Characteristic linear dynamics of kinetically controlled burning. Part I: Traditional single-reactor models

We examine combustion controlled predominantly by chemical kinetics using various incarnations of the well-stirred reactor. The model is presented in canonical forms exhibiting first- and higher-order responses to both flow rate and mixing perturbations. These behaviors are completely characterized by physically relevant dimensionless quantities. Furthermore, because of their relevance to thermo-acoustic instabilities, we generate quasi-minimal degree-of-freedom formulations relating inlet conditions and heat release rate for both single-step and generalized multi-step chemical kinetic models.