The effect of imperfect mixing on stirred combustion reactors

Abstract

Mixed gas reactors, even when special pains have been taken to ensure good mixing, often depart quite noticeably from the ideal of instantaneous mixing on the micro-scale. The present paper offers a quantitative measure of the extent of this departure, and shows how it is related to the reactor performance. The intensity of the mixing is characterized by a single parameter that measures the time scale of decay of nonuniformities in composition in the reactor. This is related to the design parameters of a gas reactor by dimensional arguments drawn from the theory of isotropic turbulence. The analysis of reactor performance is carried out in terms of a coalescence model for the micro-mixing that incorporates this time scale. The mixing model is borrowed from chemical engineering studies. Calculations are presented for adiabatic reaction systems, showing the shift in the effective reaction-rate curve, and especially the reduction in blow-out limit, with decreasing mixing intensity. Such calculations permit one to see how high a mixing intensity is needed to approximate perfect mixing, and how this level depends on the reaction kineties.