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

Abstract

Three-dimensional Direct Numerical Simulation (DNS) data of statistically planar turbulent spray flames propagating into mono-disperse droplets for different values of droplet diameter ad and droplet equivalence ratio ϕd has been used to analyse the statistical behaviour of the fuel mass fraction dissipation rate $$ \overset{\sim }{\upvarepsilon_Y} $$εY~ 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 $$ \overset{\sim }{\upvarepsilon_Y} $$εY~ 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 $$ \overset{\sim }{\upvarepsilon_Y} $$εY~ transport equation (i.e. the turbulent transport term T1, the density variation term T2, the scalar turbulence interaction term T3, the reaction rate term T4, the evaporation contribution terms T5 and T6, and the dissipation rate term −D2) 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 T1, T2, T31, T32, T33, [T4 − D2 + f(D)] and [T5 + T6], which have been shown to perform generally satisfactorily for all cases considered here.

Physical effects of water droplets interacting with turbulent premixed flames: A Direct Numerical Simulation analysis

“…The canonical setup used for the present study is similar to several earlier DNS analyses on fuel spray combustion [35,36,37,38,39]. Here, a premixed and statistically planar stoichiometric n-heptane/air flame is subjected to a constant water droplet stream from the inlet.…”