Predicting The Consumption Speed Of A Premixed Flame Subjected To An Unsteady Stretch Rate

The stretched laminar flame model provides a convenient approach to embed realistic chemical kinetics when simulating turbulent premixed flames. When positive-only periodic strain rates are applied to a laminar flame there is a notable phase lag and diminished amplitude in heat release rate. Similar results have been observed with respect to the other component of stretch rate, namely the unsteady motion of a curved flame front when the stretch rates are periodic about zero. Both cases showed that the heat release rate or consumption speed of these laminar premixed flames can vary significantly from the quasi-steady flamelet model. Deviation from quasi-steady behaviour increases for conditions further from stoichiometric such that unsteady time scales of the flow are of the same magnitude as the chemistry. A challenge remains in how to use such results predictively for local and instantaneous consumption speed for small segments of turbulent flames where their stretch history is not periodic. This paper uses a frequency response analysis as a characterization tool to simplify the complex non-linear behaviour of premixed methane air flames for equivalence ratios from 1.0 down to 0.7, and frequencies from quasi-steady up to 2000 Hz using flame transfer functions. Various linear and nonlinear models were studied to identify appropriate flame transfer functions for low and higher frequency regimes, as well as to extend the predictive capabilities of these models. Linear models were only able to accurately predict the flame behaviour below a threshold of when the fluid and chemistry time scales are the same order of magnitude.