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} 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} 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} 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.
Highlights
The closure of the mean reaction rate in the context of Reynolds Averaged Navier Stokes (RANS) simulations in turbulent combustion often requires the knowledge of the scalar dissipation rate of Extended author information available on the last page of the articleFlow, Turbulence and Combustion (2020) 105:237–266 the fuel mass fraction YF
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 f εY and its transport in the context of Reynolds Averaged Navier-Stokes (RANS) simulations
The current study considers a-priori DNS modelling of the fuel mass fraction dissipation rate εfY and the unclosed terms of its transport equation following a similar approach to several previous analyses [5, 6, 33, 39,40,41,42,43,44,45, 48,49,50, 54,55,56,57,58]
Summary
The closure of the mean reaction rate in the context of Reynolds Averaged Navier Stokes (RANS) simulations in turbulent combustion often requires the knowledge of the scalar dissipation rate of. Previous studies on droplet combustion analysed the statistical behaviour of the terms of the scalar dissipation rate transport equation [8], but the statistical analysis of εeY is yet to be addressed in detail. The validity of existing closures of εeY and the unclosed terms of its transport equation, which were originally proposed for purely gaseous phase combustion, is yet to be assessed for turbulent spray flames. The activation energy and heat of combustion are taken to be functions of the gaseous equivalence ratio, φg, so that a realistic φg-dependence of unstrained laminar burning velocity SbðφgÞ can be obtained [13] It has been shown by Tarrazo et al [13] that the mechanism compares favourably with both experiments and detailed chemistry simulations for all hydrocarbon-air flames. To generalise the results, all the terms and model predictions are shown as a function of ec 1⁄4 f ðx1Þ
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