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 ~ $$ \overset{\sim }{\upvarepsilon_Y} $$ 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 ε Y ~ $$ \overset{\sim }{\upvarepsilon_Y} $$ 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 ε Y ~ $$ \overset{\sim }{\upvarepsilon_Y} $$ 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.

中文翻译：

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湍流火焰-液滴相互作用中燃料质量分数耗散率传递的统计行为和建模：直接数值模拟研究

对于不同液滴直径 ad 和液滴当量比 ϕ d 值，统计平面湍流喷雾火焰传播成单分散液滴的三维直接数值模拟 (DNS) 数据已用于分析燃料质量分数耗散率的统计行为ε Y ~ $$ \overset{\sim }{\upvarepsilon_Y} $$ 及其在雷诺平均纳维-斯托克斯 (RANS) 模拟背景下的传输。先前为高 Damköhler 数湍流分层混合物燃烧导出的闭包已被证明不能捕获 ε Y ~ $$ \overset{\sim }{\upvarepsilon_Y} $$ 的湍流喷射火焰的统计行为，因为原始假设背后的基本假设对于本分析中考虑的情况，建模是无效的。燃料质量分数耗散率ε Y ~ $$ \overset{\sim }{\upvarepsilon_Y} $$ 输运方程（即湍流输运项T 1 ，密度变化项T 2 ，标量湍流相互作用项 T 3 、反应速率项 T 4 、蒸发贡献项 T 5 和 T 6 以及耗散率项 - D 2 已在 RANS 模拟的上下文中进行了分析。先前在湍流气态分层火焰背景下提出的模型已在此处考虑以评估它们对湍流喷射火焰的适用性。基于先验 DNS 分析，已经为 T 1 , T 2 , T 31 , T 32 , T 33 , [ T 4 − D 2 + f ( D )] 和 [ T 5 + T 6 ] 确定了合适的模型表达式，已证明对于此处考虑的所有情况总体上都令人满意。