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Statistical behavior of fuel mass fraction variance transport in turbulent flame–droplet interaction: A direct numerical simulation analysis

ABSTRACT Three-dimensional direct numerical simulations (DNS) data of statistically planar turbulent spray flames propagating into monodisperse droplets for different values of droplet diameter ad and droplet equivalence ratio ϕd have been used to analyze the statistical behavior of the fuel mass fraction variance and its transport in the context of Reynolds-averaged Navier–Stokes (RANS) simulations. The algebraic closure, which was previously derived for high Damköhler number turbulent stratified mixture combustion, has been shown not to capture statistical behavior of for turbulent spray flames, because the underlying assumptions behind the original modeling are invalid for the cases considered in this analysis. The modeling of the unclosed terms of the variance transport equation (i.e., the turbulent transport term T1, the reaction rate contribution T3, the evaporation contribution T4, and the dissipation rate term –D2) has been analyzed in the context of RANS simulations. The models previously proposed in the context of turbulent gaseous stratified flames have been considered here to assess their suitability for turbulent spray flames. Model expressions have been identified for and −D2 which have been shown to perform satisfactorily in all cases considered in the current study. However, the model previously proposed for T3 in the context of turbulent gaseous stratified flames has been found to be inadequate for turbulent spray flames and further consideration of the modeling of this unclosed term is therefore necessary.