New quasi-steady-state and partial-equilibrium methods for integrating chemically reacting systems.

Abstract

We present new quasi-steady-state (QSS) and partial-equilibrium (PE) methods for integrating systems of ordinary differential equations (ODEs) that arise from chemical reactions. These methods were developed for use in process-split reacting-flow simulations. The new QSS integrator is a second-order predictor-corrector method that is A-stable for linear equations. The method is accurate regardless of the timescales of the individual ODEs in the system and works well for problems typical of hydrocarbon combustion. The method has very low start-up costs, making it ideal for process-split reacting-flow simulations which require the solution of an initial-value problem in each computational cell in the flowfield for every global timestep. For problems of extreme stiffness, PE tools can be used in combination with the QSS integrator. PE methods remove the fastest reactions in the mechanism from the kinetic integration when their effects can be calculated using algebraic equilibrium constraints. Conservation constraints are used to write an ODE for the reaction's progress variable. The solution of this equation provides a new method for identifying reactions in equilibrium. A systematic method for finding a set of conserved scalars for an arbitrary group of reactions is presented, and this method is used to eliminate reactions that produce redundant equilibrium constraints. Since the equilibrium reactions must compensate for changes in the system that disturb their equilibrium, the equilibrium source terms are not forced identically to zero. Equilibrium is imposed by driving these source terms to the average value required to compensate for the perturbations caused by the other processes. Integration results for a cesium-air mechanism, a hydrogen-air mechanism, and a thermonuclear mechanism used in astrophysics are presented. One-dimensional flame and detonation results are presented for a single-step hydrogen mechanism and the thermonuclear mechanism, respectively. The new QSS method outperforms the integrator CHEMEQ in speed, accuracy, and stability, and is recommended for reacting-flow applications in the stiffness range of typical hydrocarbon combustion problems. The new PE tools broaden the range for which a partial-equilibrium calculation will maintain the accuracy of the solution.