Development of a low-order model of turbulent non-premixed flame global blow-off

A novel model for the global extinction of recirculating non-premixed flames has been developed and validated. This model is based on the imperfectly stirred reactor approach, derived from the spatially integrated conditional moment closure equation, and enhanced with a stochastic model for the scalar dissipation rate, the key characteristics of which can be inferred from computational fluid dynamics data or experimental measurements. We refer to this new model as the stochastic imperfectly stirred reactor. The model’s output is the probability of extinction, which corresponds to the proportion of a flame’s stoichiometric isosurface experiencing local extinctions. A review of the literature suggests that for a flame to blow off globally, about 30% of the stoichiometric isosurface must be extinguished. This criterion was tested against two atmospheric Cambridge swirl spray flame experiments using ethanol and kerosene as fuels. Time-averaged computational fluid dynamics data for these experiments, at conditions far from blow-off, allowed for a calculation of the blow-off velocity within 13% of the experimental values. The stochastic imperfectly stirred reactor model can in principle predict a combustor’s complete blow-off curve with only a limited number of computational fluid dynamics solutions which can be obtained even without a finite-rate turbulent combustion model, as long as the mixture fraction field is reasonably well captured.