dimensional flows. Static combustion and steady supersonic combustion cases illustrate the ability of the method to accurately capture the ignition delay for hydrogen-air mixtures.; Demonstration studies are presented to illustrate the capabilities of the method. One-dimensional flow in a shock tube predicts species dissociation behind the main shock wave. One-dimension flow in supersonic nozzles predicts the well-known chemical freezing effect in an expanding flow. Two-dimensional cases consisted of a model of a scramjet combustor and a rocket motor nozzle. A parametric study was performed on a model of a scramjet combustor. The parameters studied were; wall angle, inlet Mach number, inlet temperature, and inlet equivalence ratio. The scramjet case demonstrates the usefulness of the method as a predictive tool for reacting flows. The rocket motor nozzle case demonstrates the capability of the method to handle mixed subsonic/transonic/supersonic flow environments. Five different chemical reaction mechanisms were studied illustrating the flexibility of the method.