A Criterion for Quasi-Steadiness of the Laminar Diffusion Flamelet Model

The laminar diffusion flamelet model is a well-established approach to modeling turbulent non-premixed combustion. Its quasi-steady version, referred to as the steady flamelet model, is very useful in engineering CFD calculations due to its low computational cost. However, previous studies have shown that unsteadiness of flamelets needs to be taken into account under certain circumstances. In this study, we derive a flamelet time scale, which is a characteristic time period needed for a flamelet structure to reach its quasi-steady state, and we use this time scale to propose a criterion to test quasi-steadiness of the flamelet. Although this criterion is rather conservative in that the predicted steady-flamelet regime tends to be smaller than it should be, the criterion is easy to use because it only requires the information from the mixing field.