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 turbulent premixed Bunsen burner flames at different pressure levels. An algebraic expression for sub-grid variance, 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, has been found to be inadequate for the purpose of prediction of sub-grid variance even for the flames in the wrinkled flamelets/corrugated flamelets regime. Moreover, 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 all the cases considered here. The modelling of the unclosed terms of the sub-grid variance transport equation has been analysed in detail. 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. It has been found that the alternation of pressure does not have any significant impact on the closures of sub-grid flux of variance but a model parameter for the Favre-filtered scalar dissipation rate needs to be modified to account for the variation of pressure.

中文翻译：

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不同压力水平湍流本生燃烧器火焰反应进程变量亚网格尺度变化的闭合分析

基于对不同压力水平下湍流预混本生灯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。已发现子网格方差的代数表达式不能基于预测的反应进程变量的双峰子网格分布推导出，该变量具有未燃烧的反应物和完全燃烧的产物的脉冲，已发现不足以预测即使对于皱纹小火焰/波纹小火焰区域中的火焰，子网格方差也是如此。此外，经常用于对被动标量的子网格方差进行建模的代数模型已被发现显着高估了此处考虑的所有情况下反应进程变量的子网格方差。详细分析了子网格方差传输方程的非闭合项的建模。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。已经发现，压力的变化对子网格方差通量的闭合没有任何显着影响，但需要修改 Favre 滤波标量耗散率的模型参数以考虑压力的变化。