Numerical solution technique for transient, two-dimensional combustion with multi-step kinetics

Abstract

For numerical combustion problems, computational time and storage requirements scale approximately with the square of the number of chemical species. Therefore, the most difficult cases that can be solved using elementary chemical kinetics have been one-dimensional transient and two-dimensional steady formulations. This limitation and the established shortcomings of global reactions have encouraged recent development of simplified but accurate multi-step kinetics schemes. The present investigation uses one of these simplified reaction mechanisms to determine if solution of a multi-dimensional, transient, reacting flow problem is possible without resort to overly simplified, global kinetics. A laminar, two-dimensional, transient, viscous flow model has been developed which incorporates a chemical kinetics mechanism for propane consisting of four reversible reactions and only seven species. The model is used to investigate the initiation and propagation of a flame subjected to heat transfer, wall motion and shear flow. The mathematical model simulates the physical and chemical processes occurring near the centerline of a thin-gap formed by two cold, solid surfaces as one surface moves first toward and then away from the other. The governing conservation equations for mass, momentum, energy and chemical species are simplified using the thin-gap approximation. The problem is transformed to eliminate the continuity equation by using a compressible stream function formulation. The resulting mixed order system of nonlinear, boundary value problems is solved by a semi-discrete numerical procedure which employs a finite element collocation method and adaptive grid technique. Both non-reacting and reacting cases are solved to demonstrate the effect of the shear flow and cold surfaces on the flow field and on the developing laminar flame. The results reveal a complex flow with numerous substructures caused by the interaction of the developing flame with cold fluid trapped in the boundary layer adjacent to the stationary wall. The reacting flow results represent the first calculation of a laminar, reacting flow in a moving wall geometry using nonequilibrium, multi-step chemistry while simultaneously resolving the momentum and thermal boundary layers.