Abstract
Three techniques which employ different approaches for obtaining a method of characteristics solution for chemical non-equilibrium flows are reviewed and compared. Two features of the solution process are evaluated to determine their effect on the accuracy of the solution. The first aspect to be considered is the integration of the stiff conservation equations in a unit process. A new fifth-order accurate, multi-step integration routine is contrasted with a first-order accurate, single-step forward differencing scheme. The second comparison is designed to determine if a solution of the flowfield along continuous streamlines is superior to one along discontinuous segments of the streamlines. Tests are performed, using a chemical model describing the supersonic combustion of H2-air. Calculations of single unit processes are used to validate the techniques and to determine suitable grid sizes. Solutions for constant area duct flow show that the techniques which use the multi-step integration routine are more accurate. Results from the constant area duct test, for an initial pressure of 3.685 atm, show that a method of characteristics technique which utilizes continuous streamlines is able to converge at a grid size two orders of magnitude larger than that needed by a technique which uses discontinuous segments of streamlines.
Convergence of an accurate scheme for first order quasi linear equations