Low-dimensional modeling of flame dynamics in heated microchannels

We report on numerical simulations of stoichiometric methane/air premixed flames into a micro-tube at atmospheric pressure. These simulations result from numerical resolutions of reduced-order models. Former experimental and numerical studies reported the occurrence of a Flame Repetitive Extinction/Ignition (FREI) phenomenon provided that a temperature gradient is sustained at the walls. Conducting unsteady one-dimensional simulations including complex chemistry, a late numerical study tried to explain the occurrence of this phenomenon in terms of chemical balance. The present study aims to point out the main mechanisms underlying the arising of this instability. Provided a calibration of some empirical constants, an unsteady two-dimensional model including one-step chemical reaction is shown to quantitatively reproduce the FREI regime all along the range of flow rates investigated by the experimental studies. Interestingly, the stability diagram of the configuration investigated can be decently captured combining a very simple reaction model with an elementary hydrodynamical feature consisting of non-uniform velocity profile. Complementing the aforementioned numerical study, it is shown that, when the tube diameter is varied, the two-dimensional model unveils an unstable regime that a one-dimensional model cannot capture. As two-dimensional hydrodynamics appears to play a key role into the flame׳s dynamics, one-dimensional models are not believed to deliver in general an adequate strategy of combustion control into such microchannels.