Integral method solution of time-dependent strained diffusion-reaction layers with multistep kinetics

Multiple coupled chemical reactions occurring within strained diffusion layers are key to a wide range of reactive flow problems. An integral approach is presented here to allow calculations of global properties of such reactive layers for complex multistep chemical kinetics and time-varying strain rates. The infinite-degree-of-freedom partial differential equations (PDEs) governing the dynamics of the species concentration profiles for reactants, intermediates, and products as well as the temperature are projected onto a set of ordinary differential equations having just a few degrees of freedom for the evolution of integral moments of these profiles. The presence of multistep reaction kinetics leads to a set of highly coupled nonlinear moment equations. Numerical solutions are presented for four-step methane-air kinetics coupled with thermal nitric oxide kinetics and are compared with direct solutions of the original PDEs. Some properties and numerical illustrations of key features of the internal layer structure and global flame properties, including the extinction phenomenon characteristic of large Zel'dovich number reaction kinetics, are discussed. The method presented brings comparatively detailed parametric studies of such problems within reach of rather modest computational requirements.