Relevance of the Bray number in the small-scale modeling of turbulent premixed flames

The present study is devoted to the analysis of the influence of expansion phenomena on turbulent small scales in premixed reactive flows. It is shown that, under certain conditions, the expansion that takes place across wrinkled laminar flamelets can be sufficient to control the fluctuating velocity gradients and associated dissipation rate functions. These conditions are fixed by the respective values of a set of nondimensional parameters, namely the turbulence Reynolds number ReTReT, the Bray number, and the ratio between integral length scale of turbulence and thermal flame front thickness. A new criterion is introduced that makes it possible to delineate the influence of expansion phenomena on small-scale turbulent premixed reactive flows. The relevance of this criterion is analyzed in the light of experimental results represented in the classical diagram of combustion regime. The present analysis confirms that special care is required to represent and include the influence of expansion phenomena when using either RANS or LES closures to model turbulent premixed combustion.