Statistical Behaviour and Modelling of Fuel Mass Fraction Dissipation Rate Transport in Turbulent Flame-Droplet Interaction: A Direct Numerical Simulation study

Three-dimensional Direct Numerical Simulation (DNS) data of statistically planar turbulent spray flames propagating into mono-disperse droplets for different values of droplet diameter a d and droplet equivalence ratio ϕ d has been used to analyse the statistical behaviour of the fuel mass fraction dissipation rate ε Y ~ and its transport in the context of Reynolds Averaged Navier-Stokes (RANS) simulations. Closures previously derived for high Damköhler number turbulent stratified mixture combustion have been shown not to capture the statistical behaviour of ε Y ~ for turbulent spray flames, because the underlying assumptions behind the original modelling are invalid for the cases considered in this analysis. The modelling of the unclosed terms of the fuel mass fraction dissipation rate ε Y ~ transport equation (i.e. the turbulent transport term T 1 , the density variation term T 2 , the scalar turbulence interaction term T 3 , the reaction rate term T 4 , the evaporation contribution terms T 5 and T 6 , and the dissipation rate term − D 2 ) has been analysed 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. Based on a-priori DNS analysis, suitable model expressions have been identified for T 1 , T 2 , T 31 , T 32 , T 33 , [ T 4 − D 2 + f ( D )] and [ T 5 + T 6 ], which have been shown to perform generally satisfactorily for all cases considered here.