The statistical behaviour and modelling of the sub-grid variance of reaction progress variable have been analysed based on a priori analysis of Direct Numerical Simulation (DNS) data of freely propagating statistically planar turbulent premixed flames with different turbulence intensities. It has been found that an algebraic expression, which can be derived based on a presumed bi-modal sub-grid distribution of reaction progress variable with impulses at unburned reactants and fully burned products, is inadequate for the purpose of prediction of sub-grid variance. An algebraic model, which is often used for modelling sub-grid variance of passive scalars, has been found to significantly overpredict the sub-grid variance of reaction progress variable for the cases considered here. The statistical behaviours of the terms of the sub-grid variance have been analysed in detail and explained based on scaling arguments. It has been found that reaction rate and molecular dissipation contributions play leading order roles in the transport of sub-grid reaction progress variable variance and they remain in approximate equilibrium for large filter widths. Suitable model expressions have been identified for the sub-grid flux of variance, reaction rate contribution and scalar dissipation rate based on a priori analysis of DNS data.

中文翻译：

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湍流预混火焰中的亚网格反应进程变方差闭合

基于对具有不同湍流强度的自由传播的统计平面湍流预混火焰的直接数值模拟 (DNS) 数据的先验分析，分析了反应进程变量的子网格方差的统计行为和建模。已经发现，可以基于具有未燃烧反应物和完全燃烧产物脉冲的反应进程变量的假定双峰子网格分布导出的代数表达式不足以预测子网格方差. 代数模型通常用于对被动标量的子网格方差进行建模，已发现对于此处考虑的情况，显着高估了反应进程变量的子网格方差。已经详细分析了子网格方差项的统计行为，并基于缩放参数进行了解释。已经发现，反应速率和分子耗散贡献在子网格反应进程变量方差的传输中起主导作用，并且它们在大过滤器宽度下保持近似平衡。基于 DNS 数据的先验分析，已经为子网格的方差通量、反应速率贡献和标量耗散率确定了合适的模型表达式。