Simulation of the Transient, Compressible, Gas-dynamic Behavior of Catalytic-combustion Ignition in Stagnation Flows

This paper develops and uses a computation model to explore the transient ignition dynamics of catalytic combustion in a stagnation-flow configuration. The analysis considers the elementary heterogeneous chemistry associated with catalytic behavior at the surface. It also considers gas-dynamic effects in the boundary layer, including temporal and spatial pressure variations. The gas-dynamic effects are included through the axial momentum equation, which has been neglected in previous analyses of unsteady stagnation flows. In addition to the physical interpretation of ignition transients, the paper presents a mathematical and computational analysis and comparison of the constant-pressure and compressible stagnation-flow equations. The constant-pressure equations, as commonly formulated and used, are a system of differential-algebraic equations (DAE) that have an index greater than two. This high-index behavior is responsible for severe numerical difficulties in regions of fast transients or stringent numerical error control. This paper relaxes the constant-pressure assumption using a compressible-flow formulation, which extends the range of physical validity and reduces the index of the transient stagnation-flow problem while preserving stagnationflow “similarity.”